%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA139-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:48 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.45s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA139-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:12:53 EDT 2026
% 0.15/0.32 % CPUTime :
% 1.23/1.45 % SZS status Unsatisfiable
% 1.23/1.45 % SZS output start Proof
% 1.23/1.45 tff(elem_1_type, type, (
% 1.23/1.45 elem_1: $i)).
% 1.23/1.45 tff(s_type, type, (
% 1.23/1.45 s: $i > $i)).
% 1.23/1.45 tff(z_type, type, (
% 1.23/1.45 z: $i)).
% 1.23/1.45 tff(b_type, type, (
% 1.23/1.45 b: ( $i * $i ) > $o)).
% 1.23/1.45 tff(r_type, type, (
% 1.23/1.45 r: ( $i * $i ) > $o)).
% 1.23/1.45 tff(inj_0_type, type, (
% 1.23/1.45 inj_0: $i > $i)).
% 1.23/1.45 tff(1,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.23/1.45 tff(2,plain,
% 1.23/1.45 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(3,assumption,(~r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.45 tff(4,assumption,(~r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.45 tff(5,plain,
% 1.23/1.45 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(6,plain,
% 1.23/1.45 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5])).
% 1.23/1.45 tff(7,plain,
% 1.23/1.45 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(8,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(9,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(10,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.23/1.45 tff(11,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.23/1.45 tff(12,plain,(
% 1.23/1.45 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.45 inference(skolemize,[status(sab)],[11])).
% 1.23/1.45 tff(13,plain,
% 1.23/1.45 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.23/1.45 tff(14,plain,
% 1.23/1.45 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[13, 7])).
% 1.23/1.45 tff(15,plain,
% 1.23/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(16,plain,
% 1.23/1.45 (inj_0(s(z)) = z),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[15, 14])).
% 1.23/1.45 tff(17,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 1.23/1.45 tff(18,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[17])).
% 1.23/1.45 tff(19,plain,
% 1.23/1.45 ((~![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)))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(20,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[19, 14])).
% 1.23/1.45 tff(21,plain,
% 1.23/1.45 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[20])).
% 1.23/1.45 tff(22,plain,
% 1.23/1.45 (s(s(s(s(s(s(z)))))) = z),
% 1.23/1.45 inference(transitivity,[status(thm)],[21, 18, 16])).
% 1.23/1.45 tff(23,plain,
% 1.23/1.45 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(24,plain,
% 1.23/1.45 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[23])).
% 1.23/1.45 tff(25,plain,
% 1.23/1.45 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(26,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.23/1.45 tff(27,plain,
% 1.23/1.45 (![X: $i] : (~(s(X) = z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.23/1.45 tff(28,plain,(
% 1.23/1.45 ![X: $i] : (~(s(X) = z))),
% 1.23/1.45 inference(skolemize,[status(sab)],[27])).
% 1.23/1.45 tff(29,plain,
% 1.23/1.45 (![X: $i] : (~(s(X) = z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.23/1.45 tff(30,plain,
% 1.23/1.45 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(31,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.23/1.45 tff(32,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[31, 22])).
% 1.23/1.45 tff(33,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(34,plain,
% 1.23/1.45 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[33, 6])).
% 1.23/1.45 tff(35,plain,
% 1.23/1.45 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(36,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[35])).
% 1.23/1.45 tff(37,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(38,plain,
% 1.23/1.45 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(39,plain,
% 1.23/1.45 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[38])).
% 1.23/1.45 tff(40,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.23/1.45 tff(41,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.23/1.45 tff(42,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.23/1.45 tff(43,plain,(
% 1.23/1.45 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(skolemize,[status(sab)],[42])).
% 1.23/1.45 tff(44,plain,
% 1.23/1.45 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.23/1.45 tff(45,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(46,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(47,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.23/1.45 tff(48,plain,
% 1.23/1.45 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[47, 44])).
% 1.23/1.45 tff(49,plain,
% 1.23/1.45 (b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[48, 34])).
% 1.23/1.45 tff(50,plain,
% 1.23/1.45 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[49, 4])).
% 1.23/1.45 tff(51,assumption,(r(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.45 tff(52,plain,
% 1.23/1.45 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(53,plain,
% 1.23/1.45 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[52])).
% 1.23/1.45 tff(54,assumption,(~r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(55,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(56,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.23/1.45 tff(57,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.23/1.45 tff(58,plain,
% 1.23/1.45 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[57])).
% 1.23/1.45 tff(59,plain,
% 1.23/1.45 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[58])).
% 1.23/1.45 tff(60,plain,
% 1.23/1.45 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(z)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[59])).
% 1.23/1.45 tff(61,plain,
% 1.23/1.45 (~b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[55, 60])).
% 1.23/1.45 tff(62,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[56, 61])).
% 1.23/1.45 tff(63,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(64,plain,
% 1.23/1.45 (~(s(z) = elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[63, 56, 55])).
% 1.23/1.45 tff(65,plain,
% 1.23/1.45 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2])).
% 1.23/1.45 tff(66,assumption,(z = elem!1), introduced(assumption)).
% 1.23/1.45 tff(67,plain,
% 1.23/1.45 (s(z) = s(elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[66])).
% 1.23/1.45 tff(68,plain,
% 1.23/1.45 (s(elem!1) = s(z)),
% 1.23/1.45 inference(symmetry,[status(thm)],[67])).
% 1.23/1.45 tff(69,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1, 68])).
% 1.23/1.45 tff(70,plain,((~(z = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(71,plain,
% 1.23/1.45 (~(z = elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[70, 1])).
% 1.23/1.45 tff(72,assumption,(elem!1 = z), introduced(assumption)).
% 1.23/1.45 tff(73,plain,
% 1.23/1.45 (z = elem!1),
% 1.23/1.45 inference(symmetry,[status(thm)],[72])).
% 1.23/1.45 tff(74,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.23/1.45 tff(75,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 1.23/1.45 tff(76,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(77,plain,
% 1.23/1.45 (~(elem!1 = z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[76, 71])).
% 1.23/1.45 tff(78,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.23/1.45 tff(79,plain,
% 1.23/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(80,plain,
% 1.23/1.45 (inj_0(s(s(z))) = s(z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[79, 14])).
% 1.23/1.45 tff(81,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 1.23/1.45 tff(82,plain,
% 1.23/1.45 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[81])).
% 1.23/1.45 tff(83,plain,
% 1.23/1.45 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[78, 82])).
% 1.23/1.45 tff(84,plain,
% 1.23/1.45 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[83])).
% 1.23/1.45 tff(85,plain,
% 1.23/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(86,plain,
% 1.23/1.45 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[85, 14])).
% 1.23/1.45 tff(87,plain,
% 1.23/1.45 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[86])).
% 1.23/1.45 tff(88,plain,
% 1.23/1.45 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[87, 84, 20])).
% 1.23/1.45 tff(89,plain,
% 1.23/1.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[88])).
% 1.23/1.45 tff(90,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.23/1.45 inference(symmetry,[status(thm)],[89])).
% 1.23/1.45 tff(91,plain,
% 1.23/1.45 ((~![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))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(92,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[91, 14])).
% 1.23/1.45 tff(93,plain,
% 1.23/1.45 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[92])).
% 1.23/1.45 tff(94,plain,
% 1.23/1.45 (s(s(s(s(z)))) = s(elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.45 tff(95,plain,
% 1.23/1.45 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[94])).
% 1.23/1.45 tff(96,plain,
% 1.23/1.45 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[95])).
% 1.23/1.45 tff(97,plain,
% 1.23/1.45 (s(s(elem!1)) = s(z)),
% 1.23/1.45 inference(transitivity,[status(thm)],[96, 93, 90, 80])).
% 1.23/1.45 tff(98,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.23/1.45 tff(99,plain,
% 1.23/1.45 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[98])).
% 1.23/1.45 tff(100,plain,
% 1.23/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(101,plain,
% 1.23/1.45 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[100, 14])).
% 1.23/1.45 tff(102,plain,
% 1.23/1.45 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.23/1.45 inference(symmetry,[status(thm)],[101])).
% 1.23/1.45 tff(103,plain,
% 1.23/1.45 (s(elem!1) = z),
% 1.23/1.45 inference(transitivity,[status(thm)],[102, 99, 16])).
% 1.23/1.45 tff(104,plain,
% 1.23/1.45 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(105,plain,
% 1.23/1.45 (~(s(elem!1) = z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[104, 29])).
% 1.23/1.45 tff(106,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[105, 103])).
% 1.23/1.45 tff(107,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(108,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[107, 97])).
% 1.23/1.45 tff(109,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(110,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[109, 78])).
% 1.23/1.45 tff(111,plain,
% 1.23/1.45 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(112,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.23/1.45 tff(113,plain,
% 1.23/1.45 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.23/1.45 tff(114,assumption,(~(s(s(s(s(s(s(s(z))))))) = elem!1)), introduced(assumption)).
% 1.23/1.45 tff(115,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[114, 113])).
% 1.23/1.45 tff(116,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(117,plain,
% 1.23/1.45 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[116, 110])).
% 1.23/1.45 tff(118,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(119,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(120,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.23/1.45 tff(121,plain,
% 1.23/1.45 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[120, 44])).
% 1.23/1.45 tff(122,plain,
% 1.23/1.45 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[121, 117, 3])).
% 1.23/1.45 tff(123,assumption,(b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.45 tff(124,plain,
% 1.23/1.45 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.45 tff(125,plain,
% 1.23/1.45 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[124])).
% 1.23/1.45 tff(126,plain,
% 1.23/1.45 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[125])).
% 1.23/1.45 tff(127,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(128,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(129,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.23/1.45 tff(130,plain,
% 1.23/1.45 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[129, 44])).
% 1.23/1.45 tff(131,plain,
% 1.23/1.45 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[130, 110, 54])).
% 1.23/1.45 tff(132,assumption,(b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.45 tff(133,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(134,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(135,plain,
% 1.23/1.45 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(136,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[135])).
% 1.23/1.45 tff(137,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(138,plain,
% 1.23/1.45 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(139,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[138])).
% 1.23/1.45 tff(140,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.23/1.45 tff(141,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.23/1.45 tff(142,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.23/1.45 tff(143,plain,(
% 1.23/1.45 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(skolemize,[status(sab)],[142])).
% 1.23/1.45 tff(144,plain,
% 1.23/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[143, 136])).
% 1.23/1.45 tff(145,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(146,plain,
% 1.23/1.45 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(147,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[146])).
% 1.23/1.46 tff(148,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[147, 145])).
% 1.23/1.46 tff(149,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(150,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.23/1.46 tff(151,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[150, 144, 134, 123, 133, 132])).
% 1.23/1.46 tff(152,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(153,plain,
% 1.23/1.46 (~b(s(z), elem!1)),
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% 1.23/1.46 tff(156,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
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% 1.23/1.46 inference(symmetry,[status(thm)],[212])).
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% 1.23/1.46 inference(unit_resolution,[status(thm)],[217, 210])).
% 1.23/1.46 tff(219,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(220,plain,
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% 1.23/1.46 inference(modus_ponens,[status(thm)],[219, 206])).
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% 1.23/1.46 inference(modus_ponens,[status(thm)],[220, 202])).
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% 1.23/1.46 inference(monotonicity,[status(thm)],[78])).
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% 1.23/1.46 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
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% 1.23/1.46 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[232])).
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% 1.23/1.46 (s(z) = s(s(s(s(s(z)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[193, 233, 92])).
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% 1.23/1.46 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
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% 1.23/1.46 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
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% 1.23/1.46 inference(unit_resolution,[status(thm)],[237, 14])).
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% 1.23/1.46 inference(unit_resolution,[status(thm)],[242, 240])).
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% 1.23/1.46 tff(250,plain,
% 1.23/1.46 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[249, 228])).
% 1.23/1.46 tff(251,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.23/1.46 tff(252,plain,
% 1.23/1.46 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.46 tff(253,plain,
% 1.23/1.46 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[252])).
% 1.23/1.46 tff(254,plain,
% 1.23/1.46 (b(z, s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[251, 253])).
% 1.23/1.46 tff(255,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(256,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[255, 254])).
% 1.23/1.46 tff(257,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(258,plain,
% 1.23/1.46 (b(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[257, 251, 78])).
% 1.23/1.46 tff(259,assumption,(b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.46 tff(260,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(261,plain,
% 1.23/1.46 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(262,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[261])).
% 1.23/1.46 tff(263,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[262, 260])).
% 1.23/1.46 tff(264,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(265,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.23/1.46 tff(266,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[265, 144, 251, 133, 132, 259])).
% 1.23/1.46 tff(267,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(268,plain,
% 1.23/1.46 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[267, 251, 131, 122])).
% 1.23/1.46 tff(269,plain,
% 1.23/1.46 ((z = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 1.23/1.46 inference(commutativity,[status(thm)],[])).
% 1.23/1.46 tff(270,plain,
% 1.23/1.46 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[269])).
% 1.23/1.46 tff(271,plain,
% 1.23/1.46 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[270])).
% 1.23/1.46 tff(272,plain,
% 1.23/1.46 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(273,plain,
% 1.23/1.46 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[272, 29])).
% 1.23/1.46 tff(274,plain,
% 1.23/1.46 (~(z = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[273, 271])).
% 1.23/1.46 tff(275,plain,
% 1.23/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(276,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(277,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.23/1.46 tff(278,plain,
% 1.23/1.46 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[277, 44])).
% 1.23/1.46 tff(279,plain,
% 1.23/1.46 (b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[278, 274])).
% 1.23/1.46 tff(280,plain,
% 1.23/1.46 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[279, 268])).
% 1.23/1.46 tff(281,plain,
% 1.23/1.46 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.46 tff(282,plain,
% 1.23/1.46 (b(elem!1, s(z))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[56, 281])).
% 1.23/1.46 tff(283,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(284,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(285,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.23/1.46 tff(286,assumption,(b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.23/1.47 tff(287,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(288,plain,
% 1.23/1.47 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(289,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[288])).
% 1.23/1.47 tff(290,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[289, 287])).
% 1.23/1.47 tff(291,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(292,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.23/1.47 tff(293,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[292, 144, 285, 284, 283, 286])).
% 1.23/1.47 tff(294,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(295,plain,
% 1.23/1.47 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[294, 285, 284, 283])).
% 1.23/1.47 tff(296,assumption,(~b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.23/1.47 tff(297,assumption,(~r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.23/1.47 tff(298,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(299,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(300,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.23/1.47 tff(301,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[300, 44, 273, 297, 296])).
% 1.23/1.47 tff(302,plain,(b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(303,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[302, 295])).
% 1.23/1.47 tff(304,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.23/1.47 tff(305,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.23/1.47 tff(306,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(307,plain,
% 1.23/1.47 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(308,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[307])).
% 1.23/1.47 tff(309,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[308, 306])).
% 1.23/1.47 tff(310,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(311,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.23/1.47 tff(312,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[311, 144, 305, 123, 132, 304])).
% 1.23/1.47 tff(313,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(314,plain,
% 1.23/1.47 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[313, 282, 123, 132])).
% 1.23/1.47 tff(315,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(316,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(317,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.23/1.47 tff(318,plain,
% 1.23/1.47 ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[317, 44])).
% 1.23/1.47 tff(319,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[318, 33])).
% 1.23/1.47 tff(320,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[319, 314])).
% 1.23/1.47 tff(321,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.23/1.47 tff(322,assumption,(r(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.23/1.47 tff(323,assumption,(r(s(z), z)), introduced(assumption)).
% 1.23/1.47 tff(324,plain,
% 1.23/1.47 (^[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))))),
% 1.23/1.47 inference(bind,[status(th)],[])).
% 1.23/1.47 tff(325,plain,
% 1.23/1.47 (![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)))),
% 1.23/1.47 inference(quant_intro,[status(thm)],[324])).
% 1.23/1.47 tff(326,plain,
% 1.23/1.47 (![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)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(327,plain,
% 1.23/1.47 (^[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)))))),
% 1.23/1.47 inference(bind,[status(th)],[])).
% 1.23/1.47 tff(328,plain,
% 1.23/1.47 (![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)))),
% 1.23/1.47 inference(quant_intro,[status(thm)],[327])).
% 1.23/1.47 tff(329,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')).
% 1.23/1.47 tff(330,plain,
% 1.23/1.47 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.23/1.47 tff(331,plain,
% 1.23/1.47 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[330, 326])).
% 1.23/1.47 tff(332,plain,(
% 1.23/1.47 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.23/1.47 inference(skolemize,[status(sab)],[331])).
% 1.23/1.47 tff(333,plain,
% 1.23/1.47 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[332, 325])).
% 1.23/1.47 tff(334,plain,
% 1.23/1.47 (((~![X0: $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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(335,plain,
% 1.23/1.47 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(336,plain,
% 1.23/1.47 (((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, 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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[335])).
% 1.23/1.47 tff(337,plain,
% 1.23/1.47 (((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, 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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[336, 334])).
% 1.23/1.47 tff(338,plain,
% 1.23/1.47 ((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(339,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.23/1.47 tff(340,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[339, 333, 323, 322, 321, 51])).
% 1.23/1.47 tff(341,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(342,plain,
% 1.23/1.47 (~r(s(z), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[341, 320, 51, 303])).
% 1.23/1.47 tff(343,plain,
% 1.23/1.47 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(344,plain,
% 1.23/1.47 (~(s(z) = z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[343, 29])).
% 1.23/1.47 tff(345,plain,
% 1.23/1.47 (((~![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))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(346,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(347,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.23/1.47 tff(348,plain,
% 1.23/1.47 (b(s(z), z) | r(s(z), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[347, 44, 344])).
% 1.23/1.47 tff(349,plain,
% 1.23/1.47 (b(s(z), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[348, 342])).
% 1.23/1.47 tff(350,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.23/1.47 tff(351,plain,
% 1.23/1.47 (~b(s(z), s(s(s(z))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[350, 126])).
% 1.23/1.47 tff(352,plain,
% 1.23/1.47 (r(s(z), s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[172, 351])).
% 1.23/1.47 tff(353,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.23/1.47 tff(354,assumption,(r(z, s(z))), introduced(assumption)).
% 1.23/1.47 tff(355,plain,
% 1.23/1.47 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(356,plain,
% 1.23/1.47 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(357,plain,
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% 1.23/1.47 inference(monotonicity,[status(thm)],[356])).
% 1.23/1.47 tff(358,plain,
% 1.23/1.47 (((~![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(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[357, 355])).
% 1.23/1.47 tff(359,plain,
% 1.23/1.47 ((~![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(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(360,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.23/1.47 tff(361,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[360, 333, 354, 353, 322, 321])).
% 1.23/1.47 tff(362,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(363,plain,
% 1.23/1.47 (~r(z, s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[362, 352, 303, 320])).
% 1.23/1.47 tff(364,plain,
% 1.23/1.47 ((z = s(z)) <=> (s(z) = z)),
% 1.23/1.47 inference(commutativity,[status(thm)],[])).
% 1.23/1.47 tff(365,plain,
% 1.23/1.47 ((s(z) = z) <=> (z = s(z))),
% 1.23/1.47 inference(symmetry,[status(thm)],[364])).
% 1.23/1.47 tff(366,plain,
% 1.23/1.47 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[365])).
% 1.23/1.47 tff(367,plain,
% 1.23/1.47 (~(z = s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[344, 366])).
% 1.23/1.47 tff(368,plain,
% 1.23/1.47 (((~![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)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(369,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(370,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.23/1.47 tff(371,plain,
% 1.23/1.47 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[370, 44])).
% 1.23/1.47 tff(372,plain,
% 1.23/1.47 (b(z, s(z)) | r(z, s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[371, 367])).
% 1.23/1.47 tff(373,plain,
% 1.23/1.47 (b(z, s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[372, 363])).
% 1.23/1.47 tff(374,plain,
% 1.23/1.47 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.47 tff(375,plain,
% 1.23/1.47 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.23/1.47 inference(symmetry,[status(thm)],[374])).
% 1.23/1.47 tff(376,plain,
% 1.23/1.47 ((~b(elem!1, z)) <=> (~b(s(s(s(z))), z))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[375])).
% 1.23/1.47 tff(377,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.23/1.47 tff(378,plain,
% 1.23/1.47 (~b(s(s(s(z))), z)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.23/1.48 tff(379,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[285, 378])).
% 1.23/1.48 tff(380,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(381,plain,
% 1.23/1.48 (b(elem!1, z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[380, 285, 78])).
% 1.23/1.48 tff(382,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(383,plain,
% 1.23/1.48 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(384,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[383])).
% 1.23/1.48 tff(385,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[384, 382])).
% 1.23/1.48 tff(386,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(387,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.23/1.48 tff(388,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[387, 144, 381, 373, 349, 282])).
% 1.23/1.48 tff(389,plain,((~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(390,plain,
% 1.23/1.48 (~b(s(s(s(z))), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[389, 280, 123, 122, 153, 78, 56, 258, 250])).
% 1.23/1.48 tff(391,plain,
% 1.23/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(392,plain,
% 1.23/1.48 (~(s(s(s(z))) = z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[391, 29])).
% 1.23/1.48 tff(393,plain,
% 1.23/1.48 (((~![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))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(394,plain,
% 1.23/1.48 ((~![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))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(395,plain,
% 1.23/1.48 ((~![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)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.23/1.48 tff(396,plain,
% 1.23/1.48 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[395, 44, 392])).
% 1.23/1.48 tff(397,plain,
% 1.23/1.48 (r(s(s(s(z))), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[396, 390])).
% 1.23/1.48 tff(398,plain,
% 1.23/1.48 (r(elem!1, z)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[397, 222])).
% 1.23/1.48 tff(399,plain,
% 1.23/1.48 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[78])).
% 1.23/1.48 tff(400,plain,
% 1.23/1.48 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.23/1.48 inference(transitivity,[status(thm)],[399, 52])).
% 1.23/1.48 tff(401,plain,
% 1.23/1.48 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[400])).
% 1.23/1.48 tff(402,plain,
% 1.23/1.48 (~(s(z) = elem!1)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[166, 401])).
% 1.23/1.48 tff(403,plain,
% 1.23/1.48 (((~![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))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(404,plain,
% 1.23/1.48 ((~![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))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(405,plain,
% 1.23/1.48 ((~![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)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[404, 403])).
% 1.23/1.48 tff(406,plain,
% 1.23/1.48 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[405, 44])).
% 1.23/1.48 tff(407,plain,
% 1.23/1.48 (r(s(z), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[406, 402, 153])).
% 1.23/1.48 tff(408,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.23/1.48 tff(409,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(410,plain,
% 1.23/1.48 (((~![X0: $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), elem!1)) | (~r(elem!1, z)) | (~r(z, 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(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(411,plain,
% 1.23/1.48 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(412,plain,
% 1.23/1.48 (((~![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(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(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[411])).
% 1.23/1.48 tff(413,plain,
% 1.23/1.48 (((~![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(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(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[412, 410])).
% 1.23/1.48 tff(414,plain,
% 1.23/1.48 ((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(415,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.23/1.48 tff(416,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[415, 333, 409, 323, 408, 51])).
% 1.23/1.48 tff(417,plain,((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(418,plain,
% 1.23/1.48 (~r(s(z), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[417, 407, 398, 280])).
% 1.23/1.48 tff(419,plain,
% 1.23/1.48 (b(s(z), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[348, 418])).
% 1.23/1.48 tff(420,plain,
% 1.23/1.48 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[313, 282, 123, 122])).
% 1.23/1.48 tff(421,plain,
% 1.23/1.48 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[319, 420])).
% 1.23/1.48 tff(422,plain,
% 1.23/1.48 (((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(423,plain,
% 1.23/1.48 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(424,plain,
% 1.23/1.48 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[423])).
% 1.23/1.48 tff(425,plain,
% 1.23/1.48 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[424, 422])).
% 1.23/1.48 tff(426,plain,
% 1.23/1.48 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(427,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.23/1.48 tff(428,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[427, 333, 409, 354, 322, 51])).
% 1.23/1.48 tff(429,plain,((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(430,plain,
% 1.23/1.48 (~r(z, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[429, 421, 280, 407])).
% 1.23/1.48 tff(431,plain,
% 1.23/1.48 (b(z, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[372, 430])).
% 1.23/1.48 tff(432,assumption,(~(s(elem!1) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.48 tff(433,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.23/1.48 tff(434,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.23/1.48 tff(435,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(436,plain,
% 1.23/1.48 (((~![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(elem!1), elem!1)) | (~r(s(elem!1), 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(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(437,plain,
% 1.23/1.48 (((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(438,plain,
% 1.23/1.48 (((~![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(elem!1), 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[437])).
% 1.23/1.48 tff(439,plain,
% 1.23/1.48 (((~![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(elem!1), 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(transitivity,[status(thm)],[438, 436])).
% 1.23/1.48 tff(440,plain,
% 1.23/1.48 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(441,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[440, 439])).
% 1.23/1.48 tff(442,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[441, 333, 435, 409, 434, 408])).
% 1.23/1.48 tff(443,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(444,plain,
% 1.23/1.48 (~r(s(elem!1), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[443, 434, 409, 408])).
% 1.23/1.48 tff(445,plain,
% 1.23/1.48 (((~![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))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(446,plain,
% 1.23/1.48 ((~![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))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(447,plain,
% 1.23/1.48 ((~![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)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.23/1.48 tff(448,plain,
% 1.23/1.48 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[447, 44])).
% 1.23/1.48 tff(449,plain,
% 1.23/1.48 (b(s(elem!1), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[448, 444, 433])).
% 1.23/1.48 tff(450,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.48 tff(451,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(452,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[130, 114, 54])).
% 1.23/1.48 tff(453,plain,
% 1.23/1.48 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[116, 114])).
% 1.23/1.48 tff(454,plain,
% 1.23/1.48 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[121, 453, 3])).
% 1.23/1.48 tff(455,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(456,plain,
% 1.23/1.48 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(457,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[456])).
% 1.23/1.49 tff(458,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[457, 455])).
% 1.23/1.49 tff(459,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(460,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.23/1.49 tff(461,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[460, 144, 451, 133, 132, 450])).
% 1.23/1.49 tff(462,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(463,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[462, 454, 452, 451, 450])).
% 1.23/1.49 tff(464,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(465,plain,
% 1.23/1.49 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[464, 449, 54, 114, 3])).
% 1.23/1.49 tff(466,assumption,(~r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.49 tff(467,assumption,(~b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.49 tff(468,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(469,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(470,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.23/1.49 tff(471,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[470, 44, 467, 466, 432])).
% 1.23/1.49 tff(472,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(473,plain,
% 1.23/1.49 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[472, 465, 432])).
% 1.23/1.49 tff(474,plain,
% 1.23/1.49 (((~![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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), 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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(475,plain,
% 1.23/1.49 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(476,plain,
% 1.23/1.49 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[475])).
% 1.23/1.49 tff(477,plain,
% 1.23/1.49 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[476, 474])).
% 1.23/1.49 tff(478,plain,
% 1.23/1.49 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(479,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.23/1.49 tff(480,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[479, 333, 409, 434, 322, 473])).
% 1.23/1.49 tff(481,plain,((~r(s(elem!1), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(482,plain,
% 1.23/1.49 (~r(s(elem!1), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[481, 407, 421, 197, 54, 110, 3, 221, 398])).
% 1.23/1.49 tff(483,plain,
% 1.23/1.49 (((~![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)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(484,plain,
% 1.23/1.49 ((~![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)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(485,plain,
% 1.23/1.49 ((~![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))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.23/1.49 tff(486,plain,
% 1.23/1.49 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[485, 44])).
% 1.23/1.49 tff(487,plain,
% 1.23/1.49 (b(s(elem!1), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[486, 482, 1])).
% 1.23/1.49 tff(488,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.23/1.49 tff(489,assumption,(b(s(z), z)), introduced(assumption)).
% 1.23/1.49 tff(490,assumption,(b(z, s(z))), introduced(assumption)).
% 1.23/1.49 tff(491,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.23/1.49 tff(492,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(493,plain,
% 1.23/1.49 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(494,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[493])).
% 1.23/1.49 tff(495,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[494, 492])).
% 1.23/1.49 tff(496,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(497,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.23/1.49 tff(498,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[497, 144, 491, 490, 489, 488])).
% 1.23/1.49 tff(499,plain,((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(500,plain,
% 1.23/1.49 (~b(s(elem!1), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[499, 487, 431, 419])).
% 1.23/1.49 tff(501,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.23/1.49 tff(502,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.23/1.49 tff(503,plain,
% 1.23/1.49 (((~![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))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(504,plain,
% 1.23/1.49 ((~![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))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(505,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.23/1.49 tff(506,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[505, 44, 105, 502, 501])).
% 1.23/1.49 tff(507,plain,(r(s(elem!1), z) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(508,plain,
% 1.23/1.49 (r(s(elem!1), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[507, 500])).
% 1.23/1.49 tff(509,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.23/1.49 tff(510,plain,
% 1.23/1.49 (((~![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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, 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(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(511,plain,
% 1.23/1.49 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(512,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[511])).
% 1.23/1.49 tff(513,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[512, 510])).
% 1.23/1.49 tff(514,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(515,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.23/1.49 tff(516,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[515, 333, 435, 408, 509, 51])).
% 1.23/1.49 tff(517,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(518,plain,
% 1.23/1.49 (~r(s(elem!1), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[517, 508, 280, 398])).
% 1.23/1.49 tff(519,plain,
% 1.23/1.49 (b(s(elem!1), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[448, 518, 221])).
% 1.23/1.49 tff(520,plain,
% 1.23/1.49 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[464, 519, 54, 110, 3])).
% 1.23/1.49 tff(521,plain,
% 1.23/1.49 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[472, 520, 197])).
% 1.23/1.49 tff(522,plain,
% 1.23/1.49 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[177])).
% 1.23/1.49 tff(523,plain,
% 1.23/1.49 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[196, 522])).
% 1.23/1.49 tff(524,assumption,(r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.23/1.49 tff(525,assumption,(r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.23/1.49 tff(526,plain,
% 1.23/1.49 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(527,plain,
% 1.23/1.49 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(528,plain,
% 1.23/1.49 (((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[527])).
% 1.23/1.49 tff(529,plain,
% 1.23/1.49 (((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[528, 526])).
% 1.23/1.49 tff(530,plain,
% 1.23/1.49 ((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(531,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.23/1.49 tff(532,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[531, 333, 509, 51, 525, 524])).
% 1.23/1.49 tff(533,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(534,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[533, 521, 280, 508])).
% 1.23/1.49 tff(535,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.23/1.49 tff(536,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.23/1.49 tff(537,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(elem!1))), introduced(assumption)).
% 1.23/1.49 tff(538,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(539,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.23/1.50 inference(quant_inst,[status(thm)],[])).
% 1.23/1.50 tff(540,plain,
% 1.23/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.23/1.50 tff(541,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[540, 44, 537, 536, 535])).
% 1.23/1.50 tff(542,plain,(b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(543,plain,
% 1.23/1.50 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[542, 534, 523])).
% 1.23/1.50 tff(544,plain,
% 1.23/1.50 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(elem!1 = s(elem!1)))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[200])).
% 1.23/1.50 tff(545,plain,
% 1.23/1.50 (~(elem!1 = s(elem!1))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[220, 544])).
% 1.23/1.50 tff(546,assumption,(b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(547,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(548,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(549,plain,
% 1.32/1.50 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(550,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[549])).
% 1.32/1.50 tff(551,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[550, 548])).
% 1.32/1.50 tff(552,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(553,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.32/1.50 tff(554,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[553, 144, 547, 451, 133, 546])).
% 1.32/1.50 tff(555,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(556,plain,
% 1.32/1.50 (~b(elem!1, s(elem!1))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[555, 543, 131, 519])).
% 1.32/1.50 tff(557,plain,
% 1.32/1.50 (((~![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)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(558,plain,
% 1.32/1.50 ((~![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)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(559,plain,
% 1.32/1.50 ((~![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))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.32/1.50 tff(560,plain,
% 1.32/1.50 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[559, 44])).
% 1.32/1.50 tff(561,plain,
% 1.32/1.50 (r(elem!1, s(elem!1))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[560, 556, 545])).
% 1.32/1.50 tff(562,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(563,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(564,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(565,plain,
% 1.32/1.50 (((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(566,plain,
% 1.32/1.50 (((~![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), z)) | (~r(elem!1, 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(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[565])).
% 1.32/1.50 tff(567,plain,
% 1.32/1.50 (((~![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), z)) | (~r(elem!1, 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(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[566, 564])).
% 1.32/1.50 tff(568,plain,
% 1.32/1.50 ((~![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), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(569,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.32/1.50 tff(570,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[569, 333, 563, 562, 408, 509])).
% 1.32/1.50 tff(571,plain,((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(572,plain,
% 1.32/1.50 (~r(z, s(elem!1))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[571, 561, 508, 398])).
% 1.32/1.50 tff(573,assumption,(z = s(elem!1)), introduced(assumption)).
% 1.32/1.50 tff(574,plain,
% 1.32/1.50 (s(elem!1) = z),
% 1.32/1.50 inference(symmetry,[status(thm)],[573])).
% 1.32/1.50 tff(575,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[105, 574])).
% 1.32/1.50 tff(576,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(577,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(578,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(579,plain,
% 1.32/1.50 (((~![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)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(580,plain,
% 1.32/1.50 ((~![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)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(581,plain,
% 1.32/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.32/1.50 tff(582,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[581, 44, 578, 577, 576])).
% 1.32/1.50 tff(583,plain,(b(z, s(elem!1)) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(584,plain,
% 1.32/1.50 (b(z, s(elem!1))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[583, 572])).
% 1.32/1.50 tff(585,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.32/1.50 tff(586,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(587,plain,
% 1.32/1.50 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(588,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[587])).
% 1.32/1.50 tff(589,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[588, 586])).
% 1.32/1.50 tff(590,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(591,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.32/1.50 tff(592,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[591, 144, 451, 585, 133, 286, 546])).
% 1.32/1.50 tff(593,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(594,plain,
% 1.32/1.50 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[593, 584, 131, 543, 519])).
% 1.32/1.50 tff(595,plain,
% 1.32/1.50 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[302, 594])).
% 1.32/1.50 tff(596,plain,
% 1.32/1.50 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(597,plain,
% 1.32/1.50 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(598,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[597])).
% 1.32/1.50 tff(599,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[598, 596])).
% 1.32/1.50 tff(600,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(601,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.32/1.50 tff(602,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[601, 333, 508, 595, 280, 521])).
% 1.32/1.50 tff(603,plain,((~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(604,plain,
% 1.32/1.50 (~b(z, elem!1)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[603, 78, 3, 1, 123, 54, 56])).
% 1.32/1.50 tff(605,plain,
% 1.32/1.50 ((~b(z, elem!1)) <=> (~b(z, s(s(s(z)))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[253])).
% 1.32/1.50 tff(606,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.32/1.50 tff(607,plain,
% 1.32/1.50 (~b(z, s(s(s(z))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.32/1.50 tff(608,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[284, 607])).
% 1.32/1.50 tff(609,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(z))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(610,plain,
% 1.32/1.50 (~b(z, s(s(s(z))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[609, 604, 78])).
% 1.32/1.50 tff(611,plain,
% 1.32/1.50 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.32/1.50 inference(commutativity,[status(thm)],[])).
% 1.32/1.50 tff(612,plain,
% 1.32/1.50 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.32/1.50 inference(symmetry,[status(thm)],[611])).
% 1.32/1.50 tff(613,plain,
% 1.32/1.50 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[612])).
% 1.32/1.50 tff(614,plain,
% 1.32/1.50 (~(z = s(s(s(z))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[392, 613])).
% 1.32/1.50 tff(615,plain,
% 1.32/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(616,plain,
% 1.32/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(617,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.32/1.51 tff(618,plain,
% 1.32/1.51 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[617, 44])).
% 1.32/1.51 tff(619,plain,
% 1.32/1.51 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[618, 614])).
% 1.32/1.51 tff(620,plain,
% 1.32/1.51 (r(z, s(s(s(z))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[619, 610])).
% 1.32/1.51 tff(621,plain,
% 1.32/1.51 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[313, 305, 123, 132])).
% 1.32/1.51 tff(622,plain,
% 1.32/1.51 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[319, 621])).
% 1.32/1.51 tff(623,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.32/1.51 tff(624,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.32/1.51 tff(625,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(626,plain,
% 1.32/1.51 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(627,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[626])).
% 1.32/1.51 tff(628,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[627, 625])).
% 1.32/1.51 tff(629,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(630,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.32/1.51 tff(631,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[630, 144, 624, 305, 123, 132, 286])).
% 1.32/1.51 tff(632,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(633,plain,
% 1.32/1.51 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[632, 624, 305, 123, 132])).
% 1.32/1.51 tff(634,plain,
% 1.32/1.51 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[302, 633])).
% 1.32/1.51 tff(635,plain,
% 1.32/1.51 (((~![X0: $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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(636,plain,
% 1.32/1.51 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(637,plain,
% 1.32/1.51 (((~![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(s(s(z))))))), z)) | (~r(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[636])).
% 1.32/1.51 tff(638,plain,
% 1.32/1.51 (((~![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(s(s(z))))))), z)) | (~r(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[637, 635])).
% 1.32/1.51 tff(639,plain,
% 1.32/1.51 ((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(640,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.32/1.51 tff(641,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[640, 333, 323, 623, 322, 321])).
% 1.32/1.51 tff(642,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(643,plain,
% 1.32/1.51 (~r(s(z), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[642, 634, 623, 622])).
% 1.32/1.51 tff(644,plain,
% 1.32/1.51 (b(s(z), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[348, 643])).
% 1.32/1.51 tff(645,plain,
% 1.32/1.51 (~r(z, s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[362, 634, 353, 622])).
% 1.32/1.51 tff(646,plain,
% 1.32/1.51 (b(z, s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[372, 645])).
% 1.32/1.51 tff(647,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[387, 144, 624, 646, 644, 305])).
% 1.32/1.51 tff(648,plain,((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(649,plain,
% 1.32/1.51 (~b(elem!1, z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[648, 282, 620, 173, 123, 122])).
% 1.32/1.51 tff(650,plain,
% 1.32/1.51 (((~![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))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(651,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(652,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.32/1.51 tff(653,plain,
% 1.32/1.51 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[652, 44])).
% 1.32/1.51 tff(654,plain,
% 1.32/1.51 (r(elem!1, z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[653, 649, 77])).
% 1.32/1.51 tff(655,plain,
% 1.32/1.51 (((~![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))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(656,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(657,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.32/1.51 tff(658,plain,
% 1.32/1.51 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[657, 44])).
% 1.32/1.51 tff(659,plain,
% 1.32/1.51 (r(z, elem!1)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[658, 604, 71])).
% 1.32/1.51 tff(660,plain,
% 1.32/1.51 (~r(s(elem!1), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[481, 654, 407, 197, 54, 110, 3, 221, 421])).
% 1.32/1.51 tff(661,plain,
% 1.32/1.51 (b(s(elem!1), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[486, 660, 1])).
% 1.32/1.51 tff(662,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(663,plain,
% 1.32/1.51 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(664,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[663])).
% 1.32/1.51 tff(665,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[664, 662])).
% 1.32/1.51 tff(666,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(667,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.32/1.51 tff(668,plain,
% 1.32/1.51 (~b(elem!1, s(elem!1))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[667, 144, 661, 282, 123, 122])).
% 1.32/1.51 tff(669,plain,
% 1.32/1.51 (r(elem!1, s(elem!1))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[560, 668, 545])).
% 1.32/1.51 tff(670,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.32/1.51 tff(671,plain,
% 1.32/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(672,plain,
% 1.32/1.51 (((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(673,plain,
% 1.32/1.51 (((~![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(elem!1, 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(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[672])).
% 1.32/1.51 tff(674,plain,
% 1.32/1.51 (((~![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(elem!1, 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(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[673, 671])).
% 1.32/1.51 tff(675,plain,
% 1.32/1.51 ((~![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(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(676,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.32/1.51 tff(677,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[676, 333, 563, 670, 408, 509])).
% 1.32/1.51 tff(678,plain,((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(679,plain,
% 1.32/1.51 (~r(s(elem!1), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[678, 669, 659, 654])).
% 1.32/1.51 tff(680,plain,
% 1.32/1.51 (((~![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(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, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(681,plain,
% 1.32/1.51 ((~![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(z), elem!1)) | (~r(s(z), z)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(682,plain,
% 1.32/1.51 ((~![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(z), elem!1)) | (~r(s(z), z))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.32/1.51 tff(683,plain,
% 1.32/1.51 (~r(s(z), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[682, 333, 659, 407, 654])).
% 1.32/1.51 tff(684,plain,
% 1.32/1.51 (b(s(z), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[348, 683])).
% 1.32/1.51 tff(685,plain,
% 1.32/1.51 (((~![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(z, s(z))) | (~r(z, elem!1)) | (~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(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(686,plain,
% 1.32/1.52 (((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(687,plain,
% 1.32/1.52 (((~![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(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[686])).
% 1.32/1.52 tff(688,plain,
% 1.32/1.52 (((~![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(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[687, 685])).
% 1.32/1.52 tff(689,plain,
% 1.32/1.52 ((~![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))))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(690,plain,
% 1.32/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[689, 688])).
% 1.32/1.52 tff(691,plain,
% 1.32/1.52 (~r(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[690, 333, 659, 407, 654])).
% 1.32/1.52 tff(692,plain,
% 1.32/1.52 (b(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[372, 691])).
% 1.32/1.52 tff(693,plain,
% 1.32/1.52 (~b(s(elem!1), z)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[499, 692, 661, 684])).
% 1.32/1.52 tff(694,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[507, 693, 679])).
% 1.32/1.52 tff(695,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(696,plain,
% 1.32/1.52 (~(s(s(s(z))) = elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[695, 56, 1, 54, 3, 50])).
% 1.32/1.52 tff(697,plain,
% 1.32/1.52 (~(elem!1 = s(s(s(z))))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[696, 65])).
% 1.32/1.52 tff(698,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.32/1.52 tff(699,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.32/1.52 tff(700,plain,
% 1.32/1.52 (((~![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))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(701,plain,
% 1.32/1.52 ((~![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))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(702,plain,
% 1.32/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.32/1.52 tff(703,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[702, 44, 699, 698, 55])).
% 1.32/1.52 tff(704,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,[]))).
% 1.32/1.52 tff(705,plain,
% 1.32/1.52 (r(s(s(s(z))), elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[704, 696, 55])).
% 1.32/1.52 tff(706,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.32/1.52 tff(707,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.32/1.52 tff(708,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.32/1.52 tff(709,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.32/1.52 tff(710,plain,
% 1.32/1.52 (s(z) = elem!1),
% 1.32/1.52 inference(symmetry,[status(thm)],[709])).
% 1.32/1.52 tff(711,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[706, 710])).
% 1.32/1.52 tff(712,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(713,plain,
% 1.32/1.52 (~(elem!1 = s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[712, 706])).
% 1.32/1.52 tff(714,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.32/1.52 tff(715,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.32/1.52 tff(716,plain,
% 1.32/1.52 (((~![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)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(717,plain,
% 1.32/1.52 ((~![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)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(718,plain,
% 1.32/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.32/1.52 tff(719,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[718, 44, 715, 708, 714])).
% 1.32/1.52 tff(720,plain,(r(elem!1, s(z)) | b(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(721,plain,
% 1.32/1.52 (r(elem!1, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[720, 708, 713])).
% 1.32/1.52 tff(722,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.32/1.52 tff(723,plain,
% 1.32/1.52 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(724,plain,
% 1.32/1.52 ((~![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(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(725,plain,
% 1.32/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.32/1.52 tff(726,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[725, 333, 670, 354, 323, 722])).
% 1.32/1.52 tff(727,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(728,plain,
% 1.32/1.52 (~r(z, elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[727, 354, 721, 323])).
% 1.32/1.52 tff(729,plain,
% 1.32/1.52 (b(z, elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[658, 728, 71])).
% 1.32/1.52 tff(730,plain,
% 1.32/1.52 (~(elem!1 = z)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[76, 74])).
% 1.32/1.52 tff(731,plain,
% 1.32/1.52 (r(elem!1, z)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[653, 377, 730])).
% 1.32/1.52 tff(732,plain,
% 1.32/1.52 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[81])).
% 1.32/1.52 tff(733,plain,
% 1.32/1.52 (b(elem!1, s(z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[304, 732])).
% 1.32/1.52 tff(734,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[708, 733])).
% 1.32/1.52 tff(735,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(elem!1, s(z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(736,plain,
% 1.32/1.52 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[735, 304, 708])).
% 1.32/1.52 tff(737,plain,
% 1.32/1.52 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[130, 736, 54])).
% 1.32/1.52 tff(738,plain,
% 1.32/1.52 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[116, 736])).
% 1.32/1.52 tff(739,plain,
% 1.32/1.52 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[121, 738, 3])).
% 1.32/1.52 tff(740,plain,
% 1.32/1.52 (((~![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(elem!1, s(z))) | (~r(z, 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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(741,plain,
% 1.32/1.52 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(742,plain,
% 1.32/1.52 (((~![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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[741])).
% 1.32/1.52 tff(743,plain,
% 1.32/1.52 (((~![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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[742, 740])).
% 1.32/1.52 tff(744,plain,
% 1.32/1.52 ((~![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))))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(745,plain,
% 1.32/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.32/1.52 tff(746,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[745, 333, 354, 323, 408, 722])).
% 1.32/1.52 tff(747,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(748,plain,
% 1.32/1.52 (~r(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[747, 408, 323, 721])).
% 1.32/1.52 tff(749,plain,
% 1.32/1.52 (b(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[372, 748])).
% 1.32/1.52 tff(750,plain,
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% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(751,plain,
% 1.32/1.52 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(752,plain,
% 1.32/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[751])).
% 1.32/1.52 tff(753,plain,
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% 1.32/1.52 inference(transitivity,[status(thm)],[752, 750])).
% 1.32/1.52 tff(754,plain,
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% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(755,plain,
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% 1.32/1.52 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.32/1.52 tff(756,plain,
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% 1.32/1.52 inference(unit_resolution,[status(thm)],[755, 144, 490, 123, 304, 259])).
% 1.32/1.52 tff(757,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(758,plain,
% 1.32/1.52 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[757, 304, 123, 749])).
% 1.32/1.52 tff(759,plain,
% 1.32/1.52 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[279, 758])).
% 1.32/1.52 tff(760,plain,
% 1.32/1.52 (~r(s(z), elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[417, 759, 323, 408])).
% 1.32/1.52 tff(761,plain,
% 1.32/1.52 (b(s(z), elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[406, 760, 706])).
% 1.32/1.52 tff(762,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[152, 761, 739, 123, 737])).
% 1.32/1.52 tff(763,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(764,plain,
% 1.32/1.52 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[763, 731, 706, 3, 323, 123, 54, 708])).
% 1.32/1.52 tff(765,plain,
% 1.32/1.52 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[319, 764])).
% 1.32/1.52 tff(766,plain,
% 1.32/1.52 (~r(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[747, 731, 323, 721])).
% 1.32/1.52 tff(767,plain,
% 1.32/1.52 (b(z, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[372, 766])).
% 1.32/1.52 tff(768,plain,
% 1.32/1.52 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[341, 321, 323, 322])).
% 1.32/1.52 tff(769,plain,
% 1.32/1.52 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[279, 768])).
% 1.32/1.52 tff(770,plain,
% 1.32/1.52 (~r(z, s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[642, 321, 323, 322])).
% 1.32/1.52 tff(771,plain,
% 1.32/1.52 (b(z, s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[619, 770])).
% 1.32/1.52 tff(772,plain,
% 1.32/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(773,plain,
% 1.32/1.52 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(774,plain,
% 1.32/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[773])).
% 1.32/1.52 tff(775,plain,
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% 1.32/1.52 inference(transitivity,[status(thm)],[774, 772])).
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% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
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% 1.32/1.53 inference(modus_ponens,[status(thm)],[776, 775])).
% 1.32/1.53 tff(778,plain,
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[777, 144, 490, 771, 56, 123, 769])).
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% 1.32/1.53 tff(780,plain,
% 1.32/1.53 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[779, 767, 56, 123, 323, 765])).
% 1.32/1.53 tff(781,plain,
% 1.32/1.53 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[302, 780])).
% 1.32/1.53 tff(782,plain,
% 1.32/1.53 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(elem!1, z)),
% 1.32/1.53 inference(monotonicity,[status(thm)],[81])).
% 1.32/1.53 tff(783,plain,
% 1.32/1.53 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.53 inference(symmetry,[status(thm)],[782])).
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% 1.32/1.53 ((~b(elem!1, z)) <=> (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[783])).
% 1.32/1.53 tff(785,plain,
% 1.32/1.53 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[377, 784])).
% 1.32/1.53 tff(786,plain,
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[286, 785])).
% 1.32/1.53 tff(787,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(788,plain,
% 1.32/1.53 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[787, 781, 377])).
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[130, 788, 54])).
% 1.32/1.53 tff(790,plain,
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[116, 788])).
% 1.32/1.53 tff(791,plain,
% 1.32/1.53 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[121, 790, 3])).
% 1.32/1.53 tff(792,plain,
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[152, 791, 123, 789])).
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[406, 792, 706])).
% 1.32/1.53 tff(794,plain,
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% 1.32/1.53 inference(unit_resolution,[status(thm)],[417, 793, 323, 731])).
% 1.32/1.53 tff(795,plain,
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% 1.32/1.53 tff(797,plain,
% 1.32/1.53 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
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% 1.32/1.53 inference(monotonicity,[status(thm)],[797])).
% 1.32/1.53 tff(799,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[798, 796])).
% 1.32/1.53 tff(800,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(801,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.32/1.53 tff(802,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[801, 144, 251, 490, 123, 133, 259])).
% 1.32/1.53 tff(803,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(804,plain,
% 1.32/1.53 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[803, 123, 490, 251, 259])).
% 1.32/1.53 tff(805,plain,
% 1.32/1.53 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[130, 804, 114])).
% 1.32/1.53 tff(806,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(807,plain,
% 1.32/1.53 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(808,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[807])).
% 1.32/1.53 tff(809,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[808, 806])).
% 1.32/1.53 tff(810,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(811,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.32/1.53 tff(812,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[811, 144, 251, 490, 305, 123, 259])).
% 1.32/1.53 tff(813,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(814,plain,
% 1.32/1.53 (~b(elem!1, s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[813, 123, 490, 251, 259])).
% 1.32/1.53 tff(815,plain,
% 1.32/1.53 (r(elem!1, s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[720, 814, 714])).
% 1.32/1.53 tff(816,plain,
% 1.32/1.53 (((~![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(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(817,plain,
% 1.32/1.53 ((~![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(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(818,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[817, 816])).
% 1.32/1.53 tff(819,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[818, 333, 323, 815, 805, 322])).
% 1.32/1.53 tff(820,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(821,plain,
% 1.32/1.53 (~b(z, elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[820, 795, 123, 788, 713, 765, 323, 767])).
% 1.32/1.53 tff(822,plain,
% 1.32/1.53 (r(z, elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[658, 821, 74])).
% 1.32/1.53 tff(823,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[682, 333, 822, 793, 323, 731])).
% 1.32/1.53 tff(824,plain,(b(elem!1, z) | (~r(s(z), z)) | (z = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(825,plain,
% 1.32/1.53 (b(elem!1, z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[824, 323, 71, 123, 706, 3, 54, 56, 708])).
% 1.32/1.53 tff(826,plain,
% 1.32/1.53 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[267, 737, 729, 739])).
% 1.32/1.53 tff(827,plain,
% 1.32/1.53 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[279, 826])).
% 1.32/1.53 tff(828,plain,
% 1.32/1.53 (~b(s(z), elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[152, 739, 123, 737])).
% 1.32/1.53 tff(829,plain,
% 1.32/1.53 (r(s(z), elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[406, 828, 706])).
% 1.32/1.53 tff(830,plain,
% 1.32/1.53 (((~![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))), 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(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(831,plain,
% 1.32/1.53 (((~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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(832,plain,
% 1.32/1.53 (((~![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(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(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[831])).
% 1.32/1.53 tff(833,plain,
% 1.32/1.53 (((~![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(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(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[832, 830])).
% 1.32/1.53 tff(834,plain,
% 1.32/1.53 ((~![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(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(835,plain,
% 1.32/1.53 ((~![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))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.32/1.53 tff(836,plain,
% 1.32/1.53 (~r(s(z), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[835, 333, 829, 721, 707])).
% 1.32/1.53 tff(837,plain,
% 1.32/1.53 (b(s(z), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[172, 836])).
% 1.32/1.53 tff(838,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.32/1.53 tff(839,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(840,plain,
% 1.32/1.53 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(841,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[840])).
% 1.32/1.53 tff(842,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[841, 839])).
% 1.32/1.53 tff(843,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(844,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[843, 842])).
% 1.32/1.53 tff(845,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[844, 144, 56, 838, 283, 304])).
% 1.32/1.53 tff(846,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(847,plain,
% 1.32/1.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[846, 837, 56, 304])).
% 1.32/1.53 tff(848,plain,
% 1.32/1.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[249, 847])).
% 1.32/1.53 tff(849,plain,
% 1.32/1.53 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(850,plain,
% 1.32/1.53 (inj_0(s(elem!1)) = elem!1),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[849, 14])).
% 1.32/1.53 tff(851,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.32/1.53 tff(852,plain,
% 1.32/1.53 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[851])).
% 1.32/1.53 tff(853,plain,
% 1.32/1.53 (s(z) = elem!1),
% 1.32/1.53 inference(transitivity,[status(thm)],[193, 852, 850])).
% 1.32/1.53 tff(854,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[706, 853])).
% 1.32/1.53 tff(855,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(856,plain,
% 1.32/1.53 (~(s(s(z)) = s(elem!1))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[855, 706])).
% 1.32/1.53 tff(857,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.32/1.53 tff(858,plain,
% 1.32/1.53 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[857])).
% 1.32/1.53 tff(859,plain,
% 1.32/1.53 (s(s(z)) = s(elem!1)),
% 1.32/1.53 inference(transitivity,[status(thm)],[87, 858, 101])).
% 1.32/1.53 tff(860,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.32/1.53 tff(861,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[860, 859])).
% 1.32/1.53 tff(862,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(863,plain,
% 1.32/1.53 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[862, 856])).
% 1.32/1.53 tff(864,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(865,plain,
% 1.32/1.54 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(866,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[865])).
% 1.32/1.54 tff(867,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.54 inference(transitivity,[status(thm)],[866, 864])).
% 1.32/1.54 tff(868,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(869,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.32/1.54 tff(870,plain,
% 1.32/1.54 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[869, 144, 488, 123, 304])).
% 1.32/1.54 tff(871,plain,
% 1.32/1.54 (~r(z, elem!1)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[727, 354, 722, 323])).
% 1.32/1.54 tff(872,plain,
% 1.32/1.54 (b(z, elem!1)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[658, 871, 71])).
% 1.32/1.54 tff(873,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(874,plain,
% 1.32/1.54 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(875,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[874])).
% 1.32/1.54 tff(876,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.32/1.54 inference(transitivity,[status(thm)],[875, 873])).
% 1.32/1.54 tff(877,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(878,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[877, 876])).
% 1.32/1.54 tff(879,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[878, 144, 251, 624, 133, 286])).
% 1.32/1.54 tff(880,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(881,plain,
% 1.32/1.54 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[880, 133, 624, 872])).
% 1.32/1.54 tff(882,plain,
% 1.32/1.54 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[302, 881])).
% 1.32/1.54 tff(883,plain,
% 1.32/1.54 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[267, 133, 872, 132])).
% 1.32/1.54 tff(884,plain,
% 1.32/1.54 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[279, 883])).
% 1.32/1.54 tff(885,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.32/1.54 tff(886,plain,
% 1.32/1.54 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[885])).
% 1.32/1.54 tff(887,plain,
% 1.32/1.54 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.32/1.54 inference(symmetry,[status(thm)],[886])).
% 1.32/1.54 tff(888,plain,
% 1.32/1.54 (b(elem!1, s(z))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[488, 887])).
% 1.32/1.54 tff(889,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[708, 888])).
% 1.32/1.54 tff(890,plain,((~b(s(elem!1), s(z))) | b(elem!1, s(z)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(891,plain,
% 1.32/1.54 (~(elem!1 = s(elem!1))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[890, 488, 708])).
% 1.32/1.54 tff(892,plain,
% 1.32/1.54 (~r(s(z), s(s(s(z))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[835, 333, 409, 722, 707])).
% 1.32/1.54 tff(893,plain,
% 1.32/1.54 (b(s(z), s(s(s(z))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[172, 892])).
% 1.32/1.54 tff(894,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(895,plain,
% 1.32/1.54 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(896,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[895])).
% 1.32/1.54 tff(897,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.54 inference(transitivity,[status(thm)],[896, 894])).
% 1.32/1.54 tff(898,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(899,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.32/1.54 tff(900,plain,
% 1.32/1.54 (~b(s(elem!1), s(s(s(z))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[899, 144, 488, 56, 893])).
% 1.32/1.54 tff(901,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.32/1.54 tff(902,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.32/1.54 tff(903,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.32/1.54 tff(904,plain,
% 1.32/1.54 (elem!1 = s(elem!1)),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[903, 198])).
% 1.32/1.54 tff(905,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[902, 904])).
% 1.32/1.54 tff(906,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(907,plain,
% 1.32/1.54 (~(s(elem!1) = elem!1)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[906, 902])).
% 1.32/1.54 tff(908,plain,
% 1.32/1.54 (b(s(elem!1), z)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[507, 501])).
% 1.32/1.54 tff(909,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(910,plain,
% 1.32/1.54 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(911,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[910])).
% 1.32/1.54 tff(912,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.32/1.54 inference(transitivity,[status(thm)],[911, 909])).
% 1.32/1.54 tff(913,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(914,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[913, 912])).
% 1.32/1.54 tff(915,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[914, 144, 451, 251, 624, 491])).
% 1.32/1.54 tff(916,plain,((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(917,plain,
% 1.32/1.54 (~b(s(elem!1), elem!1)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[916, 908, 624, 251])).
% 1.32/1.54 tff(918,plain,
% 1.32/1.54 (r(s(elem!1), elem!1)),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[448, 917, 907])).
% 1.32/1.54 tff(919,assumption,(s(s(s(s(s(s(s(z))))))) = s(elem!1)), introduced(assumption)).
% 1.32/1.54 tff(920,plain,
% 1.32/1.54 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(elem!1), z)),
% 1.32/1.54 inference(monotonicity,[status(thm)],[919])).
% 1.32/1.54 tff(921,plain,
% 1.32/1.54 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.54 inference(symmetry,[status(thm)],[920])).
% 1.32/1.54 tff(922,plain,
% 1.32/1.54 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[921])).
% 1.32/1.54 tff(923,plain,
% 1.32/1.54 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[501, 922])).
% 1.32/1.54 tff(924,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[321, 923])).
% 1.32/1.54 tff(925,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(926,plain,
% 1.32/1.54 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[925, 501, 321])).
% 1.32/1.54 tff(927,assumption,(s(elem!1) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.32/1.54 tff(928,plain,
% 1.32/1.54 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.32/1.54 inference(symmetry,[status(thm)],[927])).
% 1.32/1.54 tff(929,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[537, 928])).
% 1.32/1.54 tff(930,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(931,plain,
% 1.32/1.54 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[930, 926])).
% 1.32/1.54 tff(932,plain,
% 1.32/1.54 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[472, 931, 467])).
% 1.32/1.54 tff(933,plain,
% 1.32/1.54 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(934,plain,
% 1.32/1.54 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(935,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[934])).
% 1.32/1.54 tff(936,plain,
% 1.32/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[935, 933])).
% 1.32/1.55 tff(937,plain,
% 1.32/1.55 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(938,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.32/1.55 tff(939,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[938, 333, 562, 321, 51, 525])).
% 1.32/1.55 tff(940,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(941,plain,
% 1.32/1.55 (~r(z, s(elem!1))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[940, 932, 321, 51])).
% 1.32/1.55 tff(942,plain,
% 1.32/1.55 (b(z, s(elem!1))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[583, 941])).
% 1.32/1.55 tff(943,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(944,plain,
% 1.32/1.55 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(945,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[944])).
% 1.32/1.55 tff(946,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[945, 943])).
% 1.32/1.55 tff(947,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(948,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1)))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.32/1.55 tff(949,plain,
% 1.32/1.55 ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[948, 144])).
% 1.32/1.55 tff(950,plain,
% 1.32/1.55 (~b(elem!1, s(elem!1))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[949, 942, 624, 908])).
% 1.32/1.55 tff(951,plain,
% 1.32/1.55 (r(elem!1, s(elem!1))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[560, 950, 902])).
% 1.32/1.55 tff(952,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(953,plain,
% 1.32/1.55 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(954,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[953])).
% 1.32/1.55 tff(955,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[954, 952])).
% 1.32/1.55 tff(956,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(957,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.32/1.55 tff(958,plain,
% 1.32/1.55 (~r(s(elem!1), s(s(s(z))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[957, 333, 951, 918, 707])).
% 1.32/1.55 tff(959,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.32/1.55 tff(960,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.32/1.55 tff(961,plain,
% 1.32/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(962,plain,
% 1.32/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(963,plain,
% 1.32/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.32/1.55 tff(964,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[963, 44, 960, 901, 959])).
% 1.32/1.55 tff(965,plain,(b(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(966,plain,
% 1.32/1.55 (s(elem!1) = s(s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[965, 958, 901])).
% 1.32/1.55 tff(967,plain,
% 1.32/1.55 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[966])).
% 1.32/1.55 tff(968,plain,
% 1.32/1.55 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[967])).
% 1.32/1.55 tff(969,plain,
% 1.32/1.55 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.32/1.55 inference(symmetry,[status(thm)],[968])).
% 1.32/1.55 tff(970,plain,
% 1.32/1.55 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[969])).
% 1.32/1.55 tff(971,plain,
% 1.32/1.55 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.32/1.55 inference(symmetry,[status(thm)],[970])).
% 1.32/1.55 tff(972,plain,
% 1.32/1.55 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.32/1.55 inference(commutativity,[status(thm)],[])).
% 1.32/1.55 tff(973,plain,
% 1.32/1.55 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[966])).
% 1.32/1.55 tff(974,plain,
% 1.32/1.55 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[973, 972])).
% 1.32/1.55 tff(975,plain,
% 1.32/1.55 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[974])).
% 1.32/1.55 tff(976,plain,
% 1.32/1.55 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(977,plain,
% 1.32/1.55 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[976, 14])).
% 1.32/1.55 tff(978,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.32/1.55 tff(979,plain,
% 1.32/1.55 (s(s(s(elem!1))) = s(elem!1)),
% 1.32/1.55 inference(symmetry,[status(thm)],[978])).
% 1.32/1.55 tff(980,plain,
% 1.32/1.55 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[979])).
% 1.32/1.55 tff(981,plain,
% 1.32/1.55 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.32/1.55 inference(symmetry,[status(thm)],[980])).
% 1.32/1.55 tff(982,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.32/1.55 tff(983,plain,
% 1.32/1.55 (s(s(s(z))) = s(elem!1)),
% 1.32/1.55 inference(symmetry,[status(thm)],[982])).
% 1.32/1.55 tff(984,plain,
% 1.32/1.55 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[983])).
% 1.32/1.55 tff(985,plain,
% 1.32/1.55 (s(s(z)) = s(s(elem!1))),
% 1.32/1.55 inference(transitivity,[status(thm)],[87, 984, 981, 977])).
% 1.32/1.55 tff(986,plain,
% 1.32/1.55 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[985])).
% 1.32/1.55 tff(987,plain,
% 1.32/1.55 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.32/1.55 inference(symmetry,[status(thm)],[986])).
% 1.32/1.55 tff(988,plain,
% 1.32/1.55 (s(elem!1) = s(z)),
% 1.32/1.55 inference(transitivity,[status(thm)],[102, 987, 80])).
% 1.32/1.55 tff(989,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1, 988])).
% 1.32/1.55 tff(990,plain,((~(s(elem!1) = s(s(s(z))))) | (s(elem!1) = s(z)) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(991,plain,
% 1.32/1.55 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[990, 966, 1])).
% 1.32/1.55 tff(992,plain,
% 1.32/1.55 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[991, 975])).
% 1.32/1.55 tff(993,plain,
% 1.32/1.55 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[969])).
% 1.32/1.55 tff(994,plain,
% 1.32/1.55 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[993])).
% 1.32/1.55 tff(995,plain,
% 1.32/1.55 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[969])).
% 1.32/1.55 tff(996,plain,
% 1.32/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.32/1.55 inference(symmetry,[status(thm)],[995])).
% 1.32/1.55 tff(997,plain,
% 1.32/1.55 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.32/1.55 inference(commutativity,[status(thm)],[])).
% 1.32/1.55 tff(998,plain,
% 1.32/1.55 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.32/1.55 inference(symmetry,[status(thm)],[997])).
% 1.32/1.55 tff(999,plain,
% 1.32/1.55 (s(s(s(z))) = s(elem!1)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[966, 998])).
% 1.32/1.55 tff(1000,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.32/1.55 tff(1001,plain,
% 1.32/1.55 (elem!1 = s(s(s(elem!1)))),
% 1.32/1.55 inference(symmetry,[status(thm)],[1000])).
% 1.32/1.55 tff(1002,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.32/1.55 tff(1003,plain,
% 1.32/1.55 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1002])).
% 1.32/1.55 tff(1004,plain,
% 1.32/1.55 (s(s(z)) = s(s(s(elem!1)))),
% 1.32/1.55 inference(transitivity,[status(thm)],[87, 1003, 850, 1001])).
% 1.32/1.55 tff(1005,plain,
% 1.32/1.55 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1004])).
% 1.32/1.55 tff(1006,plain,
% 1.32/1.55 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.32/1.55 inference(symmetry,[status(thm)],[1005])).
% 1.32/1.55 tff(1007,plain,
% 1.32/1.55 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.32/1.55 inference(symmetry,[status(thm)],[977])).
% 1.32/1.55 tff(1008,plain,
% 1.32/1.55 (s(s(elem!1)) = s(z)),
% 1.32/1.55 inference(transitivity,[status(thm)],[1007, 1006, 80])).
% 1.32/1.55 tff(1009,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[107, 1008])).
% 1.32/1.55 tff(1010,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1011,plain,
% 1.32/1.55 (~(s(s(s(elem!1))) = elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1010, 999])).
% 1.32/1.55 tff(1012,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.32/1.55 tff(1013,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.32/1.55 tff(1014,plain,
% 1.32/1.55 (s(s(s(elem!1))) = elem!1),
% 1.32/1.55 inference(symmetry,[status(thm)],[1013])).
% 1.32/1.55 tff(1015,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1012, 1014])).
% 1.32/1.55 tff(1016,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1017,plain,
% 1.32/1.55 (~(elem!1 = s(s(s(elem!1))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1016, 1012])).
% 1.32/1.55 tff(1018,plain,
% 1.32/1.55 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.32/1.55 inference(commutativity,[status(thm)],[])).
% 1.32/1.55 tff(1019,plain,
% 1.32/1.55 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.32/1.55 inference(symmetry,[status(thm)],[1018])).
% 1.32/1.55 tff(1020,plain,
% 1.32/1.55 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.55 tff(1021,plain,
% 1.32/1.55 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1022,plain,
% 1.32/1.55 (~(s(s(s(elem!1))) = z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1021, 29])).
% 1.32/1.55 tff(1023,plain,
% 1.32/1.55 (~(z = s(s(s(elem!1))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1022, 1020])).
% 1.32/1.55 tff(1024,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.32/1.55 tff(1025,plain,
% 1.32/1.55 (((~![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(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1026,plain,
% 1.32/1.55 ((~![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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1027,plain,
% 1.32/1.55 ((~![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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.32/1.55 tff(1028,plain,
% 1.32/1.55 (~r(z, s(s(s(elem!1))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1027, 333, 354, 1024, 323])).
% 1.32/1.55 tff(1029,plain,
% 1.32/1.55 (((~![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)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1030,plain,
% 1.32/1.55 ((~![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)))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1031,plain,
% 1.32/1.55 ((~![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))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 1.32/1.55 tff(1032,plain,
% 1.32/1.55 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1031, 44, 1028])).
% 1.32/1.55 tff(1033,plain,
% 1.32/1.55 (b(z, s(s(s(elem!1))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1032, 1023])).
% 1.32/1.55 tff(1034,plain,
% 1.32/1.55 (((~![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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(elem!1))), z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1035,plain,
% 1.32/1.55 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1036,plain,
% 1.32/1.55 (((~![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(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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1035])).
% 1.32/1.55 tff(1037,plain,
% 1.32/1.55 (((~![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(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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.32/1.55 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.32/1.55 tff(1038,plain,
% 1.32/1.55 ((~![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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1039,plain,
% 1.32/1.55 ((~![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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.32/1.55 tff(1040,plain,
% 1.32/1.55 (~r(s(s(s(elem!1))), z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1039, 333, 354, 1024, 323])).
% 1.32/1.55 tff(1041,plain,
% 1.32/1.55 (((~![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))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1042,plain,
% 1.32/1.55 ((~![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))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1043,plain,
% 1.32/1.55 ((~![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)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.32/1.55 tff(1044,plain,
% 1.32/1.55 (b(s(s(s(elem!1))), z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 1040])).
% 1.32/1.55 tff(1045,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1046,plain,
% 1.32/1.55 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1047,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1046])).
% 1.32/1.56 tff(1048,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.32/1.56 inference(transitivity,[status(thm)],[1047, 1045])).
% 1.32/1.56 tff(1049,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1050,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 1.32/1.56 tff(1051,plain,
% 1.32/1.56 (~b(elem!1, s(s(s(elem!1))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1050, 144, 624, 1044, 1033])).
% 1.32/1.56 tff(1052,plain,
% 1.32/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1053,plain,
% 1.32/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1054,plain,
% 1.32/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.32/1.56 tff(1055,plain,
% 1.32/1.56 (r(elem!1, s(s(s(elem!1))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1054, 44, 1051, 1017])).
% 1.32/1.56 tff(1056,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.32/1.56 tff(1057,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1058,plain,
% 1.32/1.56 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1059,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1058])).
% 1.32/1.56 tff(1060,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.32/1.56 inference(transitivity,[status(thm)],[1059, 1057])).
% 1.32/1.56 tff(1061,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1062,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.32/1.56 tff(1063,plain,
% 1.32/1.56 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1062, 144, 491, 1044, 1033])).
% 1.32/1.56 tff(1064,plain,
% 1.32/1.56 (((~![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)))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1065,plain,
% 1.32/1.56 ((~![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)))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1066,plain,
% 1.32/1.56 ((~![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))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 1.32/1.56 tff(1067,plain,
% 1.32/1.56 ((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))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1066, 44])).
% 1.32/1.56 tff(1068,plain,
% 1.32/1.56 (r(s(elem!1), s(s(s(elem!1))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1067, 1063, 1056])).
% 1.32/1.56 tff(1069,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1070,plain,
% 1.32/1.56 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1071,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1070])).
% 1.32/1.56 tff(1072,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)))),
% 1.32/1.56 inference(transitivity,[status(thm)],[1071, 1069])).
% 1.32/1.56 tff(1073,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1074,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 1.32/1.56 tff(1075,plain,
% 1.32/1.56 (~b(s(s(s(elem!1))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1074, 144, 251, 624, 1044])).
% 1.32/1.56 tff(1076,plain,
% 1.32/1.56 (((~![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))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1077,plain,
% 1.32/1.56 ((~![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))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1078,plain,
% 1.32/1.56 ((~![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)),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 1.32/1.56 tff(1079,plain,
% 1.32/1.56 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1078, 44])).
% 1.32/1.56 tff(1080,plain,
% 1.32/1.56 (r(s(s(s(elem!1))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1079, 1075, 1012])).
% 1.32/1.56 tff(1081,plain,
% 1.32/1.56 (((~![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(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~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), elem!1)) | (~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))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1082,plain,
% 1.32/1.56 (((~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(s(elem!1), elem!1)) | (~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))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1083,plain,
% 1.32/1.56 (((~![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(s(elem!1), elem!1)) | (~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)))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1082])).
% 1.32/1.56 tff(1084,plain,
% 1.32/1.56 (((~![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(s(elem!1), elem!1)) | (~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))))))),
% 1.32/1.56 inference(transitivity,[status(thm)],[1083, 1081])).
% 1.32/1.56 tff(1085,plain,
% 1.32/1.56 ((~![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)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1086,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 1.32/1.56 tff(1087,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1086, 333, 435, 1080, 1068, 1055])).
% 1.32/1.56 tff(1088,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(1089,plain,
% 1.32/1.56 (~r(s(s(s(elem!1))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1088, 1011, 354, 251, 918, 624, 908, 991, 323])).
% 1.32/1.56 tff(1090,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.32/1.56 tff(1091,plain,
% 1.32/1.56 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1090])).
% 1.32/1.56 tff(1092,plain,
% 1.32/1.56 (s(s(elem!1)) = z),
% 1.32/1.56 inference(transitivity,[status(thm)],[1007, 1091, 16])).
% 1.32/1.56 tff(1093,plain,
% 1.32/1.56 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1094,plain,
% 1.32/1.56 (~(s(s(elem!1)) = z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1093, 29])).
% 1.32/1.56 tff(1095,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1094, 1092])).
% 1.32/1.56 tff(1096,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(1097,plain,
% 1.32/1.56 (((~![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)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1098,plain,
% 1.32/1.56 ((~![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)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(1099,plain,
% 1.32/1.56 ((~![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))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 1.32/1.56 tff(1100,plain,
% 1.32/1.56 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1099, 44])).
% 1.32/1.56 tff(1101,plain,
% 1.32/1.56 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1100, 1096])).
% 1.32/1.56 tff(1102,plain,
% 1.32/1.56 (b(s(s(s(elem!1))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1101, 1089])).
% 1.32/1.56 tff(1103,plain,
% 1.32/1.56 (b(s(s(s(s(s(z))))), s(z))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[1102, 996])).
% 1.32/1.56 tff(1104,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1105,plain,
% 1.32/1.56 (((~b(s(s(s(z))), 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(z), 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))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(1106,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[1105])).
% 1.32/1.56 tff(1107,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.32/1.57 tff(1108,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(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))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1109,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.32/1.57 tff(1110,plain,
% 1.32/1.57 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1109, 144, 56, 838])).
% 1.32/1.57 tff(1111,plain,
% 1.32/1.57 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1110, 1103])).
% 1.32/1.57 tff(1112,plain,
% 1.32/1.57 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1111, 994])).
% 1.32/1.57 tff(1113,plain,
% 1.32/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1114,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1115,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.32/1.57 tff(1116,plain,
% 1.32/1.57 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1115, 44])).
% 1.32/1.57 tff(1117,plain,
% 1.32/1.57 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1116, 1112, 992])).
% 1.32/1.57 tff(1118,plain,
% 1.32/1.57 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1117, 971])).
% 1.32/1.57 tff(1119,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1120,plain,
% 1.32/1.57 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1121,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[1120])).
% 1.32/1.57 tff(1122,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.32/1.57 tff(1123,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1124,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.32/1.57 tff(1125,plain,
% 1.32/1.57 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1124, 144, 56, 123, 304])).
% 1.32/1.57 tff(1126,plain,
% 1.32/1.57 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.32/1.57 inference(commutativity,[status(thm)],[])).
% 1.32/1.57 tff(1127,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.32/1.57 tff(1128,plain,
% 1.32/1.57 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.32/1.57 tff(1129,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))), introduced(assumption)).
% 1.32/1.57 tff(1130,plain,
% 1.32/1.57 ($false),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1129, 1128])).
% 1.32/1.57 tff(1131,plain,((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.57 tff(1132,plain,
% 1.32/1.57 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1131, 244])).
% 1.32/1.57 tff(1133,plain,
% 1.32/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1134,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1135,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.32/1.57 tff(1136,plain,
% 1.32/1.57 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1135, 44])).
% 1.32/1.57 tff(1137,plain,
% 1.32/1.57 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1136, 1132])).
% 1.32/1.57 tff(1138,plain,
% 1.32/1.57 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1137, 1125])).
% 1.32/1.57 tff(1139,plain,
% 1.32/1.57 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[846, 838, 56, 304])).
% 1.32/1.57 tff(1140,plain,
% 1.32/1.57 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[249, 1139])).
% 1.32/1.57 tff(1141,plain,
% 1.32/1.57 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1142,plain,
% 1.32/1.57 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1143,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[1142])).
% 1.32/1.57 tff(1144,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[1143, 1141])).
% 1.32/1.57 tff(1145,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1146,plain,
% 1.32/1.57 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.32/1.57 tff(1147,plain,
% 1.32/1.57 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1146, 333, 1140, 1138])).
% 1.32/1.57 tff(1148,plain,
% 1.32/1.57 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1147, 1118])).
% 1.32/1.57 tff(1149,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1150,plain,
% 1.32/1.57 (((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1151,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[1150])).
% 1.32/1.57 tff(1152,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[1151, 1149])).
% 1.32/1.57 tff(1153,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1154,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.32/1.57 tff(1155,plain,
% 1.32/1.57 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1154, 144, 123, 304])).
% 1.32/1.57 tff(1156,plain,
% 1.32/1.57 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1155, 1103])).
% 1.32/1.57 tff(1157,plain,
% 1.32/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(1158,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(1159,plain,
% 1.32/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 1.32/1.57 tff(1160,plain,
% 1.32/1.57 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1159, 44, 1156])).
% 1.32/1.57 tff(1161,plain,
% 1.32/1.57 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1160, 1148])).
% 1.32/1.57 tff(1162,plain,
% 1.32/1.57 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.32/1.57 inference(symmetry,[status(thm)],[1161])).
% 1.32/1.57 tff(1163,plain,
% 1.32/1.57 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[1162])).
% 1.32/1.57 tff(1164,plain,
% 1.32/1.57 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1163])).
% 1.32/1.58 tff(1165,plain,
% 1.32/1.58 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[239, 1164, 20])).
% 1.32/1.58 tff(1166,plain,
% 1.32/1.58 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1165])).
% 1.32/1.58 tff(1167,plain,
% 1.32/1.58 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1166])).
% 1.32/1.58 tff(1168,plain,
% 1.32/1.58 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[968, 93, 1167, 183])).
% 1.32/1.58 tff(1169,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[992, 1168])).
% 1.32/1.58 tff(1170,plain,(r(s(elem!1), z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1171,plain,
% 1.32/1.58 (r(s(elem!1), z)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1170, 900, 304, 56, 893, 354, 872, 624, 323, 1, 123, 707, 891, 882, 884, 870])).
% 1.32/1.58 tff(1172,plain,
% 1.32/1.58 (((~![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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1173,plain,
% 1.32/1.58 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1174,plain,
% 1.32/1.58 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1173])).
% 1.32/1.58 tff(1175,plain,
% 1.32/1.58 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[1174, 1172])).
% 1.32/1.58 tff(1176,plain,
% 1.32/1.58 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1177,plain,
% 1.32/1.58 ((~![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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.32/1.58 tff(1178,plain,
% 1.32/1.58 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1177, 333, 354, 1171, 882])).
% 1.32/1.58 tff(1179,plain,
% 1.32/1.58 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[472, 1178, 870])).
% 1.32/1.58 tff(1180,plain,
% 1.32/1.58 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1179])).
% 1.32/1.58 tff(1181,plain,
% 1.32/1.58 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1180])).
% 1.32/1.58 tff(1182,plain,
% 1.32/1.58 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1181])).
% 1.32/1.58 tff(1183,plain,
% 1.32/1.58 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1182])).
% 1.32/1.58 tff(1184,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.32/1.58 tff(1185,plain,
% 1.32/1.58 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1181])).
% 1.32/1.58 tff(1186,plain,
% 1.32/1.58 ((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1185])).
% 1.32/1.58 tff(1187,plain,
% 1.32/1.58 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1181])).
% 1.32/1.58 tff(1188,plain,
% 1.32/1.58 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1187])).
% 1.32/1.58 tff(1189,plain,
% 1.32/1.58 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1179])).
% 1.32/1.58 tff(1190,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.32/1.58 tff(1191,plain,
% 1.32/1.58 (s(elem!1) = s(s(elem!1))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1190])).
% 1.32/1.58 tff(1192,plain,
% 1.32/1.58 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1191])).
% 1.32/1.58 tff(1193,plain,
% 1.32/1.58 (elem!1 = inj_0(s(elem!1))),
% 1.32/1.58 inference(symmetry,[status(thm)],[850])).
% 1.32/1.58 tff(1194,plain,
% 1.32/1.58 (elem!1 = s(elem!1)),
% 1.32/1.58 inference(transitivity,[status(thm)],[1193, 1192, 101])).
% 1.32/1.58 tff(1195,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[902, 1194])).
% 1.32/1.58 tff(1196,plain,((~(s(s(elem!1)) = s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1197,plain,
% 1.32/1.58 (~(s(s(elem!1)) = s(elem!1))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1196, 891])).
% 1.32/1.58 tff(1198,plain,
% 1.32/1.58 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1179])).
% 1.32/1.58 tff(1199,plain,
% 1.32/1.58 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1198])).
% 1.32/1.58 tff(1200,plain,
% 1.32/1.58 (b(elem!1, s(elem!1))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[132, 1199])).
% 1.32/1.58 tff(1201,plain,
% 1.32/1.58 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[930, 1179])).
% 1.32/1.58 tff(1202,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1203,plain,
% 1.32/1.58 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[919])).
% 1.32/1.58 tff(1204,plain,
% 1.32/1.58 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.32/1.58 inference(transitivity,[status(thm)],[21, 1203, 850, 1202])).
% 1.32/1.58 tff(1205,plain,
% 1.32/1.58 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1204])).
% 1.32/1.58 tff(1206,plain,
% 1.32/1.58 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.32/1.58 inference(transitivity,[status(thm)],[93, 1205, 101])).
% 1.32/1.58 tff(1207,plain,
% 1.32/1.58 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1206])).
% 1.32/1.58 tff(1208,plain,
% 1.32/1.58 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.32/1.58 inference(transitivity,[status(thm)],[239, 1207, 850, 1202])).
% 1.32/1.58 tff(1209,plain,
% 1.32/1.58 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1208])).
% 1.32/1.58 tff(1210,plain,
% 1.32/1.58 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[1209])).
% 1.32/1.58 tff(1211,plain,
% 1.32/1.58 (s(elem!1) = s(s(s(z)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[102, 1210, 183])).
% 1.32/1.58 tff(1212,plain,
% 1.32/1.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[919])).
% 1.32/1.58 tff(1213,plain,
% 1.32/1.58 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1212])).
% 1.32/1.58 tff(1214,plain,
% 1.32/1.58 (~(s(elem!1) = s(s(s(z))))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[244, 1213])).
% 1.32/1.58 tff(1215,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1214, 1211])).
% 1.32/1.58 tff(1216,plain,((~(elem!1 = s(s(elem!1)))) | (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1217,plain,
% 1.32/1.58 (~(elem!1 = s(s(elem!1)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1216, 1201])).
% 1.32/1.58 tff(1218,plain,
% 1.32/1.58 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.32/1.58 inference(commutativity,[status(thm)],[])).
% 1.32/1.58 tff(1219,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.32/1.58 tff(1220,plain,
% 1.32/1.58 (elem!1 = s(s(elem!1))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 1.32/1.58 tff(1221,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.32/1.58 tff(1222,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1221, 1220])).
% 1.32/1.58 tff(1223,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1224,plain,
% 1.32/1.58 (~(s(s(elem!1)) = elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1223, 1217])).
% 1.32/1.58 tff(1225,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.32/1.58 tff(1226,plain,
% 1.32/1.58 (s(elem!1) = s(z)),
% 1.32/1.58 inference(symmetry,[status(thm)],[1225])).
% 1.32/1.58 tff(1227,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1, 1226])).
% 1.32/1.58 tff(1228,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1229,plain,
% 1.32/1.58 (~(s(z) = s(elem!1))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1228, 1])).
% 1.32/1.58 tff(1230,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1231,plain,
% 1.32/1.58 (((~![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(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, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1232,plain,
% 1.32/1.58 ((~![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(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1233,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.32/1.58 tff(1234,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1233, 333, 354, 323, 509, 1230])).
% 1.32/1.58 tff(1235,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1236,plain,
% 1.32/1.58 (~r(s(z), s(elem!1))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1235, 1171, 354, 323])).
% 1.32/1.58 tff(1237,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1238,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1239,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1240,plain,
% 1.32/1.58 (((~![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)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1241,plain,
% 1.32/1.58 ((~![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)))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1242,plain,
% 1.32/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.32/1.58 tff(1243,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1242, 44, 1239, 1238, 1237])).
% 1.32/1.58 tff(1244,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(1245,plain,
% 1.32/1.58 (b(s(z), s(elem!1))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1244, 1236, 1229])).
% 1.32/1.58 tff(1246,plain,
% 1.32/1.58 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1179])).
% 1.32/1.58 tff(1247,plain,
% 1.32/1.58 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.32/1.58 inference(symmetry,[status(thm)],[1246])).
% 1.32/1.58 tff(1248,plain,
% 1.32/1.58 (b(s(elem!1), elem!1)),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[133, 1247])).
% 1.32/1.58 tff(1249,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1250,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1251,plain,
% 1.32/1.58 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1252,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1251])).
% 1.32/1.58 tff(1253,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[1252, 1250])).
% 1.32/1.58 tff(1254,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1255,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.32/1.58 tff(1256,plain,
% 1.32/1.58 (~b(s(s(elem!1)), elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1255, 144, 547, 451, 1249])).
% 1.32/1.58 tff(1257,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.32/1.58 tff(1258,plain,
% 1.32/1.58 (((~![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))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1259,plain,
% 1.32/1.58 ((~![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))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1260,plain,
% 1.32/1.58 ((~![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)),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.32/1.58 tff(1261,plain,
% 1.32/1.58 (r(s(s(elem!1)), elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1260, 44, 1257, 1256])).
% 1.32/1.58 tff(1262,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.58 tff(1263,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1264,plain,
% 1.32/1.58 (((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1265,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1264])).
% 1.32/1.58 tff(1266,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[1265, 1263])).
% 1.32/1.58 tff(1267,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1268,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 1.32/1.58 tff(1269,plain,
% 1.32/1.58 (~b(s(s(elem!1)), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1268, 144, 1249, 488, 1262])).
% 1.32/1.58 tff(1270,plain,
% 1.32/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1271,plain,
% 1.32/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(1272,plain,
% 1.32/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.32/1.58 tff(1273,plain,
% 1.32/1.58 (r(s(s(elem!1)), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1272, 44, 107, 1269])).
% 1.32/1.58 tff(1274,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(1275,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1276,plain,
% 1.32/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 1.32/1.59 tff(1277,plain,
% 1.32/1.59 ($false),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1276, 333, 409, 1273, 1261, 722])).
% 1.32/1.59 tff(1278,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.59 tff(1279,plain,
% 1.32/1.59 (~b(s(s(elem!1)), s(elem!1))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1278, 1248, 722, 1245, 1224, 1200, 488, 409])).
% 1.32/1.59 tff(1280,plain,
% 1.32/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1281,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1282,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.32/1.59 tff(1283,plain,
% 1.32/1.59 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1282, 44])).
% 1.32/1.59 tff(1284,plain,
% 1.32/1.59 (r(s(s(elem!1)), s(elem!1))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1283, 1279, 1197])).
% 1.32/1.59 tff(1285,plain,
% 1.32/1.59 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1284, 1189])).
% 1.32/1.59 tff(1286,plain,
% 1.32/1.59 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1285, 1188])).
% 1.32/1.59 tff(1287,plain,
% 1.32/1.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[846, 893, 56, 304])).
% 1.32/1.59 tff(1288,plain,
% 1.32/1.59 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[249, 1287])).
% 1.32/1.59 tff(1289,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1290,plain,
% 1.32/1.59 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1291,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1290])).
% 1.32/1.59 tff(1292,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.32/1.59 tff(1293,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1294,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.32/1.59 tff(1295,plain,
% 1.32/1.59 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1294, 333, 1288, 1138])).
% 1.32/1.59 tff(1296,plain,
% 1.32/1.59 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1295, 1286])).
% 1.32/1.59 tff(1297,plain,
% 1.32/1.59 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1296, 1186])).
% 1.32/1.59 tff(1298,plain,
% 1.32/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1299,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1300,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.32/1.59 tff(1301,plain,
% 1.32/1.59 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1300, 44])).
% 1.32/1.59 tff(1302,plain,
% 1.32/1.59 (b(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1301, 1297, 1184])).
% 1.32/1.59 tff(1303,plain,
% 1.32/1.59 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1302, 1183])).
% 1.32/1.59 tff(1304,plain,
% 1.32/1.59 ((z = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = z)),
% 1.32/1.59 inference(commutativity,[status(thm)],[])).
% 1.32/1.59 tff(1305,plain,
% 1.32/1.59 ((s(s(s(s(s(s(s(s(z)))))))) = z) <=> (z = s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(symmetry,[status(thm)],[1304])).
% 1.32/1.59 tff(1306,plain,
% 1.32/1.59 ((~(s(s(s(s(s(s(s(s(z)))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1305])).
% 1.32/1.59 tff(1307,plain,
% 1.32/1.59 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(z)))))))) = z))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1308,plain,
% 1.32/1.59 (~(s(s(s(s(s(s(s(s(z)))))))) = z)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1307, 29])).
% 1.32/1.59 tff(1309,plain,
% 1.32/1.59 (~(z = s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1308, 1306])).
% 1.32/1.59 tff(1310,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1311,plain,
% 1.32/1.59 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1312,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1311])).
% 1.32/1.59 tff(1313,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.32/1.59 tff(1314,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1315,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.32/1.59 tff(1316,plain,
% 1.32/1.59 ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1315, 333, 1288, 884])).
% 1.32/1.59 tff(1317,plain,
% 1.32/1.59 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1316, 1286])).
% 1.32/1.59 tff(1318,plain,
% 1.32/1.59 (((~![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))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1319,plain,
% 1.32/1.59 ((~![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))))))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1320,plain,
% 1.32/1.59 ((~![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)))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.32/1.59 tff(1321,plain,
% 1.32/1.59 ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1320, 44, 1317])).
% 1.32/1.59 tff(1322,plain,
% 1.32/1.59 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1321, 1309])).
% 1.32/1.59 tff(1323,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1324,plain,
% 1.32/1.59 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1325,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1324])).
% 1.32/1.59 tff(1326,plain,
% 1.32/1.59 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.32/1.59 tff(1327,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1328,plain,
% 1.32/1.59 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.32/1.59 tff(1329,plain,
% 1.32/1.59 ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1328, 333, 1288, 884])).
% 1.32/1.59 tff(1330,plain,
% 1.32/1.59 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1329, 1286])).
% 1.32/1.59 tff(1331,plain,
% 1.32/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(1332,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(1333,plain,
% 1.32/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.43/1.60 tff(1334,plain,
% 1.43/1.60 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1333, 44, 1308, 1330])).
% 1.43/1.60 tff(1335,plain,
% 1.43/1.60 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1336,plain,
% 1.43/1.60 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1337,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1336])).
% 1.43/1.60 tff(1338,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1337, 1335])).
% 1.43/1.60 tff(1339,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1340,plain,
% 1.43/1.60 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 1.43/1.60 tff(1341,plain,
% 1.43/1.60 (~r(s(s(s(z))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1340, 333, 1288, 1138, 884])).
% 1.43/1.60 tff(1342,plain,
% 1.43/1.60 (b(s(s(s(z))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[396, 1341])).
% 1.43/1.60 tff(1343,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1344,plain,
% 1.43/1.60 (((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1345,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1344])).
% 1.43/1.60 tff(1346,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.43/1.60 tff(1347,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1348,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.43/1.60 tff(1349,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1348, 144, 1342, 1334, 1322, 1303])).
% 1.43/1.60 tff(1350,plain,((~b(s(elem!1), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1351,plain,
% 1.43/1.60 (~b(s(elem!1), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1350, 829, 721, 863, 737, 739, 354, 323, 304, 56, 825, 1, 123, 707, 708])).
% 1.43/1.60 tff(1352,plain,
% 1.43/1.60 (r(s(elem!1), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[486, 1351, 1])).
% 1.43/1.60 tff(1353,plain,
% 1.43/1.60 (((~![X0: $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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1354,plain,
% 1.43/1.60 ((~![X0: $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))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1355,plain,
% 1.43/1.60 ((~![X0: $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)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 1.43/1.60 tff(1356,plain,
% 1.43/1.60 (~r(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1355, 333, 354, 323, 434])).
% 1.43/1.60 tff(1357,plain,
% 1.43/1.60 (b(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[583, 1356])).
% 1.43/1.60 tff(1358,plain,
% 1.43/1.60 (((~![X0: $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(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(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1359,plain,
% 1.43/1.60 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1360,plain,
% 1.43/1.60 (((~![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(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1359])).
% 1.43/1.60 tff(1361,plain,
% 1.43/1.60 (((~![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(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1360, 1358])).
% 1.43/1.60 tff(1362,plain,
% 1.43/1.60 ((~![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(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1363,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 1.43/1.60 tff(1364,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1363, 333, 354, 323, 434, 509])).
% 1.43/1.60 tff(1365,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1366,plain,
% 1.43/1.60 (~r(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1365, 354, 323, 434])).
% 1.43/1.60 tff(1367,plain,
% 1.43/1.60 (b(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[507, 1366])).
% 1.43/1.60 tff(1368,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.43/1.60 tff(1369,plain,
% 1.43/1.60 (((~![X0: $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), elem!1)) | (~r(z, 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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1370,plain,
% 1.43/1.60 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1371,plain,
% 1.43/1.60 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1370])).
% 1.43/1.60 tff(1372,plain,
% 1.43/1.60 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.43/1.60 tff(1373,plain,
% 1.43/1.60 ((~![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)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1374,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.43/1.60 tff(1375,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1374, 333, 409, 354, 323, 408])).
% 1.43/1.60 tff(1376,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1377,plain,
% 1.43/1.60 (~r(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1376, 409, 354, 323])).
% 1.43/1.60 tff(1378,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.43/1.60 tff(1379,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[652, 44, 377, 1368, 1378])).
% 1.43/1.60 tff(1380,plain,(r(elem!1, z) | b(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1381,plain,
% 1.43/1.60 (b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1380, 1377, 1368])).
% 1.43/1.60 tff(1382,plain,
% 1.43/1.60 (~b(elem!1, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[949, 1381, 1367, 1357])).
% 1.43/1.60 tff(1383,plain,
% 1.43/1.60 (r(elem!1, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[560, 1382, 902])).
% 1.43/1.60 tff(1384,plain,
% 1.43/1.60 (~b(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[916, 1381, 251, 1367])).
% 1.43/1.60 tff(1385,plain,
% 1.43/1.60 (r(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[448, 1384, 907])).
% 1.43/1.60 tff(1386,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1387,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1388,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.43/1.60 tff(1389,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1388, 333, 563, 435, 409, 434])).
% 1.43/1.60 tff(1390,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1391,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1390, 1385, 1383, 409, 434])).
% 1.43/1.60 tff(1392,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | (elem!1 = z) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1393,plain,
% 1.43/1.60 (elem!1 = s(elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1392, 1352, 354, 729, 77, 829, 323])).
% 1.43/1.60 tff(1394,plain,
% 1.43/1.60 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1393])).
% 1.43/1.60 tff(1395,plain,
% 1.43/1.60 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[739, 1394])).
% 1.43/1.60 tff(1396,plain,
% 1.43/1.60 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1393])).
% 1.43/1.60 tff(1397,plain,
% 1.43/1.60 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[737, 1396])).
% 1.43/1.60 tff(1398,assumption,(b(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.43/1.60 tff(1399,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1400,plain,
% 1.43/1.61 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1401,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1400])).
% 1.43/1.61 tff(1402,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1401, 1399])).
% 1.43/1.61 tff(1403,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1404,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.43/1.61 tff(1405,plain,
% 1.43/1.61 (~b(s(s(z)), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1404, 144, 1398, 546, 450])).
% 1.43/1.61 tff(1406,plain,
% 1.43/1.61 (((~![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)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1407,plain,
% 1.43/1.61 ((~![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)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1408,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.43/1.61 tff(1409,plain,
% 1.43/1.61 (r(s(s(z)), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1408, 44, 860, 1405])).
% 1.43/1.61 tff(1410,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.43/1.61 tff(1411,plain,
% 1.43/1.61 (s(z) = s(s(z))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1410])).
% 1.43/1.61 tff(1412,plain,
% 1.43/1.61 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1411])).
% 1.43/1.61 tff(1413,plain,
% 1.43/1.61 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1412])).
% 1.43/1.61 tff(1414,plain,
% 1.43/1.61 (s(z) = z),
% 1.43/1.61 inference(transitivity,[status(thm)],[193, 1413, 16])).
% 1.43/1.61 tff(1415,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[344, 1414])).
% 1.43/1.61 tff(1416,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1417,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.43/1.61 tff(1418,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1419,plain,
% 1.43/1.61 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1420,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1419])).
% 1.43/1.61 tff(1421,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1420, 1418])).
% 1.43/1.61 tff(1422,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1423,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.43/1.61 tff(1424,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1423, 144, 1417, 1398, 123, 304])).
% 1.43/1.61 tff(1425,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1426,plain,
% 1.43/1.61 (~b(s(s(z)), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1425, 1398, 123, 304])).
% 1.43/1.61 tff(1427,plain,
% 1.43/1.61 (((~![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)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1428,plain,
% 1.43/1.61 ((~![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)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1429,plain,
% 1.43/1.61 ((~![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))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.43/1.61 tff(1430,plain,
% 1.43/1.61 (r(s(s(z)), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1429, 44, 1426, 1416])).
% 1.43/1.61 tff(1431,plain,
% 1.43/1.61 (((~![X0: $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(s(s(z)), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1432,plain,
% 1.43/1.61 ((~![X0: $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(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1433,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.43/1.61 tff(1434,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1433, 333, 323, 434, 1430, 1409])).
% 1.43/1.61 tff(1435,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1436,plain,
% 1.43/1.61 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1435, 1352, 323, 856, 1397, 1395, 123, 304])).
% 1.43/1.61 tff(1437,assumption,(s(s(z)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.43/1.61 tff(1438,plain,
% 1.43/1.61 (s(s(s(s(s(s(s(z))))))) = s(s(z))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1437])).
% 1.43/1.61 tff(1439,plain,
% 1.43/1.61 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1438])).
% 1.43/1.61 tff(1440,plain,
% 1.43/1.61 (s(s(s(s(s(s(z)))))) = s(z)),
% 1.43/1.61 inference(transitivity,[status(thm)],[21, 1439, 80])).
% 1.43/1.61 tff(1441,plain,
% 1.43/1.61 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1440])).
% 1.43/1.61 tff(1442,plain,
% 1.43/1.61 (s(s(s(s(s(z))))) = z),
% 1.43/1.61 inference(transitivity,[status(thm)],[93, 1441, 16])).
% 1.43/1.61 tff(1443,plain,
% 1.43/1.61 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1444,plain,
% 1.43/1.61 (~(s(s(s(s(s(z))))) = z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1443, 29])).
% 1.43/1.61 tff(1445,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1444, 1442])).
% 1.43/1.61 tff(1446,plain,(~(s(s(z)) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1447,plain,
% 1.43/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1448,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1449,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.43/1.61 tff(1450,plain,
% 1.43/1.61 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1449, 44])).
% 1.43/1.61 tff(1451,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1450, 1446])).
% 1.43/1.61 tff(1452,plain,
% 1.43/1.61 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1451, 1436])).
% 1.43/1.61 tff(1453,plain,
% 1.43/1.61 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1454,plain,
% 1.43/1.61 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1455,plain,
% 1.43/1.61 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1454])).
% 1.43/1.61 tff(1456,plain,
% 1.43/1.61 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1455, 1453])).
% 1.43/1.61 tff(1457,plain,
% 1.43/1.61 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1458,plain,
% 1.43/1.61 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 1.43/1.61 tff(1459,plain,
% 1.43/1.61 (~r(s(s(z)), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1458, 333, 1452, 848, 827])).
% 1.43/1.61 tff(1460,plain,
% 1.43/1.61 (((~![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))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1461,plain,
% 1.43/1.61 ((~![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))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1462,plain,
% 1.43/1.61 ((~![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)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.43/1.61 tff(1463,plain,
% 1.43/1.61 (b(s(s(z)), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1462, 44, 164, 1459])).
% 1.43/1.61 tff(1464,plain,
% 1.43/1.61 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1465,plain,
% 1.43/1.61 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1466,plain,
% 1.43/1.62 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1465])).
% 1.43/1.62 tff(1467,plain,
% 1.43/1.62 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1466, 1464])).
% 1.43/1.62 tff(1468,plain,
% 1.43/1.62 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1469,plain,
% 1.43/1.62 ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.43/1.62 tff(1470,plain,
% 1.43/1.62 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1469, 333, 1452, 848, 1138])).
% 1.43/1.62 tff(1471,plain,
% 1.43/1.62 (((~![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)))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1472,plain,
% 1.43/1.62 ((~![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)))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1473,plain,
% 1.43/1.62 ((~![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))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.43/1.62 tff(1474,plain,
% 1.43/1.62 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1473, 44, 1470, 217])).
% 1.43/1.62 tff(1475,plain,
% 1.43/1.62 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1476,plain,
% 1.43/1.62 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1477,plain,
% 1.43/1.62 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1476])).
% 1.43/1.62 tff(1478,plain,
% 1.43/1.62 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1477, 1475])).
% 1.43/1.62 tff(1479,plain,
% 1.43/1.62 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1480,plain,
% 1.43/1.62 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 1.43/1.62 tff(1481,plain,
% 1.43/1.62 (~r(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1480, 333, 848, 1138, 827])).
% 1.43/1.62 tff(1482,plain,
% 1.43/1.62 (b(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[619, 1481])).
% 1.43/1.62 tff(1483,plain,
% 1.43/1.62 (~r(s(s(s(z))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1340, 333, 848, 1138, 827])).
% 1.43/1.62 tff(1484,plain,
% 1.43/1.62 (b(s(s(s(z))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[396, 1483])).
% 1.43/1.62 tff(1485,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1486,plain,
% 1.43/1.62 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1487,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1486])).
% 1.43/1.62 tff(1488,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1487, 1485])).
% 1.43/1.62 tff(1489,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1490,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 1.43/1.62 tff(1491,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1490, 144, 1484, 1482, 1474, 1463])).
% 1.43/1.62 tff(1492,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | b(elem!1, s(z)) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1493,plain,
% 1.43/1.62 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1492, 354, 123, 323, 1, 56, 707, 708, 706, 3, 54])).
% 1.43/1.62 tff(1494,plain,
% 1.43/1.62 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[319, 1493])).
% 1.43/1.62 tff(1495,plain,
% 1.43/1.62 (((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1496,plain,
% 1.43/1.62 ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1497,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.43/1.62 tff(1498,plain,
% 1.43/1.62 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1497, 333, 354, 323, 1494])).
% 1.43/1.62 tff(1499,plain,
% 1.43/1.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[302, 1498])).
% 1.43/1.62 tff(1500,plain,
% 1.43/1.62 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[880, 1499, 825, 729])).
% 1.43/1.62 tff(1501,plain,
% 1.43/1.62 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[130, 1500, 54])).
% 1.43/1.62 tff(1502,plain,
% 1.43/1.62 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1501])).
% 1.43/1.62 tff(1503,plain,
% 1.43/1.62 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1502])).
% 1.43/1.62 tff(1504,plain,
% 1.43/1.62 (~(s(s(z)) = elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1446, 1503])).
% 1.43/1.62 tff(1505,plain,
% 1.43/1.62 (s(s(z)) = elem!1),
% 1.43/1.62 inference(transitivity,[status(thm)],[87, 984, 850])).
% 1.43/1.62 tff(1506,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.43/1.62 tff(1507,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1506, 1505])).
% 1.43/1.62 tff(1508,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1509,plain,
% 1.43/1.62 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1508, 1504])).
% 1.43/1.62 tff(1510,plain,
% 1.43/1.62 (~(s(s(s(z))) = elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[695, 56, 1, 54, 3, 123])).
% 1.43/1.62 tff(1511,plain,
% 1.43/1.62 (~(elem!1 = s(s(s(z))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1510, 65])).
% 1.43/1.62 tff(1512,plain,
% 1.43/1.62 (((~![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(z))), elem!1)) | (~r(z, 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(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1513,plain,
% 1.43/1.62 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1514,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1513])).
% 1.43/1.62 tff(1515,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1514, 1512])).
% 1.43/1.62 tff(1516,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1517,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 1.43/1.62 tff(1518,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1517, 333, 354, 623, 707, 353])).
% 1.43/1.62 tff(1519,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1520,plain,
% 1.43/1.62 (~r(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1519, 353, 707, 354])).
% 1.43/1.62 tff(1521,plain,
% 1.43/1.62 (b(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[619, 1520])).
% 1.43/1.62 tff(1522,plain,
% 1.43/1.62 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[81])).
% 1.43/1.62 tff(1523,plain,
% 1.43/1.62 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[1522])).
% 1.43/1.62 tff(1524,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.43/1.62 tff(1525,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.43/1.62 tff(1526,plain,
% 1.43/1.62 (((~![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(elem!1, 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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1527,plain,
% 1.43/1.62 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1528,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1527])).
% 1.43/1.62 tff(1529,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.43/1.63 tff(1530,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1531,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.43/1.63 tff(1532,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1531, 333, 1525, 722, 707, 353])).
% 1.43/1.63 tff(1533,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1534,plain,
% 1.43/1.63 (~r(elem!1, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1533, 353, 707, 722])).
% 1.43/1.63 tff(1535,plain,
% 1.43/1.63 (((~![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)))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1536,plain,
% 1.43/1.63 ((~![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)))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1537,plain,
% 1.43/1.63 ((~![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))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 1.43/1.63 tff(1538,plain,
% 1.43/1.63 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1537, 44])).
% 1.43/1.63 tff(1539,plain,
% 1.43/1.63 (b(elem!1, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1538, 1534, 1524])).
% 1.43/1.63 tff(1540,plain,
% 1.43/1.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1539, 1523])).
% 1.43/1.63 tff(1541,plain,
% 1.43/1.63 (~b(s(s(s(z))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[294, 1540, 286, 1521])).
% 1.43/1.63 tff(1542,plain,
% 1.43/1.63 (r(s(s(s(z))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[396, 1541])).
% 1.43/1.63 tff(1543,plain,
% 1.43/1.63 (((~![X0: $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))), 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), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1544,plain,
% 1.43/1.63 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1545,plain,
% 1.43/1.63 (((~![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(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1544])).
% 1.43/1.63 tff(1546,plain,
% 1.43/1.63 (((~![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(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.43/1.63 tff(1547,plain,
% 1.43/1.63 ((~![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(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1548,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.43/1.63 tff(1549,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1548, 333, 354, 323, 1542, 353])).
% 1.43/1.63 tff(1550,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1551,plain,
% 1.43/1.63 (~r(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1550, 354, 323, 1499, 1501, 1511, 707, 721])).
% 1.43/1.63 tff(1552,plain,
% 1.43/1.63 (b(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[172, 1551])).
% 1.43/1.63 tff(1553,plain,
% 1.43/1.63 (elem!1 = s(elem!1)),
% 1.43/1.63 inference(symmetry,[status(thm)],[903])).
% 1.43/1.63 tff(1554,plain,
% 1.43/1.63 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.43/1.63 inference(transitivity,[status(thm)],[81, 1553])).
% 1.43/1.63 tff(1555,plain,
% 1.43/1.63 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1554])).
% 1.43/1.63 tff(1556,plain,
% 1.43/1.63 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.43/1.63 inference(transitivity,[status(thm)],[21, 1555, 850, 1553])).
% 1.43/1.63 tff(1557,plain,
% 1.43/1.63 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1556])).
% 1.43/1.63 tff(1558,plain,
% 1.43/1.63 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.43/1.63 inference(transitivity,[status(thm)],[93, 1557, 850, 1553])).
% 1.43/1.63 tff(1559,plain,
% 1.43/1.63 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1558])).
% 1.43/1.63 tff(1560,plain,
% 1.43/1.63 (s(s(s(s(z)))) = s(elem!1)),
% 1.43/1.63 inference(transitivity,[status(thm)],[239, 1559, 850, 1553])).
% 1.43/1.63 tff(1561,plain,
% 1.43/1.63 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1560])).
% 1.43/1.63 tff(1562,plain,
% 1.43/1.63 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1561])).
% 1.43/1.63 tff(1563,plain,
% 1.43/1.63 (elem!1 = s(s(s(z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1193, 1562, 183])).
% 1.43/1.63 tff(1564,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1524, 1563])).
% 1.43/1.63 tff(1565,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(z)))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1566,plain,
% 1.43/1.63 (~(s(elem!1) = elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1565, 1501, 1511])).
% 1.43/1.63 tff(1567,plain,
% 1.43/1.63 (s(elem!1) = elem!1),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[885, 199])).
% 1.43/1.63 tff(1568,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[433, 1567])).
% 1.43/1.63 tff(1569,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1570,plain,
% 1.43/1.63 (~(elem!1 = s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1569, 1566])).
% 1.43/1.63 tff(1571,plain,
% 1.43/1.63 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1501])).
% 1.43/1.63 tff(1572,plain,
% 1.43/1.63 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1571])).
% 1.43/1.63 tff(1573,plain,
% 1.43/1.63 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1572])).
% 1.43/1.63 tff(1574,plain,
% 1.43/1.63 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1570, 1573])).
% 1.43/1.63 tff(1575,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1576,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.43/1.63 tff(1577,plain,
% 1.43/1.63 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.43/1.63 inference(commutativity,[status(thm)],[])).
% 1.43/1.63 tff(1578,plain,
% 1.43/1.63 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1577])).
% 1.43/1.63 tff(1579,plain,
% 1.43/1.63 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1578])).
% 1.43/1.63 tff(1580,plain,
% 1.43/1.63 (~(s(z) = s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1, 1579])).
% 1.43/1.63 tff(1581,plain,
% 1.43/1.63 (r(s(elem!1), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[486, 1, 1576])).
% 1.43/1.63 tff(1582,plain,
% 1.43/1.63 (((~![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(elem!1), s(z))) | (~r(z, 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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1583,plain,
% 1.43/1.63 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1584,plain,
% 1.43/1.63 (((~![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(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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1583])).
% 1.43/1.63 tff(1585,plain,
% 1.43/1.63 (((~![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(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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1584, 1582])).
% 1.43/1.63 tff(1586,plain,
% 1.43/1.63 ((~![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(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1587,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.43/1.63 tff(1588,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1587, 333, 409, 354, 434, 509])).
% 1.43/1.63 tff(1589,plain,((~r(s(elem!1), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1590,plain,
% 1.43/1.63 (~r(s(z), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1589, 1581, 354, 509])).
% 1.43/1.63 tff(1591,plain,
% 1.43/1.63 (b(s(z), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[406, 1590, 706])).
% 1.43/1.63 tff(1592,plain,
% 1.43/1.63 (~r(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1365, 1581, 354, 509])).
% 1.43/1.63 tff(1593,plain,
% 1.43/1.63 (b(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[348, 1592])).
% 1.43/1.63 tff(1594,plain,
% 1.43/1.63 (b(z, elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[658, 71, 1575])).
% 1.43/1.63 tff(1595,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1596,plain,
% 1.43/1.63 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1597,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1596])).
% 1.43/1.63 tff(1598,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1597, 1595])).
% 1.43/1.63 tff(1599,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1600,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.43/1.63 tff(1601,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1600, 144, 251, 624, 134, 489])).
% 1.43/1.63 tff(1602,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1603,plain,
% 1.43/1.63 (~b(elem!1, z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1602, 1594, 1591, 1593])).
% 1.43/1.63 tff(1604,plain,
% 1.43/1.63 (r(elem!1, z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[653, 1603, 77])).
% 1.43/1.63 tff(1605,plain,
% 1.43/1.63 (((~![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(z))) | (~r(elem!1, 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), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1606,plain,
% 1.43/1.63 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1607,plain,
% 1.43/1.63 (((~![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(elem!1), 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(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1606])).
% 1.43/1.63 tff(1608,plain,
% 1.43/1.63 (((~![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(elem!1), 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(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.43/1.63 tff(1609,plain,
% 1.43/1.63 ((~![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(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1610,plain,
% 1.43/1.63 ((~![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(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.43/1.63 tff(1611,plain,
% 1.43/1.63 (~r(s(elem!1), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1610, 333, 354, 1604, 509])).
% 1.43/1.63 tff(1612,plain,
% 1.43/1.63 (b(s(elem!1), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[448, 1611, 907])).
% 1.43/1.63 tff(1613,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1614,plain,
% 1.43/1.63 (((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1615,plain,
% 1.43/1.63 (((~![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(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1614])).
% 1.43/1.63 tff(1616,plain,
% 1.43/1.63 (((~![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(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1615, 1613])).
% 1.43/1.63 tff(1617,plain,
% 1.43/1.63 ((~![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(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1618,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.43/1.63 tff(1619,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1618, 333, 563, 354, 408, 509])).
% 1.43/1.63 tff(1620,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1621,plain,
% 1.43/1.63 (~r(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1620, 1604, 354, 509])).
% 1.43/1.63 tff(1622,plain,
% 1.43/1.63 (b(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[560, 1621, 902])).
% 1.43/1.63 tff(1623,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1624,plain,
% 1.43/1.63 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1625,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1624])).
% 1.43/1.63 tff(1626,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1625, 1623])).
% 1.43/1.64 tff(1627,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1628,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.43/1.64 tff(1629,plain,
% 1.43/1.64 (~b(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1628, 144, 1622, 1612, 1591])).
% 1.43/1.64 tff(1630,plain,
% 1.43/1.64 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1242, 44, 1629])).
% 1.43/1.64 tff(1631,plain,
% 1.43/1.64 (r(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1630, 1580])).
% 1.43/1.64 tff(1632,plain,
% 1.43/1.64 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.43/1.64 inference(commutativity,[status(thm)],[])).
% 1.43/1.64 tff(1633,plain,
% 1.43/1.64 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1632])).
% 1.43/1.64 tff(1634,plain,
% 1.43/1.64 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1633])).
% 1.43/1.64 tff(1635,plain,
% 1.43/1.64 (~(z = s(elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[105, 1634])).
% 1.43/1.64 tff(1636,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1637,plain,
% 1.43/1.64 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1638,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1637])).
% 1.43/1.64 tff(1639,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1638, 1636])).
% 1.43/1.64 tff(1640,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1641,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 1.43/1.64 tff(1642,plain,
% 1.43/1.64 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1641, 144])).
% 1.43/1.64 tff(1643,plain,
% 1.43/1.64 (~b(z, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1642, 1612, 1594, 1622])).
% 1.43/1.64 tff(1644,plain,
% 1.43/1.64 ((z = s(elem!1)) | r(z, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[581, 44, 1643])).
% 1.43/1.64 tff(1645,plain,
% 1.43/1.64 (r(z, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1644, 1635])).
% 1.43/1.64 tff(1646,plain,
% 1.43/1.64 (((~![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(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1647,plain,
% 1.43/1.64 (((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1648,plain,
% 1.43/1.64 (((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1647])).
% 1.43/1.64 tff(1649,plain,
% 1.43/1.64 (((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.43/1.64 tff(1650,plain,
% 1.43/1.64 ((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1651,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.43/1.64 tff(1652,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1651, 333, 354, 1581, 1645, 1631])).
% 1.43/1.64 tff(1653,plain,((s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | r(z, elem!1) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1654,plain,
% 1.43/1.64 (~r(s(elem!1), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1653, 1576, 1575, 706, 902, 1, 354])).
% 1.43/1.64 tff(1655,plain,
% 1.43/1.64 (r(s(elem!1), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[486, 1576, 1])).
% 1.43/1.64 tff(1656,plain,
% 1.43/1.64 (((~![X0: $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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1657,plain,
% 1.43/1.64 ((~![X0: $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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1658,plain,
% 1.43/1.64 ((~![X0: $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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.43/1.64 tff(1659,plain,
% 1.43/1.64 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1658, 333, 323, 434, 322])).
% 1.43/1.64 tff(1660,plain,
% 1.43/1.64 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[540, 44, 537, 1659])).
% 1.43/1.64 tff(1661,plain,
% 1.43/1.64 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1497, 333, 354, 323, 322])).
% 1.43/1.64 tff(1662,plain,
% 1.43/1.64 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[300, 44, 273, 1661])).
% 1.43/1.64 tff(1663,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1664,plain,
% 1.43/1.64 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1665,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1664])).
% 1.43/1.64 tff(1666,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1665, 1663])).
% 1.43/1.64 tff(1667,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1668,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.43/1.64 tff(1669,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1668, 144, 491, 1357, 1662, 1660])).
% 1.43/1.64 tff(1670,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1671,plain,
% 1.43/1.64 (~b(s(elem!1), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1670, 1655, 354, 322, 323, 537])).
% 1.43/1.64 tff(1672,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[507, 1671, 1654])).
% 1.43/1.64 tff(1673,plain,(b(s(elem!1), s(z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(z, elem!1) | (s(z) = elem!1) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1674,plain,
% 1.43/1.64 (b(s(elem!1), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1673, 354, 1494, 323, 1574, 728, 706, 1570, 1])).
% 1.43/1.64 tff(1675,plain,
% 1.43/1.64 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[899, 144, 1674, 56, 1552])).
% 1.43/1.64 tff(1676,plain,
% 1.43/1.64 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[965, 1675, 1509])).
% 1.43/1.64 tff(1677,plain,
% 1.43/1.64 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1501])).
% 1.43/1.64 tff(1678,plain,
% 1.43/1.64 (b(s(z), elem!1)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[123, 1677])).
% 1.43/1.64 tff(1679,plain,
% 1.43/1.64 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[81])).
% 1.43/1.64 tff(1680,plain,
% 1.43/1.64 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1679])).
% 1.43/1.64 tff(1681,plain,
% 1.43/1.64 (~(s(s(z)) = elem!1)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1446, 1680])).
% 1.43/1.64 tff(1682,plain,
% 1.43/1.64 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1508, 1681])).
% 1.43/1.64 tff(1683,plain,
% 1.43/1.64 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[899, 144, 488, 56, 838])).
% 1.43/1.64 tff(1684,plain,
% 1.43/1.64 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[965, 1683, 1682])).
% 1.43/1.64 tff(1685,plain,
% 1.43/1.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[81])).
% 1.43/1.64 tff(1686,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.43/1.64 tff(1687,plain,
% 1.43/1.64 (((~![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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1688,plain,
% 1.43/1.64 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1689,plain,
% 1.43/1.64 (((~![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(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1688])).
% 1.43/1.64 tff(1690,plain,
% 1.43/1.64 (((~![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(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1689, 1687])).
% 1.43/1.64 tff(1691,plain,
% 1.43/1.64 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1692,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.43/1.64 tff(1693,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1692, 333, 435, 722, 707, 1686])).
% 1.43/1.64 tff(1694,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1695,plain,
% 1.43/1.64 (~r(s(elem!1), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1694, 1684, 707, 722])).
% 1.43/1.64 tff(1696,plain,
% 1.43/1.64 (b(s(elem!1), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[448, 1695, 433])).
% 1.43/1.65 tff(1697,plain,
% 1.43/1.65 (~b(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[916, 1696, 624, 251])).
% 1.43/1.65 tff(1698,plain,
% 1.43/1.65 (r(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[507, 1697])).
% 1.43/1.65 tff(1699,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.43/1.65 tff(1700,plain,
% 1.43/1.65 (((~![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(elem!1), s(s(s(z))))) | (~r(s(elem!1), 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(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1701,plain,
% 1.43/1.65 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1702,plain,
% 1.43/1.65 (((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(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(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1701])).
% 1.43/1.65 tff(1703,plain,
% 1.43/1.65 (((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(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(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1702, 1700])).
% 1.43/1.65 tff(1704,plain,
% 1.43/1.65 ((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1705,plain,
% 1.43/1.65 ((~![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(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 1.43/1.65 tff(1706,plain,
% 1.43/1.65 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1705, 333, 354, 509, 1699])).
% 1.43/1.65 tff(1707,plain,
% 1.43/1.65 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[965, 1706, 960])).
% 1.43/1.65 tff(1708,plain,
% 1.43/1.65 (~r(s(z), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1548, 333, 354, 323, 1699])).
% 1.43/1.65 tff(1709,plain,
% 1.43/1.65 (b(s(z), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[170, 44, 167, 1708])).
% 1.43/1.65 tff(1710,plain,
% 1.43/1.65 (((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1711,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1710])).
% 1.43/1.65 tff(1712,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1711, 894])).
% 1.43/1.65 tff(1713,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1714,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 1.43/1.65 tff(1715,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1714, 144, 488, 56, 1709, 1707])).
% 1.43/1.65 tff(1716,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1717,plain,
% 1.43/1.65 (~r(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1716, 1698, 354, 1682, 488, 56, 323])).
% 1.43/1.65 tff(1718,plain,
% 1.43/1.65 (b(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[396, 1717])).
% 1.43/1.65 tff(1719,plain,
% 1.43/1.65 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[294, 1718, 286, 284])).
% 1.43/1.65 tff(1720,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[249, 1719])).
% 1.43/1.65 tff(1721,plain,
% 1.43/1.65 (r(elem!1, s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1720, 1685])).
% 1.43/1.65 tff(1722,plain,
% 1.43/1.65 (~(elem!1 = s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1569, 433])).
% 1.43/1.65 tff(1723,plain,
% 1.43/1.65 (~r(s(z), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1235, 1698, 354, 323])).
% 1.43/1.65 tff(1724,plain,
% 1.43/1.65 (b(s(z), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1244, 1723, 1237])).
% 1.43/1.65 tff(1725,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.43/1.65 tff(1726,plain,
% 1.43/1.65 (b(elem!1, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[560, 902, 1725])).
% 1.43/1.65 tff(1727,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.43/1.65 tff(1728,plain,
% 1.43/1.65 (b(s(elem!1), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[448, 907, 1727])).
% 1.43/1.65 tff(1729,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1628, 144, 547, 451, 134, 1262])).
% 1.43/1.65 tff(1730,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1731,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1730, 1728, 1726, 1262, 134])).
% 1.43/1.65 tff(1732,plain,((elem!1 = s(elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1733,plain,
% 1.43/1.65 (r(elem!1, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1732, 1724, 1722, 134, 1695])).
% 1.43/1.65 tff(1734,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), 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(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1735,plain,
% 1.43/1.65 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1736,plain,
% 1.43/1.65 (((~![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(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(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(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1735])).
% 1.43/1.65 tff(1737,plain,
% 1.43/1.65 (((~![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(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(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(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1736, 1734])).
% 1.43/1.65 tff(1738,plain,
% 1.43/1.65 ((~![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(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1739,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.43/1.65 tff(1740,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1739, 333, 1733, 1721, 707, 1684])).
% 1.43/1.65 tff(1741,plain,((~b(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1742,plain,
% 1.43/1.65 (~b(z, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1741, 1674, 1501, 1499, 707, 1678, 1229, 354, 56, 323, 825, 729, 1566, 721, 1552])).
% 1.43/1.65 tff(1743,plain,
% 1.43/1.65 (r(z, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[619, 1742])).
% 1.43/1.65 tff(1744,plain,
% 1.43/1.65 (~r(s(elem!1), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1694, 1676, 707, 721])).
% 1.43/1.65 tff(1745,plain,
% 1.43/1.65 (b(s(elem!1), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[448, 1744, 1566])).
% 1.43/1.65 tff(1746,plain,
% 1.43/1.65 (~b(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[916, 1745, 825, 729])).
% 1.43/1.65 tff(1747,plain,
% 1.43/1.65 (r(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[507, 1746])).
% 1.43/1.65 tff(1748,plain,
% 1.43/1.65 (((~![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(elem!1), s(s(s(z))))) | (~r(s(elem!1), 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))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1749,plain,
% 1.43/1.65 (((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1750,plain,
% 1.43/1.65 (((~![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(s(elem!1), s(s(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(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1749])).
% 1.43/1.65 tff(1751,plain,
% 1.43/1.65 (((~![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(s(elem!1), s(s(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(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.43/1.65 tff(1752,plain,
% 1.43/1.65 ((~![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(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1753,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.43/1.65 tff(1754,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1753, 333, 1747, 1743, 707, 1676])).
% 1.43/1.65 tff(1755,plain,((~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1756,plain,
% 1.43/1.65 (~r(z, s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1755, 323, 56, 707, 706, 1, 123, 54, 708, 3])).
% 1.43/1.65 tff(1757,plain,
% 1.43/1.65 (b(z, s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[372, 1756])).
% 1.43/1.65 tff(1758,plain,
% 1.43/1.65 (~b(s(z), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[152, 454, 123, 452])).
% 1.43/1.65 tff(1759,plain,
% 1.43/1.65 (r(s(z), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[406, 1758, 706])).
% 1.43/1.65 tff(1760,plain,
% 1.43/1.65 (~b(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[880, 452, 624, 286])).
% 1.43/1.65 tff(1761,plain,
% 1.43/1.65 (r(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[658, 1760, 74])).
% 1.43/1.65 tff(1762,plain,
% 1.43/1.65 (((~![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), elem!1)) | (~r(elem!1, 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(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1763,plain,
% 1.43/1.65 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1764,plain,
% 1.43/1.65 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1763])).
% 1.43/1.65 tff(1765,plain,
% 1.43/1.65 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1764, 1762])).
% 1.43/1.65 tff(1766,plain,
% 1.43/1.65 ((~![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)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1767,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.43/1.65 tff(1768,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1767, 333, 1761, 1759, 323, 722])).
% 1.43/1.65 tff(1769,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (z = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1770,plain,
% 1.43/1.65 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1769, 286, 722, 706, 71, 123, 624, 323, 3, 54])).
% 1.43/1.65 tff(1771,plain,
% 1.43/1.65 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1770])).
% 1.43/1.65 tff(1772,plain,
% 1.43/1.65 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1771])).
% 1.43/1.65 tff(1773,plain,
% 1.43/1.65 (~(s(s(z)) = elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1446, 1772])).
% 1.43/1.65 tff(1774,plain,
% 1.43/1.65 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1508, 1773])).
% 1.43/1.65 tff(1775,plain,
% 1.43/1.65 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1770])).
% 1.43/1.65 tff(1776,plain,
% 1.43/1.65 (b(s(z), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[123, 1775])).
% 1.43/1.65 tff(1777,plain,
% 1.43/1.65 (~(s(elem!1) = elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1565, 1770, 1511])).
% 1.43/1.65 tff(1778,plain,
% 1.43/1.65 (((~![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(z, elem!1)) | (~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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1779,plain,
% 1.43/1.65 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1780,plain,
% 1.43/1.65 (((~![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(s(s(z))), elem!1)) | (~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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1779])).
% 1.43/1.65 tff(1781,plain,
% 1.43/1.65 (((~![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(s(s(z))), elem!1)) | (~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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1780, 1778])).
% 1.43/1.65 tff(1782,plain,
% 1.43/1.65 ((~![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(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1783,plain,
% 1.43/1.65 ((~![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(z, elem!1)) | (~r(s(s(s(z))), z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.43/1.65 tff(1784,plain,
% 1.43/1.65 (~r(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1783, 333, 670, 722, 707])).
% 1.43/1.65 tff(1785,plain,
% 1.43/1.65 (b(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[396, 1784])).
% 1.43/1.65 tff(1786,plain,
% 1.43/1.65 (((~![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(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, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1787,plain,
% 1.43/1.65 ((~![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(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1788,plain,
% 1.43/1.66 ((~![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(z, elem!1)) | (~r(z, s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.43/1.66 tff(1789,plain,
% 1.43/1.66 (~r(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1788, 333, 670, 722, 707])).
% 1.43/1.66 tff(1790,plain,
% 1.43/1.66 (b(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[619, 1789])).
% 1.43/1.66 tff(1791,plain,
% 1.43/1.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[294, 1790, 286, 1785])).
% 1.43/1.66 tff(1792,plain,
% 1.43/1.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[249, 1791])).
% 1.43/1.66 tff(1793,plain,
% 1.43/1.66 (r(elem!1, s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1792, 1685])).
% 1.43/1.66 tff(1794,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.43/1.66 tff(1795,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1796,plain,
% 1.43/1.66 (((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1797,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1796])).
% 1.43/1.66 tff(1798,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.43/1.66 tff(1799,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1800,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.43/1.66 tff(1801,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1800, 144, 491, 285, 284, 1794])).
% 1.43/1.66 tff(1802,plain,((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1803,plain,
% 1.43/1.66 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1802, 491, 284, 285])).
% 1.43/1.66 tff(1804,plain,
% 1.43/1.66 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[965, 1803, 960])).
% 1.43/1.66 tff(1805,plain,
% 1.43/1.66 (~r(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1694, 1804, 707, 722])).
% 1.43/1.66 tff(1806,plain,
% 1.43/1.66 (~r(elem!1, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1739, 333, 1525, 707, 1804])).
% 1.43/1.66 tff(1807,plain,
% 1.43/1.66 (~b(s(z), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1732, 1806, 1722, 134, 1805])).
% 1.43/1.66 tff(1808,plain,
% 1.43/1.66 (r(s(z), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1244, 1807, 1229])).
% 1.43/1.66 tff(1809,plain,
% 1.43/1.66 (b(elem!1, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[560, 1806, 1722])).
% 1.43/1.66 tff(1810,plain,
% 1.43/1.66 (~b(z, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[949, 1809, 624, 491])).
% 1.43/1.66 tff(1811,plain,
% 1.43/1.66 (r(z, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[583, 1810])).
% 1.43/1.66 tff(1812,plain,
% 1.43/1.66 (b(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[448, 1805, 433])).
% 1.43/1.66 tff(1813,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1814,plain,
% 1.43/1.66 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1815,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1814])).
% 1.43/1.66 tff(1816,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1815, 1813])).
% 1.43/1.66 tff(1817,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1818,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.43/1.66 tff(1819,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1818, 144, 451, 491, 134, 490, 488])).
% 1.43/1.66 tff(1820,plain,((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1821,plain,
% 1.43/1.66 (~b(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1820, 1812, 490, 134, 491])).
% 1.43/1.66 tff(1822,plain,
% 1.43/1.66 (r(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[486, 1821, 1])).
% 1.43/1.66 tff(1823,plain,
% 1.43/1.66 (((~![X0: $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(elem!1))) | (~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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1824,plain,
% 1.43/1.66 (((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1825,plain,
% 1.43/1.66 (((~![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(z))) | (~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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1824])).
% 1.43/1.66 tff(1826,plain,
% 1.43/1.66 (((~![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(z))) | (~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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1825, 1823])).
% 1.43/1.66 tff(1827,plain,
% 1.43/1.66 ((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1828,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 1.43/1.66 tff(1829,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1828, 333, 323, 1822, 1811, 1808])).
% 1.43/1.66 tff(1830,plain,((~b(s(elem!1), z)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (s(elem!1) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1831,plain,
% 1.43/1.66 (~b(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1830, 1793, 624, 134, 323, 707, 1, 490, 433, 722, 1682, 1790, 1785])).
% 1.43/1.66 tff(1832,plain,
% 1.43/1.66 (r(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[507, 1831])).
% 1.43/1.66 tff(1833,plain,
% 1.43/1.66 (((~![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))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1834,plain,
% 1.43/1.66 ((~![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))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1835,plain,
% 1.43/1.66 ((~![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)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 1.43/1.66 tff(1836,plain,
% 1.43/1.66 (~r(s(z), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1835, 333, 670, 323, 1832])).
% 1.43/1.66 tff(1837,plain,
% 1.43/1.66 (b(s(z), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1244, 1836, 1229])).
% 1.43/1.66 tff(1838,plain,
% 1.43/1.66 (((~![X0: $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, elem!1)) | (~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(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1839,plain,
% 1.43/1.66 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1840,plain,
% 1.43/1.66 (((~![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(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1839])).
% 1.43/1.66 tff(1841,plain,
% 1.43/1.66 (((~![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(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1840, 1838])).
% 1.43/1.66 tff(1842,plain,
% 1.43/1.66 ((~![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(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1843,plain,
% 1.43/1.66 ((~![X0: $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, elem!1)) | (~r(s(elem!1), z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 1.43/1.66 tff(1844,plain,
% 1.43/1.66 (~r(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1843, 333, 670, 323, 1832])).
% 1.43/1.66 tff(1845,plain,
% 1.43/1.66 (b(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[486, 1844, 1])).
% 1.43/1.66 tff(1846,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1847,plain,
% 1.43/1.66 (((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1848,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1847])).
% 1.43/1.66 tff(1849,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1848, 1846])).
% 1.43/1.66 tff(1850,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1851,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 1.43/1.66 tff(1852,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1851, 144, 585, 490, 488, 1262])).
% 1.43/1.66 tff(1853,plain,((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1854,plain,
% 1.43/1.67 (~b(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1853, 1845, 490, 1837])).
% 1.43/1.67 tff(1855,plain,
% 1.43/1.67 (r(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[583, 1854])).
% 1.43/1.67 tff(1856,plain,
% 1.43/1.67 (((~![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(elem!1, s(z))) | (~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(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1857,plain,
% 1.43/1.67 (((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1858,plain,
% 1.43/1.67 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1857])).
% 1.43/1.67 tff(1859,plain,
% 1.43/1.67 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1858, 1856])).
% 1.43/1.67 tff(1860,plain,
% 1.43/1.67 ((~![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(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1861,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.43/1.67 tff(1862,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1861, 333, 435, 670, 562, 722])).
% 1.43/1.67 tff(1863,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1864,plain,
% 1.43/1.67 (~r(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1863, 1855, 722, 670])).
% 1.43/1.67 tff(1865,plain,
% 1.43/1.67 (r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1732, 1864, 1722, 134, 1837])).
% 1.43/1.67 tff(1866,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1867,plain,
% 1.43/1.67 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1868,plain,
% 1.43/1.67 (((~![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(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1867])).
% 1.43/1.67 tff(1869,plain,
% 1.43/1.67 (((~![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(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1868, 1866])).
% 1.43/1.67 tff(1870,plain,
% 1.43/1.67 ((~![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(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1871,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 1.43/1.67 tff(1872,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1871, 333, 1865, 670, 1832, 1855])).
% 1.43/1.67 tff(1873,plain,((~r(z, elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1874,plain,
% 1.43/1.67 (~r(z, elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1873, 1776, 722, 490, 1, 323, 624, 707, 1777, 1770, 286])).
% 1.43/1.67 tff(1875,plain,
% 1.43/1.67 (b(z, elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[658, 1874, 71])).
% 1.43/1.67 tff(1876,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1877,plain,
% 1.43/1.67 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1878,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1877])).
% 1.43/1.67 tff(1879,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1878, 1876])).
% 1.43/1.67 tff(1880,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1881,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 1.43/1.67 tff(1882,plain,
% 1.43/1.67 (~b(z, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1881, 144, 1875, 1776, 490, 56])).
% 1.43/1.67 tff(1883,plain,
% 1.43/1.67 (r(z, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[619, 1882])).
% 1.43/1.67 tff(1884,plain,
% 1.43/1.67 (((~![X0: $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), elem!1)) | (~r(elem!1, 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(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1885,plain,
% 1.43/1.67 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1886,plain,
% 1.43/1.67 (((~![X0: $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(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1885])).
% 1.43/1.67 tff(1887,plain,
% 1.43/1.67 (((~![X0: $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(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1886, 1884])).
% 1.43/1.67 tff(1888,plain,
% 1.43/1.67 ((~![X0: $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)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1889,plain,
% 1.43/1.67 ((~![X0: $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), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 1.43/1.67 tff(1890,plain,
% 1.43/1.67 (~r(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1889, 333, 323, 434, 722])).
% 1.43/1.67 tff(1891,plain,
% 1.43/1.67 (b(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[448, 1890, 433])).
% 1.43/1.67 tff(1892,plain,
% 1.43/1.67 (((~![X0: $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(elem!1))) | (~r(elem!1, 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(z), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1893,plain,
% 1.43/1.67 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1894,plain,
% 1.43/1.67 (((~![X0: $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(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(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1893])).
% 1.43/1.67 tff(1895,plain,
% 1.43/1.67 (((~![X0: $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(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(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1894, 1892])).
% 1.43/1.67 tff(1896,plain,
% 1.43/1.67 ((~![X0: $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(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1897,plain,
% 1.43/1.67 ((~![X0: $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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.43/1.67 tff(1898,plain,
% 1.43/1.67 (~r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1897, 333, 323, 434, 722])).
% 1.43/1.67 tff(1899,plain,
% 1.43/1.67 (b(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[560, 1898, 1722])).
% 1.43/1.67 tff(1900,plain,
% 1.43/1.67 (~b(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1642, 1899, 1891, 251])).
% 1.43/1.67 tff(1901,plain,
% 1.43/1.67 (r(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[583, 1900])).
% 1.43/1.67 tff(1902,plain,
% 1.43/1.67 (~b(s(elem!1), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[916, 1891, 624, 251])).
% 1.43/1.67 tff(1903,plain,
% 1.43/1.67 (r(s(elem!1), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[507, 1902])).
% 1.43/1.67 tff(1904,plain,
% 1.43/1.67 (((~![X0: $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(s(elem!1), 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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1905,plain,
% 1.43/1.67 (((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1906,plain,
% 1.43/1.67 (((~![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(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1905])).
% 1.43/1.67 tff(1907,plain,
% 1.43/1.67 (((~![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(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1906, 1904])).
% 1.43/1.67 tff(1908,plain,
% 1.43/1.67 ((~![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(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1909,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.43/1.67 tff(1910,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1909, 333, 323, 434, 1903, 1901])).
% 1.43/1.67 tff(1911,plain,((~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1912,plain,
% 1.43/1.67 (~r(s(elem!1), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1911, 1875, 323, 624, 1777, 722])).
% 1.43/1.67 tff(1913,plain,
% 1.43/1.67 (b(s(elem!1), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[486, 1912, 1])).
% 1.43/1.67 tff(1914,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1915,plain,
% 1.43/1.67 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1916,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1915])).
% 1.43/1.67 tff(1917,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.43/1.67 tff(1918,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(1919,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.43/1.67 tff(1920,plain,
% 1.43/1.67 (~b(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1919, 144, 1875, 1776, 490, 1913])).
% 1.43/1.67 tff(1921,plain,
% 1.43/1.67 (r(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[583, 1920])).
% 1.43/1.67 tff(1922,plain,
% 1.43/1.67 (((~![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))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1923,plain,
% 1.43/1.67 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(1924,plain,
% 1.43/1.67 (((~![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))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1923])).
% 1.43/1.67 tff(1925,plain,
% 1.43/1.67 (((~![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))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[1924, 1922])).
% 1.43/1.67 tff(1926,plain,
% 1.43/1.67 ((~![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))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1927,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.43/1.68 tff(1928,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1927, 333, 562, 623, 707, 1686])).
% 1.43/1.68 tff(1929,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(1930,plain,
% 1.43/1.68 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1929, 1921, 707, 1883])).
% 1.43/1.68 tff(1931,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[965, 1930, 1774])).
% 1.43/1.68 tff(1932,plain,
% 1.43/1.68 (s(elem!1) = s(s(s(z)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1002, 997])).
% 1.43/1.68 tff(1933,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[960, 1932])).
% 1.43/1.68 tff(1934,plain,((~(s(s(s(z))) = s(elem!1))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(1935,plain,
% 1.43/1.68 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1934, 1774])).
% 1.43/1.68 tff(1936,plain,
% 1.43/1.68 (((~![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), 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, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1937,plain,
% 1.43/1.68 ((~![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), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1938,plain,
% 1.43/1.68 ((~![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), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.43/1.68 tff(1939,plain,
% 1.43/1.68 (~r(s(z), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1938, 333, 323, 509, 562])).
% 1.43/1.68 tff(1940,plain,
% 1.43/1.68 (b(s(z), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1244, 1939, 1237])).
% 1.43/1.68 tff(1941,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1942,plain,
% 1.43/1.68 (((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1943,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1942])).
% 1.43/1.68 tff(1944,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[1943, 1941])).
% 1.43/1.68 tff(1945,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1946,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 1.43/1.68 tff(1947,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1946, 144, 488, 1940, 56])).
% 1.43/1.68 tff(1948,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.43/1.68 tff(1949,plain,
% 1.43/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1950,plain,
% 1.43/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1951,plain,
% 1.43/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 1.43/1.68 tff(1952,plain,
% 1.43/1.68 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 1947])).
% 1.43/1.68 tff(1953,plain,
% 1.43/1.68 (((~![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(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(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(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1954,plain,
% 1.43/1.68 (((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1955,plain,
% 1.43/1.68 (((~![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(s(s(z))), s(elem!1))) | (~r(z, s(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(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1954])).
% 1.43/1.68 tff(1956,plain,
% 1.43/1.68 (((~![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(s(s(z))), s(elem!1))) | (~r(z, s(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(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[1955, 1953])).
% 1.43/1.68 tff(1957,plain,
% 1.43/1.68 ((~![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(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1958,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.43/1.68 tff(1959,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1958, 333, 509, 562, 623, 1952])).
% 1.43/1.68 tff(1960,plain,((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(1961,plain,
% 1.43/1.68 (~r(s(elem!1), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1960, 1921, 1883, 1935, 1913, 56, 1229, 323])).
% 1.43/1.68 tff(1962,plain,
% 1.43/1.68 (b(s(elem!1), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[507, 1961])).
% 1.43/1.68 tff(1963,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.43/1.68 tff(1964,plain,
% 1.43/1.68 (r(s(s(s(z))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[396, 1963])).
% 1.43/1.68 tff(1965,plain,
% 1.43/1.68 (((~![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(z))))) | (~r(z, s(elem!1))) | (~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(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1966,plain,
% 1.43/1.68 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1967,plain,
% 1.43/1.68 (((~![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))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1966])).
% 1.43/1.68 tff(1968,plain,
% 1.43/1.68 (((~![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))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.43/1.68 tff(1969,plain,
% 1.43/1.68 ((~![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))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1970,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.43/1.68 tff(1971,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1970, 333, 562, 1699, 623, 1686])).
% 1.43/1.68 tff(1972,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(1973,plain,
% 1.43/1.68 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1972, 1964, 562, 623])).
% 1.43/1.68 tff(1974,plain,
% 1.43/1.68 (((~![X0: $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(elem!1))) | (~r(s(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(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1975,plain,
% 1.43/1.68 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1976,plain,
% 1.43/1.68 (((~![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(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1975])).
% 1.43/1.68 tff(1977,plain,
% 1.43/1.68 (((~![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(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[1976, 1974])).
% 1.43/1.68 tff(1978,plain,
% 1.43/1.68 ((~![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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1979,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.43/1.68 tff(1980,plain,
% 1.43/1.68 (~r(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1979, 333, 323, 562, 1964])).
% 1.43/1.68 tff(1981,plain,
% 1.43/1.68 (b(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[170, 44, 167, 1980])).
% 1.43/1.68 tff(1982,plain,
% 1.43/1.68 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[899, 144, 488, 56, 1981])).
% 1.43/1.68 tff(1983,plain,
% 1.43/1.68 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[963, 44, 1982])).
% 1.43/1.68 tff(1984,plain,
% 1.43/1.68 (s(elem!1) = s(s(s(z)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1983, 1973])).
% 1.43/1.68 tff(1985,plain,
% 1.43/1.68 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1984])).
% 1.43/1.68 tff(1986,plain,
% 1.43/1.68 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.43/1.68 inference(symmetry,[status(thm)],[1985])).
% 1.43/1.68 tff(1987,plain,
% 1.43/1.68 ((~b(s(s(s(z))), z)) <=> (~b(s(elem!1), z))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1986])).
% 1.43/1.68 tff(1988,plain,
% 1.43/1.68 (~b(s(elem!1), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1963, 1987])).
% 1.43/1.68 tff(1989,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[491, 1988])).
% 1.43/1.68 tff(1990,plain,(b(s(s(s(z))), z) | (~b(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(1991,plain,
% 1.43/1.68 (b(s(s(s(z))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1990, 1962, 1883, 56, 1921, 1913, 323])).
% 1.43/1.68 tff(1992,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1993,plain,
% 1.43/1.68 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(1994,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1993])).
% 1.43/1.68 tff(1995,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[1994, 1992])).
% 1.43/1.68 tff(1996,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(1997,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 1.43/1.68 tff(1998,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1997, 144, 1962, 490, 1913, 1991, 1931])).
% 1.43/1.68 tff(1999,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2000,plain,
% 1.43/1.68 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1999, 1757, 56, 323, 707, 1, 825, 721, 123, 706, 3, 54])).
% 1.43/1.68 tff(2001,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[302, 2000])).
% 1.43/1.68 tff(2002,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[779, 2001, 56, 123, 323, 1757])).
% 1.43/1.68 tff(2003,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[319, 2002])).
% 1.43/1.68 tff(2004,plain,
% 1.43/1.68 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[735, 2003, 708])).
% 1.43/1.68 tff(2005,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[130, 2004, 54])).
% 1.43/1.68 tff(2006,plain,
% 1.43/1.68 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[116, 2004])).
% 1.43/1.68 tff(2007,plain,
% 1.43/1.68 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[121, 2006, 3])).
% 1.43/1.68 tff(2008,plain,
% 1.43/1.68 (~b(s(z), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[152, 2007, 123, 2005])).
% 1.43/1.68 tff(2009,plain,
% 1.43/1.68 (r(s(z), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[406, 2008, 706])).
% 1.43/1.68 tff(2010,plain,
% 1.43/1.68 (~r(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[835, 333, 2009, 721, 707])).
% 1.43/1.68 tff(2011,plain,
% 1.43/1.68 (b(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[172, 2010])).
% 1.43/1.68 tff(2012,plain,
% 1.43/1.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[757, 2003, 123, 1757])).
% 1.43/1.68 tff(2013,plain,
% 1.43/1.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[279, 2012])).
% 1.43/1.68 tff(2014,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1124, 144, 56, 123, 2003])).
% 1.43/1.68 tff(2015,plain,
% 1.43/1.68 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1137, 2014])).
% 1.43/1.68 tff(2016,plain,
% 1.43/1.68 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[846, 2011, 56, 2003])).
% 1.43/1.68 tff(2017,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[249, 2016])).
% 1.43/1.68 tff(2018,plain,
% 1.43/1.68 (~r(z, s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1480, 333, 2017, 2015, 2013])).
% 1.43/1.69 tff(2019,plain,
% 1.43/1.69 (b(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[619, 2018])).
% 1.43/1.69 tff(2020,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2021,plain,
% 1.43/1.69 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2022,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2021])).
% 1.43/1.69 tff(2023,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2022, 2020])).
% 1.43/1.69 tff(2024,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(z, s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2025,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 1.43/1.69 tff(2026,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2025, 144, 1757, 2019, 56, 2011])).
% 1.43/1.69 tff(2027,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2028,plain,
% 1.43/1.69 (~r(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2027, 708, 707, 50, 706, 3, 54, 56, 1])).
% 1.43/1.69 tff(2029,plain,
% 1.43/1.69 (b(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[348, 2028])).
% 1.43/1.69 tff(2030,plain,
% 1.43/1.69 (((~![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))), elem!1)) | (~r(elem!1, 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), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2031,plain,
% 1.43/1.69 (((~r(elem!1, 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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2032,plain,
% 1.43/1.69 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2031])).
% 1.43/1.69 tff(2033,plain,
% 1.43/1.69 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2032, 2030])).
% 1.43/1.69 tff(2034,plain,
% 1.43/1.69 ((~![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(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2035,plain,
% 1.43/1.69 ((~![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))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 1.43/1.69 tff(2036,plain,
% 1.43/1.69 (~r(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2035, 333, 409, 408, 707])).
% 1.43/1.69 tff(2037,plain,
% 1.43/1.69 (b(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[172, 2036])).
% 1.43/1.69 tff(2038,plain,
% 1.43/1.69 (~b(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2025, 144, 490, 56, 838])).
% 1.43/1.69 tff(2039,plain,
% 1.43/1.69 (r(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[619, 2038])).
% 1.43/1.69 tff(2040,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2041,plain,
% 1.43/1.69 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2042,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2041])).
% 1.43/1.69 tff(2043,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.43/1.69 tff(2044,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2045,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.43/1.69 tff(2046,plain,
% 1.43/1.69 (~b(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2045, 144, 490, 489, 56])).
% 1.43/1.69 tff(2047,plain,
% 1.43/1.69 (r(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[396, 2046])).
% 1.43/1.69 tff(2048,plain,
% 1.43/1.69 (((~![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, 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))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2049,plain,
% 1.43/1.69 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2050,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2049])).
% 1.43/1.69 tff(2051,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2050, 2048])).
% 1.43/1.69 tff(2052,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2053,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 1.43/1.69 tff(2054,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2053, 333, 408, 2047, 2039, 707])).
% 1.43/1.69 tff(2055,plain,((~b(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2056,plain,
% 1.43/1.69 (~b(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2055, 2037, 707, 489, 56, 408])).
% 1.43/1.69 tff(2057,plain,
% 1.43/1.69 (r(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[372, 2056])).
% 1.43/1.69 tff(2058,plain,
% 1.43/1.69 (((~![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(z, 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2059,plain,
% 1.43/1.69 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2060,plain,
% 1.43/1.69 (((~![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(z, s(z))) | (~r(elem!1, 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2059])).
% 1.43/1.69 tff(2061,plain,
% 1.43/1.69 (((~![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(z, s(z))) | (~r(elem!1, 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2060, 2058])).
% 1.43/1.69 tff(2062,plain,
% 1.43/1.69 ((~![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(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2063,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.43/1.69 tff(2064,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2063, 333, 409, 2057, 408, 722])).
% 1.43/1.69 tff(2065,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2066,plain,
% 1.43/1.69 (~r(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2065, 408, 721, 707, 489, 56])).
% 1.43/1.69 tff(2067,plain,
% 1.43/1.69 (b(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[406, 2066, 706])).
% 1.43/1.69 tff(2068,plain,
% 1.43/1.69 (~b(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2055, 490, 707, 489, 56, 408])).
% 1.43/1.69 tff(2069,plain,
% 1.43/1.69 (r(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[172, 2068])).
% 1.43/1.69 tff(2070,plain,
% 1.43/1.69 (~r(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1533, 2069, 707, 722])).
% 1.43/1.69 tff(2071,plain,
% 1.43/1.69 (b(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1538, 2070, 1524])).
% 1.43/1.69 tff(2072,plain,
% 1.43/1.69 (((~![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, elem!1)) | (~r(elem!1, 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))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2073,plain,
% 1.43/1.69 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2074,plain,
% 1.43/1.69 (((~![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(z))), 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2073])).
% 1.43/1.69 tff(2075,plain,
% 1.43/1.69 (((~![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(z))), 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2074, 2072])).
% 1.43/1.69 tff(2076,plain,
% 1.43/1.69 ((~![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(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2077,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.43/1.69 tff(2078,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2077, 333, 670, 408, 1699, 707])).
% 1.43/1.69 tff(2079,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2080,plain,
% 1.43/1.69 (~r(z, elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2079, 2047, 707, 408])).
% 1.43/1.69 tff(2081,plain,
% 1.43/1.69 (b(z, elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[658, 2080, 74])).
% 1.43/1.69 tff(2082,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.43/1.69 tff(2083,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2084,plain,
% 1.43/1.69 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2085,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2084])).
% 1.43/1.69 tff(2086,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2085, 2083])).
% 1.43/1.69 tff(2087,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2088,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 1.43/1.69 tff(2089,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2088, 144, 251, 134, 490, 2082, 284])).
% 1.43/1.69 tff(2090,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2091,plain,
% 1.43/1.69 (~b(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2090, 2081, 134, 490, 2071])).
% 1.43/1.69 tff(2092,plain,
% 1.43/1.69 (r(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[619, 2091])).
% 1.43/1.69 tff(2093,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2053, 333, 408, 2047, 2092, 707])).
% 1.43/1.69 tff(2094,plain,((~b(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (z = elem!1) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2095,plain,
% 1.43/1.69 (~b(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2094, 408, 707, 2067, 74, 489, 56, 1524, 721])).
% 1.43/1.69 tff(2096,plain,
% 1.43/1.69 (r(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[372, 2095])).
% 1.43/1.69 tff(2097,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[302, 297])).
% 1.43/1.69 tff(2098,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2099,plain,
% 1.43/1.69 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2100,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2099])).
% 1.43/1.69 tff(2101,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.43/1.69 tff(2102,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2103,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.43/1.69 tff(2104,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2103, 144, 134, 489, 123, 132, 286])).
% 1.43/1.69 tff(2105,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2106,plain,
% 1.43/1.69 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2105, 2097, 489, 123, 134])).
% 1.43/1.69 tff(2107,plain,
% 1.43/1.69 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[121, 2106, 3])).
% 1.43/1.69 tff(2108,plain,
% 1.43/1.69 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2107])).
% 1.43/1.69 tff(2109,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 1.43/1.69 inference(symmetry,[status(thm)],[2108])).
% 1.43/1.69 tff(2110,plain,
% 1.43/1.69 ((~r(s(s(s(s(s(s(s(z))))))), z)) <=> (~r(elem!1, z))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2109])).
% 1.43/1.69 tff(2111,plain,
% 1.43/1.69 (~r(elem!1, z)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[297, 2110])).
% 1.43/1.69 tff(2112,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[408, 2111])).
% 1.43/1.69 tff(2113,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~r(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2114,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2113, 2067, 3, 489, 123, 408])).
% 1.43/1.69 tff(2115,plain,
% 1.43/1.69 (((~![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(z))), elem!1)) | (~r(elem!1, 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(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2116,plain,
% 1.53/1.70 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2117,plain,
% 1.53/1.70 (((~![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(s(s(z))), 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(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2116])).
% 1.53/1.70 tff(2118,plain,
% 1.53/1.70 (((~![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(s(s(z))), 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(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2117, 2115])).
% 1.53/1.70 tff(2119,plain,
% 1.53/1.70 ((~![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(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2120,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 1.53/1.70 tff(2121,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2120, 333, 354, 408, 1699, 707])).
% 1.53/1.70 tff(2122,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2123,plain,
% 1.53/1.70 (~r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2122, 2096, 707, 408])).
% 1.53/1.70 tff(2124,plain,
% 1.53/1.70 (b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[396, 2123])).
% 1.53/1.70 tff(2125,plain,
% 1.53/1.70 (~r(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1519, 623, 707, 354])).
% 1.53/1.70 tff(2126,plain,
% 1.53/1.70 (b(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[172, 2125])).
% 1.53/1.70 tff(2127,plain,
% 1.53/1.70 (~r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2122, 354, 707, 408])).
% 1.53/1.70 tff(2128,plain,
% 1.53/1.70 (b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[396, 2127])).
% 1.53/1.70 tff(2129,plain,
% 1.53/1.70 (((~![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))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, 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))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2130,plain,
% 1.53/1.70 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2131,plain,
% 1.53/1.70 (((~![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(z))), elem!1)) | (~r(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(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2130])).
% 1.53/1.70 tff(2132,plain,
% 1.53/1.70 (((~![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(z))), elem!1)) | (~r(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(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.53/1.70 tff(2133,plain,
% 1.53/1.70 ((~![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(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2134,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.53/1.70 tff(2135,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2134, 333, 670, 408, 623, 707])).
% 1.53/1.70 tff(2136,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2137,plain,
% 1.53/1.70 (~r(z, elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2136, 623, 707, 408])).
% 1.53/1.70 tff(2138,plain,
% 1.53/1.70 (b(z, elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[658, 2137, 74])).
% 1.53/1.70 tff(2139,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2140,plain,
% 1.53/1.70 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2141,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2140])).
% 1.53/1.70 tff(2142,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2141, 2139])).
% 1.53/1.70 tff(2143,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2144,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.53/1.70 tff(2145,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2144, 144, 2138, 134, 489, 2128, 2126])).
% 1.53/1.70 tff(2146,plain,((~r(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (z = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2147,plain,
% 1.53/1.70 (~r(z, s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2146, 2067, 489, 74, 707, 2096, 408])).
% 1.53/1.70 tff(2148,plain,
% 1.53/1.70 (b(z, s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[619, 2147])).
% 1.53/1.70 tff(2149,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2150,plain,
% 1.53/1.70 (((~b(s(s(s(z))), z)) | (~b(s(z), 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))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2151,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2150])).
% 1.53/1.70 tff(2152,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2151, 2149])).
% 1.53/1.70 tff(2153,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2154,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2153, 2152])).
% 1.53/1.70 tff(2155,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2154, 144, 489, 285, 284, 838])).
% 1.53/1.70 tff(2156,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2157,plain,
% 1.53/1.70 (~b(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2156, 2148, 489, 2124])).
% 1.53/1.70 tff(2158,plain,
% 1.53/1.70 (r(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[172, 2157])).
% 1.53/1.70 tff(2159,plain,
% 1.53/1.70 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[362, 2158, 2114, 2096])).
% 1.53/1.70 tff(2160,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[319, 2159])).
% 1.53/1.70 tff(2161,plain,
% 1.53/1.70 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[735, 2160, 708])).
% 1.53/1.70 tff(2162,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[130, 2161, 54])).
% 1.53/1.70 tff(2163,plain,
% 1.53/1.70 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[116, 2161])).
% 1.53/1.70 tff(2164,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[121, 2163, 3])).
% 1.53/1.70 tff(2165,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[152, 2164, 2162, 123, 2067])).
% 1.53/1.70 tff(2166,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(z)) | (~b(s(z), z)) | (z = elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2167,plain,
% 1.53/1.70 (~r(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2166, 708, 3, 54, 50, 2029, 71, 707, 56, 697, 706])).
% 1.53/1.70 tff(2168,plain,
% 1.53/1.70 (b(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1380, 2167, 77])).
% 1.53/1.70 tff(2169,plain,
% 1.53/1.70 (r(s(z), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[406, 350, 706])).
% 1.53/1.70 tff(2170,plain,
% 1.53/1.70 (~r(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[835, 333, 2169, 721, 707])).
% 1.53/1.70 tff(2171,plain,
% 1.53/1.70 (b(s(z), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[172, 2170])).
% 1.53/1.70 tff(2172,plain,
% 1.53/1.70 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2173,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2172])).
% 1.53/1.70 tff(2174,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2173, 2020])).
% 1.53/1.70 tff(2175,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2176,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 1.53/1.70 tff(2177,plain,
% 1.53/1.70 (~b(z, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2176, 144, 284, 56, 838])).
% 1.53/1.70 tff(2178,plain,
% 1.53/1.70 (r(z, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[372, 2177])).
% 1.53/1.70 tff(2179,plain,
% 1.53/1.70 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2180,plain,
% 1.53/1.70 ((~![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(z, s(z))) | (~r(z, elem!1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2181,plain,
% 1.53/1.70 ((~![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(z, s(z))) | (~r(z, elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.53/1.70 tff(2182,plain,
% 1.53/1.70 (~r(z, elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2181, 333, 409, 2178, 721])).
% 1.53/1.70 tff(2183,plain,
% 1.53/1.70 (b(z, elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[658, 2182, 74])).
% 1.53/1.70 tff(2184,plain,
% 1.53/1.70 (~b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2156, 284, 489, 838])).
% 1.53/1.70 tff(2185,plain,
% 1.53/1.70 (r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[396, 2184])).
% 1.53/1.70 tff(2186,plain,
% 1.53/1.70 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[267, 452, 251, 454])).
% 1.53/1.70 tff(2187,plain,
% 1.53/1.70 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[279, 2186])).
% 1.53/1.70 tff(2188,plain,
% 1.53/1.70 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[880, 452, 624, 251])).
% 1.53/1.70 tff(2189,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[302, 2188])).
% 1.53/1.70 tff(2190,plain,
% 1.53/1.70 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[429, 2187, 409, 354])).
% 1.53/1.70 tff(2191,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[319, 2190])).
% 1.53/1.70 tff(2192,plain,
% 1.53/1.70 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[846, 2191, 56, 838])).
% 1.53/1.70 tff(2193,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[249, 2192])).
% 1.53/1.70 tff(2194,plain,
% 1.53/1.70 (((~![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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, 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(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2195,plain,
% 1.53/1.70 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2196,plain,
% 1.53/1.70 (((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2195])).
% 1.53/1.70 tff(2197,plain,
% 1.53/1.70 (((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.53/1.70 tff(2198,plain,
% 1.53/1.70 ((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2199,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.53/1.70 tff(2200,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2199, 333, 1699, 2193, 2189, 2187])).
% 1.53/1.70 tff(2201,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2202,plain,
% 1.53/1.70 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2201, 2185, 56, 838, 409, 2178, 624, 2183, 3, 54])).
% 1.53/1.70 tff(2203,plain,
% 1.53/1.70 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[735, 2202, 708])).
% 1.53/1.70 tff(2204,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[319, 2203])).
% 1.53/1.70 tff(2205,plain,
% 1.53/1.70 (~b(s(z), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1602, 489, 624, 251])).
% 1.53/1.71 tff(2206,plain,
% 1.53/1.71 (r(s(z), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[406, 2205, 706])).
% 1.53/1.71 tff(2207,plain,
% 1.53/1.71 (((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2208,plain,
% 1.53/1.71 ((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2209,plain,
% 1.53/1.71 ((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 1.53/1.71 tff(2210,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2209, 333, 2206, 354, 322])).
% 1.53/1.71 tff(2211,plain,
% 1.53/1.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[302, 2210])).
% 1.53/1.71 tff(2212,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2213,plain,
% 1.53/1.71 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2214,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2213])).
% 1.53/1.71 tff(2215,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2214, 2212])).
% 1.53/1.71 tff(2216,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2217,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.53/1.71 tff(2218,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2217, 144, 489, 123, 2211, 259])).
% 1.53/1.71 tff(2219,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2220,plain,
% 1.53/1.71 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2219, 2204, 123, 489, 2178, 706, 624, 2183])).
% 1.53/1.71 tff(2221,plain,
% 1.53/1.71 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[429, 2204, 409, 2178])).
% 1.53/1.71 tff(2222,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[279, 2221, 2220])).
% 1.53/1.71 tff(2223,plain,((~b(z, s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (s(z) = elem!1) | (~b(elem!1, z)) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2224,plain,
% 1.53/1.71 (~b(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2223, 2169, 123, 489, 706, 624, 708, 56, 2171, 3, 54, 74])).
% 1.53/1.71 tff(2225,plain,
% 1.53/1.71 (r(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[619, 2224])).
% 1.53/1.71 tff(2226,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1788, 333, 670, 722, 623, 707])).
% 1.53/1.71 tff(2227,plain,((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2228,plain,
% 1.53/1.71 (~r(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2227, 2225, 721, 707])).
% 1.53/1.71 tff(2229,plain,
% 1.53/1.71 (b(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[658, 2228, 74])).
% 1.53/1.71 tff(2230,plain,
% 1.53/1.71 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[81])).
% 1.53/1.71 tff(2231,plain,
% 1.53/1.71 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[2230])).
% 1.53/1.71 tff(2232,plain,
% 1.53/1.71 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2231])).
% 1.53/1.71 tff(2233,plain,
% 1.53/1.71 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[350, 2232])).
% 1.53/1.71 tff(2234,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[123, 2233])).
% 1.53/1.71 tff(2235,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2236,plain,
% 1.53/1.71 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2235, 350, 123])).
% 1.53/1.71 tff(2237,plain,
% 1.53/1.71 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[130, 2236, 54])).
% 1.53/1.71 tff(2238,plain,
% 1.53/1.71 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[880, 2237, 624, 2229])).
% 1.53/1.71 tff(2239,plain,
% 1.53/1.71 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[302, 2238])).
% 1.53/1.71 tff(2240,plain,
% 1.53/1.71 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[116, 2236])).
% 1.53/1.71 tff(2241,plain,
% 1.53/1.71 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[121, 2240, 3])).
% 1.53/1.71 tff(2242,plain,
% 1.53/1.71 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[267, 2237, 2229, 2241])).
% 1.53/1.71 tff(2243,plain,
% 1.53/1.71 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[279, 2242])).
% 1.53/1.71 tff(2244,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2199, 333, 1699, 2189, 2187])).
% 1.53/1.71 tff(2245,plain,
% 1.53/1.71 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[249, 2244])).
% 1.53/1.71 tff(2246,plain,
% 1.53/1.71 (((~![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))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2247,plain,
% 1.53/1.71 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2248,plain,
% 1.53/1.71 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2247])).
% 1.53/1.71 tff(2249,plain,
% 1.53/1.71 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.53/1.71 tff(2250,plain,
% 1.53/1.71 ((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2251,plain,
% 1.53/1.71 ((~![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))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.53/1.71 tff(2252,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2251, 333, 1699, 2189, 2187])).
% 1.53/1.71 tff(2253,plain,
% 1.53/1.71 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1137, 2252])).
% 1.53/1.71 tff(2254,assumption,(b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.53/1.71 tff(2255,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2256,plain,
% 1.53/1.71 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2257,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2256])).
% 1.53/1.71 tff(2258,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2257, 2255])).
% 1.53/1.71 tff(2259,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2260,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 1.53/1.71 tff(2261,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2260, 144, 838, 123, 283, 2254])).
% 1.53/1.71 tff(2262,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2263,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2262, 2253, 2245, 123, 838])).
% 1.53/1.71 tff(2264,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2265,plain,
% 1.53/1.71 (~r(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2264, 2236, 2171, 123, 624, 2229, 3, 54])).
% 1.53/1.71 tff(2266,plain,
% 1.53/1.71 (b(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[396, 2265])).
% 1.53/1.71 tff(2267,plain,
% 1.53/1.71 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2268,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2267])).
% 1.53/1.71 tff(2269,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2268, 2040])).
% 1.53/1.71 tff(2270,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2271,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.53/1.71 tff(2272,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2271, 144, 490, 489, 285, 56])).
% 1.53/1.71 tff(2273,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2274,plain,
% 1.53/1.71 (~b(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2273, 2266, 489, 56])).
% 1.53/1.71 tff(2275,plain,
% 1.53/1.71 (r(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[372, 2274])).
% 1.53/1.71 tff(2276,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[429, 2275, 2169, 2243])).
% 1.53/1.71 tff(2277,plain,
% 1.53/1.71 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[319, 2276])).
% 1.53/1.71 tff(2278,plain,
% 1.53/1.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[846, 2277, 56, 2171])).
% 1.53/1.71 tff(2279,plain,
% 1.53/1.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[249, 2278])).
% 1.53/1.71 tff(2280,plain,
% 1.53/1.71 (((~![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))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2281,plain,
% 1.53/1.71 ((~![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))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2282,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 1.53/1.71 tff(2283,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2282, 333, 2225, 707, 2279, 2239])).
% 1.53/1.71 tff(2284,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (z = elem!1) | (s(z) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2285,plain,
% 1.53/1.71 (b(s(z), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2284, 2029, 56, 707, 2168, 3, 50, 54, 71, 706, 708])).
% 1.53/1.71 tff(2286,plain,
% 1.53/1.71 (~b(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1602, 2285, 2029, 2168])).
% 1.53/1.71 tff(2287,plain,
% 1.53/1.71 (r(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[658, 2286, 71])).
% 1.53/1.71 tff(2288,plain,
% 1.53/1.71 (~r(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1783, 333, 2287, 721, 707])).
% 1.53/1.71 tff(2289,plain,
% 1.53/1.71 (b(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[396, 2288])).
% 1.53/1.71 tff(2290,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2291,plain,
% 1.53/1.71 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2292,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2291])).
% 1.53/1.71 tff(2293,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2292, 2290])).
% 1.53/1.71 tff(2294,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2295,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 1.53/1.71 tff(2296,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2295, 144, 624, 134, 489, 123, 133])).
% 1.53/1.71 tff(2297,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2298,plain,
% 1.53/1.72 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2297, 2285, 2029, 2168, 50])).
% 1.53/1.72 tff(2299,plain,
% 1.53/1.72 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[130, 2298, 54])).
% 1.53/1.72 tff(2300,plain,
% 1.53/1.72 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, elem!1)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[81])).
% 1.53/1.72 tff(2301,plain,
% 1.53/1.72 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[2300])).
% 1.53/1.72 tff(2302,plain,
% 1.53/1.72 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[670, 2301])).
% 1.53/1.72 tff(2303,assumption,(~r(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.53/1.72 tff(2304,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2303, 2302])).
% 1.53/1.72 tff(2305,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | r(z, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2306,plain,
% 1.53/1.72 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2305, 2287, 2299])).
% 1.53/1.72 tff(2307,plain,
% 1.53/1.72 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), elem!1)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2299])).
% 1.53/1.72 tff(2308,plain,
% 1.53/1.72 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(z), elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2307])).
% 1.53/1.72 tff(2309,plain,
% 1.53/1.72 (~r(s(z), elem!1)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4, 2308])).
% 1.53/1.72 tff(2310,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.53/1.72 tff(2311,plain,
% 1.53/1.72 (r(z, elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[658, 71, 606])).
% 1.53/1.72 tff(2312,plain,
% 1.53/1.72 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2313,plain,
% 1.53/1.72 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2314,plain,
% 1.53/1.72 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2313])).
% 1.53/1.72 tff(2315,plain,
% 1.53/1.72 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2314, 2312])).
% 1.53/1.72 tff(2316,plain,
% 1.53/1.72 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2317,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.53/1.72 tff(2318,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2317, 333, 354, 1230, 322, 51])).
% 1.53/1.72 tff(2319,plain,((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2320,plain,
% 1.53/1.72 (~r(s(z), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2319, 322, 354, 51])).
% 1.53/1.72 tff(2321,plain,
% 1.53/1.72 (b(s(z), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1244, 2320, 1229])).
% 1.53/1.72 tff(2322,plain,
% 1.53/1.72 (r(elem!1, z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[653, 377, 77])).
% 1.53/1.72 tff(2323,assumption,(r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.53/1.72 tff(2324,plain,
% 1.53/1.72 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2325,plain,
% 1.53/1.72 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2326,plain,
% 1.53/1.72 (((~![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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2325])).
% 1.53/1.72 tff(2327,plain,
% 1.53/1.72 (((~![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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2326, 2324])).
% 1.53/1.72 tff(2328,plain,
% 1.53/1.72 ((~![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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2329,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 1.53/1.72 tff(2330,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2329, 333, 408, 2323, 322, 51])).
% 1.53/1.72 tff(2331,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2332,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2331, 2322, 322, 51])).
% 1.53/1.72 tff(2333,plain,
% 1.53/1.72 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[787, 286, 377])).
% 1.53/1.72 tff(2334,plain,
% 1.53/1.72 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[116, 2333])).
% 1.53/1.72 tff(2335,plain,
% 1.53/1.72 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[121, 2334, 3])).
% 1.53/1.72 tff(2336,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2103, 144, 134, 489, 123, 2335, 286])).
% 1.53/1.72 tff(2337,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2338,plain,
% 1.53/1.72 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2337, 134, 489, 123, 3, 377])).
% 1.53/1.72 tff(2339,plain,
% 1.53/1.72 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[302, 2338])).
% 1.53/1.72 tff(2340,assumption,(r(s(z), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 1.53/1.72 tff(2341,plain,
% 1.53/1.72 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2342,plain,
% 1.53/1.72 (((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2343,plain,
% 1.53/1.72 (((~![X0: $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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2342])).
% 1.53/1.72 tff(2344,plain,
% 1.53/1.72 (((~![X0: $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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2343, 2341])).
% 1.53/1.72 tff(2345,plain,
% 1.53/1.72 ((~![X0: $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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2346,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 1.53/1.72 tff(2347,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2346, 333, 354, 322, 321, 2340])).
% 1.53/1.72 tff(2348,plain,((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2349,plain,
% 1.53/1.72 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2348, 2339, 322, 354])).
% 1.53/1.72 tff(2350,plain,
% 1.53/1.72 (~r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[362, 2339, 322, 354])).
% 1.53/1.72 tff(2351,plain,
% 1.53/1.72 (b(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[172, 2350])).
% 1.53/1.72 tff(2352,plain,
% 1.53/1.72 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[112])).
% 1.53/1.72 tff(2353,plain,
% 1.53/1.72 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 1.53/1.72 inference(symmetry,[status(thm)],[2352])).
% 1.53/1.72 tff(2354,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2353])).
% 1.53/1.72 tff(2355,plain,
% 1.53/1.72 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2354])).
% 1.53/1.72 tff(2356,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2353])).
% 1.53/1.72 tff(2357,plain,
% 1.53/1.72 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.53/1.72 inference(symmetry,[status(thm)],[2356])).
% 1.53/1.72 tff(2358,plain,
% 1.53/1.72 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[116, 112])).
% 1.53/1.72 tff(2359,plain,
% 1.53/1.72 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[112])).
% 1.53/1.72 tff(2360,plain,
% 1.53/1.72 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[2359])).
% 1.53/1.72 tff(2361,plain,
% 1.53/1.72 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2360])).
% 1.53/1.72 tff(2362,plain,
% 1.53/1.72 (~(elem!1 = s(s(s(z))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[244, 2361])).
% 1.53/1.72 tff(2363,plain,
% 1.53/1.72 (~(s(elem!1) = elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1565, 2362, 2358])).
% 1.53/1.72 tff(2364,plain,
% 1.53/1.72 (~(elem!1 = s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1569, 2363])).
% 1.53/1.72 tff(2365,plain,
% 1.53/1.72 (b(s(elem!1), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[448, 2363, 1727])).
% 1.53/1.72 tff(2366,plain,
% 1.53/1.72 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2352])).
% 1.53/1.72 tff(2367,plain,
% 1.53/1.72 (r(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(z), s(elem!1))),
% 1.53/1.72 inference(symmetry,[status(thm)],[2366])).
% 1.53/1.72 tff(2368,plain,
% 1.53/1.72 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(z), s(elem!1)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2367])).
% 1.53/1.72 tff(2369,assumption,(~r(s(z), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 1.53/1.72 tff(2370,plain,
% 1.53/1.72 (~r(s(z), s(elem!1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.53/1.72 tff(2371,plain,
% 1.53/1.72 (b(s(z), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1244, 2370, 1229])).
% 1.53/1.72 tff(2372,plain,
% 1.53/1.72 (~b(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1730, 2371, 134, 2365])).
% 1.53/1.72 tff(2373,plain,
% 1.53/1.72 (r(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[560, 2372, 2364])).
% 1.53/1.72 tff(2374,plain,
% 1.53/1.72 (~r(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[678, 2373, 670, 408])).
% 1.53/1.72 tff(2375,plain,
% 1.53/1.72 (b(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[507, 2374])).
% 1.53/1.72 tff(2376,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2377,plain,
% 1.53/1.72 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2378,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2377])).
% 1.53/1.72 tff(2379,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2378, 2376])).
% 1.53/1.72 tff(2380,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2381,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.53/1.72 tff(2382,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2381, 144, 491, 585, 489, 1262])).
% 1.53/1.72 tff(2383,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2384,plain,
% 1.53/1.72 (~b(z, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2383, 2375, 489, 2371])).
% 1.53/1.72 tff(2385,plain,
% 1.53/1.72 (r(z, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[583, 2384])).
% 1.53/1.72 tff(2386,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~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(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2387,plain,
% 1.53/1.72 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2388,plain,
% 1.53/1.72 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2387])).
% 1.53/1.72 tff(2389,plain,
% 1.53/1.72 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2388, 2386])).
% 1.53/1.72 tff(2390,plain,
% 1.53/1.72 ((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2391,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.53/1.72 tff(2392,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2391, 333, 563, 670, 434, 562])).
% 1.53/1.72 tff(2393,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2394,plain,
% 1.53/1.72 (~r(s(elem!1), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2393, 2385, 670, 2373])).
% 1.53/1.72 tff(2395,plain,
% 1.53/1.72 (b(s(elem!1), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[486, 2394, 1])).
% 1.53/1.72 tff(2396,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2395, 2357])).
% 1.53/1.72 tff(2397,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2353])).
% 1.53/1.72 tff(2398,plain,
% 1.53/1.72 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.53/1.72 inference(symmetry,[status(thm)],[2397])).
% 1.53/1.72 tff(2399,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2375, 2398])).
% 1.53/1.72 tff(2400,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2401,plain,
% 1.53/1.72 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2402,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2401])).
% 1.53/1.72 tff(2403,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2402, 2400])).
% 1.53/1.73 tff(2404,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2405,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 1.53/1.73 tff(2406,plain,
% 1.53/1.73 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2405, 144, 285, 838])).
% 1.53/1.73 tff(2407,plain,
% 1.53/1.73 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2406, 2399, 2396])).
% 1.53/1.73 tff(2408,plain,
% 1.53/1.73 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2407, 2355])).
% 1.53/1.73 tff(2409,plain,
% 1.53/1.73 (s(elem!1) = s(s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[965, 2408, 959])).
% 1.53/1.73 tff(2410,plain,
% 1.53/1.73 (s(s(s(z))) = s(elem!1)),
% 1.53/1.73 inference(symmetry,[status(thm)],[2409])).
% 1.53/1.73 tff(2411,plain,
% 1.53/1.73 (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2410, 2352])).
% 1.53/1.73 tff(2412,plain,
% 1.53/1.73 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2411])).
% 1.53/1.73 tff(2413,plain,
% 1.53/1.73 (s(s(z)) = s(s(s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[87, 2412, 181])).
% 1.53/1.73 tff(2414,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1446, 2413])).
% 1.53/1.73 tff(2415,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | r(s(z), s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2416,plain,
% 1.53/1.73 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2415, 2351, 285, 959, 1, 670, 489, 2322, 134, 1727, 2349])).
% 1.53/1.73 tff(2417,plain,
% 1.53/1.73 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[121, 2416, 3])).
% 1.53/1.73 tff(2418,plain,
% 1.53/1.73 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(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, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2419,plain,
% 1.53/1.73 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2420,plain,
% 1.53/1.73 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2419])).
% 1.53/1.73 tff(2421,plain,
% 1.53/1.73 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.53/1.73 tff(2422,plain,
% 1.53/1.73 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2423,plain,
% 1.53/1.73 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.53/1.73 tff(2424,plain,
% 1.53/1.73 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2423, 333, 670, 2322, 2339])).
% 1.53/1.73 tff(2425,plain,
% 1.53/1.73 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[111])).
% 1.53/1.73 tff(2426,plain,
% 1.53/1.73 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2416, 2425])).
% 1.53/1.73 tff(2427,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[130, 2426, 2424])).
% 1.53/1.73 tff(2428,plain,
% 1.53/1.73 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2429,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2428])).
% 1.53/1.73 tff(2430,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2429, 145])).
% 1.53/1.73 tff(2431,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2432,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.53/1.73 tff(2433,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2432, 144, 134, 123, 2427, 2417])).
% 1.53/1.73 tff(2434,plain,((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(s(z), z)) | r(s(elem!1), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2435,plain,
% 1.53/1.73 (~b(s(z), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2434, 2332, 123, 285, 959, 1, 670, 489, 1727, 322, 354, 377])).
% 1.53/1.73 tff(2436,plain,
% 1.53/1.73 (s(z) = elem!1),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[406, 2435, 2310])).
% 1.53/1.73 tff(2437,plain,
% 1.53/1.73 (b(s(z), z) <=> b(elem!1, z)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2436])).
% 1.53/1.73 tff(2438,plain,
% 1.53/1.73 (b(elem!1, z) <=> b(s(z), z)),
% 1.53/1.73 inference(symmetry,[status(thm)],[2437])).
% 1.53/1.73 tff(2439,plain,
% 1.53/1.73 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2438])).
% 1.53/1.73 tff(2440,plain,
% 1.53/1.73 (~b(s(z), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[377, 2439])).
% 1.53/1.73 tff(2441,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[489, 2440])).
% 1.53/1.73 tff(2442,plain,(b(elem!1, z) | (~b(s(z), z)) | r(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2443,plain,
% 1.53/1.73 (r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2442, 377, 2310, 123, 285, 959, 1, 670, 489, 322, 354, 51])).
% 1.53/1.73 tff(2444,plain,
% 1.53/1.73 (~r(s(elem!1), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[517, 2443, 51, 2322])).
% 1.53/1.73 tff(2445,plain,
% 1.53/1.73 (b(s(elem!1), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[507, 2444])).
% 1.53/1.73 tff(2446,plain,
% 1.53/1.73 (~b(z, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2383, 2445, 489, 2321])).
% 1.53/1.73 tff(2447,plain,
% 1.53/1.73 (r(z, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[583, 2446])).
% 1.53/1.73 tff(2448,plain,
% 1.53/1.73 (((~![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, elem!1)) | (~r(elem!1, 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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2449,plain,
% 1.53/1.73 (((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2450,plain,
% 1.53/1.73 (((~![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(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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2449])).
% 1.53/1.73 tff(2451,plain,
% 1.53/1.73 (((~![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(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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2450, 2448])).
% 1.53/1.73 tff(2452,plain,
% 1.53/1.73 ((~![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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2453,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 1.53/1.73 tff(2454,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2453, 333, 2443, 670, 2322, 2447])).
% 1.53/1.73 tff(2455,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2456,plain,
% 1.53/1.73 (b(elem!1, z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2455, 322, 489, 51, 2310, 123, 285, 959, 1, 670, 354])).
% 1.53/1.73 tff(2457,plain,
% 1.53/1.73 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.73 tff(2458,plain,
% 1.53/1.73 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[322, 2457])).
% 1.53/1.73 tff(2459,plain,
% 1.53/1.73 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.73 tff(2460,plain,
% 1.53/1.73 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2459, 1218])).
% 1.53/1.73 tff(2461,plain,
% 1.53/1.73 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2460])).
% 1.53/1.73 tff(2462,plain,
% 1.53/1.73 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[107, 2461])).
% 1.53/1.73 tff(2463,plain,
% 1.53/1.73 (s(z) = s(s(s(elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[57, 1001])).
% 1.53/1.73 tff(2464,plain,
% 1.53/1.73 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2463])).
% 1.53/1.73 tff(2465,plain,
% 1.53/1.73 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2464])).
% 1.53/1.73 tff(2466,plain,
% 1.53/1.73 (s(s(elem!1)) = z),
% 1.53/1.73 inference(transitivity,[status(thm)],[1007, 2465, 16])).
% 1.53/1.73 tff(2467,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1094, 2466])).
% 1.53/1.73 tff(2468,plain,((~(s(z) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2469,plain,
% 1.53/1.73 (~(s(s(s(elem!1))) = elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2468, 57])).
% 1.53/1.73 tff(2470,plain,
% 1.53/1.73 (s(elem!1) = elem!1),
% 1.53/1.73 inference(symmetry,[status(thm)],[885])).
% 1.53/1.73 tff(2471,plain,
% 1.53/1.73 (s(s(elem!1)) = s(elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2470])).
% 1.53/1.73 tff(2472,plain,
% 1.53/1.73 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2471])).
% 1.53/1.73 tff(2473,plain,
% 1.53/1.73 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2472])).
% 1.53/1.73 tff(2474,plain,
% 1.53/1.73 (s(elem!1) = s(s(elem!1))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2471])).
% 1.53/1.73 tff(2475,plain,
% 1.53/1.73 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2474, 2473])).
% 1.53/1.73 tff(2476,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.53/1.73 inference(commutativity,[status(thm)],[])).
% 1.53/1.73 tff(2477,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[885])).
% 1.53/1.73 tff(2478,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2477, 2476])).
% 1.53/1.73 tff(2479,plain,
% 1.53/1.73 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2478])).
% 1.53/1.73 tff(2480,plain,
% 1.53/1.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1012, 2479])).
% 1.53/1.73 tff(2481,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2480, 2475])).
% 1.53/1.73 tff(2482,plain,((~(elem!1 = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2483,plain,
% 1.53/1.73 (~(elem!1 = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2482, 2469])).
% 1.53/1.73 tff(2484,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.53/1.73 tff(2485,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2486,plain,
% 1.53/1.73 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2487,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2486])).
% 1.53/1.73 tff(2488,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2487, 2485])).
% 1.53/1.73 tff(2489,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2490,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 1.53/1.73 tff(2491,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2490, 333, 563, 670, 2484, 51])).
% 1.53/1.73 tff(2492,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2493,plain,
% 1.53/1.73 (~r(elem!1, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2492, 2458, 670, 51])).
% 1.53/1.73 tff(2494,plain,
% 1.53/1.73 (b(elem!1, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[560, 2493, 2483])).
% 1.53/1.73 tff(2495,plain,
% 1.53/1.73 (s(s(z)) = s(elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.73 tff(2496,plain,
% 1.53/1.73 (s(s(s(z))) = s(s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2495])).
% 1.53/1.73 tff(2497,plain,
% 1.53/1.73 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2496])).
% 1.53/1.73 tff(2498,plain,
% 1.53/1.73 (b(s(s(elem!1)), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[285, 2497])).
% 1.53/1.73 tff(2499,plain,
% 1.53/1.73 (s(s(elem!1)) = s(s(s(z)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2496])).
% 1.53/1.73 tff(2500,plain,
% 1.53/1.73 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.73 tff(2501,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2500])).
% 1.53/1.73 tff(2502,plain,
% 1.53/1.73 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.53/1.73 inference(commutativity,[status(thm)],[])).
% 1.53/1.73 tff(2503,plain,
% 1.53/1.73 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2496])).
% 1.53/1.73 tff(2504,plain,
% 1.53/1.73 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2503, 2502])).
% 1.53/1.73 tff(2505,plain,
% 1.53/1.73 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2504])).
% 1.53/1.73 tff(2506,plain,
% 1.53/1.73 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.73 tff(2507,plain,
% 1.53/1.73 (~(s(s(elem!1)) = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1196, 2483])).
% 1.53/1.73 tff(2508,plain,
% 1.53/1.73 (~(s(elem!1) = s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 1.53/1.73 tff(2509,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[965, 2508, 959])).
% 1.53/1.73 tff(2510,plain,
% 1.53/1.73 (b(s(elem!1), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2509, 2501])).
% 1.53/1.73 tff(2511,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2512,plain,
% 1.53/1.73 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2513,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2512])).
% 1.53/1.73 tff(2514,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2513, 2511])).
% 1.53/1.73 tff(2515,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2516,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 1.53/1.73 tff(2517,plain,
% 1.53/1.73 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2516, 144, 624, 2510, 2498])).
% 1.53/1.73 tff(2518,plain,
% 1.53/1.73 (~b(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2517, 2494])).
% 1.53/1.73 tff(2519,plain,
% 1.53/1.73 (((~![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))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2520,plain,
% 1.53/1.73 ((~![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))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2521,plain,
% 1.53/1.73 ((~![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)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.53/1.73 tff(2522,plain,
% 1.53/1.73 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2521, 44])).
% 1.53/1.73 tff(2523,plain,
% 1.53/1.73 (r(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2522, 2518, 2462])).
% 1.53/1.73 tff(2524,plain,
% 1.53/1.73 (((~![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(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2525,plain,
% 1.53/1.74 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2526,plain,
% 1.53/1.74 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2525])).
% 1.53/1.74 tff(2527,plain,
% 1.53/1.74 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2526, 2524])).
% 1.53/1.74 tff(2528,plain,
% 1.53/1.74 ((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2529,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.53/1.74 tff(2530,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2529, 333, 670, 2523, 2458, 51])).
% 1.53/1.74 tff(2531,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2532,plain,
% 1.53/1.74 (~(s(z) = elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2531, 2456, 51, 670, 959, 285, 322])).
% 1.53/1.74 tff(2533,plain,
% 1.53/1.74 (b(s(z), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[406, 2532, 2310])).
% 1.53/1.74 tff(2534,plain,
% 1.53/1.74 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2535,plain,
% 1.53/1.74 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2536,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2535])).
% 1.53/1.74 tff(2537,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2536, 2534])).
% 1.53/1.74 tff(2538,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2539,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 1.53/1.74 tff(2540,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2539, 333, 670, 2323, 322, 51])).
% 1.53/1.74 tff(2541,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2542,plain,
% 1.53/1.74 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2541, 322, 670, 51])).
% 1.53/1.74 tff(2543,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2297, 2456, 2533, 489, 123])).
% 1.53/1.74 tff(2544,plain,
% 1.53/1.74 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[111])).
% 1.53/1.74 tff(2545,assumption,(~b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.53/1.74 tff(2546,plain,
% 1.53/1.74 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2353])).
% 1.53/1.74 tff(2547,plain,
% 1.53/1.74 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2546])).
% 1.53/1.74 tff(2548,plain,
% 1.53/1.74 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[112])).
% 1.53/1.74 tff(2549,plain,
% 1.53/1.74 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2365, 2548])).
% 1.53/1.74 tff(2550,plain,
% 1.53/1.74 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2549, 2547])).
% 1.53/1.74 tff(2551,plain,
% 1.53/1.74 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2352])).
% 1.53/1.74 tff(2552,plain,
% 1.53/1.74 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1262, 2551])).
% 1.53/1.74 tff(2553,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[81])).
% 1.53/1.74 tff(2554,plain,
% 1.53/1.74 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(symmetry,[status(thm)],[2553])).
% 1.53/1.74 tff(2555,plain,
% 1.53/1.74 ((~r(elem!1, z)) <=> (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2554])).
% 1.53/1.74 tff(2556,plain,
% 1.53/1.74 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1378, 2555])).
% 1.53/1.74 tff(2557,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[321, 2556])).
% 1.53/1.74 tff(2558,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2559,plain,
% 1.53/1.74 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2558, 2358, 1378])).
% 1.53/1.74 tff(2560,plain,
% 1.53/1.74 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[302, 2559])).
% 1.53/1.74 tff(2561,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2562,plain,
% 1.53/1.74 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2563,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2562])).
% 1.53/1.74 tff(2564,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2563, 2561])).
% 1.53/1.74 tff(2565,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2566,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 1.53/1.74 tff(2567,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2566, 144, 489, 123, 2560, 2552])).
% 1.53/1.74 tff(2568,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2567, 2550])).
% 1.53/1.74 tff(2569,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2570,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2569, 1378, 123, 1727, 2321, 489])).
% 1.53/1.74 tff(2571,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[121, 2570, 2542])).
% 1.53/1.74 tff(2572,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2105, 2571, 489, 123, 134])).
% 1.53/1.74 tff(2573,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[302, 2572])).
% 1.53/1.74 tff(2574,plain,
% 1.53/1.74 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2558, 2573, 1378])).
% 1.53/1.74 tff(2575,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[130, 2574, 2545])).
% 1.53/1.74 tff(2576,plain,
% 1.53/1.74 (~r(elem!1, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2492, 2575, 670, 51])).
% 1.53/1.74 tff(2577,plain,
% 1.53/1.74 (elem!1 = s(elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1732, 2576, 134, 1727, 2321])).
% 1.53/1.74 tff(2578,plain,
% 1.53/1.74 (s(s(s(elem!1))) = elem!1),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2482, 2577])).
% 1.53/1.74 tff(2579,plain,
% 1.53/1.74 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1000])).
% 1.53/1.74 tff(2580,plain,
% 1.53/1.74 ((s(elem!1) = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2579, 198])).
% 1.53/1.74 tff(2581,plain,
% 1.53/1.74 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2580])).
% 1.53/1.74 tff(2582,plain,
% 1.53/1.74 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[885, 2581])).
% 1.53/1.74 tff(2583,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1056, 2582])).
% 1.53/1.74 tff(2584,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2585,plain,
% 1.53/1.74 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2584, 2578, 2577])).
% 1.53/1.74 tff(2586,plain,
% 1.53/1.74 (~(s(elem!1) = s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[990, 2585, 1])).
% 1.53/1.74 tff(2587,plain,
% 1.53/1.74 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[965, 2586, 959])).
% 1.53/1.74 tff(2588,plain,
% 1.53/1.74 (~r(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[362, 2573, 322, 354])).
% 1.53/1.74 tff(2589,plain,
% 1.53/1.74 (b(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[172, 2588])).
% 1.53/1.74 tff(2590,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2591,plain,
% 1.53/1.74 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2592,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2591])).
% 1.53/1.74 tff(2593,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2592, 2590])).
% 1.53/1.74 tff(2594,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2595,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 1.53/1.74 tff(2596,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2595, 144, 489, 2321, 285, 2589, 2587])).
% 1.53/1.74 tff(2597,plain,(r(elem!1, z) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2598,plain,
% 1.53/1.74 (r(elem!1, z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2597, 1727, 285, 959, 1, 134, 489, 670, 51, 2545, 322, 354, 123])).
% 1.53/1.74 tff(2599,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2113, 2598, 2542, 489, 123, 134])).
% 1.53/1.74 tff(2600,plain,
% 1.53/1.74 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2423, 333, 670, 2598, 2599])).
% 1.53/1.74 tff(2601,plain,
% 1.53/1.74 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[130, 2600, 2545])).
% 1.53/1.74 tff(2602,plain,
% 1.53/1.74 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2601, 2544])).
% 1.53/1.74 tff(2603,plain,
% 1.53/1.74 (((~![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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2604,plain,
% 1.53/1.74 (((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2605,plain,
% 1.53/1.74 (((~![X0: $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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2604])).
% 1.53/1.74 tff(2606,plain,
% 1.53/1.74 (((~![X0: $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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2605, 2603])).
% 1.53/1.74 tff(2607,plain,
% 1.53/1.74 ((~![X0: $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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2608,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.53/1.74 tff(2609,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2608, 333, 354, 322, 51, 2340])).
% 1.53/1.74 tff(2610,plain,((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2611,plain,
% 1.53/1.74 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2610, 322, 354, 51])).
% 1.53/1.74 tff(2612,plain,
% 1.53/1.74 (~r(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[362, 2599, 322, 354])).
% 1.53/1.74 tff(2613,plain,
% 1.53/1.74 (b(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[172, 2612])).
% 1.53/1.74 tff(2614,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2415, 2613, 285, 2611, 1, 670, 489, 2598, 134, 1727, 959])).
% 1.53/1.74 tff(2615,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2614, 2602])).
% 1.53/1.74 tff(2616,plain,(r(s(elem!1), elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | r(s(elem!1), s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2617,plain,
% 1.53/1.74 (r(s(elem!1), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2616, 2543, 670, 285, 1, 489, 2533, 959, 322, 354, 123, 51])).
% 1.53/1.74 tff(2618,plain,
% 1.53/1.74 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[112])).
% 1.53/1.74 tff(2619,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), elem!1)),
% 1.53/1.74 inference(symmetry,[status(thm)],[2618])).
% 1.53/1.74 tff(2620,plain,
% 1.53/1.74 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), elem!1))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2619])).
% 1.53/1.74 tff(2621,plain,
% 1.53/1.74 (~r(s(elem!1), elem!1)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[466, 2620])).
% 1.53/1.74 tff(2622,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[435, 2621])).
% 1.53/1.74 tff(2623,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2624,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2623, 2617, 466])).
% 1.53/1.74 tff(2625,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[121, 2624, 2542])).
% 1.53/1.74 tff(2626,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2105, 2625, 489, 123, 2533])).
% 1.53/1.74 tff(2627,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[302, 2626])).
% 1.53/1.74 tff(2628,plain,
% 1.53/1.74 (~r(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[362, 2627, 322, 354])).
% 1.53/1.74 tff(2629,plain,
% 1.53/1.74 (b(s(z), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[172, 2628])).
% 1.53/1.74 tff(2630,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2595, 144, 489, 1262, 285, 838, 1794])).
% 1.53/1.74 tff(2631,plain,((~b(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2632,plain,
% 1.53/1.74 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2631, 2321, 489, 285, 2629])).
% 1.53/1.74 tff(2633,plain,
% 1.53/1.74 (s(elem!1) = s(s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[965, 2632, 959])).
% 1.53/1.74 tff(2634,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2633])).
% 1.53/1.74 tff(2635,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2634])).
% 1.53/1.74 tff(2636,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2633])).
% 1.53/1.74 tff(2637,plain,
% 1.53/1.74 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2636])).
% 1.53/1.74 tff(2638,plain,
% 1.53/1.74 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[466, 2637])).
% 1.53/1.75 tff(2639,plain,
% 1.53/1.75 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1137, 2638])).
% 1.53/1.75 tff(2640,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2262, 2639, 123, 2629])).
% 1.53/1.75 tff(2641,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[249, 2640])).
% 1.53/1.75 tff(2642,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2641, 2635])).
% 1.53/1.75 tff(2643,plain,
% 1.53/1.75 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2633])).
% 1.53/1.75 tff(2644,plain,
% 1.53/1.75 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.53/1.75 inference(symmetry,[status(thm)],[2643])).
% 1.53/1.75 tff(2645,plain,
% 1.53/1.75 (b(s(elem!1), z)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[285, 2644])).
% 1.53/1.75 tff(2646,plain,
% 1.53/1.75 (~b(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2383, 2645, 489, 2321])).
% 1.53/1.75 tff(2647,plain,
% 1.53/1.75 (r(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[583, 2646])).
% 1.53/1.75 tff(2648,plain,
% 1.53/1.75 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2649,plain,
% 1.53/1.75 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2650,plain,
% 1.53/1.75 (((~![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(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2649])).
% 1.53/1.75 tff(2651,plain,
% 1.53/1.75 (((~![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(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2650, 2648])).
% 1.53/1.75 tff(2652,plain,
% 1.53/1.75 ((~![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(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2653,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 1.53/1.75 tff(2654,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2653, 333, 435, 562, 51, 524])).
% 1.53/1.75 tff(2655,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2656,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2655, 2647, 51, 2617])).
% 1.53/1.75 tff(2657,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2656, 2642])).
% 1.53/1.75 tff(2658,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2659,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2658, 466, 123, 489, 51, 285, 959, 354, 2311, 1, 2310])).
% 1.53/1.75 tff(2660,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[319, 2659])).
% 1.53/1.75 tff(2661,plain,
% 1.53/1.75 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.75 tff(2662,plain,
% 1.53/1.75 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2661])).
% 1.53/1.75 tff(2663,plain,
% 1.53/1.75 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2495])).
% 1.53/1.75 tff(2664,plain,
% 1.53/1.75 (b(s(s(z)), elem!1) <=> b(s(elem!1), s(z))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2663, 2662])).
% 1.53/1.75 tff(2665,plain,
% 1.53/1.75 ((~b(s(s(z)), elem!1)) <=> (~b(s(elem!1), s(z)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2664])).
% 1.53/1.75 tff(2666,plain,
% 1.53/1.75 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.75 tff(2667,plain,
% 1.53/1.75 ((~b(s(s(z)), s(z))) <=> (~b(s(s(z)), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2666])).
% 1.53/1.75 tff(2668,plain,
% 1.53/1.75 (s(elem!1) = s(s(z))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2495])).
% 1.53/1.75 tff(2669,plain,
% 1.53/1.75 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2668])).
% 1.53/1.75 tff(2670,plain,
% 1.53/1.75 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2669])).
% 1.53/1.75 tff(2671,assumption,(r(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.53/1.75 tff(2672,plain,
% 1.53/1.75 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 1.53/1.75 tff(2673,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[466, 2672])).
% 1.53/1.75 tff(2674,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2675,plain,
% 1.53/1.75 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2674, 57, 466])).
% 1.53/1.75 tff(2676,plain,
% 1.53/1.75 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1451, 2675])).
% 1.53/1.75 tff(2677,plain,
% 1.53/1.75 (~b(s(s(z)), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1425, 2676, 123, 304])).
% 1.53/1.75 tff(2678,plain,
% 1.53/1.75 (~b(s(s(z)), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2677, 2667])).
% 1.53/1.75 tff(2679,plain,
% 1.53/1.75 (~b(s(elem!1), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2678, 2665])).
% 1.53/1.75 tff(2680,plain,
% 1.53/1.75 (r(s(elem!1), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[486, 2679, 1])).
% 1.53/1.75 tff(2681,plain,
% 1.53/1.75 (~(s(elem!1) = elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[906, 2483])).
% 1.53/1.75 tff(2682,plain,
% 1.53/1.75 ((~b(s(s(z)), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2663])).
% 1.53/1.75 tff(2683,plain,
% 1.53/1.75 (~b(s(elem!1), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2678, 2682])).
% 1.53/1.75 tff(2684,plain,
% 1.53/1.75 (r(s(elem!1), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[448, 2683, 2681])).
% 1.53/1.75 tff(2685,plain,
% 1.53/1.75 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2668])).
% 1.53/1.75 tff(2686,plain,
% 1.53/1.75 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2685])).
% 1.53/1.75 tff(2687,plain,
% 1.53/1.75 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1398, 2686])).
% 1.53/1.75 tff(2688,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[467, 2687])).
% 1.53/1.75 tff(2689,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2690,plain,
% 1.53/1.75 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2689, 2676, 57])).
% 1.53/1.75 tff(2691,plain,
% 1.53/1.75 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.75 tff(2692,plain,
% 1.53/1.75 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[123, 2691])).
% 1.53/1.75 tff(2693,plain,
% 1.53/1.75 (b(s(z), z) <=> b(elem!1, z)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.75 tff(2694,plain,
% 1.53/1.75 (b(elem!1, z)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[489, 2693])).
% 1.53/1.75 tff(2695,plain,
% 1.53/1.75 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2495])).
% 1.53/1.75 tff(2696,plain,
% 1.53/1.75 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2695, 174])).
% 1.53/1.75 tff(2697,plain,
% 1.53/1.75 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2696])).
% 1.53/1.75 tff(2698,plain,
% 1.53/1.75 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1446, 2697])).
% 1.53/1.75 tff(2699,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.75 tff(2700,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[304, 2699])).
% 1.53/1.75 tff(2701,plain,
% 1.53/1.75 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.75 tff(2702,plain,
% 1.53/1.75 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2701])).
% 1.53/1.75 tff(2703,plain,
% 1.53/1.75 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2702])).
% 1.53/1.75 tff(2704,plain,
% 1.53/1.75 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[244, 2703])).
% 1.53/1.75 tff(2705,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2706,plain,
% 1.53/1.75 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2707,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2706])).
% 1.53/1.75 tff(2708,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2707, 2705])).
% 1.53/1.75 tff(2709,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2710,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 1.53/1.75 tff(2711,plain,
% 1.53/1.75 (~b(elem!1, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2710, 144, 624, 132, 286, 450])).
% 1.53/1.75 tff(2712,plain,
% 1.53/1.75 (r(elem!1, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[560, 2711, 902])).
% 1.53/1.75 tff(2713,plain,
% 1.53/1.75 (~r(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2393, 2712, 670, 434])).
% 1.53/1.75 tff(2714,plain,
% 1.53/1.75 (b(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[583, 2713])).
% 1.53/1.75 tff(2715,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2716,plain,
% 1.53/1.75 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2717,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2716])).
% 1.53/1.75 tff(2718,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2717, 2715])).
% 1.53/1.75 tff(2719,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2720,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 1.53/1.75 tff(2721,plain,
% 1.53/1.75 (~r(s(elem!1), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2720, 333, 2712, 435, 670])).
% 1.53/1.75 tff(2722,plain,
% 1.53/1.75 (b(s(elem!1), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[507, 2721])).
% 1.53/1.75 tff(2723,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1668, 144, 2722, 2714, 286])).
% 1.53/1.75 tff(2724,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[540, 44, 537, 2723])).
% 1.53/1.75 tff(2725,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), introduced(assumption)).
% 1.53/1.75 tff(2726,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.53/1.75 tff(2727,plain,
% 1.53/1.75 (~(s(s(elem!1)) = s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1196, 902])).
% 1.53/1.75 tff(2728,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2729,plain,
% 1.53/1.75 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2730,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2729])).
% 1.53/1.75 tff(2731,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2730, 2728])).
% 1.53/1.75 tff(2732,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2733,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.53/1.75 tff(2734,plain,
% 1.53/1.75 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2733, 144, 2722, 2714, 2726])).
% 1.53/1.75 tff(2735,plain,
% 1.53/1.75 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1283, 2734, 2727])).
% 1.53/1.75 tff(2736,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.53/1.75 tff(2737,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.53/1.75 tff(2738,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2739,plain,
% 1.53/1.75 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2740,plain,
% 1.53/1.75 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2739])).
% 1.53/1.75 tff(2741,plain,
% 1.53/1.75 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2740, 2738])).
% 1.53/1.75 tff(2742,plain,
% 1.53/1.75 ((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2743,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.53/1.75 tff(2744,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2743, 333, 563, 2737, 434, 2736])).
% 1.53/1.75 tff(2745,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2746,plain,
% 1.53/1.75 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2745, 2735, 434, 2712])).
% 1.53/1.75 tff(2747,plain,
% 1.53/1.75 (b(elem!1, s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2522, 2746, 1221])).
% 1.53/1.75 tff(2748,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2749,plain,
% 1.53/1.75 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2750,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2749])).
% 1.53/1.75 tff(2751,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2750, 2748])).
% 1.53/1.75 tff(2752,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2753,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 1.53/1.76 tff(2754,plain,
% 1.53/1.76 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2753, 144, 2747, 133, 286, 2726])).
% 1.53/1.76 tff(2755,plain,
% 1.53/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2756,plain,
% 1.53/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2757,plain,
% 1.53/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.53/1.76 tff(2758,plain,
% 1.53/1.76 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2757, 44])).
% 1.53/1.76 tff(2759,plain,
% 1.53/1.76 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2758, 2754, 2725])).
% 1.53/1.76 tff(2760,plain,
% 1.53/1.76 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2761,plain,
% 1.53/1.76 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2762,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 1.53/1.76 tff(2763,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2762, 333, 435, 2735, 2759, 2724])).
% 1.53/1.76 tff(2764,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2765,plain,
% 1.53/1.76 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2764, 2684, 2704, 2700, 2498, 2698, 2462, 2680, 670, 2483, 2694, 2692, 2690])).
% 1.53/1.76 tff(2766,plain,
% 1.53/1.76 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[302, 2765])).
% 1.53/1.76 tff(2767,plain,
% 1.53/1.76 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2496])).
% 1.53/1.76 tff(2768,plain,
% 1.53/1.76 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.76 tff(2769,plain,
% 1.53/1.76 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2768])).
% 1.53/1.76 tff(2770,plain,
% 1.53/1.76 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2496])).
% 1.53/1.76 tff(2771,plain,
% 1.53/1.76 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.53/1.76 inference(symmetry,[status(thm)],[2770])).
% 1.53/1.76 tff(2772,plain,
% 1.53/1.76 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2771, 2769])).
% 1.53/1.76 tff(2773,plain,
% 1.53/1.76 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2772])).
% 1.53/1.76 tff(2774,plain,
% 1.53/1.76 (~r(z, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2393, 563, 670, 434])).
% 1.53/1.76 tff(2775,plain,
% 1.53/1.76 (b(z, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[583, 2774])).
% 1.53/1.76 tff(2776,plain,
% 1.53/1.76 (~r(s(elem!1), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2720, 333, 563, 435, 670])).
% 1.53/1.76 tff(2777,plain,
% 1.53/1.76 (b(s(elem!1), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[507, 2776])).
% 1.53/1.76 tff(2778,plain,
% 1.53/1.76 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2733, 144, 2777, 2775, 2498])).
% 1.53/1.76 tff(2779,plain,
% 1.53/1.76 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1283, 2778, 2507])).
% 1.53/1.76 tff(2780,plain,
% 1.53/1.76 (((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2781,plain,
% 1.53/1.76 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2782,plain,
% 1.53/1.76 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2781])).
% 1.53/1.76 tff(2783,plain,
% 1.53/1.76 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2782, 2780])).
% 1.53/1.76 tff(2784,plain,
% 1.53/1.76 ((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2785,plain,
% 1.53/1.76 ((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2784, 2783])).
% 1.53/1.76 tff(2786,plain,
% 1.53/1.76 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2785, 333, 563, 435, 2779])).
% 1.53/1.76 tff(2787,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2786, 2773])).
% 1.53/1.76 tff(2788,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.53/1.76 tff(2789,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.53/1.76 tff(2790,plain,
% 1.53/1.76 (((~![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)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2791,plain,
% 1.53/1.76 ((~![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)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2792,plain,
% 1.53/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.53/1.76 tff(2793,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2792, 44, 166, 2789, 2788])).
% 1.53/1.76 tff(2794,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2795,plain,
% 1.53/1.76 (b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2794, 2787])).
% 1.53/1.76 tff(2796,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2797,plain,
% 1.53/1.76 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2798,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2797])).
% 1.53/1.76 tff(2799,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2798, 2796])).
% 1.53/1.76 tff(2800,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2801,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 1.53/1.76 tff(2802,plain,
% 1.53/1.76 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2801, 144, 489, 285, 304])).
% 1.53/1.76 tff(2803,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2802, 2795])).
% 1.53/1.76 tff(2804,plain,
% 1.53/1.76 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1137, 2803])).
% 1.53/1.76 tff(2805,plain,
% 1.53/1.76 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2804, 2767])).
% 1.53/1.76 tff(2806,plain,
% 1.53/1.76 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2745, 2779, 434, 563])).
% 1.53/1.76 tff(2807,plain,
% 1.53/1.76 (b(elem!1, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2522, 2806, 2462])).
% 1.53/1.76 tff(2808,plain,
% 1.53/1.76 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.76 tff(2809,plain,
% 1.53/1.76 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.53/1.76 inference(symmetry,[status(thm)],[2808])).
% 1.53/1.76 tff(2810,plain,
% 1.53/1.76 (b(s(s(elem!1)), z)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[285, 2809])).
% 1.53/1.76 tff(2811,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.53/1.76 tff(2812,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.53/1.76 tff(2813,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2814,plain,
% 1.53/1.76 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2815,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2814])).
% 1.53/1.76 tff(2816,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2815, 2813])).
% 1.53/1.76 tff(2817,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2818,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 1.53/1.76 tff(2819,plain,
% 1.53/1.76 (~b(s(s(elem!1)), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2818, 144, 624, 2812, 2811])).
% 1.53/1.76 tff(2820,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2819, 2810])).
% 1.53/1.76 tff(2821,plain,((~b(s(s(s(z))), z)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2822,plain,
% 1.53/1.76 (~b(z, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2821, 2807, 285, 2694, 57])).
% 1.53/1.76 tff(2823,plain,
% 1.53/1.76 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.76 tff(2824,plain,
% 1.53/1.76 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2823])).
% 1.53/1.76 tff(2825,plain,
% 1.53/1.76 (b(z, s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[284, 2824])).
% 1.53/1.76 tff(2826,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.53/1.76 tff(2827,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2826, 2825])).
% 1.53/1.76 tff(2828,plain,(b(z, s(s(elem!1))) | (~b(z, s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2829,plain,
% 1.53/1.76 (~b(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2828, 2822, 57])).
% 1.53/1.76 tff(2830,plain,
% 1.53/1.76 (r(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[619, 2829])).
% 1.53/1.76 tff(2831,plain,
% 1.53/1.76 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.76 tff(2832,plain,
% 1.53/1.76 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2831])).
% 1.53/1.76 tff(2833,plain,
% 1.53/1.76 (r(z, s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[623, 2832])).
% 1.53/1.76 tff(2834,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.53/1.76 tff(2835,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2834, 2833])).
% 1.53/1.76 tff(2836,plain,((~r(z, s(s(s(z))))) | r(z, s(s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2837,plain,
% 1.53/1.76 (r(z, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2836, 2830, 57])).
% 1.53/1.76 tff(2838,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2839,plain,
% 1.53/1.76 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2840,plain,
% 1.53/1.76 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2839])).
% 1.53/1.76 tff(2841,plain,
% 1.53/1.76 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2840, 2838])).
% 1.53/1.76 tff(2842,plain,
% 1.53/1.76 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2843,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 1.53/1.76 tff(2844,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2843, 333, 321, 51, 2837, 2805])).
% 1.53/1.76 tff(2845,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2846,plain,
% 1.53/1.76 (~r(elem!1, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2845, 2766, 51, 57, 489, 285, 304, 2684, 2680, 670])).
% 1.53/1.76 tff(2847,plain,
% 1.53/1.76 (b(elem!1, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[560, 2846, 2483])).
% 1.53/1.76 tff(2848,plain,
% 1.53/1.76 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2499])).
% 1.53/1.76 tff(2849,plain,
% 1.53/1.76 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2848])).
% 1.53/1.76 tff(2850,plain,
% 1.53/1.76 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2849])).
% 1.53/1.76 tff(2851,plain,
% 1.53/1.76 (~r(s(elem!1), s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[959, 2850])).
% 1.53/1.76 tff(2852,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.53/1.76 tff(2853,plain,
% 1.53/1.76 (s(s(elem!1)) = s(elem!1)),
% 1.53/1.76 inference(symmetry,[status(thm)],[2852])).
% 1.53/1.76 tff(2854,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.53/1.76 tff(2855,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2854, 2853])).
% 1.53/1.76 tff(2856,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2857,plain,
% 1.53/1.76 (~(s(elem!1) = s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2856, 2507])).
% 1.53/1.76 tff(2858,plain,
% 1.53/1.76 (((~![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))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2859,plain,
% 1.53/1.76 ((~![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))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2860,plain,
% 1.53/1.76 ((~![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)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2859, 2858])).
% 1.53/1.76 tff(2861,plain,
% 1.53/1.76 (b(s(elem!1), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2860, 44, 2857, 2851])).
% 1.53/1.76 tff(2862,plain,
% 1.53/1.76 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2516, 144, 2694, 2861, 2498])).
% 1.53/1.76 tff(2863,plain,
% 1.53/1.76 (~b(elem!1, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2862, 2847])).
% 1.53/1.76 tff(2864,plain,
% 1.53/1.76 (r(elem!1, s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2522, 2863, 2462])).
% 1.53/1.76 tff(2865,plain,
% 1.53/1.76 (((~![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(elem!1, s(s(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(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2866,plain,
% 1.53/1.76 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2867,plain,
% 1.53/1.76 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2866])).
% 1.53/1.77 tff(2868,plain,
% 1.53/1.77 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2867, 2865])).
% 1.53/1.77 tff(2869,plain,
% 1.53/1.77 ((~![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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2870,plain,
% 1.53/1.77 ((~![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(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 1.53/1.77 tff(2871,plain,
% 1.53/1.77 (~r(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2870, 333, 2684, 670, 2864])).
% 1.53/1.77 tff(2872,plain,
% 1.53/1.77 (b(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[583, 2871])).
% 1.53/1.77 tff(2873,plain,
% 1.53/1.77 (((~![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(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~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), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2874,plain,
% 1.53/1.77 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2875,plain,
% 1.53/1.77 (((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2874])).
% 1.53/1.77 tff(2876,plain,
% 1.53/1.77 (((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2875, 2873])).
% 1.53/1.77 tff(2877,plain,
% 1.53/1.77 ((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2878,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 1.53/1.77 tff(2879,plain,
% 1.53/1.77 (~r(s(elem!1), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2878, 333, 2684, 670, 2864])).
% 1.53/1.77 tff(2880,plain,
% 1.53/1.77 (b(s(elem!1), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[507, 2879])).
% 1.53/1.77 tff(2881,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[949, 2880, 2872, 2694, 2847])).
% 1.53/1.77 tff(2882,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2883,plain,
% 1.53/1.77 (~(s(z) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2882, 2660, 51, 489, 285, 2311, 1, 959, 123, 466])).
% 1.53/1.77 tff(2884,plain,
% 1.53/1.77 (b(s(z), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[406, 2883, 2310])).
% 1.53/1.77 tff(2885,plain,
% 1.53/1.77 (~(s(z) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2882, 304, 51, 489, 285, 2311, 1, 959, 123, 466])).
% 1.53/1.77 tff(2886,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2337, 377, 489, 123, 134, 2097])).
% 1.53/1.77 tff(2887,plain,
% 1.53/1.77 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2888,plain,
% 1.53/1.77 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2889,plain,
% 1.53/1.77 (((~![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(s(s(z))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2888])).
% 1.53/1.77 tff(2890,plain,
% 1.53/1.77 (((~![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(s(s(z))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.53/1.77 tff(2891,plain,
% 1.53/1.77 ((~![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(s(s(z))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2892,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.53/1.77 tff(2893,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2892, 333, 670, 2323, 51, 524])).
% 1.53/1.77 tff(2894,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2895,plain,
% 1.53/1.77 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2894, 2886, 2311, 51])).
% 1.53/1.77 tff(2896,plain,
% 1.53/1.77 (~r(elem!1, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[678, 509, 670, 408])).
% 1.53/1.77 tff(2897,plain,
% 1.53/1.77 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[509, 921])).
% 1.53/1.77 tff(2898,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[297, 2897])).
% 1.53/1.77 tff(2899,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), z) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2900,plain,
% 1.53/1.77 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2899, 509, 297])).
% 1.53/1.77 tff(2901,plain,
% 1.53/1.77 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[930, 2900])).
% 1.53/1.77 tff(2902,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[472, 2901, 466])).
% 1.53/1.77 tff(2903,plain,
% 1.53/1.77 (~b(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1732, 902, 134, 1727, 1725])).
% 1.53/1.77 tff(2904,plain,
% 1.53/1.77 (r(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1244, 2903, 1229])).
% 1.53/1.77 tff(2905,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2906,plain,
% 1.53/1.77 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2907,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2906])).
% 1.53/1.77 tff(2908,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2907, 2905])).
% 1.53/1.77 tff(2909,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2910,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.53/1.77 tff(2911,plain,
% 1.53/1.77 (~b(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2910, 144, 1728, 134, 304, 450])).
% 1.53/1.77 tff(2912,plain,
% 1.53/1.77 (r(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[486, 2911, 1])).
% 1.53/1.77 tff(2913,plain,
% 1.53/1.77 (((~![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(z))) | (~r(z, s(z))) | (~r(s(elem!1), 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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2914,plain,
% 1.53/1.77 (((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2915,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2914])).
% 1.53/1.77 tff(2916,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2915, 2913])).
% 1.53/1.77 tff(2917,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2918,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.53/1.77 tff(2919,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2918, 333, 354, 2912, 509, 2904])).
% 1.53/1.77 tff(2920,plain,((elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2921,plain,
% 1.53/1.77 (elem!1 = s(elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2920, 509, 354, 1, 134, 304, 2902, 1727, 2896])).
% 1.53/1.77 tff(2922,plain,
% 1.53/1.77 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2921])).
% 1.53/1.77 tff(2923,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[2922])).
% 1.53/1.77 tff(2924,plain,
% 1.53/1.77 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2902, 2923])).
% 1.53/1.77 tff(2925,assumption,(~b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.53/1.77 tff(2926,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2925, 2924])).
% 1.53/1.77 tff(2927,plain,((~r(s(elem!1), z)) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), z) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2928,plain,
% 1.53/1.77 (~r(s(elem!1), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2927, 2322, 354, 1, 134, 304, 1727, 466, 297, 2311, 2106])).
% 1.53/1.77 tff(2929,plain,
% 1.53/1.77 (b(s(elem!1), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[507, 2928])).
% 1.53/1.77 tff(2930,plain,
% 1.53/1.77 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[787, 377, 2097])).
% 1.53/1.77 tff(2931,plain,
% 1.53/1.77 (((~![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(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2932,plain,
% 1.53/1.77 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2933,plain,
% 1.53/1.77 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2932])).
% 1.53/1.77 tff(2934,plain,
% 1.53/1.77 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2933, 2931])).
% 1.53/1.77 tff(2935,plain,
% 1.53/1.77 ((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2936,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 1.53/1.77 tff(2937,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2936, 333, 670, 408, 2484, 51])).
% 1.53/1.77 tff(2938,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2939,plain,
% 1.53/1.77 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2938, 2322, 2311, 51])).
% 1.53/1.77 tff(2940,plain,
% 1.53/1.77 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[130, 2939, 2930])).
% 1.53/1.77 tff(2941,plain,
% 1.53/1.77 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[919])).
% 1.53/1.77 tff(2942,plain,
% 1.53/1.77 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[2941])).
% 1.53/1.77 tff(2943,plain,
% 1.53/1.77 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2942])).
% 1.53/1.77 tff(2944,plain,
% 1.53/1.77 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[1239, 2943])).
% 1.53/1.77 tff(2945,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[123, 2944])).
% 1.53/1.77 tff(2946,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2947,plain,
% 1.53/1.77 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2946, 1239, 123])).
% 1.53/1.77 tff(2948,plain,
% 1.53/1.77 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[540, 44, 535])).
% 1.53/1.77 tff(2949,plain,
% 1.53/1.77 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2948, 2947])).
% 1.53/1.77 tff(2950,plain,
% 1.53/1.77 (r(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1244, 1239, 1229])).
% 1.53/1.77 tff(2951,plain,
% 1.53/1.77 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[930, 2947])).
% 1.53/1.77 tff(2952,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[472, 2951, 466])).
% 1.53/1.77 tff(2953,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(2954,plain,
% 1.53/1.78 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(2955,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2954])).
% 1.53/1.78 tff(2956,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[2955, 2953])).
% 1.53/1.78 tff(2957,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(2958,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 1.53/1.78 tff(2959,plain,
% 1.53/1.78 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2958, 144, 491, 489, 304])).
% 1.53/1.78 tff(2960,plain,
% 1.53/1.78 (~b(s(elem!1), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2959, 2952])).
% 1.53/1.78 tff(2961,plain,
% 1.53/1.78 (r(s(elem!1), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[486, 2960, 1])).
% 1.53/1.78 tff(2962,plain,
% 1.53/1.78 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(2963,plain,
% 1.53/1.78 (((~![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(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2962])).
% 1.53/1.78 tff(2964,plain,
% 1.53/1.78 (((~![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(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[2963, 1646])).
% 1.53/1.78 tff(2965,plain,
% 1.53/1.78 ((~![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(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(2966,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[2965, 2964])).
% 1.53/1.78 tff(2967,plain,
% 1.53/1.78 (~r(z, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2966, 333, 354, 2961, 2950])).
% 1.53/1.78 tff(2968,plain,
% 1.53/1.78 (b(z, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[583, 2967])).
% 1.53/1.78 tff(2969,plain,
% 1.53/1.78 (b(z, s(elem!1)) <=> b(z, elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2470])).
% 1.53/1.78 tff(2970,plain,
% 1.53/1.78 (b(z, elem!1) <=> b(z, s(elem!1))),
% 1.53/1.78 inference(symmetry,[status(thm)],[2969])).
% 1.53/1.78 tff(2971,plain,
% 1.53/1.78 ((~b(z, elem!1)) <=> (~b(z, s(elem!1)))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2970])).
% 1.53/1.78 tff(2972,plain,
% 1.53/1.78 (~b(z, s(elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[606, 2971])).
% 1.53/1.78 tff(2973,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[585, 2972])).
% 1.53/1.78 tff(2974,plain,((~(elem!1 = s(elem!1))) | (~b(z, s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(2975,plain,
% 1.53/1.78 (~(elem!1 = s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2974, 2968, 606])).
% 1.53/1.78 tff(2976,plain,
% 1.53/1.78 (~(s(elem!1) = elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[906, 2975])).
% 1.53/1.78 tff(2977,plain,
% 1.53/1.78 (b(s(elem!1), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[448, 2976, 1727])).
% 1.53/1.78 tff(2978,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[591, 144, 2977, 2968, 133, 286, 2949])).
% 1.53/1.78 tff(2979,plain,(b(s(z), s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(elem!1), elem!1) | b(z, elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(2980,plain,
% 1.53/1.78 (b(s(z), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2979, 2940, 2097, 1727, 606, 354, 1, 2929, 489, 304, 466, 2895, 123])).
% 1.53/1.78 tff(2981,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(2982,plain,
% 1.53/1.78 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(2983,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2982])).
% 1.53/1.78 tff(2984,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.53/1.78 tff(2985,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(2986,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.53/1.78 tff(2987,plain,
% 1.53/1.78 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2986, 144, 2929, 2980, 304, 2097])).
% 1.53/1.78 tff(2988,plain,
% 1.53/1.78 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[540, 44, 2895])).
% 1.53/1.78 tff(2989,plain,
% 1.53/1.78 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2988, 2987])).
% 1.53/1.78 tff(2990,plain,
% 1.53/1.78 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2989])).
% 1.53/1.78 tff(2991,plain,
% 1.53/1.78 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2990])).
% 1.53/1.78 tff(2992,plain,
% 1.53/1.78 (~(s(elem!1) = s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[244, 2991])).
% 1.53/1.78 tff(2993,plain,
% 1.53/1.78 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[965, 2992, 959])).
% 1.53/1.78 tff(2994,plain,
% 1.53/1.78 (~b(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2631, 2993, 489, 285, 2980])).
% 1.53/1.78 tff(2995,plain,
% 1.53/1.78 (r(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[172, 2994])).
% 1.53/1.78 tff(2996,plain,
% 1.53/1.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2989])).
% 1.53/1.78 tff(2997,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[2996])).
% 1.53/1.78 tff(2998,plain,
% 1.53/1.78 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2997])).
% 1.53/1.78 tff(2999,plain,
% 1.53/1.78 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[959, 2998])).
% 1.53/1.78 tff(3000,plain,
% 1.53/1.78 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[249, 2999])).
% 1.53/1.78 tff(3001,plain,
% 1.53/1.78 (~b(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[294, 3000, 285, 2097])).
% 1.53/1.78 tff(3002,plain,
% 1.53/1.78 (r(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[619, 3001])).
% 1.53/1.78 tff(3003,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.53/1.78 tff(3004,plain,
% 1.53/1.78 (((~![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(z))), s(elem!1))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3005,plain,
% 1.53/1.78 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3006,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~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(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3005])).
% 1.53/1.78 tff(3007,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~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(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3006, 3004])).
% 1.53/1.78 tff(3008,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3009,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 1.53/1.78 tff(3010,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3009, 333, 354, 623, 353, 3003])).
% 1.53/1.78 tff(3011,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3012,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3011, 3002, 354, 2995])).
% 1.53/1.78 tff(3013,plain,
% 1.53/1.78 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.53/1.78 inference(transitivity,[status(thm)],[2990, 998])).
% 1.53/1.78 tff(3014,plain,
% 1.53/1.78 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3013])).
% 1.53/1.78 tff(3015,plain,
% 1.53/1.78 (~(s(s(s(z))) = s(elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[244, 3014])).
% 1.53/1.78 tff(3016,plain,
% 1.53/1.78 (b(s(s(s(z))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1951, 44, 3015, 3012])).
% 1.53/1.78 tff(3017,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3018,plain,
% 1.53/1.78 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3019,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3018])).
% 1.53/1.78 tff(3020,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3019, 3017])).
% 1.53/1.78 tff(3021,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3022,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3021, 3020])).
% 1.53/1.78 tff(3023,plain,
% 1.53/1.78 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3022, 144, 2929, 2980, 285])).
% 1.53/1.78 tff(3024,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3023, 3016])).
% 1.53/1.78 tff(3025,plain,
% 1.53/1.78 (r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2794, 3024])).
% 1.53/1.78 tff(3026,plain,
% 1.53/1.78 (((~![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(z))))) | (~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3027,plain,
% 1.53/1.78 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3028,plain,
% 1.53/1.78 (((~![X0: $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(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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3027])).
% 1.53/1.78 tff(3029,plain,
% 1.53/1.78 (((~![X0: $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(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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3028, 3026])).
% 1.53/1.78 tff(3030,plain,
% 1.53/1.78 ((~![X0: $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(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3031,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.53/1.78 tff(3032,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3031, 333, 354, 3002, 3025, 2995])).
% 1.53/1.78 tff(3033,plain,(b(elem!1, z) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), elem!1) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3034,plain,
% 1.53/1.78 (b(elem!1, z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3033, 297, 285, 489, 959, 304, 1727, 606, 1, 466, 123, 51, 134, 354])).
% 1.53/1.78 tff(3035,plain,
% 1.53/1.78 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2297, 3034, 134, 489, 123])).
% 1.53/1.78 tff(3036,plain,
% 1.53/1.78 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3037,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3036])).
% 1.53/1.78 tff(3038,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3037, 864])).
% 1.53/1.78 tff(3039,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3040,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.53/1.78 tff(3041,plain,
% 1.53/1.78 (~b(s(elem!1), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3040, 144, 123, 304, 2952])).
% 1.53/1.78 tff(3042,plain,
% 1.53/1.78 (r(s(elem!1), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[486, 3041, 1])).
% 1.53/1.78 tff(3043,plain,
% 1.53/1.78 (~r(z, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2966, 333, 354, 3042, 2950])).
% 1.53/1.78 tff(3044,plain,
% 1.53/1.78 (b(z, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[583, 3043])).
% 1.53/1.78 tff(3045,plain,
% 1.53/1.78 (~(elem!1 = s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2974, 3044, 606])).
% 1.53/1.78 tff(3046,plain,
% 1.53/1.78 (~r(s(elem!1), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2918, 333, 354, 3042, 2950])).
% 1.53/1.78 tff(3047,plain,
% 1.53/1.78 (b(s(elem!1), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[507, 3046])).
% 1.53/1.78 tff(3048,plain,
% 1.53/1.78 (~b(elem!1, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[949, 3044, 624, 3047])).
% 1.53/1.78 tff(3049,plain,
% 1.53/1.78 (r(elem!1, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[560, 3048, 3045])).
% 1.53/1.78 tff(3050,plain,
% 1.53/1.78 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2297, 624, 134, 489, 123])).
% 1.53/1.78 tff(3051,plain,
% 1.53/1.78 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2492, 3049, 2311, 51])).
% 1.53/1.78 tff(3052,plain,
% 1.53/1.78 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[130, 3051, 3050])).
% 1.53/1.78 tff(3053,plain,
% 1.53/1.78 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3052])).
% 1.53/1.78 tff(3054,plain,
% 1.53/1.78 (b(elem!1, s(z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[304, 3053])).
% 1.53/1.78 tff(3055,plain,
% 1.53/1.78 (s(s(s(z))) = s(elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[982, 998])).
% 1.53/1.78 tff(3056,plain,
% 1.53/1.78 (~r(z, s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2966, 333, 354, 434, 1230])).
% 1.53/1.79 tff(3057,plain,
% 1.53/1.79 (b(z, s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[583, 3056])).
% 1.53/1.79 tff(3058,plain,
% 1.53/1.79 (~r(s(elem!1), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2918, 333, 354, 434, 1230])).
% 1.53/1.79 tff(3059,plain,
% 1.53/1.79 (b(s(elem!1), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[507, 3058])).
% 1.53/1.79 tff(3060,plain,
% 1.53/1.79 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[990, 982, 1])).
% 1.53/1.79 tff(3061,plain,
% 1.53/1.79 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.53/1.79 inference(commutativity,[status(thm)],[])).
% 1.53/1.79 tff(3062,plain,
% 1.53/1.79 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3061])).
% 1.53/1.79 tff(3063,plain,
% 1.53/1.79 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3062])).
% 1.53/1.79 tff(3064,plain,
% 1.53/1.79 (~(s(z) = s(s(s(elem!1))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[1096, 3063])).
% 1.53/1.79 tff(3065,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.53/1.79 tff(3066,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3067,plain,
% 1.53/1.79 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3068,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3067])).
% 1.53/1.79 tff(3069,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3068, 3066])).
% 1.53/1.79 tff(3070,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3071,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 1.53/1.79 tff(3072,plain,
% 1.53/1.79 (~r(z, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3071, 333, 563, 670, 3065])).
% 1.53/1.79 tff(3073,plain,
% 1.53/1.79 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1031, 44, 3072])).
% 1.53/1.79 tff(3074,plain,
% 1.53/1.79 (b(z, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3073, 1023])).
% 1.53/1.79 tff(3075,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3076,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3077,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3076, 3075])).
% 1.53/1.79 tff(3078,plain,
% 1.53/1.79 (~r(s(s(s(elem!1))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3077, 333, 563, 670, 3065])).
% 1.53/1.79 tff(3079,plain,
% 1.53/1.79 (b(s(s(s(elem!1))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 3078])).
% 1.53/1.79 tff(3080,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3081,plain,
% 1.53/1.79 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3082,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3081])).
% 1.53/1.79 tff(3083,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3082, 3080])).
% 1.53/1.79 tff(3084,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3085,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.53/1.79 tff(3086,plain,
% 1.53/1.79 (~b(s(z), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3085, 144, 489, 3079, 3074])).
% 1.53/1.79 tff(3087,plain,
% 1.53/1.79 (((~![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)))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3088,plain,
% 1.53/1.79 ((~![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)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3089,plain,
% 1.53/1.79 ((~![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))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 1.53/1.79 tff(3090,plain,
% 1.53/1.79 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3089, 44, 3086])).
% 1.53/1.79 tff(3091,plain,
% 1.53/1.79 (r(s(z), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3090, 3064])).
% 1.53/1.79 tff(3092,plain,
% 1.53/1.79 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1062, 144, 491, 3079, 3074])).
% 1.53/1.79 tff(3093,plain,
% 1.53/1.79 (r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1067, 3092, 1056])).
% 1.53/1.79 tff(3094,plain,
% 1.53/1.79 (((~![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(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3095,plain,
% 1.53/1.79 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3096,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~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(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3095])).
% 1.53/1.79 tff(3097,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~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(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3096, 3094])).
% 1.53/1.79 tff(3098,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3099,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3098, 3097])).
% 1.53/1.79 tff(3100,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3099, 333, 3065, 3093, 1230, 3091])).
% 1.53/1.79 tff(3101,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3102,plain,
% 1.53/1.79 (~r(s(s(s(elem!1))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3101, 1056, 1230, 489, 491, 563, 670])).
% 1.53/1.79 tff(3103,plain,
% 1.53/1.79 (b(s(s(s(elem!1))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1079, 3102, 1012])).
% 1.53/1.79 tff(3104,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3105,plain,
% 1.53/1.79 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3106,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3105])).
% 1.53/1.79 tff(3107,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3106, 3104])).
% 1.53/1.79 tff(3108,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3109,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 1.53/1.79 tff(3110,plain,
% 1.53/1.79 (~b(s(s(s(elem!1))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3109, 144, 134, 3103, 305])).
% 1.53/1.79 tff(3111,plain,
% 1.53/1.79 (r(s(s(s(elem!1))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1101, 3110])).
% 1.53/1.79 tff(3112,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), 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(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3113,plain,
% 1.53/1.79 (((~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))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3114,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(elem!1)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3113])).
% 1.53/1.79 tff(3115,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(elem!1))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3114, 3112])).
% 1.53/1.79 tff(3116,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3117,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.53/1.79 tff(3118,plain,
% 1.53/1.79 (~r(s(s(s(elem!1))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3117, 333, 354, 1024, 1230])).
% 1.53/1.79 tff(3119,plain,
% 1.53/1.79 (b(s(s(s(elem!1))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 3118])).
% 1.53/1.79 tff(3120,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(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(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3121,plain,
% 1.53/1.79 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3122,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3121])).
% 1.53/1.79 tff(3123,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3122, 3120])).
% 1.53/1.79 tff(3124,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3125,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 1.53/1.79 tff(3126,plain,
% 1.53/1.79 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3125, 333, 1024, 434, 1230])).
% 1.53/1.79 tff(3127,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.53/1.79 tff(3128,plain,
% 1.53/1.79 (((~![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)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3129,plain,
% 1.53/1.79 ((~![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)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3130,plain,
% 1.53/1.79 ((~![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))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 1.53/1.80 tff(3131,plain,
% 1.53/1.80 (b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3130, 44, 3127, 3126])).
% 1.53/1.80 tff(3132,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(3133,plain,
% 1.53/1.80 (((~b(s(elem!1), z)) | (~b(s(s(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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(3134,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1)))))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[3133])).
% 1.53/1.80 tff(3135,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))))),
% 1.53/1.80 inference(transitivity,[status(thm)],[3134, 3132])).
% 1.53/1.80 tff(3136,plain,
% 1.53/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.80 inference(quant_inst,[status(thm)],[])).
% 1.53/1.80 tff(3137,plain,
% 1.53/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 1.53/1.80 tff(3138,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3137, 144, 491, 585, 3131, 3119])).
% 1.53/1.80 tff(3139,plain,((~r(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(3140,plain,
% 1.53/1.80 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3139, 3111, 585, 491, 1230, 434, 354])).
% 1.53/1.80 tff(3141,plain,
% 1.53/1.80 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[3140, 2476])).
% 1.53/1.80 tff(3142,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[1056, 3141])).
% 1.53/1.80 tff(3143,plain,((s(elem!1) = s(s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(3144,plain,
% 1.53/1.80 (s(s(s(elem!1))) = elem!1),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3143, 3060, 354, 489, 1230, 434, 3059, 3057, 134, 305, 563, 670])).
% 1.53/1.80 tff(3145,plain,
% 1.53/1.80 (~(s(s(s(z))) = s(elem!1))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[1010, 3144])).
% 1.53/1.80 tff(3146,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3145, 3055])).
% 1.53/1.80 tff(3147,plain,((~(s(elem!1) = s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(3148,plain,
% 1.62/1.80 (~(s(elem!1) = s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3147, 2950, 489, 354, 3042, 134, 3054, 3049, 2311, 1])).
% 1.62/1.80 tff(3149,plain,
% 1.62/1.80 (b(s(elem!1), s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[965, 3148, 959])).
% 1.62/1.80 tff(3150,plain,
% 1.62/1.80 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3052])).
% 1.62/1.80 tff(3151,plain,
% 1.62/1.80 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3150])).
% 1.62/1.80 tff(3152,plain,
% 1.62/1.80 (~(elem!1 = s(s(s(z))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[244, 3151])).
% 1.62/1.80 tff(3153,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3154,plain,
% 1.62/1.80 (((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3155,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3154])).
% 1.62/1.80 tff(3156,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.62/1.80 tff(3157,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(3158,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.62/1.80 tff(3159,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3158, 144, 491, 284, 1794, 286, 450])).
% 1.62/1.80 tff(3160,plain,((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(3161,plain,
% 1.62/1.80 (~b(z, s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3160, 3149, 286, 2952, 3047])).
% 1.62/1.80 tff(3162,plain,
% 1.62/1.80 (r(z, s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[619, 3161])).
% 1.62/1.80 tff(3163,plain,
% 1.62/1.80 (~(s(s(s(z))) = elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[109, 3052])).
% 1.62/1.80 tff(3164,plain,
% 1.62/1.80 (~(s(s(s(z))) = s(elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1934, 3148])).
% 1.62/1.80 tff(3165,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3166,plain,
% 1.62/1.80 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3167,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3166])).
% 1.62/1.80 tff(3168,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[3167, 3165])).
% 1.62/1.80 tff(3169,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(3170,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 1.62/1.80 tff(3171,plain,
% 1.62/1.80 (~b(s(s(s(z))), s(elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3170, 144, 3047, 3044, 285])).
% 1.62/1.80 tff(3172,plain,
% 1.62/1.80 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1951, 44, 3171])).
% 1.62/1.80 tff(3173,plain,
% 1.62/1.80 (r(s(s(s(z))), s(elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3172, 3164])).
% 1.62/1.80 tff(3174,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3175,plain,
% 1.62/1.80 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3176,plain,
% 1.62/1.80 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3175])).
% 1.62/1.80 tff(3177,plain,
% 1.62/1.80 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[3176, 3174])).
% 1.62/1.80 tff(3178,plain,
% 1.62/1.80 ((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(3179,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.62/1.80 tff(3180,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3179, 333, 563, 434, 707, 3003])).
% 1.62/1.80 tff(3181,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(3182,plain,
% 1.62/1.80 (~r(s(s(s(z))), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3181, 3173, 3042, 3049])).
% 1.62/1.80 tff(3183,plain,
% 1.62/1.80 (b(s(s(s(z))), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[704, 3182, 3163])).
% 1.62/1.80 tff(3184,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3185,plain,
% 1.62/1.80 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3186,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3185])).
% 1.62/1.80 tff(3187,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[3186, 3184])).
% 1.62/1.80 tff(3188,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(3189,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 1.62/1.80 tff(3190,plain,
% 1.62/1.80 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3189, 144, 624, 134, 285])).
% 1.62/1.80 tff(3191,plain,
% 1.62/1.80 (~b(s(s(s(z))), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3190, 3183])).
% 1.62/1.80 tff(3192,plain,
% 1.62/1.80 (r(s(s(s(z))), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2794, 3191])).
% 1.62/1.80 tff(3193,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.62/1.80 tff(3194,plain,
% 1.62/1.80 (((~![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(z, s(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(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3195,plain,
% 1.62/1.80 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(3196,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3195])).
% 1.62/1.80 tff(3197,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[3196, 3194])).
% 1.62/1.80 tff(3198,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(3199,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 1.62/1.80 tff(3200,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3199, 333, 670, 1525, 623, 3193])).
% 1.62/1.80 tff(3201,plain,((~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(3202,plain,
% 1.62/1.80 (~r(elem!1, s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3201, 3192, 2311, 3162])).
% 1.62/1.80 tff(3203,plain,
% 1.62/1.80 (b(elem!1, s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1538, 3202, 3152])).
% 1.62/1.80 tff(3204,plain,
% 1.62/1.80 (~(s(elem!1) = elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[906, 3045])).
% 1.62/1.80 tff(3205,plain,
% 1.62/1.80 (b(s(elem!1), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[448, 3204, 1727])).
% 1.62/1.80 tff(3206,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3207,plain,
% 1.62/1.81 (((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3208,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3207])).
% 1.62/1.81 tff(3209,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.62/1.81 tff(3210,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(3211,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.62/1.81 tff(3212,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3211, 144, 3205, 3047, 3203, 285, 3149])).
% 1.62/1.81 tff(3213,plain,(b(s(z), s(elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(z), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | b(z, elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3214,plain,
% 1.62/1.81 (b(s(z), s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3213, 3034, 285, 134, 2097, 959, 489, 354, 1, 304, 51, 1727, 606, 123, 466])).
% 1.62/1.81 tff(3215,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3216,plain,
% 1.62/1.81 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3217,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3216])).
% 1.62/1.81 tff(3218,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3217, 3215])).
% 1.62/1.81 tff(3219,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(3220,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.62/1.81 tff(3221,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3220, 144, 489, 1262, 123, 286, 450])).
% 1.62/1.81 tff(3222,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3223,plain,
% 1.62/1.81 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3222, 3214, 489, 123, 2097])).
% 1.62/1.81 tff(3224,plain,
% 1.62/1.81 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[472, 3223, 466])).
% 1.62/1.81 tff(3225,plain,
% 1.62/1.81 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3224])).
% 1.62/1.81 tff(3226,plain,
% 1.62/1.81 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3225])).
% 1.62/1.81 tff(3227,plain,
% 1.62/1.81 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[1727, 3226])).
% 1.62/1.81 tff(3228,plain,
% 1.62/1.81 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[130, 3227, 3035])).
% 1.62/1.81 tff(3229,plain,
% 1.62/1.81 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3224])).
% 1.62/1.81 tff(3230,plain,
% 1.62/1.81 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.62/1.81 inference(symmetry,[status(thm)],[3229])).
% 1.62/1.81 tff(3231,plain,
% 1.62/1.81 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3230])).
% 1.62/1.81 tff(3232,plain,
% 1.62/1.81 (~b(s(elem!1), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3035, 3231])).
% 1.62/1.81 tff(3233,plain,
% 1.62/1.81 (s(elem!1) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[448, 3232, 1727])).
% 1.62/1.81 tff(3234,plain,
% 1.62/1.81 (elem!1 = s(s(s(z)))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1565, 3233, 3228])).
% 1.62/1.81 tff(3235,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.62/1.81 tff(3236,plain,
% 1.62/1.81 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3235])).
% 1.62/1.81 tff(3237,plain,
% 1.62/1.81 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.62/1.81 inference(symmetry,[status(thm)],[3236])).
% 1.62/1.81 tff(3238,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.62/1.81 tff(3239,plain,
% 1.62/1.81 (s(s(s(z))) = elem!1),
% 1.62/1.81 inference(symmetry,[status(thm)],[3238])).
% 1.62/1.81 tff(3240,plain,
% 1.62/1.81 (s(s(s(z))) = s(s(elem!1))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3239, 1193, 3237, 977])).
% 1.62/1.81 tff(3241,plain,
% 1.62/1.81 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3240])).
% 1.62/1.81 tff(3242,plain,
% 1.62/1.81 (s(s(z)) = s(elem!1)),
% 1.62/1.81 inference(transitivity,[status(thm)],[87, 3241, 101])).
% 1.62/1.81 tff(3243,plain,
% 1.62/1.81 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3242])).
% 1.62/1.81 tff(3244,plain,
% 1.62/1.81 (s(z) = elem!1),
% 1.62/1.81 inference(transitivity,[status(thm)],[193, 3243, 850])).
% 1.62/1.81 tff(3245,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[706, 3244])).
% 1.62/1.81 tff(3246,plain,((~(elem!1 = s(s(s(z))))) | (s(z) = elem!1) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3247,plain,
% 1.62/1.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3246, 3234, 2885])).
% 1.62/1.81 tff(3248,plain,
% 1.62/1.81 (elem!1 = s(elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[906, 3233])).
% 1.62/1.81 tff(3249,plain,
% 1.62/1.81 (s(s(s(elem!1))) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2482, 3248])).
% 1.62/1.81 tff(3250,plain,
% 1.62/1.81 (s(elem!1) = s(s(s(elem!1)))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2584, 3249, 3248])).
% 1.62/1.81 tff(3251,plain,
% 1.62/1.81 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.62/1.81 inference(symmetry,[status(thm)],[2476])).
% 1.62/1.81 tff(3252,plain,
% 1.62/1.81 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[978, 3251])).
% 1.62/1.81 tff(3253,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3127, 3252])).
% 1.62/1.81 tff(3254,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3255,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3254, 3250, 3247])).
% 1.62/1.81 tff(3256,plain,(r(s(s(s(s(s(s(s(z))))))), z) | r(s(elem!1), elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3257,plain,
% 1.62/1.81 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3256, 1727, 466, 489, 123, 285, 134, 959, 354, 1, 304, 51, 606])).
% 1.62/1.81 tff(3258,plain,
% 1.62/1.81 (b(s(z), s(elem!1)) <=> b(s(z), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[903])).
% 1.62/1.81 tff(3259,plain,
% 1.62/1.81 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 1.62/1.81 inference(symmetry,[status(thm)],[3258])).
% 1.62/1.81 tff(3260,plain,
% 1.62/1.81 (b(s(z), s(elem!1))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[134, 3259])).
% 1.62/1.81 tff(3261,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1239, 3260])).
% 1.62/1.81 tff(3262,plain,((~(s(elem!1) = elem!1)) | b(s(z), s(elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3263,plain,
% 1.62/1.81 (~(s(elem!1) = elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3262, 1239, 134])).
% 1.62/1.81 tff(3264,plain,
% 1.62/1.81 (~(elem!1 = s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1569, 3263])).
% 1.62/1.81 tff(3265,plain,
% 1.62/1.81 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2558, 1378, 321])).
% 1.62/1.81 tff(3266,plain,
% 1.62/1.81 (b(elem!1, z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1380, 1378, 1368])).
% 1.62/1.81 tff(3267,plain,
% 1.62/1.81 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2297, 3266, 134, 489, 123])).
% 1.62/1.81 tff(3268,plain,
% 1.62/1.81 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[130, 3267, 3265])).
% 1.62/1.81 tff(3269,plain,
% 1.62/1.81 (~b(elem!1, s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[949, 3266, 585, 491])).
% 1.62/1.81 tff(3270,plain,
% 1.62/1.81 (r(elem!1, s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[560, 3269, 902])).
% 1.62/1.81 tff(3271,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2492, 3270, 3268, 670, 51])).
% 1.62/1.81 tff(3272,plain,(r(elem!1, z) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3273,plain,
% 1.62/1.81 (r(elem!1, z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3272, 3264, 51, 670, 3044, 3047, 134, 489, 123, 321, 77])).
% 1.62/1.81 tff(3274,plain,
% 1.62/1.81 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2938, 3273, 670, 51])).
% 1.62/1.81 tff(3275,plain,
% 1.62/1.81 (((~![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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3276,plain,
% 1.62/1.81 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3277,plain,
% 1.62/1.81 (((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3276])).
% 1.62/1.81 tff(3278,plain,
% 1.62/1.81 (((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3277, 3275])).
% 1.62/1.81 tff(3279,plain,
% 1.62/1.81 ((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(3280,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 1.62/1.81 tff(3281,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3280, 333, 670, 408, 2323, 321])).
% 1.62/1.81 tff(3282,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3283,plain,
% 1.62/1.81 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3282, 3273, 670, 321])).
% 1.62/1.81 tff(3284,plain,
% 1.62/1.81 (b(s(elem!1), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[448, 3263, 1727])).
% 1.62/1.81 tff(3285,plain,
% 1.62/1.81 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[464, 3284, 2952, 3283, 3274])).
% 1.62/1.81 tff(3286,plain,
% 1.62/1.81 (~(s(s(s(z))) = elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[109, 3285])).
% 1.62/1.81 tff(3287,plain,
% 1.62/1.81 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[81])).
% 1.62/1.81 tff(3288,plain,
% 1.62/1.81 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3287])).
% 1.62/1.81 tff(3289,plain,
% 1.62/1.81 (~(elem!1 = s(elem!1))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[537, 3288])).
% 1.62/1.81 tff(3290,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2920, 2896, 509, 354, 1, 134, 304, 902, 1727, 450])).
% 1.62/1.81 tff(3291,plain,((~r(s(elem!1), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(elem!1)) | r(s(elem!1), elem!1) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3292,plain,
% 1.62/1.81 (~r(s(elem!1), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3291, 3289, 1, 134, 304, 354, 1727, 450, 670, 408])).
% 1.62/1.81 tff(3293,plain,
% 1.62/1.81 (b(s(elem!1), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[507, 3292])).
% 1.62/1.81 tff(3294,plain,
% 1.62/1.81 (b(s(elem!1), s(s(s(z))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[965, 960, 959])).
% 1.62/1.81 tff(3295,plain,
% 1.62/1.81 (~(s(s(s(z))) = s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1934, 960])).
% 1.62/1.81 tff(3296,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.62/1.81 tff(3297,plain,
% 1.62/1.81 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1951, 44, 3296])).
% 1.62/1.81 tff(3298,plain,
% 1.62/1.81 (r(s(s(s(z))), s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3297, 3295])).
% 1.62/1.81 tff(3299,plain,
% 1.62/1.81 (((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(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(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3300,plain,
% 1.62/1.81 ((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(3301,plain,
% 1.62/1.81 ((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.62/1.81 tff(3302,plain,
% 1.62/1.81 (~r(s(s(s(z))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3301, 333, 434, 1230, 3298])).
% 1.62/1.81 tff(3303,plain,
% 1.62/1.81 (b(s(s(s(z))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2794, 3302])).
% 1.62/1.81 tff(3304,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3305,plain,
% 1.62/1.81 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(3306,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3305])).
% 1.62/1.81 tff(3307,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3306, 3304])).
% 1.62/1.81 tff(3308,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(3309,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.62/1.81 tff(3310,plain,
% 1.62/1.81 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3309, 144, 489, 305, 285])).
% 1.62/1.81 tff(3311,plain,
% 1.62/1.81 (~b(s(s(s(z))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3310, 3303])).
% 1.62/1.81 tff(3312,plain,
% 1.62/1.81 (r(s(s(s(z))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[704, 3311, 698])).
% 1.62/1.81 tff(3313,plain,
% 1.62/1.81 (~r(z, s(s(s(z))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2136, 3312, 670, 408])).
% 1.62/1.81 tff(3314,plain,
% 1.62/1.81 (b(z, s(s(s(z))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[619, 3313])).
% 1.62/1.81 tff(3315,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1800, 144, 491, 285, 3314, 3294])).
% 1.62/1.81 tff(3316,plain,((s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | b(s(s(s(z))), s(elem!1)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3317,plain,
% 1.62/1.81 (b(s(s(s(z))), s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3316, 1682, 285, 670, 408, 698, 489, 733, 434, 1230, 3293, 959])).
% 1.62/1.81 tff(3318,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3170, 144, 3293, 3057, 285, 3317])).
% 1.62/1.81 tff(3319,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), elem!1) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3320,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3319, 3286, 3285, 354, 3042, 2950, 670, 285, 3273, 489, 959, 1, 134, 304, 1727, 2952, 2947])).
% 1.62/1.81 tff(3321,plain,(b(s(z), s(elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3322,plain,
% 1.62/1.81 (b(s(z), s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3321, 1727, 2311, 285, 489, 959, 1, 134, 304, 354, 3257, 51, 123, 466])).
% 1.62/1.81 tff(3323,plain,
% 1.62/1.81 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[927])).
% 1.62/1.81 tff(3324,plain,
% 1.62/1.81 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.81 inference(transitivity,[status(thm)],[3323, 111])).
% 1.62/1.81 tff(3325,plain,
% 1.62/1.81 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[3324, 2544])).
% 1.62/1.81 tff(3326,plain,
% 1.62/1.81 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[930, 927])).
% 1.62/1.81 tff(3327,plain,
% 1.62/1.81 (r(s(elem!1), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[925, 3326, 321])).
% 1.62/1.81 tff(3328,plain,
% 1.62/1.81 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[927])).
% 1.62/1.81 tff(3329,plain,
% 1.62/1.81 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3328])).
% 1.62/1.81 tff(3330,plain,
% 1.62/1.81 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[1727, 3329])).
% 1.62/1.81 tff(3331,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[130, 3267, 3265, 54])).
% 1.62/1.81 tff(3332,plain,(r(elem!1, z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(3333,plain,
% 1.62/1.81 (r(elem!1, z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3332, 3330, 134, 489, 123, 321, 1368])).
% 1.62/1.81 tff(3334,plain,
% 1.62/1.81 (~r(elem!1, s(elem!1))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[678, 3333, 670, 3327])).
% 1.62/1.81 tff(3335,plain,
% 1.62/1.81 (elem!1 = s(elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1732, 3334, 134, 1727, 1262])).
% 1.62/1.81 tff(3336,plain,
% 1.62/1.81 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[3335, 3325])).
% 1.62/1.81 tff(3337,plain,
% 1.62/1.81 (s(elem!1) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1569, 3335])).
% 1.62/1.81 tff(3338,plain,
% 1.62/1.81 (s(s(s(elem!1))) = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2482, 3335])).
% 1.62/1.81 tff(3339,plain,
% 1.62/1.81 (s(elem!1) = s(s(s(elem!1)))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2584, 3338, 3335])).
% 1.62/1.81 tff(3340,plain,
% 1.62/1.81 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3254, 3339])).
% 1.62/1.82 tff(3341,plain,
% 1.62/1.82 (~(elem!1 = s(s(s(z))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3246, 3340, 706])).
% 1.62/1.82 tff(3342,plain,
% 1.62/1.82 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1565, 3341, 3337])).
% 1.62/1.82 tff(3343,plain,
% 1.62/1.82 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[116, 3342])).
% 1.62/1.82 tff(3344,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3343, 3336])).
% 1.62/1.82 tff(3345,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3346,plain,
% 1.62/1.82 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3345, 1727, 134, 2885, 3322, 2311, 489, 123, 3257, 77])).
% 1.62/1.82 tff(3347,plain,
% 1.62/1.82 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[472, 3346, 466])).
% 1.62/1.82 tff(3348,plain,
% 1.62/1.82 (~b(s(elem!1), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3040, 144, 123, 304, 3347])).
% 1.62/1.82 tff(3349,plain,
% 1.62/1.82 (r(s(elem!1), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[486, 3348, 1])).
% 1.62/1.82 tff(3350,plain,
% 1.62/1.82 (~r(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2492, 2484, 670, 51])).
% 1.62/1.82 tff(3351,plain,
% 1.62/1.82 (elem!1 = s(elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1732, 3350, 134, 1727, 1262])).
% 1.62/1.82 tff(3352,plain,
% 1.62/1.82 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3351])).
% 1.62/1.82 tff(3353,plain,
% 1.62/1.82 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2484, 3352])).
% 1.62/1.82 tff(3354,plain,
% 1.62/1.82 (~b(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2974, 3351, 606])).
% 1.62/1.82 tff(3355,plain,
% 1.62/1.82 (r(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[583, 3354])).
% 1.62/1.82 tff(3356,plain,
% 1.62/1.82 (((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3357,plain,
% 1.62/1.82 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3358,plain,
% 1.62/1.82 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3357])).
% 1.62/1.82 tff(3359,plain,
% 1.62/1.82 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[3358, 3356])).
% 1.62/1.82 tff(3360,plain,
% 1.62/1.82 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(3361,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 1.62/1.82 tff(3362,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3361, 333, 434, 3355, 51, 3353])).
% 1.62/1.82 tff(3363,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3364,plain,
% 1.62/1.82 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3363, 3349, 51, 606, 134, 1727, 3322, 2311])).
% 1.62/1.82 tff(3365,plain,
% 1.62/1.82 (r(elem!1, z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3332, 3364, 134, 489, 123, 3257, 77])).
% 1.62/1.82 tff(3366,plain,
% 1.62/1.82 (~r(s(elem!1), z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3291, 902, 1, 134, 304, 354, 1727, 450, 670, 408])).
% 1.62/1.82 tff(3367,plain,
% 1.62/1.82 (b(s(elem!1), z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[507, 3366])).
% 1.62/1.82 tff(3368,plain,
% 1.62/1.82 (r(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1732, 902, 134, 1727, 1262])).
% 1.62/1.82 tff(3369,plain,
% 1.62/1.82 (~r(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2393, 3368, 670, 434])).
% 1.62/1.82 tff(3370,plain,
% 1.62/1.82 (b(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[583, 3369])).
% 1.62/1.82 tff(3371,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2383, 3370, 3367, 489, 1262])).
% 1.62/1.82 tff(3372,plain,((elem!1 = s(elem!1)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | r(s(elem!1), elem!1) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3373,plain,
% 1.62/1.82 (elem!1 = s(elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3372, 3322, 489, 2311, 3349, 1, 134, 304, 354, 1727, 3347, 3365])).
% 1.62/1.82 tff(3374,plain,
% 1.62/1.82 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3373])).
% 1.62/1.82 tff(3375,plain,
% 1.62/1.82 (s(elem!1) = elem!1),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1569, 3373])).
% 1.62/1.82 tff(3376,plain,
% 1.62/1.82 (s(s(s(elem!1))) = elem!1),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2482, 3373])).
% 1.62/1.82 tff(3377,plain,
% 1.62/1.82 (s(elem!1) = s(s(s(elem!1)))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2584, 3376, 3373])).
% 1.62/1.82 tff(3378,plain,
% 1.62/1.82 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3254, 3377])).
% 1.62/1.82 tff(3379,plain,
% 1.62/1.82 (~(elem!1 = s(s(s(z))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3246, 3378, 2885])).
% 1.62/1.82 tff(3380,plain,
% 1.62/1.82 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1565, 3379, 3375])).
% 1.62/1.82 tff(3381,plain,
% 1.62/1.82 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[130, 3380, 3364])).
% 1.62/1.82 tff(3382,plain,
% 1.62/1.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3381, 3374])).
% 1.62/1.82 tff(3383,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3384,plain,
% 1.62/1.82 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3385,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3384])).
% 1.62/1.82 tff(3386,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[3385, 3383])).
% 1.62/1.82 tff(3387,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(3388,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 1.62/1.82 tff(3389,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3388, 144, 3322, 123, 3382, 3347])).
% 1.62/1.82 tff(3390,plain,(r(s(elem!1), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3391,plain,
% 1.62/1.82 (r(s(elem!1), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3390, 2884, 489, 1, 123, 2660, 354, 51, 606, 466, 285, 959])).
% 1.62/1.82 tff(3392,plain,
% 1.62/1.82 (~(s(z) = elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2882, 304, 51, 489, 285, 670, 1, 959, 123, 466])).
% 1.62/1.82 tff(3393,plain,
% 1.62/1.82 (~(elem!1 = s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[712, 3392])).
% 1.62/1.82 tff(3394,plain,
% 1.62/1.82 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2623, 435, 466])).
% 1.62/1.82 tff(3395,plain,
% 1.62/1.82 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[81, 2544])).
% 1.62/1.82 tff(3396,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.62/1.82 tff(3397,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3396, 3395])).
% 1.62/1.82 tff(3398,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3399,plain,
% 1.62/1.82 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3398, 3394])).
% 1.62/1.82 tff(3400,plain,
% 1.62/1.82 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[130, 3050, 3399])).
% 1.62/1.82 tff(3401,plain,
% 1.62/1.82 (~r(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2492, 3400, 670, 51])).
% 1.62/1.82 tff(3402,plain,
% 1.62/1.82 (b(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[560, 3401, 902])).
% 1.62/1.82 tff(3403,plain,
% 1.62/1.82 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[927])).
% 1.62/1.82 tff(3404,plain,
% 1.62/1.82 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[547, 3403])).
% 1.62/1.82 tff(3405,plain,
% 1.62/1.82 (~b(elem!1, s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[313, 3404, 123, 304])).
% 1.62/1.82 tff(3406,plain,
% 1.62/1.82 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[927])).
% 1.62/1.82 tff(3407,plain,
% 1.62/1.82 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 1.62/1.82 inference(symmetry,[status(thm)],[3406])).
% 1.62/1.82 tff(3408,plain,
% 1.62/1.82 (r(z, s(elem!1))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[51, 3407])).
% 1.62/1.82 tff(3409,plain,
% 1.62/1.82 (~r(elem!1, s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1863, 3408, 670, 435])).
% 1.62/1.82 tff(3410,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[720, 3409, 3405, 714])).
% 1.62/1.82 tff(3411,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3412,plain,
% 1.62/1.82 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3411, 3402, 670, 435, 123, 304, 51, 714])).
% 1.62/1.82 tff(3413,plain,
% 1.62/1.82 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[472, 3412, 466])).
% 1.62/1.82 tff(3414,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[949, 3044, 3047, 624, 547])).
% 1.62/1.82 tff(3415,plain,(b(s(z), s(elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3416,plain,
% 1.62/1.82 (b(s(z), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3415, 624, 3402, 354, 1, 123, 304, 466])).
% 1.62/1.82 tff(3417,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3418,plain,
% 1.62/1.82 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3419,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3418])).
% 1.62/1.82 tff(3420,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[3419, 3417])).
% 1.62/1.82 tff(3421,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(3422,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 1.62/1.82 tff(3423,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3422, 144, 3402, 134, 3416, 123, 3413])).
% 1.62/1.82 tff(3424,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3425,plain,
% 1.62/1.82 (~b(elem!1, z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3424, 902, 123, 466, 670, 435, 304, 51, 3393, 354, 1, 134, 489])).
% 1.62/1.82 tff(3426,plain,
% 1.62/1.82 (r(elem!1, z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[653, 3425, 77])).
% 1.62/1.82 tff(3427,plain,
% 1.62/1.82 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2938, 3426, 670, 51])).
% 1.62/1.82 tff(3428,plain,
% 1.62/1.82 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[130, 3427, 3399])).
% 1.62/1.82 tff(3429,plain,
% 1.62/1.82 (~r(s(elem!1), z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[517, 3426, 51, 435])).
% 1.62/1.82 tff(3430,plain,
% 1.62/1.82 (b(s(elem!1), z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[507, 3429])).
% 1.62/1.82 tff(3431,plain,
% 1.62/1.82 (~r(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2453, 333, 435, 670, 3426])).
% 1.62/1.82 tff(3432,plain,
% 1.62/1.82 (b(z, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[583, 3431])).
% 1.62/1.82 tff(3433,plain,
% 1.62/1.82 (~b(s(z), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2383, 3432, 489, 3430])).
% 1.62/1.82 tff(3434,plain,
% 1.62/1.82 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2946, 3433, 123])).
% 1.62/1.82 tff(3435,plain,
% 1.62/1.82 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[152, 3428, 123, 134])).
% 1.62/1.82 tff(3436,plain,
% 1.62/1.82 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[121, 3435, 3394])).
% 1.62/1.82 tff(3437,plain,
% 1.62/1.82 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3282, 3436, 670, 3426])).
% 1.62/1.82 tff(3438,plain,
% 1.62/1.82 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2113, 297, 408, 489, 123, 134])).
% 1.62/1.82 tff(3439,plain,
% 1.62/1.82 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2894, 3438, 670, 51])).
% 1.62/1.82 tff(3440,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3441,plain,
% 1.62/1.82 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3442,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3441])).
% 1.62/1.82 tff(3443,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[3442, 3440])).
% 1.62/1.82 tff(3444,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(3445,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 1.62/1.82 tff(3446,plain,
% 1.62/1.82 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3445, 144, 547, 491, 133, 2097])).
% 1.62/1.82 tff(3447,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[540, 44, 537, 3446, 3439])).
% 1.62/1.82 tff(3448,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3449,plain,
% 1.62/1.82 (~b(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3448, 3437, 3434, 3430, 3428, 670, 51, 3426, 489, 123, 134])).
% 1.62/1.82 tff(3450,plain,
% 1.62/1.82 (r(elem!1, s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[560, 3449, 902])).
% 1.62/1.82 tff(3451,plain,
% 1.62/1.82 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[930, 3434])).
% 1.62/1.82 tff(3452,plain,
% 1.62/1.82 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[472, 3451, 466])).
% 1.62/1.82 tff(3453,plain,
% 1.62/1.82 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2958, 144, 3430, 489, 304])).
% 1.62/1.82 tff(3454,plain,
% 1.62/1.82 (~b(s(elem!1), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3453, 3452])).
% 1.62/1.82 tff(3455,plain,
% 1.62/1.82 (r(s(elem!1), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[486, 3454, 1])).
% 1.62/1.82 tff(3456,plain,
% 1.62/1.82 (r(s(z), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1244, 3433, 1229])).
% 1.62/1.82 tff(3457,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3458,plain,
% 1.62/1.82 (((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(3459,plain,
% 1.62/1.82 (((~![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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3458])).
% 1.62/1.82 tff(3460,plain,
% 1.62/1.82 (((~![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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.62/1.82 tff(3461,plain,
% 1.62/1.82 ((~![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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(3462,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.62/1.82 tff(3463,plain,
% 1.62/1.82 (~r(elem!1, s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3462, 333, 3450, 435, 3456])).
% 1.62/1.82 tff(3464,plain,
% 1.62/1.82 (b(elem!1, s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[720, 3463, 3393])).
% 1.62/1.82 tff(3465,plain,
% 1.62/1.82 (~(s(s(s(z))) = elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[380, 3425, 285])).
% 1.62/1.82 tff(3466,plain,
% 1.62/1.82 (~b(s(s(s(z))), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3170, 144, 3430, 3432, 285])).
% 1.62/1.82 tff(3467,plain,
% 1.62/1.82 (s(elem!1) = s(s(s(z)))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3316, 3464, 285, 670, 3466, 3426, 489, 3465, 3455, 3456, 3430, 959])).
% 1.62/1.82 tff(3468,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3147, 3467, 3464, 489, 354, 3456, 134, 3455, 3450, 670, 1])).
% 1.62/1.82 tff(3469,plain,((elem!1 = s(elem!1)) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(3470,plain,
% 1.62/1.82 (elem!1 = s(elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3469, 2884, 354, 489, 2311, 1, 285, 959, 3391, 51, 123, 2660, 466])).
% 1.62/1.82 tff(3471,plain,
% 1.62/1.82 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(elem!1))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3470])).
% 1.62/1.82 tff(3472,plain,
% 1.62/1.82 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), elem!1)),
% 1.62/1.83 inference(symmetry,[status(thm)],[3471])).
% 1.62/1.83 tff(3473,plain,
% 1.62/1.83 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), elem!1))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3472])).
% 1.62/1.83 tff(3474,plain,
% 1.62/1.83 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.62/1.83 inference(bind,[status(th)],[])).
% 1.62/1.83 tff(3475,plain,
% 1.62/1.83 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.62/1.83 inference(quant_intro,[status(thm)],[3474])).
% 1.62/1.83 tff(3476,plain,
% 1.62/1.83 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3477,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.62/1.83 tff(3478,plain,
% 1.62/1.83 (![X: $i] : (~r(X, X))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3477, 3476])).
% 1.62/1.83 tff(3479,plain,(
% 1.62/1.83 ![X: $i] : (~r(X, X))),
% 1.62/1.83 inference(skolemize,[status(sab)],[3478])).
% 1.62/1.83 tff(3480,plain,
% 1.62/1.83 (![X: $i] : (~r(X, X))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3479, 3475])).
% 1.62/1.83 tff(3481,plain,
% 1.62/1.83 ((~![X: $i] : (~r(X, X))) | (~r(s(elem!1), s(elem!1)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3482,plain,
% 1.62/1.83 (~r(s(elem!1), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3481, 3480])).
% 1.62/1.83 tff(3483,plain,
% 1.62/1.83 (~r(s(elem!1), elem!1)),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3482, 3473])).
% 1.62/1.83 tff(3484,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3391, 3483])).
% 1.62/1.83 tff(3485,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(3486,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3485, 489, 354, 1, 285, 959, 51, 123, 606, 2310])).
% 1.62/1.83 tff(3487,plain,
% 1.62/1.83 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[2531, 2694, 51, 670, 959, 285, 57])).
% 1.62/1.83 tff(3488,plain,
% 1.62/1.83 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[319, 3487])).
% 1.62/1.83 tff(3489,plain,
% 1.62/1.83 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3488, 2699])).
% 1.62/1.83 tff(3490,plain,
% 1.62/1.83 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.62/1.83 inference(monotonicity,[status(thm)],[57])).
% 1.62/1.83 tff(3491,plain,
% 1.62/1.83 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[533, 509, 51, 525])).
% 1.62/1.83 tff(3492,plain,
% 1.62/1.83 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[540, 44, 537, 3491])).
% 1.62/1.83 tff(3493,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3494,plain,
% 1.62/1.83 (((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3495,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3494])).
% 1.62/1.83 tff(3496,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3495, 3493])).
% 1.62/1.83 tff(3497,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3498,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 1.62/1.83 tff(3499,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3498, 144, 451, 624, 133, 286, 546])).
% 1.62/1.83 tff(3500,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(3501,plain,
% 1.62/1.83 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3500, 3492, 624, 133, 451])).
% 1.62/1.83 tff(3502,plain,
% 1.62/1.83 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[302, 3501])).
% 1.62/1.83 tff(3503,plain,
% 1.62/1.83 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3504,plain,
% 1.62/1.83 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3505,plain,
% 1.62/1.83 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3504])).
% 1.62/1.83 tff(3506,plain,
% 1.62/1.83 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3505, 3503])).
% 1.62/1.83 tff(3507,plain,
% 1.62/1.83 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3508,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 1.62/1.83 tff(3509,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3508, 333, 670, 509, 3502, 525])).
% 1.62/1.83 tff(3510,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(3511,plain,
% 1.62/1.83 (~r(s(elem!1), z)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3510, 451, 525, 2694, 133, 670, 2698, 51])).
% 1.62/1.83 tff(3512,plain,
% 1.62/1.83 (b(s(elem!1), z)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[507, 3511])).
% 1.62/1.83 tff(3513,plain,
% 1.62/1.83 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.62/1.83 inference(monotonicity,[status(thm)],[57])).
% 1.62/1.83 tff(3514,plain,
% 1.62/1.83 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3513, 2])).
% 1.62/1.83 tff(3515,plain,
% 1.62/1.83 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3514])).
% 1.62/1.83 tff(3516,plain,
% 1.62/1.83 (~(elem!1 = s(s(s(z))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[166, 3515])).
% 1.62/1.83 tff(3517,plain,
% 1.62/1.83 (s(s(elem!1)) = elem!1),
% 1.62/1.83 inference(transitivity,[status(thm)],[1007, 3236, 850])).
% 1.62/1.83 tff(3518,plain,
% 1.62/1.83 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3517])).
% 1.62/1.83 tff(3519,plain,
% 1.62/1.83 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3518, 2])).
% 1.62/1.83 tff(3520,plain,
% 1.62/1.83 (elem!1 = s(s(s(z)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[857, 3519])).
% 1.62/1.83 tff(3521,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1524, 3520])).
% 1.62/1.83 tff(3522,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (elem!1 = s(s(s(z)))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(3523,plain,
% 1.62/1.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3522, 2496, 3516])).
% 1.62/1.83 tff(3524,plain,
% 1.62/1.83 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3254, 3523])).
% 1.62/1.83 tff(3525,plain,
% 1.62/1.83 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[2499])).
% 1.62/1.83 tff(3526,plain,
% 1.62/1.83 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.62/1.83 inference(symmetry,[status(thm)],[3525])).
% 1.62/1.83 tff(3527,plain,
% 1.62/1.83 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3526])).
% 1.62/1.83 tff(3528,plain,
% 1.62/1.83 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3527])).
% 1.62/1.83 tff(3529,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.62/1.83 tff(3530,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3531,plain,
% 1.62/1.83 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3532,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3531])).
% 1.62/1.83 tff(3533,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.62/1.83 tff(3534,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3535,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.62/1.83 tff(3536,plain,
% 1.62/1.83 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3535, 144, 451, 624, 491, 3529])).
% 1.62/1.83 tff(3537,plain,
% 1.62/1.83 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3536, 3528])).
% 1.62/1.83 tff(3538,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(elem!1))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1067, 3537, 3524])).
% 1.62/1.83 tff(3539,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3526])).
% 1.62/1.83 tff(3540,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.62/1.83 inference(symmetry,[status(thm)],[3539])).
% 1.62/1.83 tff(3541,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.83 tff(3542,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(s(z)))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 1.62/1.83 tff(3543,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.83 tff(3544,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3543, 3542])).
% 1.62/1.83 tff(3545,plain,(r(s(elem!1), s(s(s(s(z))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(3546,plain,
% 1.62/1.83 (r(s(elem!1), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3545, 3538, 57])).
% 1.62/1.83 tff(3547,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3548,plain,
% 1.62/1.83 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3549,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[3548])).
% 1.62/1.83 tff(3550,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[3549, 3547])).
% 1.62/1.83 tff(3551,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3552,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3551, 3550])).
% 1.62/1.83 tff(3553,plain,
% 1.62/1.83 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3552, 144, 3529, 133, 132])).
% 1.62/1.83 tff(3554,plain,
% 1.62/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3555,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(3556,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[3555, 3554])).
% 1.62/1.83 tff(3557,plain,
% 1.62/1.83 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3556, 44, 196, 3553])).
% 1.62/1.83 tff(3558,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.83 tff(3559,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.62/1.83 tff(3560,plain,
% 1.62/1.83 (((~![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(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3561,plain,
% 1.62/1.83 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(3562,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![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(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[3561])).
% 1.62/1.84 tff(3563,plain,
% 1.62/1.84 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[3562, 3560])).
% 1.62/1.84 tff(3564,plain,
% 1.62/1.84 ((~![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(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(3565,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 1.62/1.84 tff(3566,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3565, 333, 525, 524, 3559, 3558])).
% 1.62/1.84 tff(3567,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3568,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3567, 3557, 525, 3546])).
% 1.62/1.84 tff(3569,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[540, 44, 2698, 3568])).
% 1.62/1.84 tff(3570,plain,
% 1.62/1.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3500, 3569, 624, 133, 451])).
% 1.62/1.84 tff(3571,plain,
% 1.62/1.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[302, 3570])).
% 1.62/1.84 tff(3572,plain,
% 1.62/1.84 (((~![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(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3573,plain,
% 1.62/1.84 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3574,plain,
% 1.62/1.84 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[3573])).
% 1.62/1.84 tff(3575,plain,
% 1.62/1.84 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[3574, 3572])).
% 1.62/1.84 tff(3576,plain,
% 1.62/1.84 ((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(3577,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 1.62/1.84 tff(3578,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3577, 333, 3571, 525, 3557, 3546])).
% 1.62/1.84 tff(3579,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3580,plain,
% 1.62/1.84 (~b(s(s(s(s(z)))), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3579, 451, 2694, 133, 525, 57, 132, 3512])).
% 1.62/1.84 tff(3581,plain,
% 1.62/1.84 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.62/1.84 inference(monotonicity,[status(thm)],[3525])).
% 1.62/1.84 tff(3582,plain,
% 1.62/1.84 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.62/1.84 inference(monotonicity,[status(thm)],[57])).
% 1.62/1.84 tff(3583,plain,
% 1.62/1.84 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.62/1.84 inference(transitivity,[status(thm)],[3582, 3581])).
% 1.62/1.84 tff(3584,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.62/1.84 tff(3585,plain,
% 1.62/1.84 (b(s(s(s(s(z)))), elem!1)),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3584, 3583])).
% 1.62/1.84 tff(3586,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.62/1.84 tff(3587,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3586, 3585])).
% 1.62/1.84 tff(3588,plain,((~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3589,plain,
% 1.62/1.84 (~b(s(s(s(elem!1))), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3588, 3580, 57])).
% 1.62/1.84 tff(3590,plain,
% 1.62/1.84 (r(s(s(s(elem!1))), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1101, 3589])).
% 1.62/1.84 tff(3591,plain,
% 1.62/1.84 (r(s(s(s(elem!1))), elem!1)),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3590, 3490])).
% 1.62/1.84 tff(3592,plain,
% 1.62/1.84 (~b(s(z), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2383, 585, 489, 491])).
% 1.62/1.84 tff(3593,plain,
% 1.62/1.84 (r(s(z), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1244, 3592, 1237])).
% 1.62/1.84 tff(3594,plain,
% 1.62/1.84 (~b(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[949, 585, 624, 491])).
% 1.62/1.84 tff(3595,plain,
% 1.62/1.84 (r(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[560, 3594, 902])).
% 1.62/1.84 tff(3596,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3101, 3595, 3593, 670, 489, 1056, 491, 3065])).
% 1.62/1.84 tff(3597,plain,((~b(z, s(elem!1))) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3598,plain,
% 1.62/1.84 (~b(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3597, 3512, 489, 3524, 670, 3591, 2483, 1237, 2694])).
% 1.62/1.84 tff(3599,plain,
% 1.62/1.84 (r(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[583, 3598])).
% 1.62/1.84 tff(3600,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3601,plain,
% 1.62/1.84 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3602,plain,
% 1.62/1.84 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[3601])).
% 1.62/1.84 tff(3603,plain,
% 1.62/1.84 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[3602, 3600])).
% 1.62/1.84 tff(3604,plain,
% 1.62/1.84 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(3605,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3604, 3603])).
% 1.62/1.84 tff(3606,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3605, 333, 562, 51, 525, 524])).
% 1.62/1.84 tff(3607,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3608,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3607, 3599, 51, 525])).
% 1.62/1.84 tff(3609,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[540, 44, 2698, 3608])).
% 1.62/1.84 tff(3610,plain,
% 1.62/1.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3500, 3609, 2694, 133, 451])).
% 1.62/1.84 tff(3611,plain,
% 1.62/1.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[302, 3610])).
% 1.62/1.84 tff(3612,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[938, 333, 3599, 3611, 51, 525])).
% 1.62/1.84 tff(3613,plain,((~b(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3614,plain,
% 1.62/1.84 (~b(s(elem!1), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3613, 3489, 525, 51, 489, 670, 1229, 57, 2692])).
% 1.62/1.84 tff(3615,plain,
% 1.62/1.84 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(z)))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[2662])).
% 1.62/1.84 tff(3616,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.62/1.84 tff(3617,plain,
% 1.62/1.84 (~b(s(elem!1), s(z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 1.62/1.84 tff(3618,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[488, 3617])).
% 1.62/1.84 tff(3619,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), s(z))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3620,plain,
% 1.62/1.84 (~b(s(elem!1), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3619, 3614, 57])).
% 1.62/1.84 tff(3621,plain,
% 1.62/1.84 (r(s(elem!1), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[486, 3620, 1])).
% 1.62/1.84 tff(3622,plain,
% 1.62/1.84 (r(s(elem!1), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[448, 3614, 2681])).
% 1.62/1.84 tff(3623,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2720, 333, 563, 435, 670, 509])).
% 1.62/1.84 tff(3624,plain,((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3625,plain,
% 1.62/1.84 (~r(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3624, 509, 670, 435])).
% 1.62/1.84 tff(3626,plain,
% 1.62/1.84 (b(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[560, 3625, 902])).
% 1.62/1.84 tff(3627,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.84 tff(3628,plain,
% 1.62/1.84 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2516, 144, 624, 3627, 2726])).
% 1.62/1.84 tff(3629,plain,
% 1.62/1.84 (~b(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3628, 3626])).
% 1.62/1.84 tff(3630,plain,
% 1.62/1.84 (r(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2522, 3629, 1221])).
% 1.62/1.84 tff(3631,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2878, 333, 435, 670, 509, 3630])).
% 1.62/1.84 tff(3632,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3633,plain,
% 1.62/1.84 (~r(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3632, 3622, 670, 2462, 2694, 2861, 2498, 2483])).
% 1.62/1.84 tff(3634,plain,
% 1.62/1.84 (b(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[507, 3633])).
% 1.62/1.84 tff(3635,plain,
% 1.62/1.84 (~b(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3628, 547])).
% 1.62/1.84 tff(3636,plain,
% 1.62/1.84 (r(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2522, 3635, 1221])).
% 1.62/1.84 tff(3637,plain,
% 1.62/1.84 (~b(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[949, 547, 624, 491])).
% 1.62/1.84 tff(3638,plain,
% 1.62/1.84 (r(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[583, 3637])).
% 1.62/1.84 tff(3639,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2870, 333, 435, 670, 3638, 3636])).
% 1.62/1.84 tff(3640,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3641,plain,
% 1.62/1.84 (~b(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3640, 3622, 670, 2462, 2694, 3634, 2861, 2498])).
% 1.62/1.84 tff(3642,plain,
% 1.62/1.84 (r(elem!1, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[560, 3641, 2483])).
% 1.62/1.84 tff(3643,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2845, 3642, 51, 57, 489, 285, 3488, 3622, 3621, 670])).
% 1.62/1.84 tff(3644,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[302, 3643])).
% 1.62/1.84 tff(3645,plain,
% 1.62/1.84 (~r(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2393, 3642, 670, 3621])).
% 1.62/1.84 tff(3646,plain,
% 1.62/1.84 (b(z, s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[583, 3645])).
% 1.62/1.84 tff(3647,plain,
% 1.62/1.84 (~b(s(s(elem!1)), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2733, 144, 3634, 3646, 2498])).
% 1.62/1.84 tff(3648,plain,
% 1.62/1.84 (r(s(s(elem!1)), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1283, 3647, 2507])).
% 1.62/1.84 tff(3649,plain,
% 1.62/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2745, 3648, 3621, 3642])).
% 1.62/1.84 tff(3650,plain,
% 1.62/1.84 (b(elem!1, s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2522, 3649, 2462])).
% 1.62/1.84 tff(3651,plain,
% 1.62/1.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2753, 144, 3650, 3489, 3644, 2498])).
% 1.62/1.84 tff(3652,plain,
% 1.62/1.84 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1668, 144, 3634, 3646, 3644])).
% 1.62/1.84 tff(3653,plain,
% 1.62/1.84 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[540, 44, 2698, 3652])).
% 1.62/1.84 tff(3654,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.84 tff(3655,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3656,plain,
% 1.62/1.84 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3657,plain,
% 1.62/1.84 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[3656])).
% 1.62/1.84 tff(3658,plain,
% 1.62/1.84 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[3657, 3655])).
% 1.62/1.84 tff(3659,plain,
% 1.62/1.84 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(3660,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3659, 3658])).
% 1.62/1.84 tff(3661,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3660, 333, 2737, 3654, 525, 524])).
% 1.62/1.84 tff(3662,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3663,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3662, 3653, 525, 3648])).
% 1.62/1.84 tff(3664,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2758, 3663, 3651, 2704])).
% 1.62/1.84 tff(3665,plain,((~(s(z) = elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(3666,plain,
% 1.62/1.84 (~(s(z) = elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3665, 3486, 51, 489, 285, 2311, 1, 959, 123])).
% 1.62/1.84 tff(3667,plain,
% 1.62/1.84 (b(s(z), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[406, 3666, 2310])).
% 1.62/1.84 tff(3668,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2455, 377, 489, 51, 2310, 123, 285, 959, 1, 670, 354])).
% 1.62/1.84 tff(3669,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[319, 3668])).
% 1.62/1.84 tff(3670,plain,
% 1.62/1.84 (~(s(z) = elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3665, 525, 51, 489, 285, 670, 1, 959, 123])).
% 1.62/1.84 tff(3671,plain,
% 1.62/1.84 (b(s(z), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[406, 3670, 2310])).
% 1.62/1.84 tff(3672,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[885])).
% 1.62/1.84 tff(3673,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2938, 408, 670, 51])).
% 1.62/1.84 tff(3674,plain,
% 1.62/1.84 (s(elem!1) = elem!1),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1569, 885])).
% 1.62/1.84 tff(3675,plain,
% 1.62/1.84 (s(s(s(elem!1))) = elem!1),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2482, 885])).
% 1.62/1.84 tff(3676,plain,
% 1.62/1.84 (s(elem!1) = s(s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[2584, 3675, 885])).
% 1.62/1.84 tff(3677,plain,
% 1.62/1.84 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3254, 3676])).
% 1.62/1.84 tff(3678,plain,
% 1.62/1.84 (~(elem!1 = s(s(s(z))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3246, 3677, 706])).
% 1.62/1.84 tff(3679,plain,
% 1.62/1.84 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[1565, 3678, 3674])).
% 1.62/1.84 tff(3680,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[130, 3679, 3673])).
% 1.62/1.84 tff(3681,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[3680, 3672])).
% 1.62/1.84 tff(3682,plain,
% 1.62/1.84 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[116, 3679])).
% 1.62/1.84 tff(3683,plain,
% 1.62/1.84 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[152, 3680, 123, 134])).
% 1.62/1.84 tff(3684,plain,
% 1.62/1.84 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[121, 3683, 3682])).
% 1.62/1.84 tff(3685,plain,
% 1.62/1.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[3282, 3684, 670, 408])).
% 1.62/1.84 tff(3686,plain,
% 1.62/1.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[302, 3685])).
% 1.62/1.84 tff(3687,plain,
% 1.62/1.84 (~(s(elem!1) = s(s(s(z))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[990, 3676, 1])).
% 1.62/1.84 tff(3688,plain,
% 1.62/1.84 (b(s(elem!1), s(s(s(z))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[965, 3687, 959])).
% 1.62/1.84 tff(3689,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(3690,plain,
% 1.62/1.84 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3691,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[3690])).
% 1.62/1.85 tff(3692,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.85 inference(transitivity,[status(thm)],[3691, 3689])).
% 1.62/1.85 tff(3693,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3694,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 1.62/1.85 tff(3695,plain,
% 1.62/1.85 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3694, 144, 285, 3688, 3686, 3681])).
% 1.62/1.85 tff(3696,plain,
% 1.62/1.85 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[249, 3695])).
% 1.62/1.85 tff(3697,plain,
% 1.62/1.85 (r(elem!1, z) <=> r(s(elem!1), z)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[885])).
% 1.62/1.85 tff(3698,plain,
% 1.62/1.85 (r(s(elem!1), z)),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[408, 3697])).
% 1.62/1.85 tff(3699,plain,
% 1.62/1.85 (((~![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(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3700,plain,
% 1.62/1.85 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3701,plain,
% 1.62/1.85 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[3700])).
% 1.62/1.85 tff(3702,plain,
% 1.62/1.85 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.62/1.85 tff(3703,plain,
% 1.62/1.85 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3704,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.62/1.85 tff(3705,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3704, 333, 3698, 3696, 51, 525])).
% 1.62/1.85 tff(3706,plain,((~(elem!1 = s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | r(s(elem!1), s(s(s(z)))) | (s(z) = elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3707,plain,
% 1.62/1.85 (~(elem!1 = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3706, 2322, 525, 285, 51, 670, 123, 3671, 959, 3670, 1])).
% 1.62/1.85 tff(3708,plain,
% 1.62/1.85 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3291, 509, 1, 134, 304, 354, 1727, 902, 670, 408])).
% 1.62/1.85 tff(3709,plain,
% 1.62/1.85 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[81])).
% 1.62/1.85 tff(3710,plain,
% 1.62/1.85 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(symmetry,[status(thm)],[3709])).
% 1.62/1.85 tff(3711,plain,
% 1.62/1.85 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[451, 3710])).
% 1.62/1.85 tff(3712,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[467, 3711])).
% 1.62/1.85 tff(3713,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3714,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3713, 3708, 1728])).
% 1.62/1.85 tff(3715,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[130, 3714, 3673])).
% 1.62/1.85 tff(3716,plain,
% 1.62/1.85 (b(elem!1, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[560, 2896, 902])).
% 1.62/1.85 tff(3717,plain,
% 1.62/1.85 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[553, 144, 3716, 1728, 3715])).
% 1.62/1.85 tff(3718,plain,
% 1.62/1.85 (~b(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1732, 2896, 134, 1727, 902])).
% 1.62/1.85 tff(3719,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2946, 3718, 123])).
% 1.62/1.85 tff(3720,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[540, 44, 3719, 3717, 3491])).
% 1.62/1.85 tff(3721,plain,((~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3722,plain,
% 1.62/1.85 (~r(s(elem!1), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3721, 902, 123, 134, 1727, 51, 525, 670, 2322, 1, 304, 354])).
% 1.62/1.85 tff(3723,plain,
% 1.62/1.85 (b(s(elem!1), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[507, 3722])).
% 1.62/1.85 tff(3724,plain,
% 1.62/1.85 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3713, 81, 1728])).
% 1.62/1.85 tff(3725,plain,
% 1.62/1.85 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2910, 144, 1728, 134, 304])).
% 1.62/1.85 tff(3726,plain,
% 1.62/1.85 (~b(s(elem!1), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3725, 3724])).
% 1.62/1.85 tff(3727,plain,
% 1.62/1.85 (r(s(elem!1), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[486, 3726, 1])).
% 1.62/1.85 tff(3728,plain,
% 1.62/1.85 (~b(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3372, 3727, 489, 670, 134, 1, 1727, 304, 354, 902, 3724, 2322])).
% 1.62/1.85 tff(3729,plain,
% 1.62/1.85 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[787, 81, 377])).
% 1.62/1.85 tff(3730,plain,
% 1.62/1.85 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[302, 3729])).
% 1.62/1.85 tff(3731,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[925, 3730, 501])).
% 1.62/1.85 tff(3732,plain,
% 1.62/1.85 (~(s(s(s(z))) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[380, 377, 285])).
% 1.62/1.85 tff(3733,plain,
% 1.62/1.85 (~r(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3319, 3727, 354, 2322, 3732, 670, 285, 3724, 489, 959, 1, 134, 304, 1727, 81, 3731])).
% 1.62/1.85 tff(3734,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1244, 3733, 3728, 1229])).
% 1.62/1.85 tff(3735,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | r(s(elem!1), z) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3736,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3735, 902, 670, 285, 489, 959, 1, 134, 304, 1727, 354, 3722, 377])).
% 1.62/1.85 tff(3737,plain,
% 1.62/1.85 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[116, 3736])).
% 1.62/1.85 tff(3738,plain,
% 1.62/1.85 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2938, 2322, 670, 51])).
% 1.62/1.85 tff(3739,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[130, 3736, 3738])).
% 1.62/1.85 tff(3740,plain,
% 1.62/1.85 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[152, 3739, 123, 134])).
% 1.62/1.85 tff(3741,plain,
% 1.62/1.85 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[121, 3740, 3737])).
% 1.62/1.85 tff(3742,plain,
% 1.62/1.85 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2894, 3741, 670, 51])).
% 1.62/1.85 tff(3743,plain,
% 1.62/1.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3282, 3741, 670, 2322])).
% 1.62/1.85 tff(3744,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[302, 3743])).
% 1.62/1.85 tff(3745,plain,
% 1.62/1.85 (b(elem!1, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[560, 1725, 902])).
% 1.62/1.85 tff(3746,plain,
% 1.62/1.85 (~b(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1732, 1725, 134, 1727, 902])).
% 1.62/1.85 tff(3747,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2946, 3746, 123])).
% 1.62/1.85 tff(3748,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3448, 3747, 3745, 408, 491, 133, 670, 51, 297, 489, 123, 134])).
% 1.62/1.85 tff(3749,plain,(r(elem!1, s(elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), z) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (elem!1 = s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3750,plain,
% 1.62/1.85 (r(elem!1, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3749, 3723, 2322, 3739, 670, 51, 3743, 489, 123, 134, 902, 1727])).
% 1.62/1.85 tff(3751,plain,
% 1.62/1.85 (~b(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[593, 546, 133, 286, 451])).
% 1.62/1.85 tff(3752,plain,
% 1.62/1.85 (r(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[583, 3751])).
% 1.62/1.85 tff(3753,plain,
% 1.62/1.85 (~r(s(elem!1), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2393, 3752, 670, 563])).
% 1.62/1.85 tff(3754,plain,
% 1.62/1.85 (b(s(elem!1), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[486, 3753, 1])).
% 1.62/1.85 tff(3755,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3756,plain,
% 1.62/1.85 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3757,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[3756])).
% 1.62/1.85 tff(3758,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[3757, 3755])).
% 1.62/1.85 tff(3759,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3760,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3759, 3758])).
% 1.62/1.85 tff(3761,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3760, 144, 134, 3754, 133, 304, 546])).
% 1.62/1.85 tff(3762,plain,((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3763,plain,
% 1.62/1.85 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3762, 3739, 134, 304, 1, 670, 3750, 3744, 1728])).
% 1.62/1.85 tff(3764,plain,
% 1.62/1.85 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[542, 3763, 3742])).
% 1.62/1.85 tff(3765,plain,
% 1.62/1.85 (b(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2946, 3764, 123])).
% 1.62/1.85 tff(3766,plain,
% 1.62/1.85 (~b(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2383, 3765, 489, 3723])).
% 1.62/1.85 tff(3767,plain,
% 1.62/1.85 (r(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[583, 3766])).
% 1.62/1.85 tff(3768,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3769,plain,
% 1.62/1.85 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3770,plain,
% 1.62/1.85 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[3769])).
% 1.62/1.85 tff(3771,plain,
% 1.62/1.85 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[3770, 3768])).
% 1.62/1.85 tff(3772,plain,
% 1.62/1.85 ((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3773,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3772, 3771])).
% 1.62/1.85 tff(3774,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3773, 333, 3750, 670, 3767, 525])).
% 1.62/1.85 tff(3775,plain,((elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3776,plain,
% 1.62/1.85 (r(s(elem!1), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3775, 3707, 525, 489, 123, 3671, 3669, 1, 51, 670, 285, 959, 354, 377])).
% 1.62/1.85 tff(3777,plain,
% 1.62/1.85 (~r(s(elem!1), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[517, 3776, 51, 2322])).
% 1.62/1.85 tff(3778,plain,
% 1.62/1.85 (b(s(elem!1), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[507, 3777])).
% 1.62/1.85 tff(3779,plain,
% 1.62/1.85 (~r(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2453, 333, 3776, 670, 2322])).
% 1.62/1.85 tff(3780,plain,
% 1.62/1.85 (b(z, s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[583, 3779])).
% 1.62/1.85 tff(3781,plain,
% 1.62/1.85 (~b(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2383, 3780, 489, 3778])).
% 1.62/1.85 tff(3782,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2946, 3781, 123])).
% 1.62/1.85 tff(3783,plain,
% 1.62/1.85 (~b(s(s(s(z))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3170, 144, 3778, 3780, 285])).
% 1.62/1.85 tff(3784,plain,
% 1.62/1.85 (r(s(z), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1244, 3781, 1229])).
% 1.62/1.85 tff(3785,plain,
% 1.62/1.85 (~(s(s(s(z))) = s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1934, 1682])).
% 1.62/1.85 tff(3786,plain,
% 1.62/1.85 (r(s(s(s(z))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3297, 3785])).
% 1.62/1.85 tff(3787,plain,
% 1.62/1.85 (((~![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(s(z), s(elem!1))) | (~r(s(s(s(z))), s(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(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3788,plain,
% 1.62/1.85 ((~![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(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3789,plain,
% 1.62/1.85 ((~![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(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3788, 3787])).
% 1.62/1.85 tff(3790,plain,
% 1.62/1.85 (~r(s(s(s(z))), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3789, 333, 435, 1230, 3786])).
% 1.62/1.85 tff(3791,plain,
% 1.62/1.85 (b(s(s(s(z))), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2794, 3790])).
% 1.62/1.85 tff(3792,plain,
% 1.62/1.85 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3309, 144, 489, 733, 285])).
% 1.62/1.85 tff(3793,plain,
% 1.62/1.85 (~b(s(s(s(z))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3792, 3791])).
% 1.62/1.85 tff(3794,plain,
% 1.62/1.85 (r(s(s(s(z))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[704, 3793, 698])).
% 1.62/1.85 tff(3795,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(3796,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(3797,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 1.62/1.85 tff(3798,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3797, 333, 435, 408, 3794, 3786])).
% 1.62/1.85 tff(3799,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3800,plain,
% 1.62/1.85 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3799, 3776, 2322, 3732, 489, 285, 3784, 3783, 3669])).
% 1.62/1.85 tff(3801,plain,
% 1.62/1.85 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[116, 3800])).
% 1.62/1.85 tff(3802,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[130, 3800, 3738])).
% 1.62/1.85 tff(3803,plain,
% 1.62/1.85 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[152, 3802, 123, 3671])).
% 1.62/1.85 tff(3804,plain,
% 1.62/1.85 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[121, 3803, 3801])).
% 1.62/1.85 tff(3805,plain,
% 1.62/1.85 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2894, 3804, 670, 51])).
% 1.62/1.85 tff(3806,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[542, 3805, 3782])).
% 1.62/1.85 tff(3807,plain,
% 1.62/1.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3282, 3804, 670, 2322])).
% 1.62/1.85 tff(3808,plain,
% 1.62/1.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[302, 3807])).
% 1.62/1.85 tff(3809,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1668, 144, 3778, 3780, 3808, 3806])).
% 1.62/1.85 tff(3810,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(3811,plain,
% 1.62/1.85 (b(elem!1, z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3810, 489, 51, 123, 2311, 285, 3486, 1, 959, 354, 2310])).
% 1.62/1.85 tff(3812,plain,
% 1.62/1.85 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2297, 3811, 3667, 489, 123])).
% 1.62/1.85 tff(3813,plain,
% 1.62/1.85 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3814,plain,
% 1.62/1.86 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3815,plain,
% 1.62/1.86 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3814])).
% 1.62/1.86 tff(3816,plain,
% 1.62/1.86 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3815, 3813])).
% 1.62/1.86 tff(3817,plain,
% 1.62/1.86 ((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3818,plain,
% 1.62/1.86 ((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 1.62/1.86 tff(3819,plain,
% 1.62/1.86 (~r(z, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3818, 333, 2484, 51, 525])).
% 1.62/1.86 tff(3820,plain,
% 1.62/1.86 (b(z, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[583, 3819])).
% 1.62/1.86 tff(3821,plain,
% 1.62/1.86 (~(elem!1 = s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[2974, 3820, 606])).
% 1.62/1.86 tff(3822,plain,
% 1.62/1.86 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3823,plain,
% 1.62/1.86 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3824,plain,
% 1.62/1.86 (((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3823])).
% 1.62/1.86 tff(3825,plain,
% 1.62/1.86 (((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3824, 3822])).
% 1.62/1.86 tff(3826,plain,
% 1.62/1.86 ((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3827,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3826, 3825])).
% 1.62/1.86 tff(3828,plain,
% 1.62/1.86 (~r(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3827, 333, 2484, 51, 525])).
% 1.62/1.86 tff(3829,plain,
% 1.62/1.86 (b(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[507, 3828])).
% 1.62/1.86 tff(3830,plain,
% 1.62/1.86 (~b(elem!1, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[949, 3820, 624, 3829])).
% 1.62/1.86 tff(3831,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[560, 3830, 3821, 3350])).
% 1.62/1.86 tff(3832,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3833,plain,
% 1.62/1.86 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3832, 3811, 606, 51, 3486, 2311])).
% 1.62/1.86 tff(3834,plain,
% 1.62/1.86 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[130, 3833, 3812])).
% 1.62/1.86 tff(3835,plain,
% 1.62/1.86 (~(s(s(s(z))) = elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[109, 3834])).
% 1.62/1.86 tff(3836,plain,
% 1.62/1.86 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3834])).
% 1.62/1.86 tff(3837,plain,
% 1.62/1.86 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3836])).
% 1.62/1.86 tff(3838,plain,
% 1.62/1.86 (~(s(s(z)) = elem!1)),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1446, 3837])).
% 1.62/1.86 tff(3839,plain,
% 1.62/1.86 (~(s(elem!1) = s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1508, 3838])).
% 1.62/1.86 tff(3840,plain,
% 1.62/1.86 (b(s(elem!1), s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[965, 3839, 959])).
% 1.62/1.86 tff(3841,plain,
% 1.62/1.86 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[81])).
% 1.62/1.86 tff(3842,plain,
% 1.62/1.86 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3841])).
% 1.62/1.86 tff(3843,plain,
% 1.62/1.86 (~(elem!1 = s(s(s(z))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[244, 3842])).
% 1.62/1.86 tff(3844,plain,
% 1.62/1.86 (~(s(elem!1) = elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1565, 3843, 81])).
% 1.62/1.86 tff(3845,plain,
% 1.62/1.86 (~(elem!1 = s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1569, 3844])).
% 1.62/1.86 tff(3846,plain,
% 1.62/1.86 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3607, 562, 51, 525])).
% 1.62/1.86 tff(3847,plain,
% 1.62/1.86 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[81])).
% 1.62/1.86 tff(3848,plain,
% 1.62/1.86 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.86 inference(symmetry,[status(thm)],[3847])).
% 1.62/1.86 tff(3849,plain,
% 1.62/1.86 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[563, 3848])).
% 1.62/1.86 tff(3850,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[535, 3849])).
% 1.62/1.86 tff(3851,plain,((~r(elem!1, s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3852,plain,
% 1.62/1.86 (~r(elem!1, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3851, 3846, 81])).
% 1.62/1.86 tff(3853,plain,
% 1.62/1.86 (b(elem!1, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[560, 3852, 3845])).
% 1.62/1.86 tff(3854,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3855,plain,
% 1.62/1.86 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3856,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3855])).
% 1.62/1.86 tff(3857,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3856, 3854])).
% 1.62/1.86 tff(3858,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3859,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3858, 3857])).
% 1.62/1.86 tff(3860,plain,
% 1.62/1.86 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3859, 144, 624, 285, 1794])).
% 1.62/1.86 tff(3861,plain,
% 1.62/1.86 (~b(elem!1, s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3860, 3853])).
% 1.62/1.86 tff(3862,plain,
% 1.62/1.86 (r(elem!1, s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1538, 3861, 3843])).
% 1.62/1.86 tff(3863,plain,
% 1.62/1.86 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), elem!1)),
% 1.62/1.86 inference(monotonicity,[status(thm)],[81])).
% 1.62/1.86 tff(3864,plain,
% 1.62/1.86 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.86 inference(symmetry,[status(thm)],[3863])).
% 1.62/1.86 tff(3865,plain,
% 1.62/1.86 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3864])).
% 1.62/1.86 tff(3866,plain,
% 1.62/1.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1727, 3865])).
% 1.62/1.86 tff(3867,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[525, 3866])).
% 1.62/1.86 tff(3868,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3869,plain,
% 1.62/1.86 (r(s(elem!1), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3868, 81, 525])).
% 1.62/1.86 tff(3870,plain,
% 1.62/1.86 (((~![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, elem!1)) | (~r(z, s(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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3871,plain,
% 1.62/1.86 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3872,plain,
% 1.62/1.86 (((~![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(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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3871])).
% 1.62/1.86 tff(3873,plain,
% 1.62/1.86 (((~![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(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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3872, 3870])).
% 1.62/1.86 tff(3874,plain,
% 1.62/1.86 ((~![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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3875,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 1.62/1.86 tff(3876,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3875, 333, 3869, 670, 562, 3862])).
% 1.62/1.86 tff(3877,plain,((~r(z, s(elem!1))) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3878,plain,
% 1.62/1.86 (~r(z, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3877, 3811, 2311, 285, 3840, 3834, 51, 3486])).
% 1.62/1.86 tff(3879,plain,
% 1.62/1.86 (b(z, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[583, 3878])).
% 1.62/1.86 tff(3880,plain,
% 1.62/1.86 (r(s(elem!1), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3868, 3834, 3486])).
% 1.62/1.86 tff(3881,plain,
% 1.62/1.86 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3834])).
% 1.62/1.86 tff(3882,plain,
% 1.62/1.86 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3881])).
% 1.62/1.86 tff(3883,plain,
% 1.62/1.86 (~(elem!1 = s(s(s(z))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[244, 3882])).
% 1.62/1.86 tff(3884,plain,
% 1.62/1.86 (~(s(elem!1) = elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1565, 3883, 3834])).
% 1.62/1.86 tff(3885,plain,
% 1.62/1.86 (~(elem!1 = s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1569, 3884])).
% 1.62/1.86 tff(3886,plain,
% 1.62/1.86 (~b(elem!1, s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3860, 547])).
% 1.62/1.86 tff(3887,plain,
% 1.62/1.86 (r(elem!1, s(s(s(z))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1538, 3886, 1524])).
% 1.62/1.86 tff(3888,plain,
% 1.62/1.86 (~b(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[949, 547, 624, 585])).
% 1.62/1.86 tff(3889,plain,
% 1.62/1.86 (r(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[507, 3888])).
% 1.62/1.86 tff(3890,plain,
% 1.62/1.86 (((~![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, elem!1)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3891,plain,
% 1.62/1.86 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3892,plain,
% 1.62/1.86 (((~![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(elem!1), elem!1)) | (~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), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3891])).
% 1.62/1.86 tff(3893,plain,
% 1.62/1.86 (((~![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(elem!1), elem!1)) | (~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), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3892, 3890])).
% 1.62/1.86 tff(3894,plain,
% 1.62/1.86 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3895,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 1.62/1.86 tff(3896,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3895, 333, 435, 670, 3889, 3887])).
% 1.62/1.86 tff(3897,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3898,plain,
% 1.62/1.86 (~b(elem!1, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3897, 3880, 2311, 3883, 3811, 285, 3840, 3879])).
% 1.62/1.86 tff(3899,plain,
% 1.62/1.86 (r(elem!1, s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[560, 3898, 3885])).
% 1.62/1.86 tff(3900,plain,
% 1.62/1.86 (~r(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3624, 3899, 2311, 3880])).
% 1.62/1.86 tff(3901,plain,
% 1.62/1.86 (b(s(elem!1), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[507, 3900])).
% 1.62/1.86 tff(3902,plain,
% 1.62/1.86 (~b(s(s(s(z))), s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3170, 144, 3901, 3879, 285])).
% 1.62/1.86 tff(3903,plain,
% 1.62/1.86 (~(s(s(s(z))) = s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1934, 3839])).
% 1.62/1.86 tff(3904,plain,
% 1.62/1.86 (r(s(s(s(z))), s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1951, 44, 3903, 3902])).
% 1.62/1.86 tff(3905,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3906,plain,
% 1.62/1.86 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(3907,plain,
% 1.62/1.86 (((~![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(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[3906])).
% 1.62/1.86 tff(3908,plain,
% 1.62/1.86 (((~![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(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[3907, 3905])).
% 1.62/1.86 tff(3909,plain,
% 1.62/1.86 ((~![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(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(3910,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[3909, 3908])).
% 1.62/1.86 tff(3911,plain,
% 1.62/1.86 (~r(s(s(s(z))), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3910, 333, 3899, 3880, 3904])).
% 1.62/1.86 tff(3912,plain,
% 1.62/1.86 (b(s(s(s(z))), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[704, 3911, 3835])).
% 1.62/1.86 tff(3913,plain,
% 1.62/1.86 (~b(s(z), s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[2383, 3901, 489, 3879])).
% 1.62/1.86 tff(3914,plain,
% 1.62/1.86 (r(s(z), s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1244, 3913, 1229])).
% 1.62/1.86 tff(3915,plain,
% 1.62/1.86 (~r(s(s(s(z))), s(z))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3789, 333, 3880, 3914, 3904])).
% 1.62/1.86 tff(3916,plain,
% 1.62/1.86 (b(s(s(s(z))), s(z))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[2794, 3915])).
% 1.62/1.86 tff(3917,plain,
% 1.62/1.86 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3189, 144, 3811, 3667, 285])).
% 1.62/1.86 tff(3918,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3917, 3916, 3912])).
% 1.62/1.86 tff(3919,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(z)))) | b(z, elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(3920,plain,
% 1.62/1.86 (~b(s(z), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3919, 959, 51, 285, 606, 123, 1, 354, 2310])).
% 1.62/1.86 tff(3921,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.62/1.86 tff(3922,plain,
% 1.62/1.86 (r(s(z), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[348, 3921])).
% 1.62/1.86 tff(3923,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[130, 3673, 114])).
% 1.62/1.87 tff(3924,plain,
% 1.62/1.87 (b(s(elem!1), s(z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[451, 2662])).
% 1.62/1.87 tff(3925,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3926,plain,
% 1.62/1.87 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3927,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[3926])).
% 1.62/1.87 tff(3928,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[3927, 3925])).
% 1.62/1.87 tff(3929,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(3930,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 1.62/1.87 tff(3931,plain,
% 1.62/1.87 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3930, 144, 451, 123, 133])).
% 1.62/1.87 tff(3932,plain,
% 1.62/1.87 (~b(s(elem!1), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3931, 2690])).
% 1.62/1.87 tff(3933,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3932, 3924])).
% 1.62/1.87 tff(3934,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3935,plain,
% 1.62/1.87 (~(s(z) = elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3934, 3923, 123, 451, 466])).
% 1.62/1.87 tff(3936,plain,
% 1.62/1.87 (b(s(z), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[406, 3935, 2310])).
% 1.62/1.87 tff(3937,plain,
% 1.62/1.87 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[152, 3936, 123, 3923])).
% 1.62/1.87 tff(3938,plain,
% 1.62/1.87 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[121, 3937, 453])).
% 1.62/1.87 tff(3939,plain,
% 1.62/1.87 (((~![X0: $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, elem!1)) | (~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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3940,plain,
% 1.62/1.87 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3941,plain,
% 1.62/1.87 (((~![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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[3940])).
% 1.62/1.87 tff(3942,plain,
% 1.62/1.87 (((~![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(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.62/1.87 inference(transitivity,[status(thm)],[3941, 3939])).
% 1.62/1.87 tff(3943,plain,
% 1.62/1.87 ((~![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))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(3944,plain,
% 1.62/1.87 ((~![X0: $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, elem!1)) | (~r(elem!1, z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.62/1.87 tff(3945,plain,
% 1.62/1.87 (~r(elem!1, s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3944, 333, 670, 323, 408])).
% 1.62/1.87 tff(3946,plain,
% 1.62/1.87 (~(elem!1 = s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[712, 3935])).
% 1.62/1.87 tff(3947,plain,
% 1.62/1.87 (b(elem!1, s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[720, 3946, 3945])).
% 1.62/1.87 tff(3948,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3949,plain,
% 1.62/1.87 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3950,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[3949])).
% 1.62/1.87 tff(3951,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.62/1.87 tff(3952,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(3953,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 1.62/1.87 tff(3954,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3953, 144, 134, 305, 133, 304])).
% 1.62/1.87 tff(3955,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3956,plain,
% 1.62/1.87 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3955, 3947, 3923, 3936])).
% 1.62/1.87 tff(3957,plain,
% 1.62/1.87 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[319, 3956])).
% 1.62/1.87 tff(3958,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2331, 3957, 3938, 408, 51])).
% 1.62/1.87 tff(3959,plain,((~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~b(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3960,plain,
% 1.62/1.87 (~r(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3959, 466, 123, 2310, 1728, 51, 670, 3922, 114])).
% 1.62/1.87 tff(3961,plain,
% 1.62/1.87 (b(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1380, 3960, 77])).
% 1.62/1.87 tff(3962,plain,
% 1.62/1.87 (b(elem!1, z) <=> b(s(z), z)),
% 1.62/1.87 inference(symmetry,[status(thm)],[2693])).
% 1.62/1.87 tff(3963,plain,
% 1.62/1.87 (b(s(z), z)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[624, 3962])).
% 1.62/1.87 tff(3964,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3921, 3963])).
% 1.62/1.87 tff(3965,plain,((~(s(z) = elem!1)) | b(s(z), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3966,plain,
% 1.62/1.87 (~(s(z) = elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3965, 3961, 3921])).
% 1.62/1.87 tff(3967,plain,
% 1.62/1.87 (b(s(z), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[406, 3966, 2310])).
% 1.62/1.87 tff(3968,plain,
% 1.62/1.87 (~b(s(z), s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1732, 1725, 1727, 902, 134])).
% 1.62/1.87 tff(3969,plain,
% 1.62/1.87 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3415, 3968, 466, 354, 1, 123, 624, 3745])).
% 1.62/1.87 tff(3970,plain,
% 1.62/1.87 (r(s(z), s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1244, 3968, 1229])).
% 1.62/1.87 tff(3971,plain,
% 1.62/1.87 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2319, 3970, 354, 51])).
% 1.62/1.87 tff(3972,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[319, 3971, 3969])).
% 1.62/1.87 tff(3973,plain,(r(elem!1, s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3974,plain,
% 1.62/1.87 (r(elem!1, s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3973, 466, 51, 354, 1, 123, 3961, 1727, 902, 3967])).
% 1.62/1.87 tff(3975,plain,
% 1.62/1.87 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2492, 3974, 670, 51])).
% 1.62/1.87 tff(3976,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[130, 3975, 114])).
% 1.62/1.87 tff(3977,plain,
% 1.62/1.87 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[152, 3976, 123, 3967])).
% 1.62/1.87 tff(3978,plain,
% 1.62/1.87 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[121, 3977, 453])).
% 1.62/1.87 tff(3979,plain,
% 1.62/1.87 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2541, 3978, 670, 51])).
% 1.62/1.87 tff(3980,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[319, 3979])).
% 1.62/1.87 tff(3981,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3982,plain,
% 1.62/1.87 (((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3983,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[3982])).
% 1.62/1.87 tff(3984,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.87 inference(transitivity,[status(thm)],[3983, 3981])).
% 1.62/1.87 tff(3985,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(3986,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 1.62/1.87 tff(3987,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3986, 144, 624, 134, 133, 304, 286])).
% 1.62/1.87 tff(3988,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3989,plain,
% 1.62/1.87 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3988, 3961, 3967, 3976, 3980])).
% 1.62/1.87 tff(3990,plain,
% 1.62/1.87 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[302, 3989])).
% 1.62/1.87 tff(3991,plain,
% 1.62/1.87 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3992,plain,
% 1.62/1.87 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(3993,plain,
% 1.62/1.87 (((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[3992])).
% 1.62/1.87 tff(3994,plain,
% 1.62/1.87 (((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[3993, 3991])).
% 1.62/1.87 tff(3995,plain,
% 1.62/1.87 ((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(3996,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 1.62/1.87 tff(3997,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3996, 333, 670, 3978, 3990, 51])).
% 1.62/1.87 tff(3998,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | r(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(3999,plain,
% 1.62/1.87 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3998, 902, 51, 123, 114, 354, 1, 1727, 2311, 2310, 3920])).
% 1.62/1.87 tff(4000,plain,
% 1.62/1.87 (~r(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2938, 2484, 670, 51])).
% 1.62/1.87 tff(4001,plain,
% 1.62/1.87 (~b(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3832, 2484, 606, 51, 525, 670])).
% 1.62/1.87 tff(4002,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1380, 4001, 4000, 1368])).
% 1.62/1.87 tff(4003,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = z) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(4004,plain,
% 1.62/1.87 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4003, 3999, 606, 51, 77, 2311])).
% 1.62/1.87 tff(4005,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[130, 4004, 114])).
% 1.62/1.87 tff(4006,plain,
% 1.62/1.87 (r(s(z), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[348, 3920])).
% 1.62/1.87 tff(4007,plain,
% 1.62/1.87 (~(s(elem!1) = s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2856, 2727])).
% 1.62/1.87 tff(4008,plain,
% 1.62/1.87 (b(s(elem!1), s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2860, 44, 4007, 2851])).
% 1.62/1.87 tff(4009,plain,
% 1.62/1.87 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[2496])).
% 1.62/1.87 tff(4010,plain,
% 1.62/1.87 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 1.62/1.87 inference(symmetry,[status(thm)],[4009])).
% 1.62/1.87 tff(4011,plain,
% 1.62/1.87 (~r(z, s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3607, 524, 51, 525])).
% 1.62/1.87 tff(4012,plain,
% 1.62/1.87 (b(z, s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[583, 4011])).
% 1.62/1.87 tff(4013,plain,
% 1.62/1.87 (~r(s(elem!1), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[533, 524, 51, 525])).
% 1.62/1.87 tff(4014,plain,
% 1.62/1.87 (b(s(elem!1), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[507, 4013])).
% 1.62/1.87 tff(4015,plain,
% 1.62/1.87 (~b(s(s(elem!1)), s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2733, 144, 4014, 4012, 2726])).
% 1.62/1.87 tff(4016,plain,
% 1.62/1.87 (r(s(s(elem!1)), s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1283, 4015, 2854])).
% 1.62/1.87 tff(4017,plain,
% 1.62/1.87 (r(s(s(s(z))), s(elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4016, 4010])).
% 1.62/1.87 tff(4018,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[2496])).
% 1.62/1.87 tff(4019,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.62/1.87 inference(symmetry,[status(thm)],[4018])).
% 1.62/1.87 tff(4020,plain,
% 1.62/1.87 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[3662, 4016, 525, 524])).
% 1.62/1.87 tff(4021,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[2758, 4020, 2704])).
% 1.62/1.87 tff(4022,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4021, 4019])).
% 1.62/1.87 tff(4023,plain,
% 1.62/1.87 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(symmetry,[status(thm)],[2767])).
% 1.62/1.87 tff(4024,plain,
% 1.62/1.87 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4023])).
% 1.62/1.87 tff(4025,plain,
% 1.62/1.87 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4026,plain,
% 1.62/1.87 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4027,plain,
% 1.62/1.87 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4026])).
% 1.62/1.87 tff(4028,plain,
% 1.62/1.87 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4027, 4025])).
% 1.62/1.88 tff(4029,plain,
% 1.62/1.88 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4030,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.62/1.88 tff(4031,plain,
% 1.62/1.88 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4030, 333, 4016, 525, 524])).
% 1.62/1.88 tff(4032,plain,
% 1.62/1.88 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4031, 4024])).
% 1.62/1.88 tff(4033,plain,
% 1.62/1.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1137, 4032])).
% 1.62/1.88 tff(4034,plain,
% 1.62/1.88 (~b(s(z), s(s(s(z))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2262, 4033, 123, 4022])).
% 1.62/1.88 tff(4035,plain,
% 1.62/1.88 (r(s(z), s(s(s(z))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[172, 4034])).
% 1.62/1.88 tff(4036,plain,
% 1.62/1.88 (~r(z, s(s(s(z))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3011, 4035, 354, 4017])).
% 1.62/1.88 tff(4037,plain,
% 1.62/1.88 (b(z, s(s(s(z))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[619, 4036])).
% 1.62/1.88 tff(4038,plain,
% 1.62/1.88 (b(z, s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2828, 4037, 57])).
% 1.62/1.88 tff(4039,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4040,plain,
% 1.62/1.88 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4041,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4040])).
% 1.62/1.88 tff(4042,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4041, 4039])).
% 1.62/1.88 tff(4043,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4044,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4043, 4042])).
% 1.62/1.88 tff(4045,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4044, 144, 4014, 4038, 3627, 2726])).
% 1.62/1.88 tff(4046,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4047,plain,
% 1.62/1.88 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4046, 4008, 2498, 57, 354, 123, 525, 2727, 51])).
% 1.62/1.88 tff(4048,plain,
% 1.62/1.88 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[542, 4047, 2698])).
% 1.62/1.88 tff(4049,plain,
% 1.62/1.88 (~b(elem!1, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[555, 4048, 133, 451])).
% 1.62/1.88 tff(4050,plain,
% 1.62/1.88 (r(elem!1, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[560, 4049, 902])).
% 1.62/1.88 tff(4051,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3773, 333, 563, 670, 562, 525])).
% 1.62/1.88 tff(4052,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4053,plain,
% 1.62/1.88 (~r(z, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4052, 4050, 670, 525])).
% 1.62/1.88 tff(4054,plain,
% 1.62/1.88 (b(z, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[583, 4053])).
% 1.62/1.88 tff(4055,plain,
% 1.62/1.88 (~r(s(elem!1), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[678, 4050, 670, 408])).
% 1.62/1.88 tff(4056,plain,
% 1.62/1.88 (b(s(elem!1), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[507, 4055])).
% 1.62/1.88 tff(4057,plain,
% 1.62/1.88 (~b(s(s(elem!1)), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2733, 144, 4056, 4054, 2498])).
% 1.62/1.88 tff(4058,plain,
% 1.62/1.88 (r(s(s(elem!1)), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1283, 4057, 2727])).
% 1.62/1.88 tff(4059,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4060,plain,
% 1.62/1.88 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4061,plain,
% 1.62/1.88 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4060])).
% 1.62/1.88 tff(4062,plain,
% 1.62/1.88 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4061, 4059])).
% 1.62/1.88 tff(4063,plain,
% 1.62/1.88 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4064,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4063, 4062])).
% 1.62/1.88 tff(4065,plain,
% 1.62/1.88 (~r(elem!1, s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4064, 333, 4050, 4058, 525])).
% 1.62/1.88 tff(4066,plain,
% 1.62/1.88 (b(elem!1, s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2522, 4065, 2462])).
% 1.62/1.88 tff(4067,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4068,plain,
% 1.62/1.88 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4069,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4068])).
% 1.62/1.88 tff(4070,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4069, 4067])).
% 1.62/1.88 tff(4071,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4072,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 1.62/1.88 tff(4073,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4072, 144, 451, 4056, 4066, 4008, 2498])).
% 1.62/1.88 tff(4074,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4075,plain,
% 1.62/1.88 (~(s(z) = elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4074, 408, 525, 670, 451, 902, 133, 354, 123, 51, 959, 285])).
% 1.62/1.88 tff(4076,plain,
% 1.62/1.88 (b(s(z), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[406, 4075, 2310])).
% 1.62/1.88 tff(4077,plain,
% 1.62/1.88 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[152, 4076, 123, 133])).
% 1.62/1.88 tff(4078,plain,
% 1.62/1.88 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[121, 4077, 3396])).
% 1.62/1.88 tff(4079,plain,
% 1.62/1.88 (~(elem!1 = s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[712, 4075])).
% 1.62/1.88 tff(4080,plain,
% 1.62/1.88 (b(elem!1, s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[720, 4079, 3945])).
% 1.62/1.88 tff(4081,plain,
% 1.62/1.88 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3955, 4080, 133, 4076])).
% 1.62/1.88 tff(4082,plain,
% 1.62/1.88 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[319, 4081])).
% 1.62/1.88 tff(4083,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2541, 4082, 4078, 670, 51])).
% 1.62/1.88 tff(4084,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4085,plain,
% 1.62/1.88 (~r(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4084, 4005, 51, 453, 2311, 123, 2310, 3999, 1728, 902, 354, 959, 285, 4006])).
% 1.62/1.88 tff(4086,plain,
% 1.62/1.88 (b(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1380, 4085, 77])).
% 1.62/1.88 tff(4087,plain,
% 1.62/1.88 (~(s(z) = elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3965, 4086, 3920])).
% 1.62/1.88 tff(4088,plain,
% 1.62/1.88 (b(s(z), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[406, 4087, 2310])).
% 1.62/1.88 tff(4089,plain,
% 1.62/1.88 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[152, 4088, 123, 4005])).
% 1.62/1.88 tff(4090,plain,
% 1.62/1.88 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[121, 4089, 453])).
% 1.62/1.88 tff(4091,plain,
% 1.62/1.88 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2894, 4090, 2311, 51])).
% 1.62/1.88 tff(4092,plain,
% 1.62/1.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2541, 4090, 2311, 51])).
% 1.62/1.88 tff(4093,plain,
% 1.62/1.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[319, 4092])).
% 1.62/1.88 tff(4094,plain,
% 1.62/1.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3988, 4093, 4086, 4005, 4088])).
% 1.62/1.88 tff(4095,plain,
% 1.62/1.88 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[302, 4094])).
% 1.62/1.88 tff(4096,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4097,plain,
% 1.62/1.88 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4098,plain,
% 1.62/1.88 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4097])).
% 1.62/1.88 tff(4099,plain,
% 1.62/1.88 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4098, 4096])).
% 1.62/1.88 tff(4100,plain,
% 1.62/1.88 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4101,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 1.62/1.88 tff(4102,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4101, 333, 563, 2323, 321, 525])).
% 1.62/1.88 tff(4103,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4104,plain,
% 1.62/1.88 (~r(elem!1, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4103, 4095, 3999, 4090])).
% 1.62/1.88 tff(4105,plain,
% 1.62/1.88 (b(elem!1, s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[560, 4104, 902])).
% 1.62/1.88 tff(4106,plain,
% 1.62/1.88 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[555, 4105, 4005, 1728])).
% 1.62/1.88 tff(4107,plain,
% 1.62/1.88 (~b(s(z), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1732, 4104, 1727, 902, 4088])).
% 1.62/1.88 tff(4108,plain,
% 1.62/1.88 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2946, 4107, 123])).
% 1.62/1.88 tff(4109,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[542, 4108, 4106, 4091])).
% 1.62/1.88 tff(4110,plain,((elem!1 = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~r(z, s(z))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(z, elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4111,plain,
% 1.62/1.88 (elem!1 = s(elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4110, 114, 1727, 51, 2310, 354, 959, 285, 123, 606, 1])).
% 1.62/1.88 tff(4112,plain,
% 1.62/1.88 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4111])).
% 1.62/1.88 tff(4113,plain,
% 1.62/1.88 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4112, 175])).
% 1.62/1.88 tff(4114,plain,
% 1.62/1.88 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4113])).
% 1.62/1.88 tff(4115,plain,
% 1.62/1.88 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[114, 4114])).
% 1.62/1.88 tff(4116,plain,
% 1.62/1.88 (s(s(s(elem!1))) = elem!1),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2482, 4111])).
% 1.62/1.88 tff(4117,plain,
% 1.62/1.88 (~(s(z) = elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2468, 4116])).
% 1.62/1.88 tff(4118,plain,
% 1.62/1.88 (b(s(z), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[406, 4117, 2310])).
% 1.62/1.88 tff(4119,plain,
% 1.62/1.88 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[885])).
% 1.62/1.88 tff(4120,plain,
% 1.62/1.88 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(symmetry,[status(thm)],[4119])).
% 1.62/1.88 tff(4121,plain,
% 1.62/1.88 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[450, 4120])).
% 1.62/1.88 tff(4122,plain,
% 1.62/1.88 (b(s(z), s(elem!1))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3262, 134, 3674])).
% 1.62/1.88 tff(4123,plain,
% 1.62/1.88 (~r(s(elem!1), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3363, 2484, 51, 606, 1727, 134, 4122, 2311])).
% 1.62/1.88 tff(4124,plain,
% 1.62/1.88 (b(s(elem!1), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[486, 4123, 1])).
% 1.62/1.88 tff(4125,plain,
% 1.62/1.88 (b(elem!1, s(z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4124, 887])).
% 1.62/1.88 tff(4126,plain,
% 1.62/1.88 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[885])).
% 1.62/1.88 tff(4127,plain,
% 1.62/1.88 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[2484, 4126])).
% 1.62/1.88 tff(4128,plain,
% 1.62/1.88 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2894, 4127, 2311, 51])).
% 1.62/1.88 tff(4129,plain,
% 1.62/1.88 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[121, 4128, 3396])).
% 1.62/1.88 tff(4130,plain,
% 1.62/1.88 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[313, 4129, 123, 4125])).
% 1.62/1.88 tff(4131,plain,
% 1.62/1.88 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[319, 4130])).
% 1.62/1.88 tff(4132,plain,
% 1.62/1.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[341, 4131, 51, 323])).
% 1.62/1.88 tff(4133,plain,
% 1.62/1.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[302, 4132])).
% 1.62/1.88 tff(4134,plain,
% 1.62/1.88 (b(elem!1, z) <=> b(s(elem!1), z)),
% 1.62/1.88 inference(monotonicity,[status(thm)],[885])).
% 1.62/1.88 tff(4135,plain,
% 1.62/1.88 (~r(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2938, 2484, 2311, 51])).
% 1.62/1.88 tff(4136,plain,
% 1.62/1.88 (b(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1380, 4135, 77])).
% 1.62/1.88 tff(4137,plain,
% 1.62/1.88 (b(s(elem!1), z)),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4136, 4134])).
% 1.62/1.88 tff(4138,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4139,plain,
% 1.62/1.88 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4140,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4139])).
% 1.62/1.88 tff(4141,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4140, 4138])).
% 1.62/1.88 tff(4142,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4143,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 1.62/1.89 tff(4144,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4143, 144, 4137, 4124, 123, 4133, 450])).
% 1.62/1.89 tff(4145,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(elem!1))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(elem!1), elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4146,plain,
% 1.62/1.89 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4145, 450, 123, 51, 323, 453, 885, 1, 606, 1727, 134])).
% 1.62/1.89 tff(4147,plain,
% 1.62/1.89 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[130, 4146, 114])).
% 1.62/1.89 tff(4148,plain,
% 1.62/1.89 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[152, 4147, 123, 134])).
% 1.62/1.89 tff(4149,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4148, 4121])).
% 1.62/1.89 tff(4150,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4151,plain,
% 1.62/1.89 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4150, 4111, 123, 4118, 114, 51, 4006, 1, 606, 1727])).
% 1.62/1.89 tff(4152,plain,
% 1.62/1.89 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[472, 4151, 4115])).
% 1.62/1.89 tff(4153,plain,
% 1.62/1.89 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4003, 4152, 606, 51, 77, 2311])).
% 1.62/1.89 tff(4154,plain,
% 1.62/1.89 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[130, 4153, 114])).
% 1.62/1.89 tff(4155,plain,
% 1.62/1.89 (~r(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3706, 4152, 4111, 285, 51, 2311, 123, 4118, 959, 4117, 1])).
% 1.62/1.89 tff(4156,plain,
% 1.62/1.89 (b(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1380, 4155, 77])).
% 1.62/1.89 tff(4157,plain,
% 1.62/1.89 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[152, 4154, 123, 4118])).
% 1.62/1.89 tff(4158,plain,
% 1.62/1.89 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[121, 4157, 453])).
% 1.62/1.89 tff(4159,plain,
% 1.62/1.89 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2541, 4158, 2311, 51])).
% 1.62/1.89 tff(4160,plain,
% 1.62/1.89 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[319, 4159])).
% 1.62/1.89 tff(4161,plain,
% 1.62/1.89 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3988, 4160, 4156, 4154, 4118])).
% 1.62/1.89 tff(4162,plain,
% 1.62/1.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[302, 4161])).
% 1.62/1.89 tff(4163,plain,
% 1.62/1.89 (~b(z, s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2974, 4111, 606])).
% 1.62/1.89 tff(4164,plain,
% 1.62/1.89 (r(z, s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[583, 4163])).
% 1.62/1.89 tff(4165,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[938, 333, 4164, 4162, 51, 4152])).
% 1.62/1.89 tff(4166,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(elem!1), elem!1) | r(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4167,plain,
% 1.62/1.89 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4166, 1727, 123, 285, 959, 1, 606, 51, 2310, 354])).
% 1.62/1.89 tff(4168,plain,
% 1.62/1.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4167])).
% 1.62/1.89 tff(4169,plain,
% 1.62/1.89 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4168])).
% 1.62/1.89 tff(4170,plain,
% 1.62/1.89 (~(s(s(z)) = elem!1)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1446, 4169])).
% 1.62/1.89 tff(4171,plain,
% 1.62/1.89 (~(s(elem!1) = s(s(s(z))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1508, 4170])).
% 1.62/1.89 tff(4172,plain,
% 1.62/1.89 (b(s(elem!1), s(s(s(z))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[965, 4171, 959])).
% 1.62/1.89 tff(4173,plain,
% 1.62/1.89 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4167])).
% 1.62/1.89 tff(4174,plain,
% 1.62/1.89 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4173])).
% 1.62/1.89 tff(4175,plain,
% 1.62/1.89 (~(elem!1 = s(s(s(z))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[244, 4174])).
% 1.62/1.89 tff(4176,plain,
% 1.62/1.89 (~r(elem!1, s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[727, 4006, 354, 2311])).
% 1.62/1.89 tff(4177,plain,
% 1.62/1.89 (~b(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3965, 57, 3920])).
% 1.62/1.89 tff(4178,plain,
% 1.62/1.89 (r(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[653, 4177, 77])).
% 1.62/1.89 tff(4179,plain,
% 1.62/1.89 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[57])).
% 1.62/1.89 tff(4180,plain,
% 1.62/1.89 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.89 inference(transitivity,[status(thm)],[4179, 111])).
% 1.62/1.89 tff(4181,plain,
% 1.62/1.89 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4180])).
% 1.62/1.89 tff(4182,plain,
% 1.62/1.89 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[34, 4181])).
% 1.62/1.89 tff(4183,plain,
% 1.62/1.89 (r(s(elem!1), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4110, 4182, 2483, 51, 2310, 354, 959, 285, 123, 606, 1])).
% 1.62/1.89 tff(4184,plain,
% 1.62/1.89 (~r(s(elem!1), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[517, 4183, 51, 4178])).
% 1.62/1.89 tff(4185,plain,
% 1.62/1.89 (b(s(elem!1), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[507, 4184])).
% 1.62/1.89 tff(4186,plain,
% 1.62/1.89 (~b(z, s(s(s(z))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1802, 4185, 285, 2509])).
% 1.62/1.89 tff(4187,plain,
% 1.62/1.89 (r(z, s(s(s(z))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[619, 4186])).
% 1.62/1.89 tff(4188,plain,
% 1.62/1.89 (r(z, s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2836, 4187, 57])).
% 1.62/1.89 tff(4189,plain,
% 1.62/1.89 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2938, 4178, 2311, 51])).
% 1.62/1.89 tff(4190,plain,
% 1.62/1.89 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[130, 4182, 4189])).
% 1.62/1.89 tff(4191,plain,
% 1.62/1.89 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.62/1.89 inference(monotonicity,[status(thm)],[57])).
% 1.62/1.89 tff(4192,plain,
% 1.62/1.89 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.62/1.89 inference(symmetry,[status(thm)],[4191])).
% 1.62/1.89 tff(4193,plain,
% 1.62/1.89 (r(s(elem!1), s(z))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4183, 4192])).
% 1.62/1.89 tff(4194,plain,
% 1.62/1.89 (~r(z, s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2453, 333, 4183, 2311, 4178])).
% 1.62/1.89 tff(4195,plain,
% 1.62/1.89 (b(z, s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[583, 4194])).
% 1.62/1.89 tff(4196,plain,
% 1.62/1.89 (((~![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(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4197,plain,
% 1.62/1.89 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4198,plain,
% 1.62/1.89 (((~![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(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4197])).
% 1.62/1.89 tff(4199,plain,
% 1.62/1.89 (((~![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(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4198, 4196])).
% 1.62/1.89 tff(4200,plain,
% 1.62/1.89 ((~![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(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4201,plain,
% 1.62/1.89 ((~![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(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4200, 4199])).
% 1.62/1.89 tff(4202,plain,
% 1.62/1.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4201, 333, 1024, 323, 434])).
% 1.62/1.89 tff(4203,plain,
% 1.62/1.89 (b(s(s(s(elem!1))), s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3130, 44, 3127, 4202])).
% 1.62/1.89 tff(4204,plain,
% 1.62/1.89 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4205,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1)))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4204])).
% 1.62/1.89 tff(4206,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4205, 3132])).
% 1.62/1.89 tff(4207,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4208,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), s(elem!1)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4207, 4206])).
% 1.62/1.89 tff(4209,plain,
% 1.62/1.89 (~b(s(s(s(elem!1))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4208, 144, 491, 585, 4203])).
% 1.62/1.89 tff(4210,plain,
% 1.62/1.89 (r(s(s(s(elem!1))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 4209])).
% 1.62/1.89 tff(4211,plain,
% 1.62/1.89 (((~![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(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, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4212,plain,
% 1.62/1.89 ((~![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(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4213,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 1.62/1.89 tff(4214,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4213, 333, 670, 1024, 323, 4210])).
% 1.62/1.89 tff(4215,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4216,plain,
% 1.62/1.89 (~r(s(s(s(elem!1))), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4215, 4195, 2311, 4006, 3523, 4193, 4185])).
% 1.62/1.89 tff(4217,plain,
% 1.62/1.89 (b(s(s(s(elem!1))), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1101, 4216])).
% 1.62/1.89 tff(4218,plain,
% 1.62/1.89 (b(s(s(s(s(z)))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3588, 4217, 57])).
% 1.62/1.89 tff(4219,plain,
% 1.62/1.89 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3552, 144, 4218, 4190, 2692])).
% 1.62/1.89 tff(4220,plain,
% 1.62/1.89 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[3556, 44, 196, 4219])).
% 1.62/1.89 tff(4221,plain,
% 1.62/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2733, 144, 4185, 4195, 2498])).
% 1.62/1.89 tff(4222,plain,
% 1.62/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1283, 4221, 2507])).
% 1.62/1.89 tff(4223,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.62/1.89 tff(4224,plain,
% 1.62/1.89 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(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, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4225,plain,
% 1.62/1.89 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4226,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4225])).
% 1.62/1.89 tff(4227,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4226, 4224])).
% 1.62/1.89 tff(4228,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4229,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 1.62/1.89 tff(4230,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4229, 333, 670, 2737, 2736, 4223])).
% 1.62/1.89 tff(4231,plain,((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4232,plain,
% 1.62/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4231, 4222, 4188, 2311])).
% 1.62/1.89 tff(4233,plain,
% 1.62/1.89 (b(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2522, 4232, 2462])).
% 1.62/1.89 tff(4234,plain,
% 1.62/1.89 (((~![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(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4235,plain,
% 1.62/1.89 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4236,plain,
% 1.62/1.89 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4235])).
% 1.62/1.89 tff(4237,plain,
% 1.62/1.89 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4236, 4234])).
% 1.62/1.89 tff(4238,plain,
% 1.62/1.89 ((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4239,plain,
% 1.62/1.89 ((~![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(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.62/1.89 tff(4240,plain,
% 1.62/1.89 (~r(s(s(s(s(z)))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4239, 333, 321, 51, 3559])).
% 1.62/1.89 tff(4241,plain,
% 1.62/1.89 (((~![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))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4242,plain,
% 1.62/1.89 ((~![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))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4243,plain,
% 1.62/1.89 ((~![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)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 1.62/1.89 tff(4244,plain,
% 1.62/1.89 (b(s(s(s(s(z)))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4243, 44, 242, 4240])).
% 1.62/1.89 tff(4245,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4246,plain,
% 1.62/1.89 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4247,plain,
% 1.62/1.89 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4246])).
% 1.62/1.89 tff(4248,plain,
% 1.62/1.89 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4247, 4245])).
% 1.62/1.89 tff(4249,plain,
% 1.62/1.89 ((~![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(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4250,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4249, 4248])).
% 1.62/1.89 tff(4251,plain,
% 1.62/1.89 (~r(z, s(s(s(s(z)))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4250, 333, 321, 51, 3559])).
% 1.62/1.89 tff(4252,plain,
% 1.62/1.89 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.62/1.89 inference(commutativity,[status(thm)],[])).
% 1.62/1.89 tff(4253,plain,
% 1.62/1.89 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.62/1.89 inference(symmetry,[status(thm)],[4252])).
% 1.62/1.89 tff(4254,plain,
% 1.62/1.89 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4253])).
% 1.62/1.89 tff(4255,plain,
% 1.62/1.89 (~(z = s(s(s(s(z)))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[242, 4254])).
% 1.62/1.89 tff(4256,plain,
% 1.62/1.89 (((~![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))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4257,plain,
% 1.62/1.89 ((~![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))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4258,plain,
% 1.72/1.90 ((~![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)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4257, 4256])).
% 1.72/1.90 tff(4259,plain,
% 1.72/1.90 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4258, 44])).
% 1.72/1.90 tff(4260,plain,
% 1.72/1.90 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4259, 4255])).
% 1.72/1.90 tff(4261,plain,
% 1.72/1.90 (b(z, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4260, 4251])).
% 1.72/1.90 tff(4262,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4263,plain,
% 1.72/1.90 (((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4264,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4263])).
% 1.72/1.90 tff(4265,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4264, 4262])).
% 1.72/1.90 tff(4266,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4267,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.72/1.90 tff(4268,plain,
% 1.72/1.90 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4267, 144, 491, 4261, 4244])).
% 1.72/1.90 tff(4269,plain,
% 1.72/1.90 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4268, 3528])).
% 1.72/1.90 tff(4270,plain,
% 1.72/1.90 (r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1067, 4269, 3524])).
% 1.72/1.90 tff(4271,plain,
% 1.72/1.90 (r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3545, 4270, 57])).
% 1.72/1.90 tff(4272,plain,
% 1.72/1.90 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[3525, 2496])).
% 1.72/1.90 tff(4273,plain,
% 1.72/1.90 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[2499])).
% 1.72/1.90 tff(4274,plain,
% 1.72/1.90 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4273, 972])).
% 1.72/1.90 tff(4275,plain,
% 1.72/1.90 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4274])).
% 1.72/1.90 tff(4276,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.72/1.90 tff(4277,plain,
% 1.72/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4276])).
% 1.72/1.90 tff(4278,plain,
% 1.72/1.90 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4277])).
% 1.72/1.90 tff(4279,plain,
% 1.72/1.90 (s(s(elem!1)) = s(elem!1)),
% 1.72/1.90 inference(transitivity,[status(thm)],[1007, 4278, 101])).
% 1.72/1.90 tff(4280,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[2854, 4279])).
% 1.72/1.90 tff(4281,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4282,plain,
% 1.72/1.90 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4281, 2507])).
% 1.72/1.90 tff(4283,plain,
% 1.72/1.90 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4282, 4275])).
% 1.72/1.90 tff(4284,plain,
% 1.72/1.90 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[3526, 2499])).
% 1.72/1.90 tff(4285,plain,
% 1.72/1.90 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4284])).
% 1.72/1.90 tff(4286,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4287,plain,
% 1.72/1.90 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4288,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4287])).
% 1.72/1.90 tff(4289,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4288, 4286])).
% 1.72/1.90 tff(4290,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4291,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 1.72/1.90 tff(4292,plain,
% 1.72/1.90 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4291, 144, 2812, 3529, 2726, 4244])).
% 1.72/1.90 tff(4293,plain,
% 1.72/1.90 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4292, 4285])).
% 1.72/1.90 tff(4294,plain,
% 1.72/1.90 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1116, 4293, 4283])).
% 1.72/1.90 tff(4295,plain,
% 1.72/1.90 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4294, 4272])).
% 1.72/1.90 tff(4296,plain,
% 1.72/1.90 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[3526])).
% 1.72/1.90 tff(4297,plain,
% 1.72/1.90 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4296])).
% 1.72/1.90 tff(4298,plain,
% 1.72/1.90 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[3526])).
% 1.72/1.90 tff(4299,plain,
% 1.72/1.90 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4298])).
% 1.72/1.90 tff(4300,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4301,plain,
% 1.72/1.90 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4302,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4301])).
% 1.72/1.90 tff(4303,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4302, 4300])).
% 1.72/1.90 tff(4304,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4305,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 1.72/1.90 tff(4306,plain,
% 1.72/1.90 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4305, 144, 4261, 2726, 4244])).
% 1.72/1.90 tff(4307,plain,
% 1.72/1.90 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4306, 4299])).
% 1.72/1.90 tff(4308,plain,
% 1.72/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4309,plain,
% 1.72/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4310,plain,
% 1.72/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 1.72/1.90 tff(4311,plain,
% 1.72/1.90 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4310, 44])).
% 1.72/1.90 tff(4312,plain,
% 1.72/1.90 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4311, 4307, 4282])).
% 1.72/1.90 tff(4313,plain,
% 1.72/1.90 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4312, 4297])).
% 1.72/1.90 tff(4314,plain,
% 1.72/1.90 (((~![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(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(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(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4315,plain,
% 1.72/1.90 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4316,plain,
% 1.72/1.90 (((~![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(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4315])).
% 1.72/1.90 tff(4317,plain,
% 1.72/1.90 (((~![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(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4316, 4314])).
% 1.72/1.90 tff(4318,plain,
% 1.72/1.90 ((~![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(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4319,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4318, 4317])).
% 1.72/1.90 tff(4320,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4319, 333, 2737, 4313, 4295, 4271])).
% 1.72/1.90 tff(4321,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4322,plain,
% 1.72/1.90 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4321, 4222, 57, 2498, 4185, 4233, 4218, 51, 4220])).
% 1.72/1.90 tff(4323,plain,
% 1.72/1.90 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[302, 4322])).
% 1.72/1.90 tff(4324,plain,
% 1.72/1.90 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[2753, 144, 4233, 4190, 4323, 2498])).
% 1.72/1.90 tff(4325,plain,
% 1.72/1.90 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[2758, 4324, 2704])).
% 1.72/1.90 tff(4326,plain,
% 1.72/1.90 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4327,plain,
% 1.72/1.90 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4328,plain,
% 1.72/1.90 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4327])).
% 1.72/1.90 tff(4329,plain,
% 1.72/1.90 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4328, 4326])).
% 1.72/1.90 tff(4330,plain,
% 1.72/1.90 ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4331,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.72/1.90 tff(4332,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4331, 333, 4222, 4325, 51, 4188])).
% 1.72/1.90 tff(4333,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | r(s(z), elem!1) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4334,plain,
% 1.72/1.90 (~(s(z) = elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4333, 959, 285, 51, 2310, 354, 123, 606, 1])).
% 1.72/1.90 tff(4335,plain,
% 1.72/1.90 (~(elem!1 = s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[712, 4334])).
% 1.72/1.90 tff(4336,plain,
% 1.72/1.90 (b(elem!1, s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[720, 4335, 4176])).
% 1.72/1.90 tff(4337,plain,
% 1.72/1.90 (b(s(z), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[406, 4334, 2310])).
% 1.72/1.90 tff(4338,plain,
% 1.72/1.90 (b(s(elem!1), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[448, 1727, 907])).
% 1.72/1.91 tff(4339,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4340,plain,
% 1.72/1.91 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4341,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4340])).
% 1.72/1.91 tff(4342,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4341, 4339])).
% 1.72/1.91 tff(4343,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4344,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 1.72/1.91 tff(4345,plain,
% 1.72/1.91 (~b(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4344, 144, 4338, 4337, 4336])).
% 1.72/1.91 tff(4346,plain,
% 1.72/1.91 (r(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[486, 4345, 1])).
% 1.72/1.91 tff(4347,plain,
% 1.72/1.91 (~r(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1365, 4346, 354, 4006])).
% 1.72/1.91 tff(4348,plain,
% 1.72/1.91 (b(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[507, 4347])).
% 1.72/1.91 tff(4349,plain,
% 1.72/1.91 (~b(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1802, 4348, 285, 4172])).
% 1.72/1.91 tff(4350,plain,
% 1.72/1.91 (r(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[619, 4349])).
% 1.72/1.91 tff(4351,plain,
% 1.72/1.91 (~(s(s(s(z))) = elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[109, 4167])).
% 1.72/1.91 tff(4352,plain,
% 1.72/1.91 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3868, 4167, 1727])).
% 1.72/1.91 tff(4353,plain,
% 1.72/1.91 (b(s(elem!1), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[448, 3844, 1727])).
% 1.72/1.91 tff(4354,plain,
% 1.72/1.91 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3713, 4353, 81])).
% 1.72/1.91 tff(4355,plain,
% 1.72/1.91 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[787, 377, 81])).
% 1.72/1.91 tff(4356,plain,
% 1.72/1.91 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[302, 4355])).
% 1.72/1.91 tff(4357,plain,
% 1.72/1.91 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[341, 4356, 51, 323])).
% 1.72/1.91 tff(4358,plain,
% 1.72/1.91 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[319, 4357])).
% 1.72/1.91 tff(4359,plain,
% 1.72/1.91 (~r(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3291, 4358, 1, 134, 3845, 354, 1727, 4354, 670, 2322])).
% 1.72/1.91 tff(4360,plain,
% 1.72/1.91 (b(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[507, 4359])).
% 1.72/1.91 tff(4361,plain,
% 1.72/1.91 (~b(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1802, 4360, 285, 1794])).
% 1.72/1.91 tff(4362,plain,
% 1.72/1.91 (r(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[619, 4361])).
% 1.72/1.91 tff(4363,plain,
% 1.72/1.91 (~(s(s(s(z))) = elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[109, 81])).
% 1.72/1.91 tff(4364,plain,
% 1.72/1.91 (~r(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2136, 4362, 670, 2322])).
% 1.72/1.91 tff(4365,plain,
% 1.72/1.91 (b(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[704, 4364, 4363])).
% 1.72/1.91 tff(4366,plain,
% 1.72/1.91 (b(elem!1, s(z))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4358, 732])).
% 1.72/1.91 tff(4367,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.72/1.91 tff(4368,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4369,plain,
% 1.72/1.91 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4370,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4369])).
% 1.72/1.91 tff(4371,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4370, 4368])).
% 1.72/1.91 tff(4372,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4373,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 1.72/1.91 tff(4374,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4373, 144, 134, 305, 56, 4367])).
% 1.72/1.91 tff(4375,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4376,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4375, 4366, 134, 4365])).
% 1.72/1.91 tff(4377,plain,
% 1.72/1.91 (r(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2794, 4376])).
% 1.72/1.91 tff(4378,plain,
% 1.72/1.91 (~r(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3201, 4377, 670, 4362])).
% 1.72/1.91 tff(4379,plain,
% 1.72/1.91 (b(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1538, 4378, 3843])).
% 1.72/1.91 tff(4380,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3211, 144, 4353, 4360, 4379, 285, 1794])).
% 1.72/1.91 tff(4381,plain,(b(elem!1, z) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4382,plain,
% 1.72/1.91 (b(elem!1, z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4381, 4172, 285, 2311, 4337, 4167, 1, 354, 1727, 51, 4006])).
% 1.72/1.91 tff(4383,plain,
% 1.72/1.91 (r(elem!1, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3973, 4382, 51, 354, 1, 123, 902, 1727, 4352, 4337])).
% 1.72/1.91 tff(4384,plain,
% 1.72/1.91 (~r(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2393, 4383, 2311, 4346])).
% 1.72/1.91 tff(4385,plain,
% 1.72/1.91 (b(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[583, 4384])).
% 1.72/1.91 tff(4386,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3170, 144, 4348, 4385, 285])).
% 1.72/1.91 tff(4387,plain,
% 1.72/1.91 (~(s(s(s(z))) = s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1934, 4171])).
% 1.72/1.91 tff(4388,plain,
% 1.72/1.91 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1951, 44, 4387, 4386])).
% 1.72/1.91 tff(4389,plain,
% 1.72/1.91 (~r(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3181, 4388, 4346, 4383])).
% 1.72/1.91 tff(4390,plain,
% 1.72/1.91 (b(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[704, 4389, 4351])).
% 1.72/1.91 tff(4391,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4375, 4390, 4337, 4336])).
% 1.72/1.91 tff(4392,plain,
% 1.72/1.91 (r(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2794, 4391])).
% 1.72/1.91 tff(4393,plain,
% 1.72/1.91 (~r(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3201, 4392, 2311, 4350])).
% 1.72/1.91 tff(4394,plain,
% 1.72/1.91 (b(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1538, 4393, 4175])).
% 1.72/1.91 tff(4395,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3211, 144, 4338, 4348, 4394, 285, 4172])).
% 1.72/1.91 tff(4396,plain,(r(s(elem!1), elem!1) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | r(s(elem!1), s(s(s(z)))) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4397,plain,
% 1.72/1.91 (r(s(elem!1), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4396, 902, 51, 354, 1, 123, 285, 959, 606, 2310])).
% 1.72/1.91 tff(4398,plain,
% 1.72/1.91 (~r(s(z), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1235, 509, 354, 323])).
% 1.72/1.91 tff(4399,plain,
% 1.72/1.91 (b(s(z), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1244, 4398, 1229])).
% 1.72/1.91 tff(4400,plain,
% 1.72/1.91 (~r(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1365, 509, 354, 323])).
% 1.72/1.91 tff(4401,plain,
% 1.72/1.91 (b(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[486, 4400, 1])).
% 1.72/1.91 tff(4402,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4403,plain,
% 1.72/1.91 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4404,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4403])).
% 1.72/1.91 tff(4405,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4404, 4402])).
% 1.72/1.91 tff(4406,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4407,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4406, 4405])).
% 1.72/1.91 tff(4408,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4407, 144, 547, 488, 1262, 305])).
% 1.72/1.91 tff(4409,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4410,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4409, 4401, 3626, 305, 4399])).
% 1.72/1.91 tff(4411,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4412,plain,
% 1.72/1.91 (~r(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4411, 902, 1, 4336, 354, 4006, 2311, 4397])).
% 1.72/1.91 tff(4413,plain,
% 1.72/1.91 (b(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[507, 4412])).
% 1.72/1.91 tff(4414,plain,
% 1.72/1.91 (r(elem!1, z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[653, 377, 1368])).
% 1.72/1.91 tff(4415,plain,
% 1.72/1.91 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2938, 4414, 670, 51])).
% 1.72/1.91 tff(4416,plain,
% 1.72/1.91 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3398, 3396])).
% 1.72/1.91 tff(4417,plain,
% 1.72/1.91 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[130, 4416, 54])).
% 1.72/1.91 tff(4418,plain,
% 1.72/1.91 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[152, 4417, 123, 134])).
% 1.72/1.91 tff(4419,plain,
% 1.72/1.91 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[121, 4418, 3396])).
% 1.72/1.91 tff(4420,plain,
% 1.72/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3955, 4417, 305, 134])).
% 1.72/1.91 tff(4421,plain,
% 1.72/1.91 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[319, 4420])).
% 1.72/1.91 tff(4422,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2541, 4421, 4419, 670, 51])).
% 1.72/1.91 tff(4423,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4424,plain,
% 1.72/1.91 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4423, 4415, 51, 305, 134, 123, 670])).
% 1.72/1.91 tff(4425,plain,
% 1.72/1.91 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4424])).
% 1.72/1.91 tff(4426,plain,
% 1.72/1.91 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[4425])).
% 1.72/1.91 tff(4427,plain,
% 1.72/1.91 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4424])).
% 1.72/1.91 tff(4428,plain,
% 1.72/1.91 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[4427])).
% 1.72/1.91 tff(4429,plain,
% 1.72/1.91 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4428])).
% 1.72/1.91 tff(4430,plain,
% 1.72/1.91 (~(s(s(z)) = elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1446, 4429])).
% 1.72/1.91 tff(4431,plain,
% 1.72/1.91 (~(s(elem!1) = s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1508, 4430])).
% 1.72/1.91 tff(4432,plain,
% 1.72/1.91 (~(s(s(s(z))) = s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1934, 4431])).
% 1.72/1.91 tff(4433,plain,
% 1.72/1.91 (~r(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2453, 333, 435, 670, 4414])).
% 1.72/1.91 tff(4434,plain,
% 1.72/1.91 (b(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[583, 4433])).
% 1.72/1.91 tff(4435,plain,
% 1.72/1.91 (~r(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[517, 4414, 51, 435])).
% 1.72/1.91 tff(4436,plain,
% 1.72/1.91 (b(s(elem!1), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[507, 4435])).
% 1.72/1.91 tff(4437,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3170, 144, 4436, 4434, 285])).
% 1.72/1.91 tff(4438,plain,
% 1.72/1.91 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1951, 44, 4437])).
% 1.72/1.91 tff(4439,plain,
% 1.72/1.91 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4438, 4432])).
% 1.72/1.91 tff(4440,plain,
% 1.72/1.91 (b(s(elem!1), s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[965, 4431, 959])).
% 1.72/1.91 tff(4441,plain,
% 1.72/1.91 (~b(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1802, 4440, 285, 4436])).
% 1.72/1.91 tff(4442,plain,
% 1.72/1.91 (r(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[619, 4441])).
% 1.72/1.91 tff(4443,plain,
% 1.72/1.91 (~r(s(z), s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3011, 4442, 354, 4439])).
% 1.72/1.91 tff(4444,plain,
% 1.72/1.91 (b(s(z), s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[172, 4443])).
% 1.72/1.91 tff(4445,plain,
% 1.72/1.91 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4424])).
% 1.72/1.91 tff(4446,plain,
% 1.72/1.91 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4424])).
% 1.72/1.91 tff(4447,plain,
% 1.72/1.91 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.72/1.91 inference(symmetry,[status(thm)],[4446])).
% 1.72/1.91 tff(4448,plain,
% 1.72/1.91 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4447])).
% 1.72/1.91 tff(4449,plain,
% 1.72/1.91 (~(elem!1 = s(s(s(z))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[244, 4448])).
% 1.72/1.91 tff(4450,plain,
% 1.72/1.91 (~r(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2136, 4442, 670, 4414])).
% 1.72/1.91 tff(4451,plain,
% 1.72/1.91 (b(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[704, 4450, 3732])).
% 1.72/1.91 tff(4452,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4375, 4451, 134, 305])).
% 1.72/1.91 tff(4453,plain,
% 1.72/1.91 (r(s(s(s(z))), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2794, 4452])).
% 1.72/1.91 tff(4454,plain,
% 1.72/1.91 (~r(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3201, 4453, 670, 4442])).
% 1.72/1.91 tff(4455,plain,
% 1.72/1.91 (b(elem!1, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1538, 4454, 4449])).
% 1.72/1.91 tff(4456,plain,
% 1.72/1.91 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4455, 4445])).
% 1.72/1.91 tff(4457,plain,
% 1.72/1.91 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2262, 4456, 123, 4444])).
% 1.72/1.91 tff(4458,plain,
% 1.72/1.91 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1137, 4457])).
% 1.72/1.91 tff(4459,plain,
% 1.72/1.91 (r(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4458, 4426])).
% 1.72/1.91 tff(4460,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4450, 4459])).
% 1.72/1.91 tff(4461,plain,(b(elem!1, z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4462,plain,
% 1.72/1.91 (b(elem!1, z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4461, 4397, 2311, 4337, 4336, 354, 285, 959, 51, 123, 77])).
% 1.72/1.91 tff(4463,plain,
% 1.72/1.91 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[53])).
% 1.72/1.91 tff(4464,plain,
% 1.72/1.91 (~(elem!1 = s(z))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[706, 4463])).
% 1.72/1.91 tff(4465,plain,
% 1.72/1.91 (~r(elem!1, s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1863, 435, 670, 562])).
% 1.72/1.91 tff(4466,plain,
% 1.72/1.91 ((elem!1 = s(z)) | b(elem!1, s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[718, 44, 4465])).
% 1.72/1.91 tff(4467,plain,
% 1.72/1.91 (b(elem!1, s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4466, 4464])).
% 1.72/1.91 tff(4468,plain,
% 1.72/1.91 (~b(s(z), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4409, 4467, 488, 547])).
% 1.72/1.91 tff(4469,plain,
% 1.72/1.91 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1242, 44, 4468])).
% 1.72/1.91 tff(4470,plain,
% 1.72/1.91 (r(s(z), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4469, 1580])).
% 1.72/1.91 tff(4471,plain,
% 1.72/1.91 (((~![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), elem!1)) | (~r(z, s(elem!1))) | (~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(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4472,plain,
% 1.72/1.91 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4473,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4472])).
% 1.72/1.91 tff(4474,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4473, 4471])).
% 1.72/1.91 tff(4475,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4476,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 1.72/1.91 tff(4477,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4476, 333, 435, 323, 562, 4470])).
% 1.72/1.91 tff(4478,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4479,plain,
% 1.72/1.91 (~b(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4478, 3638, 670, 1, 323, 706, 547, 435])).
% 1.72/1.91 tff(4480,plain,
% 1.72/1.91 (r(s(elem!1), s(z))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[486, 4479, 1])).
% 1.72/1.91 tff(4481,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1355, 333, 354, 323, 4480, 3638])).
% 1.72/1.91 tff(4482,plain,((~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4483,plain,
% 1.72/1.91 (~b(elem!1, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4482, 4397, 4006, 1, 2311, 4334, 354, 4462, 4413])).
% 1.72/1.91 tff(4484,plain,
% 1.72/1.91 (r(elem!1, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[560, 4483, 902])).
% 1.72/1.91 tff(4485,plain,
% 1.72/1.91 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2492, 4484, 2311, 51])).
% 1.72/1.91 tff(4486,plain,
% 1.72/1.91 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4423, 4485, 51, 4336, 4337, 123, 2311])).
% 1.72/1.91 tff(4487,plain,
% 1.72/1.91 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4486])).
% 1.72/1.91 tff(4488,plain,
% 1.72/1.91 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[4487])).
% 1.72/1.91 tff(4489,plain,
% 1.72/1.91 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4488])).
% 1.72/1.91 tff(4490,plain,
% 1.72/1.91 (~(s(s(z)) = elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1446, 4489])).
% 1.72/1.91 tff(4491,plain,
% 1.72/1.91 (~(s(elem!1) = s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1508, 4490])).
% 1.72/1.91 tff(4492,plain,
% 1.72/1.91 (b(s(elem!1), s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[965, 4491, 959])).
% 1.72/1.91 tff(4493,plain,
% 1.72/1.91 (~b(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1802, 4492, 285, 4413])).
% 1.72/1.91 tff(4494,plain,
% 1.72/1.91 (r(z, s(s(s(z))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[619, 4493])).
% 1.72/1.91 tff(4495,plain,
% 1.72/1.91 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4486])).
% 1.72/1.91 tff(4496,plain,
% 1.72/1.91 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[4495])).
% 1.72/1.91 tff(4497,plain,
% 1.72/1.91 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(z))), s(elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.91 tff(4498,plain,
% 1.72/1.91 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.91 tff(4499,plain,
% 1.72/1.91 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(z))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4498, 997])).
% 1.72/1.91 tff(4500,plain,
% 1.72/1.91 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.91 inference(symmetry,[status(thm)],[4499])).
% 1.72/1.91 tff(4501,plain,
% 1.72/1.91 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4500])).
% 1.72/1.91 tff(4502,plain,
% 1.72/1.91 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4491, 4501])).
% 1.72/1.91 tff(4503,plain,
% 1.72/1.91 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.91 tff(4504,plain,
% 1.72/1.91 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.91 inference(symmetry,[status(thm)],[4503])).
% 1.72/1.91 tff(4505,plain,
% 1.72/1.91 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[116, 4486])).
% 1.72/1.91 tff(4506,plain,
% 1.72/1.91 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3851, 4505, 4484])).
% 1.72/1.91 tff(4507,plain,
% 1.72/1.91 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2623, 4486, 4397])).
% 1.72/1.91 tff(4508,plain,
% 1.72/1.91 (~r(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3607, 4507, 51, 4506])).
% 1.72/1.91 tff(4509,plain,
% 1.72/1.91 (b(z, s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[583, 4508])).
% 1.72/1.91 tff(4510,plain,
% 1.72/1.92 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4509, 4504])).
% 1.72/1.92 tff(4511,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.92 tff(4512,plain,
% 1.72/1.92 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.72/1.92 inference(symmetry,[status(thm)],[4511])).
% 1.72/1.92 tff(4513,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4413, 4512])).
% 1.72/1.92 tff(4514,plain,
% 1.72/1.92 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1348, 144, 285])).
% 1.72/1.92 tff(4515,plain,
% 1.72/1.92 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4514, 4513, 4510])).
% 1.72/1.92 tff(4516,plain,
% 1.72/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4517,plain,
% 1.72/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4518,plain,
% 1.72/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4517, 4516])).
% 1.72/1.92 tff(4519,plain,
% 1.72/1.92 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4518, 44, 4515])).
% 1.72/1.92 tff(4520,plain,
% 1.72/1.92 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4519, 4502])).
% 1.72/1.92 tff(4521,plain,
% 1.72/1.92 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4520, 4497])).
% 1.72/1.92 tff(4522,plain,
% 1.72/1.92 (~r(s(z), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3011, 4521, 354, 4494])).
% 1.72/1.92 tff(4523,plain,
% 1.72/1.92 (b(s(z), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[172, 4522])).
% 1.72/1.92 tff(4524,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.92 tff(4525,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4524])).
% 1.72/1.92 tff(4526,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4507, 4525])).
% 1.72/1.92 tff(4527,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4496])).
% 1.72/1.92 tff(4528,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4527])).
% 1.72/1.92 tff(4529,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4506, 4528])).
% 1.72/1.92 tff(4530,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4531,plain,
% 1.72/1.92 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4532,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4531])).
% 1.72/1.92 tff(4533,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4532, 4530])).
% 1.72/1.92 tff(4534,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4535,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4534, 4533])).
% 1.72/1.92 tff(4536,plain,
% 1.72/1.92 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4535, 333, 4529, 4526, 4520])).
% 1.72/1.92 tff(4537,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1137, 4536])).
% 1.72/1.92 tff(4538,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4539,plain,
% 1.72/1.92 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4540,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4539])).
% 1.72/1.92 tff(4541,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4540, 4538])).
% 1.72/1.92 tff(4542,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4543,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 1.72/1.92 tff(4544,plain,
% 1.72/1.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4543, 333, 4529, 4526, 4520])).
% 1.72/1.92 tff(4545,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[249, 4544])).
% 1.72/1.92 tff(4546,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2262, 4545, 4537, 123, 4523])).
% 1.72/1.92 tff(4547,plain,((elem!1 = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(4548,plain,
% 1.72/1.92 (elem!1 = s(elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4547, 959, 354, 285, 123, 51, 1, 606, 2310])).
% 1.72/1.92 tff(4549,plain,
% 1.72/1.92 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4548])).
% 1.72/1.92 tff(4550,plain,
% 1.72/1.92 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), elem!1)),
% 1.72/1.92 inference(symmetry,[status(thm)],[4549])).
% 1.72/1.92 tff(4551,plain,
% 1.72/1.92 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4550])).
% 1.72/1.92 tff(4552,plain,
% 1.72/1.92 (~r(s(elem!1), elem!1)),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[3482, 4551])).
% 1.72/1.92 tff(4553,plain,
% 1.72/1.92 (s(elem!1) = elem!1),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1569, 4548])).
% 1.72/1.92 tff(4554,plain,
% 1.72/1.92 (s(s(s(elem!1))) = elem!1),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2482, 4548])).
% 1.72/1.92 tff(4555,plain,
% 1.72/1.92 (s(elem!1) = s(s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2584, 4554, 4548])).
% 1.72/1.92 tff(4556,plain,
% 1.72/1.92 (s(s(s(elem!1))) = s(elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3254, 4555])).
% 1.72/1.92 tff(4557,plain,
% 1.72/1.92 (~(elem!1 = s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3246, 4556, 4334])).
% 1.72/1.92 tff(4558,plain,
% 1.72/1.92 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1565, 4557, 4553])).
% 1.72/1.92 tff(4559,plain,
% 1.72/1.92 (r(s(elem!1), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4166, 4558, 123, 285, 959, 1, 606, 51, 2310, 354])).
% 1.72/1.92 tff(4560,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4559, 4552])).
% 1.72/1.92 tff(4561,plain,(r(s(elem!1), s(s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(z)) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(4562,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4561, 285, 123, 1, 606, 51, 2310, 354])).
% 1.72/1.92 tff(4563,plain,
% 1.72/1.92 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[57])).
% 1.72/1.92 tff(4564,plain,
% 1.72/1.92 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4563])).
% 1.72/1.92 tff(4565,plain,
% 1.72/1.92 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[2496])).
% 1.72/1.92 tff(4566,plain,
% 1.72/1.92 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4565])).
% 1.72/1.92 tff(4567,plain,
% 1.72/1.92 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4566, 4564])).
% 1.72/1.92 tff(4568,plain,
% 1.72/1.92 (r(s(elem!1), s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1686, 2849])).
% 1.72/1.92 tff(4569,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[130, 3673, 4182])).
% 1.72/1.92 tff(4570,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3934, 4569, 123, 451, 57])).
% 1.72/1.92 tff(4571,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.72/1.92 tff(4572,plain,
% 1.72/1.92 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(symmetry,[status(thm)],[1218])).
% 1.72/1.92 tff(4573,plain,
% 1.72/1.92 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(transitivity,[status(thm)],[2460, 4572])).
% 1.72/1.92 tff(4574,plain,
% 1.72/1.92 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4573])).
% 1.72/1.92 tff(4575,plain,
% 1.72/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[107, 4574])).
% 1.72/1.92 tff(4576,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[542, 3491, 537])).
% 1.72/1.92 tff(4577,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[555, 4576, 3716, 451, 133])).
% 1.72/1.92 tff(4578,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(4579,plain,
% 1.72/1.92 (~r(s(elem!1), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4578, 4569, 451, 2698, 902, 51, 4570, 670, 408])).
% 1.72/1.92 tff(4580,plain,
% 1.72/1.92 (b(s(elem!1), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[507, 4579])).
% 1.72/1.92 tff(4581,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[3525])).
% 1.72/1.92 tff(4582,plain,
% 1.72/1.92 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4581])).
% 1.72/1.92 tff(4583,plain,
% 1.72/1.92 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4582])).
% 1.72/1.92 tff(4584,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[2496])).
% 1.72/1.92 tff(4585,plain,
% 1.72/1.92 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[555, 547, 451, 4569])).
% 1.72/1.92 tff(4586,plain,
% 1.72/1.92 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[542, 4585, 2698])).
% 1.72/1.92 tff(4587,plain,
% 1.72/1.92 (~r(z, s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3607, 4586, 51, 4570])).
% 1.72/1.92 tff(4588,plain,
% 1.72/1.92 (b(z, s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[583, 4587])).
% 1.72/1.92 tff(4589,plain,
% 1.72/1.92 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2733, 144, 491, 4588, 2498])).
% 1.72/1.92 tff(4590,plain,
% 1.72/1.92 (r(s(s(elem!1)), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1283, 4589, 2854])).
% 1.72/1.92 tff(4591,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), 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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4592,plain,
% 1.72/1.92 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4593,plain,
% 1.72/1.92 (((~![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(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), 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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4592])).
% 1.72/1.92 tff(4594,plain,
% 1.72/1.92 (((~![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(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), 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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4593, 4591])).
% 1.72/1.92 tff(4595,plain,
% 1.72/1.92 ((~![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(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4596,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 1.72/1.92 tff(4597,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4596, 333, 4590, 4571, 4586])).
% 1.72/1.92 tff(4598,plain,
% 1.72/1.92 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4597, 4024])).
% 1.72/1.92 tff(4599,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1137, 4598])).
% 1.72/1.92 tff(4600,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4599, 4584])).
% 1.72/1.92 tff(4601,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4602,plain,
% 1.72/1.92 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4603,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4602])).
% 1.72/1.92 tff(4604,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4603, 4601])).
% 1.72/1.92 tff(4605,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4606,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 1.72/1.92 tff(4607,plain,
% 1.72/1.92 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4606, 144, 4569, 2692, 4600])).
% 1.72/1.92 tff(4608,plain,
% 1.72/1.92 (r(s(s(elem!1)), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1260, 44, 4575, 4607])).
% 1.72/1.92 tff(4609,plain,
% 1.72/1.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4281, 2854])).
% 1.72/1.92 tff(4610,plain,
% 1.72/1.92 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4590, 4010])).
% 1.72/1.92 tff(4611,plain,
% 1.72/1.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3662, 4590, 4570, 4586])).
% 1.72/1.92 tff(4612,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2758, 4611, 2704])).
% 1.72/1.92 tff(4613,plain,
% 1.72/1.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4612, 4019])).
% 1.72/1.92 tff(4614,plain,
% 1.72/1.92 (~b(s(z), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2262, 4599, 123, 4613])).
% 1.72/1.92 tff(4615,plain,
% 1.72/1.92 (r(s(z), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[172, 4614])).
% 1.72/1.92 tff(4616,plain,
% 1.72/1.92 (~r(z, s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3011, 4615, 354, 4610])).
% 1.72/1.92 tff(4617,plain,
% 1.72/1.92 (b(z, s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[619, 4616])).
% 1.72/1.92 tff(4618,plain,
% 1.72/1.92 (b(z, s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2828, 4617, 57])).
% 1.72/1.92 tff(4619,plain,
% 1.72/1.92 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4284])).
% 1.72/1.92 tff(4620,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.92 tff(4621,plain,
% 1.72/1.92 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4620, 4275])).
% 1.72/1.92 tff(4622,plain,
% 1.72/1.92 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4272])).
% 1.72/1.92 tff(4623,plain,
% 1.72/1.92 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4622])).
% 1.72/1.92 tff(4624,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.72/1.92 inference(monotonicity,[status(thm)],[3525])).
% 1.72/1.92 tff(4625,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 1.72/1.92 inference(transitivity,[status(thm)],[3490, 4624])).
% 1.72/1.92 tff(4626,plain,
% 1.72/1.92 (r(s(s(s(s(z)))), elem!1)),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1024, 4625])).
% 1.72/1.92 tff(4627,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.72/1.92 tff(4628,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(4629,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4630,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4629, 4628])).
% 1.72/1.93 tff(4631,plain,
% 1.72/1.93 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4630, 333, 408, 4627, 4626])).
% 1.72/1.93 tff(4632,plain,
% 1.72/1.93 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4631, 4623])).
% 1.72/1.93 tff(4633,plain,
% 1.72/1.93 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1116, 4632, 4621])).
% 1.72/1.93 tff(4634,plain,
% 1.72/1.93 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4633, 4619])).
% 1.72/1.93 tff(4635,plain,
% 1.72/1.93 (((~![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(elem!1, z)) | (~r(z, s(s(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(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4636,plain,
% 1.72/1.93 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4637,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~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, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4636])).
% 1.72/1.93 tff(4638,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~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, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.72/1.93 inference(transitivity,[status(thm)],[4637, 4635])).
% 1.72/1.93 tff(4639,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4640,plain,
% 1.72/1.93 ((~![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(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 1.72/1.93 tff(4641,plain,
% 1.72/1.93 (~r(z, s(s(s(s(z)))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4640, 333, 670, 408, 4626])).
% 1.72/1.93 tff(4642,plain,
% 1.72/1.93 (b(z, s(s(s(s(z)))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4260, 4641])).
% 1.72/1.93 tff(4643,plain,
% 1.72/1.93 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.93 inference(symmetry,[status(thm)],[4298])).
% 1.72/1.93 tff(4644,plain,
% 1.72/1.93 (r(s(s(s(elem!1))), elem!1)),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1024, 3490])).
% 1.72/1.93 tff(4645,plain,
% 1.72/1.93 (((~![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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4646,plain,
% 1.72/1.93 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4647,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4646])).
% 1.72/1.93 tff(4648,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.72/1.93 inference(transitivity,[status(thm)],[4647, 4645])).
% 1.72/1.93 tff(4649,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4650,plain,
% 1.72/1.93 ((~![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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4649, 4648])).
% 1.72/1.93 tff(4651,plain,
% 1.72/1.93 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4650, 333])).
% 1.72/1.93 tff(4652,plain,
% 1.72/1.93 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4651, 4644, 408, 4627])).
% 1.72/1.93 tff(4653,plain,
% 1.72/1.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4311, 4652, 4620])).
% 1.72/1.93 tff(4654,plain,
% 1.72/1.93 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4653, 4643])).
% 1.72/1.93 tff(4655,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4656,plain,
% 1.72/1.93 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4657,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4656])).
% 1.72/1.93 tff(4658,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[4657, 4655])).
% 1.72/1.93 tff(4659,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4660,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 1.72/1.93 tff(4661,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4660, 144, 2811, 4654, 4642, 4634])).
% 1.72/1.93 tff(4662,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(4663,plain,
% 1.72/1.93 (~r(s(s(s(elem!1))), s(z))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4662, 4618, 57, 4609, 408, 4608, 670])).
% 1.72/1.93 tff(4664,plain,
% 1.72/1.93 (b(s(s(s(elem!1))), s(z))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1101, 4663])).
% 1.72/1.93 tff(4665,plain,
% 1.72/1.93 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[3588, 4664, 57])).
% 1.72/1.93 tff(4666,plain,
% 1.72/1.93 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[3552, 144, 4665, 4569, 2692])).
% 1.72/1.93 tff(4667,plain,
% 1.72/1.93 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[3556, 44, 196, 4666])).
% 1.72/1.93 tff(4668,plain,
% 1.72/1.93 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[294, 4617, 285, 4613])).
% 1.72/1.93 tff(4669,plain,
% 1.72/1.93 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[302, 4668])).
% 1.72/1.93 tff(4670,plain,
% 1.72/1.93 (((~![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(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4671,plain,
% 1.72/1.93 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4672,plain,
% 1.72/1.93 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4671])).
% 1.72/1.93 tff(4673,plain,
% 1.72/1.93 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[4672, 4670])).
% 1.72/1.93 tff(4674,plain,
% 1.72/1.93 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4675,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 1.72/1.93 tff(4676,plain,
% 1.72/1.93 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4675, 333, 4669, 4570, 4667])).
% 1.72/1.93 tff(4677,plain,
% 1.72/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4676, 4583])).
% 1.72/1.93 tff(4678,plain,
% 1.72/1.93 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[57])).
% 1.72/1.93 tff(4679,plain,
% 1.72/1.93 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.72/1.93 inference(symmetry,[status(thm)],[4678])).
% 1.72/1.93 tff(4680,plain,
% 1.72/1.93 (b(s(z), s(elem!1))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[547, 4679])).
% 1.72/1.93 tff(4681,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1239, 4680])).
% 1.72/1.93 tff(4682,plain,((~b(elem!1, s(elem!1))) | b(s(z), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(4683,plain,
% 1.72/1.93 (b(s(z), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4682, 547, 57])).
% 1.72/1.93 tff(4684,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.72/1.93 tff(4685,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4686,plain,
% 1.72/1.93 (((~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(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4687,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4686])).
% 1.72/1.93 tff(4688,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[4687, 4685])).
% 1.72/1.93 tff(4689,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(4690,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 1.72/1.93 tff(4691,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4690, 144, 3584, 488, 1262, 4684])).
% 1.72/1.93 tff(4692,plain,((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(4693,plain,
% 1.72/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4692, 4664, 3924, 4683])).
% 1.72/1.93 tff(4694,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.72/1.93 tff(4695,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.72/1.93 tff(4696,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[3130, 44, 3127, 4695, 4694])).
% 1.72/1.93 tff(4697,plain,(b(s(s(s(elem!1))), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(4698,plain,
% 1.72/1.93 (r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4697, 4693, 3523])).
% 1.72/1.93 tff(4699,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4698, 4677])).
% 1.72/1.93 tff(4700,plain,((~b(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(4701,plain,
% 1.72/1.93 (~b(elem!1, s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4700, 408, 57, 670, 285, 354, 123, 4571, 2727, 4580, 51, 451])).
% 1.72/1.93 tff(4702,plain,
% 1.72/1.93 (r(elem!1, s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[560, 4701, 902])).
% 1.72/1.93 tff(4703,plain,
% 1.72/1.93 (~r(z, s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[4052, 4702, 670, 4570])).
% 1.72/1.93 tff(4704,plain,
% 1.72/1.93 (b(z, s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[583, 4703])).
% 1.72/1.93 tff(4705,plain,
% 1.72/1.93 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[2733, 144, 4580, 4704, 2498])).
% 1.72/1.93 tff(4706,plain,
% 1.72/1.93 (r(s(s(elem!1)), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1283, 4705, 2727])).
% 1.72/1.93 tff(4707,plain,
% 1.72/1.93 (((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4708,plain,
% 1.72/1.93 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(4709,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[4708])).
% 1.72/1.93 tff(4710,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4709, 4707])).
% 1.72/1.94 tff(4711,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4712,plain,
% 1.72/1.94 ((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 1.72/1.94 tff(4713,plain,
% 1.72/1.94 (~r(s(s(elem!1)), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4712, 333, 4702, 4706, 4571])).
% 1.72/1.94 tff(4714,plain,
% 1.72/1.94 (b(s(s(elem!1)), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1260, 44, 4713, 4575])).
% 1.72/1.94 tff(4715,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4716,plain,
% 1.72/1.94 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4717,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4716])).
% 1.72/1.94 tff(4718,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4717, 4715])).
% 1.72/1.94 tff(4719,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4720,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4719, 4718])).
% 1.72/1.94 tff(4721,plain,
% 1.72/1.94 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4720, 333, 4702, 4706, 4571])).
% 1.72/1.94 tff(4722,plain,
% 1.72/1.94 (b(elem!1, s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2522, 4721, 2462])).
% 1.72/1.94 tff(4723,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4724,plain,
% 1.72/1.94 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4725,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4724])).
% 1.72/1.94 tff(4726,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4725, 4723])).
% 1.72/1.94 tff(4727,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4728,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4727, 4726])).
% 1.72/1.94 tff(4729,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4728, 144, 4722, 4569, 4714])).
% 1.72/1.94 tff(4730,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2758, 4729, 2704])).
% 1.72/1.94 tff(4731,plain,
% 1.72/1.94 (((~![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(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4732,plain,
% 1.72/1.94 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4733,plain,
% 1.72/1.94 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), 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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4732])).
% 1.72/1.94 tff(4734,plain,
% 1.72/1.94 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), 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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4733, 4731])).
% 1.72/1.94 tff(4735,plain,
% 1.72/1.94 ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4736,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 1.72/1.94 tff(4737,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4736, 333, 4706, 4730, 4571, 4570])).
% 1.72/1.94 tff(4738,plain,((~r(elem!1, z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(4739,plain,
% 1.72/1.94 (~r(elem!1, z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4738, 4568, 670, 902, 57, 285, 354, 123, 51, 451])).
% 1.72/1.94 tff(4740,plain,
% 1.72/1.94 (b(elem!1, z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1380, 4739, 1368])).
% 1.72/1.94 tff(4741,plain,
% 1.72/1.94 (b(s(z), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3965, 4740, 57])).
% 1.72/1.94 tff(4742,plain,
% 1.72/1.94 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4003, 525, 606, 51, 1368, 670])).
% 1.72/1.94 tff(4743,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3613, 525, 57, 51, 489, 670, 1237, 451, 132])).
% 1.72/1.94 tff(4744,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[130, 4743, 4742, 4182])).
% 1.72/1.94 tff(4745,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(4746,plain,
% 1.72/1.94 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4745, 57, 51, 4741, 670, 1237, 451, 2692, 606, 1368])).
% 1.72/1.94 tff(4747,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3934, 4746, 123, 451, 57])).
% 1.72/1.94 tff(4748,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[130, 4747, 4182])).
% 1.72/1.94 tff(4749,plain,
% 1.72/1.94 (~r(elem!1, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2492, 4748, 670, 51])).
% 1.72/1.94 tff(4750,plain,
% 1.72/1.94 (b(elem!1, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[560, 4749, 902])).
% 1.72/1.94 tff(4751,plain,
% 1.72/1.94 (b(s(z), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4682, 4750, 57])).
% 1.72/1.94 tff(4752,plain,
% 1.72/1.94 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.72/1.94 inference(symmetry,[status(thm)],[2666])).
% 1.72/1.94 tff(4753,plain,
% 1.72/1.94 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.72/1.94 inference(symmetry,[status(thm)],[2663])).
% 1.72/1.94 tff(4754,plain,
% 1.72/1.94 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4753, 4752])).
% 1.72/1.94 tff(4755,plain,
% 1.72/1.94 (b(s(s(z)), s(z))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[451, 4754])).
% 1.72/1.94 tff(4756,plain,
% 1.72/1.94 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2674, 4746, 57])).
% 1.72/1.94 tff(4757,plain,
% 1.72/1.94 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1451, 4756])).
% 1.72/1.94 tff(4758,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1425, 4757, 123, 4755])).
% 1.72/1.94 tff(4759,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[319, 4758])).
% 1.72/1.94 tff(4760,plain,
% 1.72/1.94 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[2696, 175])).
% 1.72/1.94 tff(4761,plain,
% 1.72/1.94 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4760])).
% 1.72/1.94 tff(4762,plain,
% 1.72/1.94 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1446, 4761])).
% 1.72/1.94 tff(4763,plain,
% 1.72/1.94 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[472, 4746, 4762])).
% 1.72/1.94 tff(4764,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3222, 4751, 4741, 123, 4763])).
% 1.72/1.94 tff(4765,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[302, 4764])).
% 1.72/1.94 tff(4766,plain,
% 1.72/1.94 (~r(s(z), s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[362, 4765, 4759, 354])).
% 1.72/1.94 tff(4767,plain,
% 1.72/1.94 (b(s(z), s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[172, 4766])).
% 1.72/1.94 tff(4768,plain,
% 1.72/1.94 (~b(s(elem!1), s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2631, 4767, 4741, 285, 4751])).
% 1.72/1.94 tff(4769,plain,
% 1.72/1.94 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[472, 466, 4762])).
% 1.72/1.94 tff(4770,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3934, 466, 123, 451, 57])).
% 1.72/1.94 tff(4771,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[130, 4770, 4182])).
% 1.72/1.94 tff(4772,plain,
% 1.72/1.94 (~r(elem!1, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2492, 4771, 670, 51])).
% 1.72/1.94 tff(4773,plain,
% 1.72/1.94 (b(elem!1, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[560, 4772, 902])).
% 1.72/1.94 tff(4774,plain,
% 1.72/1.94 (b(s(z), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4682, 4773, 57])).
% 1.72/1.94 tff(4775,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[3222, 4774, 489, 123, 4769])).
% 1.72/1.94 tff(4776,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[302, 4775])).
% 1.72/1.94 tff(4777,plain,
% 1.72/1.94 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4778,plain,
% 1.72/1.94 ((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4779,plain,
% 1.72/1.94 ((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4778, 4777])).
% 1.72/1.94 tff(4780,plain,
% 1.72/1.94 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4779, 333, 670, 509, 4776])).
% 1.72/1.94 tff(4781,plain,
% 1.72/1.94 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[542, 4780, 2698])).
% 1.72/1.94 tff(4782,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4783,plain,
% 1.72/1.94 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4784,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4783])).
% 1.72/1.94 tff(4785,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4784, 4782])).
% 1.72/1.94 tff(4786,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4787,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4786, 4785])).
% 1.72/1.94 tff(4788,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4787, 144, 4773, 2692, 4781, 4769])).
% 1.72/1.94 tff(4789,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(4790,plain,
% 1.72/1.94 (~r(s(elem!1), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4789, 4746, 670, 4741, 123, 57, 902, 51, 451])).
% 1.72/1.94 tff(4791,plain,
% 1.72/1.94 (b(s(elem!1), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[507, 4790])).
% 1.72/1.94 tff(4792,plain,
% 1.72/1.94 (~b(z, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[949, 4750, 4740, 4791])).
% 1.72/1.94 tff(4793,plain,
% 1.72/1.94 (r(z, s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[583, 4792])).
% 1.72/1.94 tff(4794,plain,
% 1.72/1.94 (~(s(elem!1) = s(s(s(z))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[2727, 2506])).
% 1.72/1.94 tff(4795,plain,
% 1.72/1.94 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.94 inference(symmetry,[status(thm)],[2])).
% 1.72/1.94 tff(4796,plain,
% 1.72/1.94 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.94 inference(transitivity,[status(thm)],[3514, 4795])).
% 1.72/1.94 tff(4797,plain,
% 1.72/1.94 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4796])).
% 1.72/1.94 tff(4798,plain,
% 1.72/1.94 (~(s(s(s(z))) = elem!1)),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[166, 4797])).
% 1.72/1.94 tff(4799,plain,
% 1.72/1.94 (r(s(elem!1), s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[965, 960, 901])).
% 1.72/1.94 tff(4800,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(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(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4801,plain,
% 1.72/1.94 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(4802,plain,
% 1.72/1.94 (((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[4801])).
% 1.72/1.94 tff(4803,plain,
% 1.72/1.94 (((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[4802, 4800])).
% 1.72/1.94 tff(4804,plain,
% 1.72/1.94 ((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(4805,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z)))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 1.72/1.94 tff(4806,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4805, 333, 562, 623, 4799, 3298])).
% 1.72/1.94 tff(4807,plain,((s(elem!1) = s(s(s(z)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | b(s(s(s(z))), s(elem!1)) | b(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(4808,plain,
% 1.72/1.94 (b(s(s(s(z))), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[4807, 623, 960, 562, 901])).
% 1.72/1.94 tff(4809,plain,
% 1.72/1.94 (~r(s(s(s(z))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1929, 623, 1686, 562])).
% 1.72/1.94 tff(4810,plain,
% 1.72/1.94 (b(s(s(s(z))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[704, 4809, 698])).
% 1.72/1.94 tff(4811,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.72/1.94 tff(4812,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4813,plain,
% 1.72/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4814,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4813])).
% 1.72/1.95 tff(4815,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[4814, 4812])).
% 1.72/1.95 tff(4816,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(4817,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 1.72/1.95 tff(4818,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4817, 144, 547, 451, 4367, 4811])).
% 1.72/1.95 tff(4819,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4820,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4819, 4810, 4808, 451, 547])).
% 1.72/1.95 tff(4821,plain,((~r(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(elem!1))) | b(s(elem!1), s(s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4822,plain,
% 1.72/1.95 (~r(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4821, 4750, 451, 4798, 4794, 4793, 4768, 1686])).
% 1.72/1.95 tff(4823,plain,
% 1.72/1.95 (b(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[619, 4822])).
% 1.72/1.95 tff(4824,plain,
% 1.72/1.95 (b(z, s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2828, 4823, 57])).
% 1.72/1.95 tff(4825,plain,
% 1.72/1.95 (~b(elem!1, s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2821, 4824, 285, 4740, 57])).
% 1.72/1.95 tff(4826,plain,
% 1.72/1.95 (r(elem!1, s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2522, 4825, 2462])).
% 1.72/1.95 tff(4827,plain,
% 1.72/1.95 (r(s(z), s(s(s(z))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4826, 4567])).
% 1.72/1.95 tff(4828,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4766, 4827])).
% 1.72/1.95 tff(4829,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4830,plain,
% 1.72/1.95 (~(s(z) = elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4829, 1728, 285, 4562, 354, 123, 902, 2311, 51, 1229, 606, 77])).
% 1.72/1.95 tff(4831,plain,
% 1.72/1.95 (b(s(z), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[406, 4830, 2310])).
% 1.72/1.95 tff(4832,plain,
% 1.72/1.95 (~(elem!1 = s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[712, 4830])).
% 1.72/1.95 tff(4833,plain,
% 1.72/1.95 (b(elem!1, z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1380, 1378, 77])).
% 1.72/1.95 tff(4834,plain,
% 1.72/1.95 (b(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3998, 466, 51, 123, 1727, 354, 1, 902, 670, 2310, 114])).
% 1.72/1.95 tff(4835,plain,
% 1.72/1.95 (~b(elem!1, z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3973, 3350, 51, 354, 1, 123, 1727, 902, 134, 466])).
% 1.72/1.95 tff(4836,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1380, 4835, 4000, 77])).
% 1.72/1.95 tff(4837,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4838,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4837, 466, 354, 1, 123, 1727, 902, 134, 51, 670])).
% 1.72/1.95 tff(4839,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[130, 4838, 114])).
% 1.72/1.95 tff(4840,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2297, 4839, 4834, 134, 624, 123])).
% 1.72/1.95 tff(4841,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4842,plain,
% 1.72/1.95 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4841, 114, 624, 123, 134, 51, 1727, 354, 1, 902, 2311, 2310])).
% 1.72/1.95 tff(4843,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4003, 4842, 606, 51, 77, 2311])).
% 1.72/1.95 tff(4844,plain,
% 1.72/1.95 (~b(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4423, 4843, 51, 453, 134, 123, 2311])).
% 1.72/1.95 tff(4845,plain,
% 1.72/1.95 (r(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[720, 4844, 714])).
% 1.72/1.95 tff(4846,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[130, 4843, 114])).
% 1.72/1.95 tff(4847,plain,
% 1.72/1.95 (~b(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2297, 4846, 134, 624, 123])).
% 1.72/1.95 tff(4848,plain,
% 1.72/1.95 (r(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[348, 4847])).
% 1.72/1.95 tff(4849,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[727, 4848, 4845, 354, 2311])).
% 1.72/1.95 tff(4850,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(z))) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4851,plain,
% 1.72/1.95 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4850, 4833, 4832, 4831, 354, 123, 51, 606, 1727, 1, 902, 2310])).
% 1.72/1.95 tff(4852,plain,
% 1.72/1.95 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3868, 4851, 1727])).
% 1.72/1.95 tff(4853,plain,
% 1.72/1.95 (r(elem!1, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3973, 4833, 51, 354, 1, 123, 1727, 902, 134, 466])).
% 1.72/1.95 tff(4854,plain,
% 1.72/1.95 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3398, 81])).
% 1.72/1.95 tff(4855,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2319, 1230, 354, 51])).
% 1.72/1.95 tff(4856,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[319, 4855])).
% 1.72/1.95 tff(4857,plain,
% 1.72/1.95 (b(elem!1, s(z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4856, 732])).
% 1.72/1.95 tff(4858,plain,
% 1.72/1.95 (~b(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4344, 144, 451, 134, 4857])).
% 1.72/1.95 tff(4859,plain,
% 1.72/1.95 (r(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[486, 4858, 1])).
% 1.72/1.95 tff(4860,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2918, 333, 354, 4859, 509, 1230])).
% 1.72/1.95 tff(4861,plain,((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4862,plain,
% 1.72/1.95 (~r(s(z), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4861, 509, 354, 1, 451, 134, 81, 51])).
% 1.72/1.95 tff(4863,plain,
% 1.72/1.95 (b(s(z), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1244, 4862, 1229])).
% 1.72/1.95 tff(4864,plain,
% 1.72/1.95 (~b(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2569, 4863, 123, 1727, 4854, 1378])).
% 1.72/1.95 tff(4865,plain,
% 1.72/1.95 (r(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[348, 4864])).
% 1.72/1.95 tff(4866,plain,
% 1.72/1.95 (~r(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[727, 4865, 354, 670])).
% 1.72/1.95 tff(4867,plain,
% 1.72/1.95 (b(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[720, 4866, 714])).
% 1.72/1.95 tff(4868,plain,
% 1.72/1.95 (~r(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1365, 4865, 354, 509])).
% 1.72/1.95 tff(4869,plain,
% 1.72/1.95 (b(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[486, 4868, 1])).
% 1.72/1.95 tff(4870,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4344, 144, 451, 134, 4869, 4867])).
% 1.72/1.95 tff(4871,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | r(elem!1, z) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4872,plain,
% 1.72/1.95 (~r(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4871, 1378, 134, 1, 714, 354, 670, 123, 1727, 1728, 81, 51])).
% 1.72/1.95 tff(4873,plain,
% 1.72/1.95 (b(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[507, 4872])).
% 1.72/1.95 tff(4874,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4875,plain,
% 1.72/1.95 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4876,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4875])).
% 1.72/1.95 tff(4877,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[4876, 4874])).
% 1.72/1.95 tff(4878,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(4879,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4878, 4877])).
% 1.72/1.95 tff(4880,plain,
% 1.72/1.95 (~b(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4879, 144, 1728, 4833, 4873, 134])).
% 1.72/1.95 tff(4881,plain,
% 1.72/1.95 (r(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[486, 4880, 1])).
% 1.72/1.95 tff(4882,plain,
% 1.72/1.95 (~r(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2393, 4881, 670, 4853])).
% 1.72/1.95 tff(4883,plain,
% 1.72/1.95 (b(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[583, 4882])).
% 1.72/1.95 tff(4884,plain,
% 1.72/1.95 (~b(s(s(s(z))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3170, 144, 4873, 4883, 285])).
% 1.72/1.95 tff(4885,plain,
% 1.72/1.95 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 4884])).
% 1.72/1.95 tff(4886,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2558, 1378, 81])).
% 1.72/1.95 tff(4887,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[302, 4886])).
% 1.72/1.95 tff(4888,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4889,plain,
% 1.72/1.95 (((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4890,plain,
% 1.72/1.95 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4889])).
% 1.72/1.95 tff(4891,plain,
% 1.72/1.95 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[4890, 4888])).
% 1.72/1.95 tff(4892,plain,
% 1.72/1.95 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(4893,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4892, 4891])).
% 1.72/1.95 tff(4894,plain,
% 1.72/1.95 (~r(elem!1, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4893, 333, 4853, 4881, 4885])).
% 1.72/1.95 tff(4895,plain,
% 1.72/1.95 (b(elem!1, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1538, 4894, 3843])).
% 1.72/1.95 tff(4896,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4895, 1523])).
% 1.72/1.95 tff(4897,plain,
% 1.72/1.95 (~b(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[294, 4896, 285, 4887])).
% 1.72/1.95 tff(4898,plain,
% 1.72/1.95 (r(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[619, 4897])).
% 1.72/1.95 tff(4899,plain,
% 1.72/1.95 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[81])).
% 1.72/1.95 tff(4900,plain,
% 1.72/1.95 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(symmetry,[status(thm)],[4899])).
% 1.72/1.95 tff(4901,plain,
% 1.72/1.95 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4900])).
% 1.72/1.95 tff(4902,plain,
% 1.72/1.95 (~r(s(s(s(z))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3181, 4885, 4881, 4853])).
% 1.72/1.95 tff(4903,plain,
% 1.72/1.95 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 1.72/1.95 tff(4904,plain,
% 1.72/1.95 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1137, 4903])).
% 1.72/1.95 tff(4905,plain,
% 1.72/1.95 (~b(s(z), s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2262, 4904, 123, 4896])).
% 1.72/1.95 tff(4906,plain,
% 1.72/1.95 (r(s(z), s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[172, 4905])).
% 1.72/1.95 tff(4907,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3011, 4906, 4898, 354, 4885])).
% 1.72/1.95 tff(4908,plain,(r(elem!1, z) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4909,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4908, 4852, 4851, 123, 285, 354, 2311, 1, 4831, 4832, 1727, 51, 902, 1378])).
% 1.72/1.95 tff(4910,plain,(r(elem!1, z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4911,plain,
% 1.72/1.95 (r(elem!1, z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4910, 902, 285, 354, 1, 1727, 51, 123, 606, 2310])).
% 1.72/1.95 tff(4912,plain,
% 1.72/1.95 (~(s(s(z)) = s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[855, 4830])).
% 1.72/1.95 tff(4913,plain,
% 1.72/1.95 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[862, 4912])).
% 1.72/1.95 tff(4914,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.72/1.95 tff(4915,plain,
% 1.72/1.95 (s(s(s(z))) = s(s(elem!1))),
% 1.72/1.95 inference(symmetry,[status(thm)],[4914])).
% 1.72/1.95 tff(4916,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1184, 4915])).
% 1.72/1.95 tff(4917,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4918,plain,
% 1.72/1.95 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4917, 4913])).
% 1.72/1.95 tff(4919,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2938, 408, 2311, 51])).
% 1.72/1.95 tff(4920,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[130, 114, 4919])).
% 1.72/1.95 tff(4921,plain,
% 1.72/1.95 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[152, 4920, 123, 134])).
% 1.72/1.95 tff(4922,plain,
% 1.72/1.95 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[121, 4921, 453])).
% 1.72/1.95 tff(4923,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2541, 4922, 2311, 51])).
% 1.72/1.95 tff(4924,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[319, 4923])).
% 1.72/1.95 tff(4925,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3282, 4922, 2311, 408])).
% 1.72/1.95 tff(4926,plain,
% 1.72/1.95 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2894, 4922, 2311, 51])).
% 1.72/1.95 tff(4927,plain,
% 1.72/1.95 (~b(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4423, 453, 51, 4919, 134, 123, 2311])).
% 1.72/1.95 tff(4928,plain,
% 1.72/1.95 (r(elem!1, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[720, 4927, 714])).
% 1.72/1.95 tff(4929,plain,
% 1.72/1.95 (~r(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[727, 4928, 354, 2311])).
% 1.72/1.95 tff(4930,plain,
% 1.72/1.95 (b(s(z), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[348, 4929])).
% 1.72/1.95 tff(4931,plain,
% 1.72/1.95 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[152, 133, 123, 134])).
% 1.72/1.95 tff(4932,plain,
% 1.72/1.95 (~r(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2927, 466, 354, 1, 134, 297, 1727, 408, 304, 2311, 4931])).
% 1.72/1.95 tff(4933,plain,
% 1.72/1.95 (b(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[507, 4932])).
% 1.72/1.95 tff(4934,plain,
% 1.72/1.95 (b(s(z), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2979, 4933, 133, 1727, 606, 354, 1, 489, 2097, 304, 466, 535, 123])).
% 1.72/1.95 tff(4935,plain,
% 1.72/1.95 (~b(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2383, 4934, 489, 4933])).
% 1.72/1.95 tff(4936,plain,
% 1.72/1.95 (r(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[583, 4935])).
% 1.72/1.95 tff(4937,plain,
% 1.72/1.95 (r(elem!1, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3749, 4933, 1727, 408, 2311, 51, 133, 489, 123, 134, 902, 297])).
% 1.72/1.95 tff(4938,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4939,plain,
% 1.72/1.95 (((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4940,plain,
% 1.72/1.95 (((~![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(z))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4939])).
% 1.72/1.95 tff(4941,plain,
% 1.72/1.95 (((~![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(z))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[4940, 4938])).
% 1.72/1.95 tff(4942,plain,
% 1.72/1.95 ((~![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(z))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(4943,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 1.72/1.95 tff(4944,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4943, 333, 4937, 408, 4936, 1686])).
% 1.72/1.95 tff(4945,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(elem!1), elem!1) | b(z, elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (elem!1 = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4946,plain,
% 1.72/1.95 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4945, 4930, 1686, 408, 4920, 1727, 606, 354, 1, 4924, 4926, 123, 51, 134, 902, 4925])).
% 1.72/1.95 tff(4947,plain,
% 1.72/1.95 (~r(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3721, 4946, 123, 134, 1727, 51, 408, 2311, 902, 1, 4924, 354])).
% 1.72/1.95 tff(4948,plain,
% 1.72/1.95 (b(s(elem!1), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[507, 4947])).
% 1.72/1.95 tff(4949,plain,
% 1.72/1.95 (r(elem!1, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3749, 4948, 1727, 408, 2311, 51, 4920, 4930, 123, 134, 902, 4925])).
% 1.72/1.95 tff(4950,plain,
% 1.72/1.95 (~r(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4052, 4949, 2311, 4946])).
% 1.72/1.95 tff(4951,plain,
% 1.72/1.95 (b(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[583, 4950])).
% 1.72/1.95 tff(4952,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[302, 4925])).
% 1.72/1.95 tff(4953,plain,
% 1.72/1.95 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3762, 4949, 134, 4920, 1, 2311, 1728, 4952, 4924])).
% 1.72/1.95 tff(4954,plain,
% 1.72/1.95 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[542, 4953, 4926])).
% 1.72/1.95 tff(4955,plain,
% 1.72/1.95 (b(s(z), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2946, 4954, 123])).
% 1.72/1.95 tff(4956,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2383, 4955, 4951, 4930, 4948])).
% 1.72/1.95 tff(4957,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | b(z, elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(4958,plain,
% 1.72/1.95 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4957, 4831, 123, 1, 1727, 4911, 51, 902, 354, 4562, 606, 4832])).
% 1.72/1.95 tff(4959,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 1.72/1.95 tff(4960,plain,
% 1.72/1.95 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[319, 3971])).
% 1.72/1.95 tff(4961,plain,
% 1.72/1.95 (b(elem!1, s(z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[4960, 732])).
% 1.72/1.95 tff(4962,plain,
% 1.72/1.95 (~b(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4344, 144, 1728, 134, 4961])).
% 1.72/1.95 tff(4963,plain,
% 1.72/1.95 (r(s(elem!1), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[486, 4962, 1])).
% 1.72/1.95 tff(4964,plain,
% 1.72/1.95 (~r(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2966, 333, 354, 4963, 3970])).
% 1.72/1.95 tff(4965,plain,
% 1.72/1.95 (b(z, s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[583, 4964])).
% 1.72/1.95 tff(4966,plain,
% 1.72/1.95 (~b(s(s(s(z))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3170, 144, 491, 4965, 285])).
% 1.72/1.95 tff(4967,plain,
% 1.72/1.95 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 4966])).
% 1.72/1.95 tff(4968,plain,
% 1.72/1.95 (~r(s(s(s(z))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3301, 333, 4963, 3970, 4967])).
% 1.72/1.95 tff(4969,plain,
% 1.72/1.95 (b(s(s(s(z))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2794, 4968])).
% 1.72/1.95 tff(4970,plain,
% 1.72/1.95 (~b(s(s(s(z))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[4375, 4969, 134, 4961])).
% 1.72/1.95 tff(4971,plain,
% 1.72/1.95 (r(s(s(s(z))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[704, 4970, 4363])).
% 1.72/1.95 tff(4972,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.72/1.95 tff(4973,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4974,plain,
% 1.72/1.95 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(4975,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4974])).
% 1.72/1.96 tff(4976,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.96 inference(transitivity,[status(thm)],[4975, 4973])).
% 1.72/1.96 tff(4977,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(4978,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 1.72/1.96 tff(4979,plain,
% 1.72/1.96 (~b(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4978, 144, 134, 305, 4972])).
% 1.72/1.96 tff(4980,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.72/1.96 tff(4981,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.72/1.96 tff(4982,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1272, 44, 107, 4981, 4980])).
% 1.72/1.96 tff(4983,plain,(b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(4984,plain,
% 1.72/1.96 (r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4983, 4979])).
% 1.72/1.96 tff(4985,plain,
% 1.72/1.96 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(4986,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4985])).
% 1.72/1.96 tff(4987,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.96 inference(transitivity,[status(thm)],[4986, 1250])).
% 1.72/1.96 tff(4988,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(4989,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 1.72/1.96 tff(4990,plain,
% 1.72/1.96 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4989, 144, 547, 451, 4972])).
% 1.72/1.96 tff(4991,plain,
% 1.72/1.96 (r(s(s(elem!1)), s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1283, 4990, 2854])).
% 1.72/1.96 tff(4992,plain,
% 1.72/1.96 (((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(4993,plain,
% 1.72/1.96 ((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(4994,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[4993, 4992])).
% 1.72/1.96 tff(4995,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4994, 333, 4991, 434, 4984, 1230])).
% 1.72/1.96 tff(4996,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(4997,plain,
% 1.72/1.96 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4996, 4963, 3970, 2727, 134, 4961, 3745, 1728])).
% 1.72/1.96 tff(4998,plain,
% 1.72/1.96 (elem!1 = s(s(elem!1))),
% 1.72/1.96 inference(symmetry,[status(thm)],[1219])).
% 1.72/1.96 tff(4999,plain,
% 1.72/1.96 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.72/1.96 inference(transitivity,[status(thm)],[81, 4998])).
% 1.72/1.96 tff(5000,plain,
% 1.72/1.96 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4999])).
% 1.72/1.96 tff(5001,plain,
% 1.72/1.96 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.72/1.96 inference(transitivity,[status(thm)],[21, 5000, 101])).
% 1.72/1.96 tff(5002,plain,
% 1.72/1.96 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5001])).
% 1.72/1.96 tff(5003,plain,
% 1.72/1.96 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[93, 5002, 850, 82])).
% 1.72/1.96 tff(5004,plain,
% 1.72/1.96 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5003])).
% 1.72/1.96 tff(5005,plain,
% 1.72/1.96 (s(s(s(s(z)))) = s(elem!1)),
% 1.72/1.96 inference(transitivity,[status(thm)],[239, 5004, 5000, 101])).
% 1.72/1.96 tff(5006,plain,
% 1.72/1.96 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5005])).
% 1.72/1.96 tff(5007,plain,
% 1.72/1.96 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.72/1.96 inference(symmetry,[status(thm)],[5006])).
% 1.72/1.96 tff(5008,plain,
% 1.72/1.96 (elem!1 = s(s(s(z)))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1193, 5007, 183])).
% 1.72/1.96 tff(5009,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[3843, 5008])).
% 1.72/1.96 tff(5010,plain,((~(s(s(elem!1)) = elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5011,plain,
% 1.72/1.96 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5010, 81])).
% 1.72/1.96 tff(5012,plain,
% 1.72/1.96 (r(s(s(elem!1)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1260, 44, 5011, 4997])).
% 1.72/1.96 tff(5013,plain,
% 1.72/1.96 (((~![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)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, 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)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5014,plain,
% 1.72/1.96 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5015,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5014])).
% 1.72/1.96 tff(5016,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5015, 5013])).
% 1.72/1.96 tff(5017,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5018,plain,
% 1.72/1.96 ((~![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)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5017, 5016])).
% 1.72/1.96 tff(5019,plain,
% 1.72/1.96 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5018, 333, 408, 5012, 4971])).
% 1.72/1.96 tff(5020,plain,
% 1.72/1.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5021,plain,
% 1.72/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5022,plain,
% 1.72/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5021, 5020])).
% 1.72/1.96 tff(5023,plain,
% 1.72/1.96 (b(s(s(elem!1)), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5022, 44, 4959, 5019])).
% 1.72/1.96 tff(5024,plain,
% 1.72/1.96 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5025,plain,
% 1.72/1.96 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5026,plain,
% 1.72/1.96 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.72/1.96 tff(5027,plain,
% 1.72/1.96 (~r(s(z), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5026, 333, 4963, 3970, 4967])).
% 1.72/1.96 tff(5028,plain,
% 1.72/1.96 (b(s(z), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[172, 5027])).
% 1.72/1.96 tff(5029,plain,
% 1.72/1.96 (~r(z, s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2136, 4971, 670, 408])).
% 1.72/1.96 tff(5030,plain,
% 1.72/1.96 (b(z, s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[619, 5029])).
% 1.72/1.96 tff(5031,plain,
% 1.72/1.96 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5032,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5031])).
% 1.72/1.96 tff(5033,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5032, 2149])).
% 1.72/1.96 tff(5034,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(z), s(s(s(z))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5035,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5034, 5033])).
% 1.72/1.96 tff(5036,plain,
% 1.72/1.96 (~b(s(z), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5035, 144, 285, 5030, 5028])).
% 1.72/1.96 tff(5037,plain,
% 1.72/1.96 (r(s(z), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[348, 5036])).
% 1.72/1.96 tff(5038,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.72/1.96 tff(5039,plain,
% 1.72/1.96 (((~![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))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5040,plain,
% 1.72/1.96 ((~![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))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5041,plain,
% 1.72/1.96 ((~![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)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5040, 5039])).
% 1.72/1.96 tff(5042,plain,
% 1.72/1.96 (r(s(s(elem!1)), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5041, 44, 1094, 5038])).
% 1.72/1.96 tff(5043,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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)))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5044,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5045,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 1.72/1.96 tff(5046,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5045, 333, 670, 408, 4627, 5042])).
% 1.72/1.96 tff(5047,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5048,plain,
% 1.72/1.96 (~r(s(s(elem!1)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5047, 5038, 408, 670])).
% 1.72/1.96 tff(5049,plain,
% 1.72/1.96 (b(s(s(elem!1)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1260, 44, 5048, 1257])).
% 1.72/1.96 tff(5050,plain,
% 1.72/1.96 (~b(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4978, 144, 134, 305, 5049])).
% 1.72/1.96 tff(5051,plain,
% 1.72/1.96 (((~![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(s(s(elem!1)), z)) | (~r(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, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5052,plain,
% 1.72/1.96 ((~![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(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5053,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 1.72/1.96 tff(5054,plain,
% 1.72/1.96 (~r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5053, 333, 670, 323, 5042])).
% 1.72/1.96 tff(5055,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4983, 5054, 5050])).
% 1.72/1.96 tff(5056,plain,(b(s(s(elem!1)), z) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5057,plain,
% 1.72/1.96 (b(s(s(elem!1)), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5056, 5037, 670, 134, 4961, 5011, 408])).
% 1.72/1.96 tff(5058,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5059,plain,
% 1.72/1.96 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5060,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5059])).
% 1.72/1.96 tff(5061,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5060, 5058])).
% 1.72/1.96 tff(5062,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5063,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5062, 5061])).
% 1.72/1.96 tff(5064,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5063, 144, 285, 5030, 5057, 5023])).
% 1.72/1.96 tff(5065,plain,(r(elem!1, s(elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5066,plain,
% 1.72/1.96 (r(elem!1, s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5065, 491, 4959, 408, 134, 670, 285, 354, 1, 81, 51, 1727, 902])).
% 1.72/1.96 tff(5067,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5068,plain,
% 1.72/1.96 (((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5069,plain,
% 1.72/1.96 (((~![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(z))))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5068])).
% 1.72/1.96 tff(5070,plain,
% 1.72/1.96 (((~![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(z))))) | (~r(elem!1, s(elem!1))) | (~r(z, 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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5069, 5067])).
% 1.72/1.96 tff(5071,plain,
% 1.72/1.96 ((~![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(z))))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5072,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 1.72/1.96 tff(5073,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5072, 333, 563, 670, 562, 1686])).
% 1.72/1.96 tff(5074,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5075,plain,
% 1.72/1.96 (~r(z, s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5074, 5066, 670, 1686])).
% 1.72/1.96 tff(5076,plain,
% 1.72/1.96 (b(z, s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[583, 5075])).
% 1.72/1.96 tff(5077,plain,
% 1.72/1.96 (~b(s(s(s(z))), s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[3170, 144, 491, 5076, 285])).
% 1.72/1.96 tff(5078,plain,
% 1.72/1.96 (r(s(s(s(z))), s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 5077])).
% 1.72/1.96 tff(5079,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5080,plain,
% 1.72/1.97 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5081,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5080])).
% 1.72/1.97 tff(5082,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5081, 5079])).
% 1.72/1.97 tff(5083,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5084,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5083, 5082])).
% 1.72/1.97 tff(5085,plain,
% 1.72/1.97 (~r(elem!1, s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5084, 333, 5066, 1686, 5078])).
% 1.72/1.97 tff(5086,plain,
% 1.72/1.97 (b(elem!1, s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1538, 5085, 3843])).
% 1.72/1.97 tff(5087,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5086, 1523])).
% 1.72/1.97 tff(5088,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(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(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5089,plain,
% 1.72/1.97 (((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5090,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5089])).
% 1.72/1.97 tff(5091,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5090, 5088])).
% 1.72/1.97 tff(5092,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5093,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5092, 5091])).
% 1.72/1.97 tff(5094,plain,
% 1.72/1.97 (~r(s(s(s(z))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5093, 333, 5066, 1686, 5078])).
% 1.72/1.97 tff(5095,plain,
% 1.72/1.97 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5094, 4901])).
% 1.72/1.97 tff(5096,plain,
% 1.72/1.97 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1137, 5095])).
% 1.72/1.97 tff(5097,plain,
% 1.72/1.97 (~b(s(z), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2262, 5096, 123, 5087])).
% 1.72/1.97 tff(5098,plain,
% 1.72/1.97 (r(s(z), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[172, 5097])).
% 1.72/1.97 tff(5099,plain,
% 1.72/1.97 (b(s(s(s(z))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[704, 5094, 4363])).
% 1.72/1.97 tff(5100,plain,
% 1.72/1.97 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[408, 2554])).
% 1.72/1.97 tff(5101,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[362, 5098, 5100, 354])).
% 1.72/1.97 tff(5102,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[319, 5101])).
% 1.72/1.97 tff(5103,plain,
% 1.72/1.97 (b(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[735, 5102, 81])).
% 1.72/1.97 tff(5104,plain,
% 1.72/1.97 (~b(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4375, 5103, 134, 5099])).
% 1.72/1.97 tff(5105,plain,
% 1.72/1.97 (r(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2794, 5104])).
% 1.72/1.97 tff(5106,plain,
% 1.72/1.97 (~b(s(elem!1), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4344, 144, 1728, 134, 5103])).
% 1.72/1.97 tff(5107,plain,
% 1.72/1.97 (r(s(elem!1), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[486, 5106, 1])).
% 1.72/1.97 tff(5108,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), 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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5109,plain,
% 1.72/1.97 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5110,plain,
% 1.72/1.97 (((~![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(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5109])).
% 1.72/1.97 tff(5111,plain,
% 1.72/1.97 (((~![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(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5110, 5108])).
% 1.72/1.97 tff(5112,plain,
% 1.72/1.97 ((~![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(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5113,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5112, 5111])).
% 1.72/1.97 tff(5114,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5113, 333, 5107, 5105, 5098, 5078])).
% 1.72/1.97 tff(5115,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5116,plain,
% 1.72/1.97 (~b(s(elem!1), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5115, 4831, 1, 4958, 354, 123, 4562, 285, 2311, 4918, 4911, 51, 1727, 902])).
% 1.72/1.97 tff(5117,plain,
% 1.72/1.97 (r(s(elem!1), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[507, 5116])).
% 1.72/1.97 tff(5118,plain,
% 1.72/1.97 (~r(elem!1, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[678, 5117, 2311, 4911])).
% 1.72/1.97 tff(5119,plain,
% 1.72/1.97 (~r(s(z), s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4861, 5117, 354, 1, 1728, 4831, 4958, 51])).
% 1.72/1.97 tff(5120,plain,
% 1.72/1.97 (b(s(z), s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1244, 5119, 1229])).
% 1.72/1.97 tff(5121,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1732, 5120, 5118, 1727, 902, 4831])).
% 1.72/1.97 tff(5122,plain,((elem!1 = s(elem!1)) | r(s(elem!1), elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5123,plain,
% 1.72/1.97 (elem!1 = s(elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5122, 1727, 354, 1, 51, 123, 285, 606, 2310])).
% 1.72/1.97 tff(5124,plain,
% 1.72/1.97 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5123])).
% 1.72/1.97 tff(5125,plain,
% 1.72/1.97 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5124, 175])).
% 1.72/1.97 tff(5126,plain,
% 1.72/1.97 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5125])).
% 1.72/1.97 tff(5127,plain,
% 1.72/1.97 (s(elem!1) = elem!1),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1569, 5123])).
% 1.72/1.97 tff(5128,plain,
% 1.72/1.97 (s(s(s(elem!1))) = elem!1),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2482, 5123])).
% 1.72/1.97 tff(5129,plain,
% 1.72/1.97 (~(s(z) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2468, 5128])).
% 1.72/1.97 tff(5130,plain,
% 1.72/1.97 (s(elem!1) = s(s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2584, 5128, 5123])).
% 1.72/1.97 tff(5131,plain,
% 1.72/1.97 (s(s(s(elem!1))) = s(elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3254, 5130])).
% 1.72/1.97 tff(5132,plain,
% 1.72/1.97 (~(elem!1 = s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3246, 5131, 5129])).
% 1.72/1.97 tff(5133,plain,
% 1.72/1.97 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1565, 5132, 5127])).
% 1.72/1.97 tff(5134,plain,
% 1.72/1.97 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5133, 5126])).
% 1.72/1.97 tff(5135,plain,
% 1.72/1.97 (~(elem!1 = s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[712, 5129])).
% 1.72/1.97 tff(5136,plain,
% 1.72/1.97 (b(s(z), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[406, 5129, 2310])).
% 1.72/1.97 tff(5137,plain,
% 1.72/1.97 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[116, 5133])).
% 1.72/1.97 tff(5138,plain,
% 1.72/1.97 (~(s(z) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2468, 3675])).
% 1.72/1.97 tff(5139,plain,
% 1.72/1.97 (~(elem!1 = s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[712, 5138])).
% 1.72/1.97 tff(5140,plain,
% 1.72/1.97 (~(elem!1 = s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3246, 3677, 5138])).
% 1.72/1.97 tff(5141,plain,
% 1.72/1.97 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1565, 5140, 3674])).
% 1.72/1.97 tff(5142,plain,
% 1.72/1.97 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[116, 5141])).
% 1.72/1.97 tff(5143,plain,
% 1.72/1.97 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[885])).
% 1.72/1.97 tff(5144,plain,
% 1.72/1.97 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5143, 175])).
% 1.72/1.97 tff(5145,plain,
% 1.72/1.97 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5144])).
% 1.72/1.97 tff(5146,plain,
% 1.72/1.97 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5141, 5145])).
% 1.72/1.97 tff(5147,plain,
% 1.72/1.97 (~r(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4150, 450, 123, 1727, 885, 51, 134, 1, 606, 5141])).
% 1.72/1.97 tff(5148,plain,
% 1.72/1.97 (b(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[348, 5147])).
% 1.72/1.97 tff(5149,plain,
% 1.72/1.97 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2297, 5148, 134, 624, 123])).
% 1.72/1.97 tff(5150,plain,
% 1.72/1.97 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[130, 5149, 5141])).
% 1.72/1.97 tff(5151,plain,
% 1.72/1.97 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5150, 4126])).
% 1.72/1.97 tff(5152,plain,
% 1.72/1.97 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3222, 5148, 4122, 123, 450])).
% 1.72/1.97 tff(5153,plain,
% 1.72/1.97 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[302, 5152])).
% 1.72/1.97 tff(5154,plain,
% 1.72/1.97 (~b(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2974, 885, 606])).
% 1.72/1.97 tff(5155,plain,
% 1.72/1.97 (r(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[583, 5154])).
% 1.72/1.97 tff(5156,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(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(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5157,plain,
% 1.72/1.97 (((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5158,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5157])).
% 1.72/1.97 tff(5159,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5158, 5156])).
% 1.72/1.97 tff(5160,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5161,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5160, 5159])).
% 1.72/1.97 tff(5162,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5161, 333, 5155, 1686, 5153, 5151])).
% 1.72/1.97 tff(5163,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5164,plain,
% 1.72/1.97 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5163, 624, 885, 123, 134, 1686, 1727, 51, 1, 606])).
% 1.72/1.97 tff(5165,plain,
% 1.72/1.97 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[472, 5164, 5146])).
% 1.72/1.97 tff(5166,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4003, 5165, 606, 51, 77, 2311])).
% 1.72/1.97 tff(5167,plain,
% 1.72/1.97 (~b(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4423, 5166, 51, 5142, 134, 123, 2311])).
% 1.72/1.97 tff(5168,plain,
% 1.72/1.97 (r(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[720, 5167, 5139])).
% 1.72/1.97 tff(5169,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[130, 5166, 5141])).
% 1.72/1.97 tff(5170,plain,
% 1.72/1.97 (~b(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2297, 5169, 134, 624, 123])).
% 1.72/1.97 tff(5171,plain,
% 1.72/1.97 (r(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[348, 5170])).
% 1.72/1.97 tff(5172,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[727, 5171, 5168, 354, 2311])).
% 1.72/1.97 tff(5173,plain,((~b(elem!1, z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~(elem!1 = s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | r(s(elem!1), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5174,plain,
% 1.72/1.97 (~b(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5173, 5136, 354, 123, 51, 606, 5123, 4562, 1727, 1])).
% 1.72/1.97 tff(5175,plain,
% 1.72/1.97 (r(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[653, 5174, 77])).
% 1.72/1.97 tff(5176,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2938, 5175, 2311, 51])).
% 1.72/1.97 tff(5177,plain,
% 1.72/1.97 (~b(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4423, 5176, 51, 5137, 5136, 123, 2311])).
% 1.72/1.97 tff(5178,plain,
% 1.72/1.97 (r(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[720, 5177, 5135])).
% 1.72/1.97 tff(5179,plain,
% 1.72/1.97 (~r(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[727, 5178, 354, 2311])).
% 1.72/1.97 tff(5180,plain,
% 1.72/1.97 (b(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[348, 5179])).
% 1.72/1.97 tff(5181,plain,
% 1.72/1.97 (b(s(z), s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3262, 5136, 5127])).
% 1.72/1.97 tff(5182,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[130, 5176, 5133])).
% 1.72/1.97 tff(5183,plain,
% 1.72/1.97 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[152, 5182, 123, 5136])).
% 1.72/1.97 tff(5184,plain,
% 1.72/1.97 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[121, 5183, 5137])).
% 1.72/1.97 tff(5185,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3282, 5184, 2311, 5175])).
% 1.72/1.97 tff(5186,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[302, 5185])).
% 1.72/1.97 tff(5187,plain,
% 1.72/1.97 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3222, 5186, 5181, 123, 5180])).
% 1.72/1.97 tff(5188,plain,
% 1.72/1.97 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[472, 5187, 5134])).
% 1.72/1.97 tff(5189,plain,
% 1.72/1.97 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5123])).
% 1.72/1.97 tff(5190,plain,
% 1.72/1.97 (r(s(elem!1), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.72/1.97 inference(symmetry,[status(thm)],[5189])).
% 1.72/1.97 tff(5191,plain,
% 1.72/1.97 (r(elem!1, s(s(s(z))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[4562, 5190])).
% 1.72/1.97 tff(5192,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2541, 5184, 2311, 51])).
% 1.72/1.97 tff(5193,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[319, 5192])).
% 1.72/1.97 tff(5194,plain,
% 1.72/1.97 (~b(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2974, 5123, 606])).
% 1.72/1.97 tff(5195,plain,
% 1.72/1.97 (r(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[583, 5194])).
% 1.72/1.97 tff(5196,plain,
% 1.72/1.97 (~r(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3201, 623, 670, 1525])).
% 1.72/1.97 tff(5197,plain,
% 1.72/1.97 (b(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2794, 5196])).
% 1.72/1.97 tff(5198,plain,
% 1.72/1.97 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2802, 5197])).
% 1.72/1.97 tff(5199,plain,
% 1.72/1.97 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1137, 5198])).
% 1.72/1.97 tff(5200,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), 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(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5201,plain,
% 1.72/1.97 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5202,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5201])).
% 1.72/1.97 tff(5203,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5202, 5200])).
% 1.72/1.97 tff(5204,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5205,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5204, 5203])).
% 1.72/1.97 tff(5206,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5205, 333, 562, 623, 1686, 5199])).
% 1.72/1.97 tff(5207,plain,((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5208,plain,
% 1.72/1.97 (~r(z, s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5207, 5195, 4562, 5180, 285, 5193, 2311, 5191])).
% 1.72/1.97 tff(5209,plain,
% 1.72/1.97 (b(z, s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[619, 5208])).
% 1.72/1.97 tff(5210,plain,
% 1.72/1.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[294, 5209, 285, 5186])).
% 1.72/1.97 tff(5211,plain,
% 1.72/1.97 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[249, 5210])).
% 1.72/1.97 tff(5212,plain,
% 1.72/1.97 (r(elem!1, z) <=> r(s(elem!1), z)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5123])).
% 1.72/1.97 tff(5213,plain,
% 1.72/1.97 (r(s(elem!1), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5175, 5212])).
% 1.72/1.97 tff(5214,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3704, 333, 5213, 5211, 51, 5188])).
% 1.72/1.97 tff(5215,plain,(r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5216,plain,
% 1.72/1.97 (r(s(elem!1), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5215, 285, 51, 123, 354, 606, 1, 2310])).
% 1.72/1.97 tff(5217,plain,
% 1.72/1.97 (~b(s(elem!1), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4829, 57, 285, 1686, 354, 123, 902, 2311, 51, 1229, 606, 77])).
% 1.72/1.97 tff(5218,plain,
% 1.72/1.97 (~b(s(elem!1), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3619, 57, 5217])).
% 1.72/1.97 tff(5219,plain,
% 1.72/1.97 (r(s(elem!1), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[486, 5218, 1])).
% 1.72/1.97 tff(5220,plain,
% 1.72/1.97 (~b(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3965, 3921, 57])).
% 1.72/1.97 tff(5221,plain,
% 1.72/1.97 (r(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[653, 5220, 1368])).
% 1.72/1.97 tff(5222,plain,
% 1.72/1.97 (~r(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2453, 333, 435, 670, 5221])).
% 1.72/1.97 tff(5223,plain,
% 1.72/1.97 (b(z, s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[583, 5222])).
% 1.72/1.97 tff(5224,plain,
% 1.72/1.97 (~r(s(elem!1), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1365, 3922, 354, 434])).
% 1.72/1.97 tff(5225,plain,
% 1.72/1.97 (b(s(elem!1), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[507, 5224])).
% 1.72/1.97 tff(5226,plain,
% 1.72/1.97 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2733, 144, 5225, 5223, 2726])).
% 1.72/1.97 tff(5227,plain,
% 1.72/1.97 (r(s(s(elem!1)), s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1283, 5226, 2854])).
% 1.72/1.97 tff(5228,plain,
% 1.72/1.97 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2938, 5221, 670, 51])).
% 1.72/1.97 tff(5229,plain,
% 1.72/1.97 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[130, 5228, 114])).
% 1.72/1.97 tff(5230,plain,
% 1.72/1.97 (~r(s(s(s(elem!1))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4215, 5223, 670, 434, 3523, 3922, 5225])).
% 1.72/1.97 tff(5231,plain,
% 1.72/1.97 (b(s(s(s(elem!1))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1101, 5230])).
% 1.72/1.97 tff(5232,plain,
% 1.72/1.97 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3588, 5231, 57])).
% 1.72/1.97 tff(5233,plain,
% 1.72/1.97 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3552, 144, 5232, 5229, 132])).
% 1.72/1.97 tff(5234,plain,
% 1.72/1.97 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3556, 44, 196, 5233])).
% 1.72/1.97 tff(5235,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5236,plain,
% 1.72/1.97 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5237,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5236])).
% 1.72/1.98 tff(5238,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5237, 5235])).
% 1.72/1.98 tff(5239,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5240,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 1.72/1.98 tff(5241,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5240, 333, 435, 2737, 2736, 4571])).
% 1.72/1.98 tff(5242,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5243,plain,
% 1.72/1.98 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5242, 5227, 435, 4568])).
% 1.72/1.98 tff(5244,plain,
% 1.72/1.98 (b(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2522, 5243, 2462])).
% 1.72/1.98 tff(5245,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4321, 5244, 57, 2726, 5225, 5232, 5234, 51, 5227])).
% 1.72/1.98 tff(5246,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[302, 5245])).
% 1.72/1.98 tff(5247,plain,
% 1.72/1.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2753, 144, 5244, 5229, 5246, 2726])).
% 1.72/1.98 tff(5248,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2758, 5247, 2704])).
% 1.72/1.98 tff(5249,plain,
% 1.72/1.98 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1668, 144, 5225, 5223, 5246])).
% 1.72/1.98 tff(5250,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[542, 5249, 2698])).
% 1.72/1.98 tff(5251,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5252,plain,
% 1.72/1.98 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5253,plain,
% 1.72/1.98 (((~![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(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5252])).
% 1.72/1.98 tff(5254,plain,
% 1.72/1.98 (((~![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(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5253, 5251])).
% 1.72/1.98 tff(5255,plain,
% 1.72/1.98 ((~![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(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5256,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5255, 5254])).
% 1.72/1.98 tff(5257,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5256, 333, 2737, 1686, 3654, 524])).
% 1.72/1.98 tff(5258,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5259,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5258, 5250, 5248, 1686, 5227])).
% 1.72/1.98 tff(5260,plain,(b(s(z), z) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = z) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5261,plain,
% 1.72/1.98 (b(s(z), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5260, 2498, 1686, 57, 51, 435, 2727, 2692, 2311, 5219, 114, 77, 354])).
% 1.72/1.98 tff(5262,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5263,plain,
% 1.72/1.98 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5264,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5263])).
% 1.72/1.98 tff(5265,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5264, 5262])).
% 1.72/1.98 tff(5266,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5267,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5266, 5265])).
% 1.72/1.98 tff(5268,plain,
% 1.72/1.98 (~b(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5267, 144, 547, 624, 585, 2726])).
% 1.72/1.98 tff(5269,plain,
% 1.72/1.98 (r(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2522, 5268, 1221])).
% 1.72/1.98 tff(5270,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2878, 333, 435, 670, 3889, 5269])).
% 1.72/1.98 tff(5271,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5272,plain,
% 1.72/1.98 (~b(elem!1, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5271, 585, 670, 2462, 2694, 435, 2498])).
% 1.72/1.98 tff(5273,plain,
% 1.72/1.98 (r(elem!1, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[560, 5272, 902])).
% 1.72/1.98 tff(5274,plain,
% 1.72/1.98 (~r(s(elem!1), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[3624, 5273, 670, 435])).
% 1.72/1.98 tff(5275,plain,
% 1.72/1.98 (b(s(elem!1), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[507, 5274])).
% 1.72/1.98 tff(5276,plain,
% 1.72/1.98 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2733, 144, 5275, 585, 2498])).
% 1.72/1.98 tff(5277,plain,
% 1.72/1.98 (r(s(s(elem!1)), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1283, 5276, 2727])).
% 1.72/1.98 tff(5278,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.98 inference(symmetry,[status(thm)],[2699])).
% 1.72/1.98 tff(5279,plain,
% 1.72/1.98 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4003, 2484, 606, 51, 1368, 670])).
% 1.72/1.98 tff(5280,plain,
% 1.72/1.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[472, 5279, 432])).
% 1.72/1.98 tff(5281,plain,
% 1.72/1.98 (b(elem!1, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[560, 3350, 902])).
% 1.72/1.98 tff(5282,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5283,plain,
% 1.72/1.98 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5284,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5283])).
% 1.72/1.98 tff(5285,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5284, 5282])).
% 1.72/1.98 tff(5286,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5287,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5286, 5285])).
% 1.72/1.98 tff(5288,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5287, 144, 5281, 624, 585, 132, 5280])).
% 1.72/1.98 tff(5289,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(elem!1)) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5290,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5289, 585, 2694, 132, 4762, 902, 606, 51, 1368, 670])).
% 1.72/1.98 tff(5291,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[130, 5290, 114])).
% 1.72/1.98 tff(5292,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5291, 5278])).
% 1.72/1.98 tff(5293,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2845, 5273, 51, 57, 489, 285, 5292, 435, 434, 670])).
% 1.72/1.98 tff(5294,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[302, 5293])).
% 1.72/1.98 tff(5295,plain,
% 1.72/1.98 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1668, 144, 5275, 585, 5294])).
% 1.72/1.98 tff(5296,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[542, 5295, 2698])).
% 1.72/1.98 tff(5297,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5258, 5296, 1686, 5277])).
% 1.72/1.98 tff(5298,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2758, 5297, 2704])).
% 1.72/1.98 tff(5299,plain,
% 1.72/1.98 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5242, 5277, 435, 4568])).
% 1.72/1.98 tff(5300,plain,
% 1.72/1.98 (b(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2522, 5299, 2462])).
% 1.72/1.98 tff(5301,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5302,plain,
% 1.72/1.98 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5303,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5302])).
% 1.72/1.98 tff(5304,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5303, 5301])).
% 1.72/1.98 tff(5305,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5306,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5305, 5304])).
% 1.72/1.98 tff(5307,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5306, 144, 2694, 5300, 5298, 132, 2498])).
% 1.72/1.98 tff(5308,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5309,plain,
% 1.72/1.98 (~b(z, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5308, 2692, 435, 1686, 51, 57, 5261, 285, 5219, 2311, 902, 114, 606, 77])).
% 1.72/1.98 tff(5310,plain,
% 1.72/1.98 (r(z, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[583, 5309])).
% 1.72/1.98 tff(5311,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2655, 5310, 51, 435])).
% 1.72/1.98 tff(5312,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[542, 5311, 2698])).
% 1.72/1.98 tff(5313,plain,
% 1.72/1.98 (~r(elem!1, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5074, 5310, 2311, 1686])).
% 1.72/1.98 tff(5314,plain,
% 1.72/1.98 (b(elem!1, s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[560, 5313, 902])).
% 1.72/1.98 tff(5315,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4787, 144, 547, 132, 546, 450])).
% 1.72/1.98 tff(5316,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5317,plain,
% 1.72/1.98 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5316, 5314, 2692, 5312])).
% 1.72/1.98 tff(5318,plain,
% 1.72/1.98 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[472, 5317, 4762])).
% 1.72/1.98 tff(5319,plain,
% 1.72/1.98 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[940, 5310, 51, 5318])).
% 1.72/1.98 tff(5320,plain,
% 1.72/1.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[302, 5319])).
% 1.72/1.98 tff(5321,plain,
% 1.72/1.98 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2496])).
% 1.72/1.98 tff(5322,plain,
% 1.72/1.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[472, 5279, 4762])).
% 1.72/1.98 tff(5323,plain,
% 1.72/1.98 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[3222, 5322, 489, 123, 4683])).
% 1.72/1.98 tff(5324,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[302, 5323])).
% 1.72/1.98 tff(5325,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.98 inference(symmetry,[status(thm)],[2457])).
% 1.72/1.98 tff(5326,plain,
% 1.72/1.98 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2484, 5325])).
% 1.72/1.98 tff(5327,plain,
% 1.72/1.98 (~r(s(z), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[362, 5326, 5324, 354])).
% 1.72/1.98 tff(5328,plain,
% 1.72/1.98 (b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[172, 5327])).
% 1.72/1.98 tff(5329,plain,
% 1.72/1.98 (~b(s(elem!1), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2631, 5328, 489, 285, 4683])).
% 1.72/1.98 tff(5330,plain,
% 1.72/1.98 (~b(z, s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2156, 5328, 285, 489])).
% 1.72/1.98 tff(5331,plain,
% 1.72/1.98 (r(z, s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[619, 5330])).
% 1.72/1.98 tff(5332,plain,
% 1.72/1.98 (b(s(s(s(z))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4807, 5331, 960, 562, 5329])).
% 1.72/1.98 tff(5333,plain,
% 1.72/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5332, 5321])).
% 1.72/1.98 tff(5334,plain,
% 1.72/1.98 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[57])).
% 1.72/1.98 tff(5335,plain,
% 1.72/1.98 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(symmetry,[status(thm)],[5334])).
% 1.72/1.98 tff(5336,plain,
% 1.72/1.98 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2496])).
% 1.72/1.98 tff(5337,plain,
% 1.72/1.98 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.72/1.98 inference(symmetry,[status(thm)],[5336])).
% 1.72/1.98 tff(5338,plain,
% 1.72/1.98 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5337, 5335])).
% 1.72/1.98 tff(5339,plain,
% 1.72/1.98 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(z), s(s(s(z)))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5338])).
% 1.72/1.98 tff(5340,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.72/1.98 tff(5341,plain,
% 1.72/1.98 (~b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5340, 5339])).
% 1.72/1.98 tff(5342,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[838, 5341])).
% 1.72/1.98 tff(5343,plain,(b(elem!1, s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5344,plain,
% 1.72/1.98 (b(elem!1, s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5343, 5328, 57])).
% 1.72/1.98 tff(5345,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5346,plain,
% 1.72/1.98 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5347,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5346])).
% 1.72/1.99 tff(5348,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5347, 5345])).
% 1.72/1.99 tff(5349,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5350,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5349, 5348])).
% 1.72/1.99 tff(5351,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5350, 144, 547, 1249, 2812, 132, 450])).
% 1.72/1.99 tff(5352,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5353,plain,
% 1.72/1.99 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5352, 5344, 547, 2692, 5322])).
% 1.72/1.99 tff(5354,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5353, 5333])).
% 1.72/1.99 tff(5355,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5356,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5355, 57, 5314, 4794, 5310, 5261, 285, 354, 123, 606, 51, 77, 2311])).
% 1.72/1.99 tff(5357,plain,
% 1.72/1.99 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[130, 5356, 114])).
% 1.72/1.99 tff(5358,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2870, 333, 435, 670, 562, 2736])).
% 1.72/1.99 tff(5359,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5360,plain,
% 1.72/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5359, 5310, 2311, 435])).
% 1.72/1.99 tff(5361,plain,
% 1.72/1.99 (b(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2522, 5360, 2462])).
% 1.72/1.99 tff(5362,plain,
% 1.72/1.99 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2753, 144, 5361, 5357, 5320, 2498])).
% 1.72/1.99 tff(5363,plain,
% 1.72/1.99 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2758, 5362, 2704])).
% 1.72/1.99 tff(5364,plain,
% 1.72/1.99 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5365,plain,
% 1.72/1.99 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5366,plain,
% 1.72/1.99 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5365])).
% 1.72/1.99 tff(5367,plain,
% 1.72/1.99 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5366, 5364])).
% 1.72/1.99 tff(5368,plain,
% 1.72/1.99 ((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5369,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 1.72/1.99 tff(5370,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5369, 333, 5310, 5363, 51, 5318])).
% 1.72/1.99 tff(5371,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5372,plain,
% 1.72/1.99 (~(s(z) = elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5371, 114, 5216, 51, 285, 354, 123, 606, 902, 4562, 1])).
% 1.72/1.99 tff(5373,plain,
% 1.72/1.99 (b(s(z), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[406, 5372, 2310])).
% 1.72/1.99 tff(5374,plain,
% 1.72/1.99 (~(elem!1 = s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[712, 5372])).
% 1.72/1.99 tff(5375,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2492, 563, 670, 51])).
% 1.72/1.99 tff(5376,plain,
% 1.72/1.99 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[130, 5375, 114])).
% 1.72/1.99 tff(5377,plain,
% 1.72/1.99 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[152, 5376, 123, 134])).
% 1.72/1.99 tff(5378,plain,
% 1.72/1.99 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[121, 5377, 453])).
% 1.72/1.99 tff(5379,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2894, 5378, 670, 51])).
% 1.72/1.99 tff(5380,plain,
% 1.72/1.99 (~r(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3624, 563, 670, 435])).
% 1.72/1.99 tff(5381,plain,
% 1.72/1.99 (b(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[507, 5380])).
% 1.72/1.99 tff(5382,plain,
% 1.72/1.99 (~b(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4423, 5375, 51, 453, 134, 123, 670])).
% 1.72/1.99 tff(5383,plain,
% 1.72/1.99 (r(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[720, 5382, 714])).
% 1.72/1.99 tff(5384,plain,
% 1.72/1.99 (~r(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[727, 5383, 354, 670])).
% 1.72/1.99 tff(5385,plain,
% 1.72/1.99 (b(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[348, 5384])).
% 1.72/1.99 tff(5386,plain,
% 1.72/1.99 (~b(s(z), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2383, 5385, 585, 5381])).
% 1.72/1.99 tff(5387,plain,
% 1.72/1.99 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2946, 5386, 123])).
% 1.72/1.99 tff(5388,plain,
% 1.72/1.99 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[542, 5387, 5379])).
% 1.72/1.99 tff(5389,plain,
% 1.72/1.99 (~b(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2297, 5385, 134, 5376, 123])).
% 1.72/1.99 tff(5390,plain,
% 1.72/1.99 (r(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[653, 5389, 1368])).
% 1.72/1.99 tff(5391,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3282, 5390, 670, 5378])).
% 1.72/1.99 tff(5392,plain,
% 1.72/1.99 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[302, 5391])).
% 1.72/1.99 tff(5393,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1668, 144, 5381, 585, 5392, 5388])).
% 1.72/1.99 tff(5394,plain,((~r(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (elem!1 = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5395,plain,
% 1.72/1.99 (~r(elem!1, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5394, 585, 670, 123, 77, 134, 51, 354, 714, 114, 435])).
% 1.72/1.99 tff(5396,plain,
% 1.72/1.99 (b(elem!1, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[560, 5395, 902])).
% 1.72/1.99 tff(5397,plain,
% 1.72/1.99 (~r(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[727, 323, 354, 670])).
% 1.72/1.99 tff(5398,plain,
% 1.72/1.99 (b(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[720, 5397, 714])).
% 1.72/1.99 tff(5399,plain,
% 1.72/1.99 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4423, 5398, 51, 3396, 134, 123, 670])).
% 1.72/1.99 tff(5400,plain,
% 1.72/1.99 (~r(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2938, 5399, 670, 51])).
% 1.72/1.99 tff(5401,plain,
% 1.72/1.99 (~r(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4411, 5398, 1, 435, 354, 902, 670, 323])).
% 1.72/1.99 tff(5402,plain,
% 1.72/1.99 (b(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[507, 5401])).
% 1.72/1.99 tff(5403,plain,
% 1.72/1.99 (~b(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[949, 5402, 585, 547])).
% 1.72/1.99 tff(5404,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1380, 5403, 5400, 77])).
% 1.72/1.99 tff(5405,plain,((~r(s(z), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (elem!1 = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5406,plain,
% 1.72/1.99 (~r(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5405, 585, 5396, 670, 51, 453, 134, 123, 1, 435, 354, 902, 714])).
% 1.72/1.99 tff(5407,plain,
% 1.72/1.99 (b(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[348, 5406])).
% 1.72/1.99 tff(5408,plain,
% 1.72/1.99 (~b(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2297, 133, 134, 489, 123])).
% 1.72/1.99 tff(5409,plain,
% 1.72/1.99 (r(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[653, 5408, 1368])).
% 1.72/1.99 tff(5410,plain,
% 1.72/1.99 (~r(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[517, 5409, 51, 435])).
% 1.72/1.99 tff(5411,plain,
% 1.72/1.99 (b(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[507, 5410])).
% 1.72/1.99 tff(5412,plain,
% 1.72/1.99 (~b(s(z), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2383, 5411, 585, 489])).
% 1.72/1.99 tff(5413,plain,
% 1.72/1.99 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[121, 4931, 3396])).
% 1.72/1.99 tff(5414,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3282, 5409, 670, 5413])).
% 1.72/1.99 tff(5415,plain,
% 1.72/1.99 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3448, 5411, 547, 489, 5409, 670, 51, 133, 5414, 123, 134])).
% 1.72/1.99 tff(5416,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2946, 5415, 5412, 123])).
% 1.72/1.99 tff(5417,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = z) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5418,plain,
% 1.72/1.99 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5417, 5396, 123, 5407, 670, 51, 134, 585, 435, 77, 453])).
% 1.72/1.99 tff(5419,plain,
% 1.72/1.99 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[130, 5418, 114])).
% 1.72/1.99 tff(5420,plain,
% 1.72/1.99 (~r(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2938, 5419, 670, 51])).
% 1.72/1.99 tff(5421,plain,
% 1.72/1.99 (b(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1380, 5420, 77])).
% 1.72/1.99 tff(5422,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5423,plain,
% 1.72/1.99 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5424,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5423])).
% 1.72/1.99 tff(5425,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5424, 5422])).
% 1.72/1.99 tff(5426,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5427,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5426, 5425])).
% 1.72/1.99 tff(5428,plain,
% 1.72/1.99 ((~b(elem!1, z)) | (~b(elem!1, s(z)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5427, 144, 5396, 585, 5407])).
% 1.72/1.99 tff(5429,plain,
% 1.72/1.99 (~b(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5428, 5421])).
% 1.72/1.99 tff(5430,plain,
% 1.72/1.99 (r(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[720, 5429, 714])).
% 1.72/1.99 tff(5431,plain,
% 1.72/1.99 (~b(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[949, 5421, 585, 5396])).
% 1.72/1.99 tff(5432,plain,
% 1.72/1.99 (r(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[507, 5431])).
% 1.72/1.99 tff(5433,plain,
% 1.72/1.99 (((~![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(elem!1, s(z))) | (~r(z, elem!1)) | (~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), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5434,plain,
% 1.72/1.99 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5435,plain,
% 1.72/1.99 (((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5434])).
% 1.72/1.99 tff(5436,plain,
% 1.72/1.99 (((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5435, 5433])).
% 1.72/1.99 tff(5437,plain,
% 1.72/1.99 ((~![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(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5438,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5437, 5436])).
% 1.72/1.99 tff(5439,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5438, 333, 435, 670, 5432, 5430])).
% 1.72/1.99 tff(5440,plain,((~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5441,plain,
% 1.72/1.99 (~b(z, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5440, 5374, 2311, 5216, 51, 114, 123, 5373, 1, 354, 902])).
% 1.72/1.99 tff(5442,plain,
% 1.72/1.99 (r(z, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[583, 5441])).
% 1.72/1.99 tff(5443,plain,
% 1.72/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5359, 5442, 2311, 5216])).
% 1.72/1.99 tff(5444,plain,
% 1.72/1.99 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2655, 5442, 51, 5216])).
% 1.72/1.99 tff(5445,plain,
% 1.72/1.99 (~r(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1863, 5442, 2311, 5216])).
% 1.72/1.99 tff(5446,plain,
% 1.72/1.99 (b(elem!1, s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[720, 5445, 5374])).
% 1.72/1.99 tff(5447,plain,
% 1.72/1.99 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4423, 5446, 51, 453, 5373, 123, 2311])).
% 1.72/1.99 tff(5448,plain,
% 1.72/1.99 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4003, 5447, 606, 51, 77, 2311])).
% 1.72/1.99 tff(5449,plain,
% 1.72/1.99 (~r(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2938, 5447, 2311, 51])).
% 1.72/1.99 tff(5450,plain,
% 1.72/1.99 (b(elem!1, z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1380, 5449, 77])).
% 1.72/1.99 tff(5451,plain,
% 1.72/1.99 (~r(elem!1, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5074, 5442, 2311, 4562])).
% 1.72/1.99 tff(5452,plain,
% 1.72/1.99 (b(elem!1, s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[560, 5451, 902])).
% 1.72/1.99 tff(5453,plain,
% 1.72/1.99 (~r(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4411, 323, 1, 435, 354, 902, 670, 305])).
% 1.72/1.99 tff(5454,plain,
% 1.72/1.99 (~b(s(elem!1), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4482, 323, 706, 1, 670, 547, 354, 624, 435])).
% 1.72/1.99 tff(5455,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[507, 5454, 5453])).
% 1.72/1.99 tff(5456,plain,((~r(s(z), z)) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5457,plain,
% 1.72/1.99 (~r(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5456, 5372, 1, 2311, 5452, 354, 5450, 5216, 902, 5446])).
% 1.72/1.99 tff(5458,plain,
% 1.72/1.99 (b(s(z), z)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[348, 5457])).
% 1.72/1.99 tff(5459,plain,
% 1.72/1.99 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3424, 5458, 123, 5216, 2311, 902, 5374, 51, 5450, 354, 1, 5373, 5448])).
% 1.72/1.99 tff(5460,plain,
% 1.72/1.99 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[319, 5459])).
% 1.72/1.99 tff(5461,plain,
% 1.72/1.99 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2541, 5460, 2311, 51])).
% 1.72/1.99 tff(5462,plain,
% 1.72/1.99 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[121, 5461, 453])).
% 1.72/1.99 tff(5463,plain,
% 1.72/1.99 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[542, 537, 535])).
% 1.72/1.99 tff(5464,plain,
% 1.72/1.99 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[930, 537])).
% 1.72/1.99 tff(5465,plain,
% 1.72/1.99 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[472, 5464, 466])).
% 1.72/1.99 tff(5466,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5316, 5465, 5463, 547, 132])).
% 1.72/1.99 tff(5467,plain,((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5468,plain,
% 1.72/1.99 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5467, 5452, 5462, 5448, 5444])).
% 1.72/1.99 tff(5469,plain,
% 1.72/1.99 (~(elem!1 = s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1216, 5468])).
% 1.72/1.99 tff(5470,plain,
% 1.72/1.99 (b(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2522, 5469, 5443])).
% 1.72/1.99 tff(5471,plain,
% 1.72/1.99 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5468])).
% 1.72/1.99 tff(5472,plain,
% 1.72/1.99 (r(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(z), s(s(elem!1)))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5471])).
% 1.72/1.99 tff(5473,plain,
% 1.72/1.99 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(z), s(s(elem!1))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5472])).
% 1.72/1.99 tff(5474,plain,
% 1.72/1.99 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2610, 5460, 354, 51])).
% 1.72/1.99 tff(5475,plain,
% 1.72/1.99 (~r(s(z), s(s(elem!1)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5474, 5473])).
% 1.72/1.99 tff(5476,plain,
% 1.72/1.99 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.72/1.99 inference(commutativity,[status(thm)],[])).
% 1.72/1.99 tff(5477,plain,
% 1.72/1.99 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.72/1.99 inference(symmetry,[status(thm)],[5476])).
% 1.72/1.99 tff(5478,plain,
% 1.72/1.99 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5477])).
% 1.72/1.99 tff(5479,plain,
% 1.72/1.99 (~(s(z) = s(s(elem!1)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[107, 5478])).
% 1.72/1.99 tff(5480,plain,
% 1.72/1.99 (((~![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))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5481,plain,
% 1.72/1.99 ((~![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))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5482,plain,
% 1.72/1.99 ((~![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)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5481, 5480])).
% 1.72/2.00 tff(5483,plain,
% 1.72/2.00 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5482, 44])).
% 1.72/2.00 tff(5484,plain,
% 1.72/2.00 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5483, 5479])).
% 1.72/2.00 tff(5485,plain,
% 1.72/2.00 (b(s(z), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5484, 5475])).
% 1.72/2.00 tff(5486,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.72/2.00 tff(5487,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5488,plain,
% 1.72/2.00 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5489,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5488])).
% 1.72/2.00 tff(5490,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5489, 5487])).
% 1.72/2.00 tff(5491,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5492,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5491, 5490])).
% 1.72/2.00 tff(5493,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5492, 144, 547, 1249, 5486, 305, 2812])).
% 1.72/2.00 tff(5494,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5495,plain,
% 1.72/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5494, 5452, 5485, 5446, 5470])).
% 1.72/2.00 tff(5496,plain,
% 1.72/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1283, 5495, 2727])).
% 1.72/2.00 tff(5497,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.72/2.00 tff(5498,plain,
% 1.72/2.00 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), 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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5499,plain,
% 1.72/2.00 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5500,plain,
% 1.72/2.00 (((~![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(s(elem!1)), s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5499])).
% 1.72/2.00 tff(5501,plain,
% 1.72/2.00 (((~![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(s(elem!1)), s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5500, 5498])).
% 1.72/2.00 tff(5502,plain,
% 1.72/2.00 ((~![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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5503,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 1.72/2.00 tff(5504,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5503, 333, 435, 2737, 562, 5497])).
% 1.72/2.00 tff(5505,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5506,plain,
% 1.72/2.00 (~r(s(s(elem!1)), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5505, 5496, 5216, 5442])).
% 1.72/2.00 tff(5507,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.72/2.00 tff(5508,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5041, 44, 1094, 5507, 5038])).
% 1.72/2.00 tff(5509,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5510,plain,
% 1.72/2.00 (b(s(s(elem!1)), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5509, 5506])).
% 1.72/2.00 tff(5511,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5512,plain,
% 1.72/2.00 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5513,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5512])).
% 1.72/2.00 tff(5514,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5513, 5511])).
% 1.72/2.00 tff(5515,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5516,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5515, 5514])).
% 1.72/2.00 tff(5517,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5516, 144, 5450, 5485, 5446, 5470, 5510])).
% 1.72/2.00 tff(5518,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5519,plain,
% 1.72/2.00 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5518, 902, 51, 123, 354, 1, 606, 2310, 285])).
% 1.72/2.00 tff(5520,plain,
% 1.72/2.00 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5519])).
% 1.72/2.00 tff(5521,plain,
% 1.72/2.00 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5520])).
% 1.72/2.00 tff(5522,plain,
% 1.72/2.00 (~(elem!1 = s(s(s(z))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[244, 5521])).
% 1.72/2.00 tff(5523,plain,
% 1.72/2.00 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5519])).
% 1.72/2.00 tff(5524,plain,
% 1.72/2.00 (b(s(z), elem!1)),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[123, 5523])).
% 1.72/2.00 tff(5525,plain,
% 1.72/2.00 (~r(z, s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5074, 563, 670, 1686])).
% 1.72/2.00 tff(5526,plain,
% 1.72/2.00 (b(z, s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[583, 5525])).
% 1.72/2.00 tff(5527,plain,
% 1.72/2.00 (~b(s(s(s(z))), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[3170, 144, 5381, 5526, 285])).
% 1.72/2.00 tff(5528,plain,
% 1.72/2.00 (r(s(s(s(z))), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 5527])).
% 1.72/2.00 tff(5529,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5530,plain,
% 1.72/2.00 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5531,plain,
% 1.72/2.00 (((~![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(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5530])).
% 1.72/2.00 tff(5532,plain,
% 1.72/2.00 (((~![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(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5531, 5529])).
% 1.72/2.00 tff(5533,plain,
% 1.72/2.00 ((~![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(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5534,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 1.72/2.00 tff(5535,plain,
% 1.72/2.00 (~r(elem!1, s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5534, 333, 563, 435, 5528])).
% 1.72/2.00 tff(5536,plain,
% 1.72/2.00 (b(elem!1, s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1538, 5535, 3843])).
% 1.72/2.00 tff(5537,plain,
% 1.72/2.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5536, 1523])).
% 1.72/2.00 tff(5538,plain,
% 1.72/2.00 (~r(s(s(s(z))), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[3910, 333, 563, 435, 5528])).
% 1.72/2.00 tff(5539,plain,
% 1.72/2.00 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5538, 4901])).
% 1.72/2.00 tff(5540,plain,
% 1.72/2.00 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1137, 5539])).
% 1.72/2.00 tff(5541,plain,
% 1.72/2.00 (~b(s(z), s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2262, 5540, 123, 5537])).
% 1.72/2.00 tff(5542,plain,
% 1.72/2.00 (r(s(z), s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[172, 5541])).
% 1.72/2.00 tff(5543,plain,
% 1.72/2.00 (~r(z, s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[3011, 5542, 354, 5528])).
% 1.72/2.00 tff(5544,plain,
% 1.72/2.00 (b(z, s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[619, 5543])).
% 1.72/2.00 tff(5545,plain,
% 1.72/2.00 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[294, 5544, 285, 5537])).
% 1.72/2.00 tff(5546,plain,
% 1.72/2.00 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[302, 5545])).
% 1.72/2.00 tff(5547,plain,
% 1.72/2.00 (r(elem!1, z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2558, 5546, 81])).
% 1.72/2.00 tff(5548,plain,
% 1.72/2.00 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[362, 5546, 5542, 354])).
% 1.72/2.00 tff(5549,plain,
% 1.72/2.00 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[319, 5548])).
% 1.72/2.00 tff(5550,plain,
% 1.72/2.00 (b(elem!1, s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[735, 5549, 81])).
% 1.72/2.00 tff(5551,plain,
% 1.72/2.00 (b(s(z), elem!1)),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[123, 2230])).
% 1.72/2.00 tff(5552,plain,
% 1.72/2.00 (b(s(s(s(z))), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[704, 5538, 4363])).
% 1.72/2.00 tff(5553,plain,
% 1.72/2.00 (~b(s(s(s(z))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[4375, 5550, 5551, 5552])).
% 1.72/2.00 tff(5554,plain,
% 1.72/2.00 (r(s(s(s(z))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2794, 5553])).
% 1.72/2.00 tff(5555,plain,
% 1.72/2.00 (((~![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(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), 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(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5556,plain,
% 1.72/2.00 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5557,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(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(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5556])).
% 1.72/2.00 tff(5558,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(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(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5557, 5555])).
% 1.72/2.00 tff(5559,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5560,plain,
% 1.72/2.00 ((~![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(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5559, 5558])).
% 1.72/2.00 tff(5561,plain,
% 1.72/2.00 (~r(s(z), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5560, 333, 5554, 1686, 5542])).
% 1.72/2.00 tff(5562,plain,
% 1.72/2.00 (b(s(z), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1244, 5561, 1237])).
% 1.72/2.00 tff(5563,plain,
% 1.72/2.00 (~b(s(z), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2383, 5562, 5381, 5526])).
% 1.72/2.00 tff(5564,plain,
% 1.72/2.00 (r(s(z), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[348, 5563])).
% 1.72/2.00 tff(5565,plain,
% 1.72/2.00 (b(s(s(elem!1)), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5056, 5564, 670, 5551, 5011, 5550, 5547])).
% 1.72/2.00 tff(5566,plain,
% 1.72/2.00 (((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5567,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5566])).
% 1.72/2.00 tff(5568,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5567, 2728])).
% 1.72/2.00 tff(5569,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5570,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 1.72/2.00 tff(5571,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5570, 144, 491, 585, 1249, 2726])).
% 1.72/2.00 tff(5572,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5573,plain,
% 1.72/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5572, 5381, 5526, 5565])).
% 1.72/2.00 tff(5574,plain,
% 1.72/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1283, 5573, 2854])).
% 1.72/2.00 tff(5575,plain,
% 1.72/2.00 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5576,plain,
% 1.72/2.00 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5577,plain,
% 1.72/2.00 (((~![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(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5576])).
% 1.72/2.00 tff(5578,plain,
% 1.72/2.00 (((~![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(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5577, 5575])).
% 1.72/2.00 tff(5579,plain,
% 1.72/2.00 ((~![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(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5580,plain,
% 1.72/2.00 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5579, 5578])).
% 1.72/2.00 tff(5581,plain,
% 1.72/2.00 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5580, 333, 435, 5574, 5528])).
% 1.72/2.00 tff(5582,plain,
% 1.72/2.00 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = elem!1)),
% 1.72/2.00 inference(monotonicity,[status(thm)],[81])).
% 1.72/2.00 tff(5583,plain,
% 1.72/2.00 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(z) = elem!1))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5582])).
% 1.72/2.00 tff(5584,plain,
% 1.72/2.00 (~(s(z) = elem!1)),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[34, 5583])).
% 1.72/2.00 tff(5585,plain,
% 1.72/2.00 (~(s(s(z)) = s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[855, 5584])).
% 1.72/2.00 tff(5586,plain,
% 1.72/2.00 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[862, 5585])).
% 1.72/2.00 tff(5587,plain,
% 1.72/2.00 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[4917, 5586])).
% 1.72/2.00 tff(5588,plain,
% 1.72/2.00 (b(s(s(elem!1)), s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5022, 44, 5587, 5581])).
% 1.72/2.00 tff(5589,plain,
% 1.72/2.00 (~r(s(s(elem!1)), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2785, 333, 563, 435, 5574])).
% 1.72/2.01 tff(5590,plain,
% 1.72/2.01 (b(s(s(elem!1)), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1260, 44, 5589, 5011])).
% 1.72/2.01 tff(5591,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5592,plain,
% 1.72/2.01 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5593,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5592])).
% 1.72/2.01 tff(5594,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5593, 5591])).
% 1.72/2.01 tff(5595,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5596,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5595, 5594])).
% 1.72/2.01 tff(5597,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5596, 144, 5536, 5552, 5590, 5588])).
% 1.72/2.01 tff(5598,plain,((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5599,plain,
% 1.72/2.01 (~r(elem!1, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5598, 2727, 5216, 2311, 1229, 4562, 5519, 354, 285, 123])).
% 1.72/2.01 tff(5600,plain,
% 1.72/2.01 (b(elem!1, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[560, 5599, 902])).
% 1.72/2.01 tff(5601,plain,
% 1.72/2.01 (s(s(elem!1)) = elem!1),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[1202, 4572])).
% 1.72/2.01 tff(5602,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1257, 5601])).
% 1.72/2.01 tff(5603,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5604,plain,
% 1.72/2.01 (~(elem!1 = s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5603, 5011])).
% 1.72/2.01 tff(5605,plain,
% 1.72/2.01 (~r(elem!1, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5359, 562, 670, 435])).
% 1.72/2.01 tff(5606,plain,
% 1.72/2.01 (b(elem!1, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2522, 5605, 5604])).
% 1.72/2.01 tff(5607,plain,
% 1.72/2.01 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(z))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5582, 53])).
% 1.72/2.01 tff(5608,plain,
% 1.72/2.01 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(z)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5607])).
% 1.72/2.01 tff(5609,plain,
% 1.72/2.01 (~(elem!1 = s(z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[34, 5608])).
% 1.72/2.01 tff(5610,plain,
% 1.72/2.01 (~r(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1863, 562, 670, 435])).
% 1.72/2.01 tff(5611,plain,
% 1.72/2.01 (b(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[720, 5610, 5609])).
% 1.72/2.01 tff(5612,plain,
% 1.72/2.01 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2623, 4854, 435])).
% 1.72/2.01 tff(5613,plain,
% 1.72/2.01 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[940, 562, 51, 5612])).
% 1.72/2.01 tff(5614,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[302, 5613])).
% 1.72/2.01 tff(5615,plain,
% 1.72/2.01 (b(elem!1, z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[787, 5614, 81])).
% 1.72/2.01 tff(5616,plain,
% 1.72/2.01 (~r(s(s(elem!1)), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5505, 2737, 435, 562])).
% 1.72/2.01 tff(5617,plain,
% 1.72/2.01 (b(s(s(elem!1)), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5509, 5616])).
% 1.72/2.01 tff(5618,plain,
% 1.72/2.01 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.72/2.01 inference(commutativity,[status(thm)],[])).
% 1.72/2.01 tff(5619,plain,
% 1.72/2.01 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5618])).
% 1.72/2.01 tff(5620,plain,
% 1.72/2.01 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5619])).
% 1.72/2.01 tff(5621,plain,
% 1.72/2.01 (~(z = s(s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[1094, 5620])).
% 1.72/2.01 tff(5622,plain,
% 1.72/2.01 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5623,plain,
% 1.72/2.01 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5624,plain,
% 1.72/2.01 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5623])).
% 1.72/2.01 tff(5625,plain,
% 1.72/2.01 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5624, 5622])).
% 1.72/2.01 tff(5626,plain,
% 1.72/2.01 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5627,plain,
% 1.72/2.01 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5626, 5625])).
% 1.72/2.01 tff(5628,plain,
% 1.72/2.01 (~r(z, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5627, 333, 435, 2737, 562])).
% 1.72/2.01 tff(5629,plain,
% 1.72/2.01 (((~![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))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5630,plain,
% 1.72/2.01 ((~![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))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5631,plain,
% 1.72/2.01 ((~![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)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5630, 5629])).
% 1.72/2.01 tff(5632,plain,
% 1.72/2.01 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5631, 44, 5628])).
% 1.72/2.01 tff(5633,plain,
% 1.72/2.01 (b(z, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5632, 5621])).
% 1.72/2.01 tff(5634,plain,
% 1.72/2.01 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5635,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5634])).
% 1.72/2.01 tff(5636,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5635, 2813])).
% 1.72/2.01 tff(5637,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5638,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 1.72/2.01 tff(5639,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5638, 144, 624, 2812, 5633, 5617])).
% 1.72/2.01 tff(5640,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5641,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5640, 5615, 5606, 435, 562])).
% 1.72/2.01 tff(5642,plain,
% 1.72/2.01 (b(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1283, 5641, 2854])).
% 1.72/2.01 tff(5643,plain,
% 1.72/2.01 (~b(s(z), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5494, 5642, 547, 5611, 5606])).
% 1.72/2.01 tff(5644,plain,
% 1.72/2.01 (r(s(z), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5484, 5643])).
% 1.72/2.01 tff(5645,plain,
% 1.72/2.01 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(elem!1, s(z))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[81])).
% 1.72/2.01 tff(5646,plain,
% 1.72/2.01 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5645])).
% 1.72/2.01 tff(5647,plain,
% 1.72/2.01 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5646])).
% 1.72/2.01 tff(5648,plain,
% 1.72/2.01 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5610, 5647])).
% 1.72/2.01 tff(5649,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[319, 5648])).
% 1.72/2.01 tff(5650,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[81])).
% 1.72/2.01 tff(5651,plain,
% 1.72/2.01 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5650])).
% 1.72/2.01 tff(5652,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5606, 5651])).
% 1.72/2.01 tff(5653,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[81])).
% 1.72/2.01 tff(5654,plain,
% 1.72/2.01 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5653])).
% 1.72/2.01 tff(5655,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[547, 5654])).
% 1.72/2.01 tff(5656,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[536, 5655])).
% 1.72/2.01 tff(5657,plain,((~b(elem!1, s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5658,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5657, 547, 81])).
% 1.72/2.01 tff(5659,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.72/2.01 tff(5660,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5661,plain,
% 1.72/2.01 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5662,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5661])).
% 1.72/2.01 tff(5663,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5662, 5660])).
% 1.72/2.01 tff(5664,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5665,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5664, 5663])).
% 1.72/2.01 tff(5666,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5665, 144, 1249, 488, 5659, 304, 546])).
% 1.72/2.01 tff(5667,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5668,plain,
% 1.72/2.01 (~b(s(elem!1), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5667, 5642, 5658, 5652, 5649])).
% 1.72/2.01 tff(5669,plain,
% 1.72/2.01 (r(s(elem!1), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[486, 5668, 1])).
% 1.72/2.01 tff(5670,plain,
% 1.72/2.01 (((~![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(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(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5671,plain,
% 1.72/2.01 ((~![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(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5672,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5671, 5670])).
% 1.72/2.01 tff(5673,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5672, 333, 354, 5669, 562, 5644])).
% 1.72/2.01 tff(5674,plain,((~r(z, s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5675,plain,
% 1.72/2.01 (~r(z, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5674, 5600, 1, 354, 2727, 5216, 5519, 51, 2311])).
% 1.72/2.01 tff(5676,plain,
% 1.72/2.01 (b(z, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[583, 5675])).
% 1.72/2.01 tff(5677,plain,
% 1.72/2.01 (~r(s(elem!1), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[517, 408, 51, 435])).
% 1.72/2.01 tff(5678,plain,
% 1.72/2.01 (b(s(elem!1), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[507, 5677])).
% 1.72/2.01 tff(5679,plain,
% 1.72/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[735, 708, 81])).
% 1.72/2.01 tff(5680,plain,
% 1.72/2.01 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[319, 5679])).
% 1.72/2.01 tff(5681,plain,
% 1.72/2.01 (r(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[720, 708, 5609])).
% 1.72/2.01 tff(5682,plain,
% 1.72/2.01 (~r(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[727, 5681, 354, 670])).
% 1.72/2.01 tff(5683,plain,
% 1.72/2.01 (b(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[348, 5682])).
% 1.72/2.01 tff(5684,plain,
% 1.72/2.01 (r(elem!1, s(z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[322, 5645])).
% 1.72/2.01 tff(5685,plain,
% 1.72/2.01 (b(s(z), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1244, 2320, 1237])).
% 1.72/2.01 tff(5686,plain,
% 1.72/2.01 (~b(z, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2383, 5685, 489, 491])).
% 1.72/2.01 tff(5687,plain,
% 1.72/2.01 (r(z, s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[583, 5686])).
% 1.72/2.01 tff(5688,plain,
% 1.72/2.01 (~r(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1863, 5687, 670, 435])).
% 1.72/2.01 tff(5689,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5688, 5684])).
% 1.72/2.01 tff(5690,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5691,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5690, 5683, 5680, 670, 435, 81, 491, 1237, 354, 51])).
% 1.72/2.01 tff(5692,plain,(b(elem!1, s(z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5693,plain,
% 1.72/2.01 (b(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5692, 5678, 435, 81, 670, 1237, 354, 51])).
% 1.72/2.01 tff(5694,plain,
% 1.72/2.01 (~b(s(s(s(z))), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[3170, 144, 5678, 585, 285])).
% 1.72/2.01 tff(5695,plain,
% 1.72/2.01 (r(s(s(s(z))), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 5694])).
% 1.72/2.01 tff(5696,plain,
% 1.72/2.01 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5572, 2726, 585, 491])).
% 1.72/2.01 tff(5697,plain,
% 1.72/2.01 (r(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1283, 5696, 2854])).
% 1.72/2.01 tff(5698,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5580, 333, 435, 5697, 3003])).
% 1.72/2.01 tff(5699,plain,
% 1.72/2.01 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[4917, 1184])).
% 1.72/2.01 tff(5700,plain,
% 1.72/2.01 (b(s(s(elem!1)), s(s(s(z))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5022, 44, 5699, 5698])).
% 1.72/2.01 tff(5701,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.72/2.01 tff(5702,plain,
% 1.72/2.01 (((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5703,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5702])).
% 1.72/2.01 tff(5704,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5703, 5058])).
% 1.72/2.01 tff(5705,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5706,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 1.72/2.01 tff(5707,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5706, 144, 285, 284, 2726, 5701])).
% 1.72/2.01 tff(5708,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5709,plain,
% 1.72/2.01 (~b(z, s(s(s(z))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5708, 2726, 285, 5700])).
% 1.72/2.01 tff(5710,plain,
% 1.72/2.01 (r(z, s(s(s(z))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[619, 5709])).
% 1.72/2.02 tff(5711,plain,
% 1.72/2.02 (~r(s(z), s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3011, 5710, 354, 3003])).
% 1.72/2.02 tff(5712,plain,
% 1.72/2.02 (b(s(z), s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[172, 5711])).
% 1.72/2.02 tff(5713,plain,
% 1.72/2.02 (~r(s(s(s(z))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2136, 5710, 670, 408])).
% 1.72/2.02 tff(5714,plain,
% 1.72/2.02 (b(s(s(s(z))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[704, 5713, 698])).
% 1.72/2.02 tff(5715,plain,
% 1.72/2.02 (~b(s(s(s(z))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[4375, 5714, 134, 305])).
% 1.72/2.02 tff(5716,plain,
% 1.72/2.02 (r(s(s(s(z))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2794, 5715])).
% 1.72/2.02 tff(5717,plain,
% 1.72/2.02 (~r(elem!1, s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3201, 5716, 670, 5710])).
% 1.72/2.02 tff(5718,plain,
% 1.72/2.02 (b(elem!1, s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1538, 5717, 1524])).
% 1.72/2.02 tff(5719,plain,
% 1.72/2.02 (((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(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(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5720,plain,
% 1.72/2.02 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5721,plain,
% 1.72/2.02 ((~![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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5720, 5719])).
% 1.72/2.02 tff(5722,plain,
% 1.72/2.02 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5721, 333, 435, 5697, 3003])).
% 1.72/2.02 tff(5723,plain,
% 1.72/2.02 (b(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1301, 5722, 1184])).
% 1.72/2.02 tff(5724,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.72/2.02 tff(5725,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(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(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5726,plain,
% 1.72/2.02 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5727,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~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), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5726])).
% 1.72/2.02 tff(5728,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~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), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5727, 5725])).
% 1.72/2.02 tff(5729,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5730,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.72/2.02 tff(5731,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5730, 333, 354, 5724, 623, 3193])).
% 1.72/2.02 tff(5732,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5733,plain,
% 1.72/2.02 (~r(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5732, 5716, 354, 5710])).
% 1.72/2.02 tff(5734,plain,
% 1.72/2.02 (b(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5484, 5733])).
% 1.72/2.02 tff(5735,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5736,plain,
% 1.72/2.02 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5737,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5736])).
% 1.72/2.02 tff(5738,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5737, 5735])).
% 1.72/2.02 tff(5739,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5740,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5739, 5738])).
% 1.72/2.02 tff(5741,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5740, 144, 134, 5734, 5723, 5718, 5712])).
% 1.72/2.02 tff(5742,plain,((~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5743,plain,
% 1.72/2.02 (~b(s(s(elem!1)), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5742, 5693, 3843, 354, 670, 134, 4363, 408, 5695, 285, 5586, 435, 2854, 585, 5678])).
% 1.72/2.02 tff(5744,plain,
% 1.72/2.02 (~r(s(z), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5056, 5743, 670, 134, 5011, 5693, 408])).
% 1.72/2.02 tff(5745,plain,
% 1.72/2.02 (b(s(z), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[348, 5744])).
% 1.72/2.02 tff(5746,plain,
% 1.72/2.02 (~b(s(z), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2383, 5745, 585, 5678])).
% 1.72/2.02 tff(5747,plain,
% 1.72/2.02 (r(s(z), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1244, 5746, 1237])).
% 1.72/2.02 tff(5748,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5690, 5745, 670, 435, 81, 5678, 1237, 354, 51])).
% 1.72/2.02 tff(5749,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[319, 5748])).
% 1.72/2.02 tff(5750,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3799, 5749, 5747, 435, 4363, 81, 285, 5694, 408, 5745])).
% 1.72/2.02 tff(5751,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(z))), z)) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5752,plain,
% 1.72/2.02 (~r(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5751, 5519, 5216, 285, 1229, 2311, 354, 51, 5676, 5524, 2727])).
% 1.72/2.02 tff(5753,plain,
% 1.72/2.02 (b(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1380, 5752, 77])).
% 1.72/2.02 tff(5754,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5755,plain,
% 1.72/2.02 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5756,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5755])).
% 1.72/2.02 tff(5757,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5756, 5754])).
% 1.72/2.02 tff(5758,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5759,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 1.72/2.02 tff(5760,plain,
% 1.72/2.02 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5759, 144, 5600, 5676, 285])).
% 1.72/2.02 tff(5761,plain,
% 1.72/2.02 (~b(elem!1, s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5760, 5753])).
% 1.72/2.02 tff(5762,plain,
% 1.72/2.02 (r(elem!1, s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1538, 5761, 5522])).
% 1.72/2.02 tff(5763,plain,
% 1.72/2.02 (~b(s(elem!1), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[949, 5753, 5600, 5676])).
% 1.72/2.02 tff(5764,plain,
% 1.72/2.02 (r(s(elem!1), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[507, 5763])).
% 1.72/2.02 tff(5765,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3895, 333, 5216, 2311, 5764, 5762])).
% 1.72/2.02 tff(5766,plain,((elem!1 = s(elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5767,plain,
% 1.72/2.02 (elem!1 = s(elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5766, 285, 354, 51, 1, 123, 606, 2310])).
% 1.72/2.02 tff(5768,plain,
% 1.72/2.02 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(elem!1))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5767])).
% 1.72/2.02 tff(5769,plain,
% 1.72/2.02 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), elem!1)),
% 1.72/2.02 inference(symmetry,[status(thm)],[5768])).
% 1.72/2.02 tff(5770,plain,
% 1.72/2.02 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), elem!1))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5769])).
% 1.72/2.02 tff(5771,plain,
% 1.72/2.02 (~r(s(elem!1), elem!1)),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[3482, 5770])).
% 1.72/2.02 tff(5772,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5216, 5771])).
% 1.72/2.02 tff(5773,plain,((~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5774,plain,
% 1.72/2.02 (~b(s(s(s(z))), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5773, 51, 354, 1, 50, 606, 2310])).
% 1.72/2.02 tff(5775,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.72/2.02 tff(5776,plain,
% 1.72/2.02 (r(elem!1, s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[560, 2483, 5775])).
% 1.72/2.02 tff(5777,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2492, 5776, 670, 51])).
% 1.72/2.02 tff(5778,plain,
% 1.72/2.02 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[4052, 5776, 670, 562])).
% 1.72/2.02 tff(5779,plain,
% 1.72/2.02 (b(s(elem!1), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[448, 2681, 1727])).
% 1.72/2.02 tff(5780,plain,
% 1.72/2.02 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3934, 5779, 123, 57, 5778])).
% 1.72/2.02 tff(5781,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[130, 5780, 5777, 114])).
% 1.72/2.02 tff(5782,plain,((~(s(z) = elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5783,plain,
% 1.72/2.02 (~(s(z) = elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5782, 114, 123, 2311, 562, 51, 1727, 5775])).
% 1.72/2.02 tff(5784,plain,
% 1.72/2.02 (b(s(z), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[406, 5783, 2310])).
% 1.72/2.02 tff(5785,plain,
% 1.72/2.02 (~(elem!1 = s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[712, 5783])).
% 1.72/2.02 tff(5786,plain,
% 1.72/2.02 (~b(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[4850, 902, 1727, 134, 354, 123, 51, 606, 714, 1, 114, 2310])).
% 1.72/2.02 tff(5787,plain,
% 1.72/2.02 (r(elem!1, s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[560, 902, 5775])).
% 1.72/2.02 tff(5788,plain,
% 1.72/2.02 (~r(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[678, 5787, 2311, 509])).
% 1.72/2.02 tff(5789,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[653, 5788, 5786, 77])).
% 1.72/2.02 tff(5790,plain,((elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | r(s(elem!1), elem!1) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(z), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5791,plain,
% 1.72/2.02 (elem!1 = s(elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5790, 5784, 1727, 509, 354, 123, 51, 606, 5785, 1, 114, 2310, 5775])).
% 1.72/2.02 tff(5792,plain,
% 1.72/2.02 (s(elem!1) = elem!1),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1569, 5791])).
% 1.72/2.02 tff(5793,plain,
% 1.72/2.02 (b(s(z), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3262, 5792, 5784])).
% 1.72/2.02 tff(5794,plain,
% 1.72/2.02 (~b(s(elem!1), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[890, 5791, 708])).
% 1.72/2.02 tff(5795,plain,
% 1.72/2.02 (r(s(elem!1), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[486, 5794, 1])).
% 1.72/2.02 tff(5796,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3363, 5795, 51, 606, 1727, 5784, 5793, 2311])).
% 1.72/2.02 tff(5797,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[130, 5796, 114])).
% 1.72/2.02 tff(5798,plain,
% 1.72/2.02 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[152, 5797, 123, 5784])).
% 1.72/2.02 tff(5799,plain,
% 1.72/2.02 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[121, 5798, 453])).
% 1.72/2.02 tff(5800,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2541, 5799, 2311, 51])).
% 1.72/2.02 tff(5801,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[319, 5800])).
% 1.72/2.02 tff(5802,plain,
% 1.72/2.02 (r(elem!1, s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[720, 5785, 708])).
% 1.72/2.02 tff(5803,plain,
% 1.72/2.02 (~r(s(z), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[727, 5802, 354, 2311])).
% 1.72/2.02 tff(5804,plain,
% 1.72/2.02 (b(s(z), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[348, 5803])).
% 1.72/2.02 tff(5805,plain,
% 1.72/2.02 (~b(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2297, 5797, 5784, 5804, 123])).
% 1.72/2.02 tff(5806,plain,
% 1.72/2.02 (r(elem!1, z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[653, 5805, 77])).
% 1.72/2.02 tff(5807,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3282, 5806, 2311, 5799])).
% 1.72/2.02 tff(5808,plain,
% 1.72/2.02 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2927, 5807, 354, 1, 1727, 5784, 509, 5806, 5801, 2311, 5798])).
% 1.72/2.02 tff(5809,plain,
% 1.72/2.02 (s(s(elem!1)) = s(elem!1)),
% 1.72/2.02 inference(monotonicity,[status(thm)],[903])).
% 1.72/2.02 tff(5810,plain,
% 1.72/2.02 (s(elem!1) = s(s(elem!1))),
% 1.72/2.02 inference(symmetry,[status(thm)],[5809])).
% 1.72/2.02 tff(5811,plain,
% 1.72/2.02 (elem!1 = s(s(elem!1))),
% 1.72/2.02 inference(transitivity,[status(thm)],[1553, 5810])).
% 1.72/2.02 tff(5812,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1221, 5811])).
% 1.72/2.02 tff(5813,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5814,plain,
% 1.72/2.02 (elem!1 = s(s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5813, 5792])).
% 1.72/2.02 tff(5815,plain,
% 1.72/2.02 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1216, 5814])).
% 1.72/2.02 tff(5816,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2894, 5799, 2311, 51])).
% 1.72/2.02 tff(5817,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[542, 5816, 5815])).
% 1.72/2.02 tff(5818,plain,
% 1.72/2.02 (s(s(s(elem!1))) = elem!1),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[2482, 5791])).
% 1.72/2.02 tff(5819,plain,
% 1.72/2.02 (~(s(s(s(z))) = s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1010, 5818])).
% 1.72/2.02 tff(5820,plain,
% 1.72/2.02 (~b(s(s(s(z))), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5773, 51, 354, 1, 123, 606, 2310])).
% 1.72/2.02 tff(5821,plain,
% 1.72/2.02 (r(s(s(s(z))), z)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[396, 5820])).
% 1.72/2.02 tff(5822,plain,
% 1.72/2.02 (((~![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(s(s(z))), z)) | (~r(s(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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5823,plain,
% 1.72/2.02 ((~![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(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(5824,plain,
% 1.85/2.02 ((~![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(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 1.85/2.02 tff(5825,plain,
% 1.85/2.02 (~r(s(s(s(z))), s(elem!1))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[5824, 333, 2311, 509, 5821])).
% 1.85/2.02 tff(5826,plain,
% 1.85/2.02 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[1951, 44, 5825])).
% 1.85/2.02 tff(5827,plain,
% 1.85/2.02 (b(s(s(s(z))), s(elem!1))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[5826, 5819])).
% 1.85/2.02 tff(5828,plain,
% 1.85/2.02 (((~![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(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), 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(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(5829,plain,
% 1.85/2.02 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(5830,plain,
% 1.85/2.02 (((~![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(z))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[5829])).
% 1.85/2.02 tff(5831,plain,
% 1.85/2.02 (((~![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(z))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.85/2.02 inference(transitivity,[status(thm)],[5830, 5828])).
% 1.85/2.02 tff(5832,plain,
% 1.85/2.02 ((~![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(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(5833,plain,
% 1.85/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 1.85/2.02 tff(5834,plain,
% 1.85/2.02 ($false),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[5833, 333, 670, 509, 1699, 1686])).
% 1.85/2.02 tff(5835,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.02 tff(5836,plain,
% 1.85/2.02 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[5835, 509, 5821, 2311])).
% 1.85/2.02 tff(5837,plain,
% 1.85/2.02 (s(elem!1) = s(s(s(elem!1)))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[2584, 5818, 5791])).
% 1.85/2.02 tff(5838,plain,
% 1.85/2.02 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[990, 5837, 1])).
% 1.85/2.02 tff(5839,plain,
% 1.85/2.02 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[965, 5838, 5836])).
% 1.85/2.02 tff(5840,plain,
% 1.85/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(5841,plain,
% 1.85/2.03 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(5842,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[5841])).
% 1.85/2.03 tff(5843,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.85/2.03 tff(5844,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(5845,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.85/2.03 tff(5846,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5845, 144, 5839, 5827, 5817])).
% 1.85/2.03 tff(5847,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[249, 5846])).
% 1.85/2.03 tff(5848,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3704, 333, 509, 5847, 51, 5808])).
% 1.85/2.03 tff(5849,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | b(elem!1, s(z)) | r(s(z), elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5850,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5849, 5775, 51, 354, 1, 1727, 123, 606, 708, 2310, 509, 562])).
% 1.85/2.03 tff(5851,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[735, 5850, 708])).
% 1.85/2.03 tff(5852,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[319, 5851])).
% 1.85/2.03 tff(5853,plain,
% 1.85/2.03 (~r(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2319, 5852, 354, 51])).
% 1.85/2.03 tff(5854,plain,
% 1.85/2.03 (b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1244, 5853, 1229])).
% 1.85/2.03 tff(5855,plain,
% 1.85/2.03 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3398, 5850])).
% 1.85/2.03 tff(5856,plain,
% 1.85/2.03 (~(s(s(elem!1)) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5010, 5850])).
% 1.85/2.03 tff(5857,plain,
% 1.85/2.03 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5603, 5856])).
% 1.85/2.03 tff(5858,plain,
% 1.85/2.03 (~(s(elem!1) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5813, 5857])).
% 1.85/2.03 tff(5859,plain,
% 1.85/2.03 (~(elem!1 = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1569, 5858])).
% 1.85/2.03 tff(5860,plain,
% 1.85/2.03 (r(elem!1, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[560, 5859, 5775])).
% 1.85/2.03 tff(5861,plain,
% 1.85/2.03 (~r(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[678, 5860, 2311, 509])).
% 1.85/2.03 tff(5862,plain,
% 1.85/2.03 (~b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2569, 5861, 123, 1727, 5855, 5854])).
% 1.85/2.03 tff(5863,plain,
% 1.85/2.03 (r(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[348, 5862])).
% 1.85/2.03 tff(5864,plain,
% 1.85/2.03 (~r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[727, 5863, 354, 2311])).
% 1.85/2.03 tff(5865,plain,
% 1.85/2.03 (b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1380, 5861, 77])).
% 1.85/2.03 tff(5866,plain,
% 1.85/2.03 (~(s(z) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3965, 5862, 5865])).
% 1.85/2.03 tff(5867,plain,
% 1.85/2.03 (~(elem!1 = s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[712, 5866])).
% 1.85/2.03 tff(5868,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[720, 5867, 5864, 708])).
% 1.85/2.03 tff(5869,plain,(b(elem!1, s(elem!1)) | b(elem!1, s(z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5870,plain,
% 1.85/2.03 (b(elem!1, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5869, 562, 354, 123, 1727, 509, 51, 1, 606, 2310, 708])).
% 1.85/2.03 tff(5871,plain,
% 1.85/2.03 (b(elem!1, s(elem!1)) <=> b(elem!1, elem!1)),
% 1.85/2.03 inference(monotonicity,[status(thm)],[903])).
% 1.85/2.03 tff(5872,plain,
% 1.85/2.03 (b(elem!1, elem!1) <=> b(elem!1, s(elem!1))),
% 1.85/2.03 inference(symmetry,[status(thm)],[5871])).
% 1.85/2.03 tff(5873,plain,
% 1.85/2.03 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(elem!1)))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[5872])).
% 1.85/2.03 tff(5874,plain,
% 1.85/2.03 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.85/2.03 inference(bind,[status(th)],[])).
% 1.85/2.03 tff(5875,plain,
% 1.85/2.03 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.85/2.03 inference(quant_intro,[status(thm)],[5874])).
% 1.85/2.03 tff(5876,plain,
% 1.85/2.03 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(5877,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.85/2.03 tff(5878,plain,
% 1.85/2.03 (![X: $i] : (~b(X, X))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5877, 5876])).
% 1.85/2.03 tff(5879,plain,(
% 1.85/2.03 ![X: $i] : (~b(X, X))),
% 1.85/2.03 inference(skolemize,[status(sab)],[5878])).
% 1.85/2.03 tff(5880,plain,
% 1.85/2.03 (![X: $i] : (~b(X, X))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5879, 5875])).
% 1.85/2.03 tff(5881,plain,
% 1.85/2.03 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(5882,plain,
% 1.85/2.03 (~b(elem!1, elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5881, 5880])).
% 1.85/2.03 tff(5883,plain,
% 1.85/2.03 (~b(elem!1, s(elem!1))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5882, 5873])).
% 1.85/2.03 tff(5884,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[547, 5883])).
% 1.85/2.03 tff(5885,plain,((~(s(elem!1) = elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5886,plain,
% 1.85/2.03 (~(s(elem!1) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5885, 5870])).
% 1.85/2.03 tff(5887,plain,
% 1.85/2.03 (~(elem!1 = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1569, 5886])).
% 1.85/2.03 tff(5888,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[940, 525, 51, 562])).
% 1.85/2.03 tff(5889,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4578, 525, 902, 451, 133, 51, 509, 670, 408])).
% 1.85/2.03 tff(5890,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2899, 5889, 5888, 509])).
% 1.85/2.03 tff(5891,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5892,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5891, 3923, 902, 451, 509, 51, 670, 408, 562])).
% 1.85/2.03 tff(5893,plain,
% 1.85/2.03 (~(s(z) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3934, 5892, 123, 451, 3923])).
% 1.85/2.03 tff(5894,plain,
% 1.85/2.03 (b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[406, 5893, 2310])).
% 1.85/2.03 tff(5895,plain,
% 1.85/2.03 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[152, 5894, 123, 3923])).
% 1.85/2.03 tff(5896,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[121, 5895, 453])).
% 1.85/2.03 tff(5897,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[555, 3923, 547, 451])).
% 1.85/2.03 tff(5898,plain,
% 1.85/2.03 (~b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1730, 5894, 547, 451])).
% 1.85/2.03 tff(5899,plain,
% 1.85/2.03 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2946, 5898, 123])).
% 1.85/2.03 tff(5900,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[542, 5899, 5897])).
% 1.85/2.03 tff(5901,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2894, 5900, 5896, 670, 51])).
% 1.85/2.03 tff(5902,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | r(s(z), elem!1) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5903,plain,
% 1.85/2.03 (~r(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5902, 1728, 51, 123, 547, 2311, 2310, 902, 509, 562, 114])).
% 1.85/2.03 tff(5904,plain,
% 1.85/2.03 (b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1380, 5903, 77])).
% 1.85/2.03 tff(5905,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[130, 4742, 114])).
% 1.85/2.03 tff(5906,plain,
% 1.85/2.03 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2899, 5888, 509])).
% 1.85/2.03 tff(5907,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3510, 5906, 5905, 451, 624, 525, 670, 509, 51])).
% 1.85/2.03 tff(5908,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(elem!1))) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5909,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5908, 1728, 5904, 2311, 509, 51, 114, 562, 606, 77])).
% 1.85/2.03 tff(5910,plain,
% 1.85/2.03 (b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3998, 5909, 51, 123, 1727, 354, 1, 114, 2311, 2310, 902])).
% 1.85/2.03 tff(5911,plain,
% 1.85/2.03 (~b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4841, 5909, 1727, 123, 114, 51, 5904, 354, 1, 902, 2311, 2310])).
% 1.85/2.03 tff(5912,plain,
% 1.85/2.03 (s(z) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[406, 5911, 2310])).
% 1.85/2.03 tff(5913,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4789, 5912, 5910, 2311, 509, 123, 1728, 902, 51, 5909])).
% 1.85/2.03 tff(5914,plain,((elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | r(s(elem!1), elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(elem!1))) | b(z, elem!1) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5915,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5914, 5887, 123, 51, 2310, 1727, 354, 1, 509, 562, 606, 5870])).
% 1.85/2.03 tff(5916,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[735, 5915, 708])).
% 1.85/2.03 tff(5917,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[319, 5916])).
% 1.85/2.03 tff(5918,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3868, 5915, 1727])).
% 1.85/2.03 tff(5919,plain,
% 1.85/2.03 (b(s(elem!1), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[448, 5886, 1727])).
% 1.85/2.03 tff(5920,plain,
% 1.85/2.03 (~r(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2319, 5917, 354, 51])).
% 1.85/2.03 tff(5921,plain,
% 1.85/2.03 (b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1244, 5920, 1229])).
% 1.85/2.03 tff(5922,plain,
% 1.85/2.03 (~b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1730, 5921, 5870, 5919])).
% 1.85/2.03 tff(5923,plain,
% 1.85/2.03 (s(z) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[406, 5922, 2310])).
% 1.85/2.03 tff(5924,plain,
% 1.85/2.03 (~b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4789, 5923, 2311, 509, 123, 5919, 5887, 51, 5918])).
% 1.85/2.03 tff(5925,plain,
% 1.85/2.03 (r(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[348, 5924])).
% 1.85/2.03 tff(5926,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[341, 5925, 51, 5917])).
% 1.85/2.03 tff(5927,plain,
% 1.85/2.03 (~b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3965, 5924, 5923])).
% 1.85/2.03 tff(5928,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[787, 5927, 5915])).
% 1.85/2.03 tff(5929,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[302, 5928, 5926])).
% 1.85/2.03 tff(5930,plain,((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(z), elem!1) | (~r(z, s(z))) | b(elem!1, s(z)) | r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5931,plain,
% 1.85/2.03 (~r(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5930, 509, 51, 123, 2310, 354, 708, 1727, 1, 606])).
% 1.85/2.03 tff(5932,plain,
% 1.85/2.03 (b(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[583, 5931])).
% 1.85/2.03 tff(5933,plain,
% 1.85/2.03 (~(elem!1 = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2974, 5932, 606])).
% 1.85/2.03 tff(5934,plain,
% 1.85/2.03 (~r(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[678, 563, 2311, 509])).
% 1.85/2.03 tff(5935,plain,
% 1.85/2.03 (b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1380, 5934, 77])).
% 1.85/2.03 tff(5936,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2492, 563, 2311, 51])).
% 1.85/2.03 tff(5937,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[130, 114, 5936])).
% 1.85/2.03 tff(5938,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3934, 57, 123, 451, 133])).
% 1.85/2.03 tff(5939,plain,
% 1.85/2.03 (~r(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[678, 563, 670, 509])).
% 1.85/2.03 tff(5940,plain,
% 1.85/2.03 (b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1380, 5939, 1368])).
% 1.85/2.03 tff(5941,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3510, 5938, 451, 5940, 133, 670, 509, 51])).
% 1.85/2.03 tff(5942,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2899, 5941, 509])).
% 1.85/2.03 tff(5943,plain,
% 1.85/2.03 (b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3965, 57, 5940])).
% 1.85/2.03 tff(5944,plain,
% 1.85/2.03 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4745, 5943, 51, 451, 670, 1237, 57, 5938, 606, 1368])).
% 1.85/2.03 tff(5945,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[121, 5944, 3396])).
% 1.85/2.03 tff(5946,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4103, 5945, 5942, 5938, 563])).
% 1.85/2.03 tff(5947,plain,((~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | b(z, elem!1) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5948,plain,
% 1.85/2.03 (~(s(z) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5947, 453, 563, 509, 51, 1728, 2311, 1229, 606, 77, 5937, 123])).
% 1.85/2.03 tff(5949,plain,
% 1.85/2.03 (~(elem!1 = s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[712, 5948])).
% 1.85/2.03 tff(5950,plain,
% 1.85/2.03 (b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[406, 5948, 2310])).
% 1.85/2.03 tff(5951,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4850, 5950, 5949, 1727, 902, 354, 123, 51, 606, 5935, 1, 114, 2310])).
% 1.85/2.03 tff(5952,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5953,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5952, 563, 5933, 354, 123, 51, 606, 1, 2310, 1727, 509])).
% 1.85/2.03 tff(5954,plain,
% 1.85/2.03 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3398, 5953])).
% 1.85/2.03 tff(5955,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[735, 5953, 708])).
% 1.85/2.03 tff(5956,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[319, 5955])).
% 1.85/2.03 tff(5957,plain,
% 1.85/2.03 (~r(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2319, 5956, 354, 51])).
% 1.85/2.03 tff(5958,plain,
% 1.85/2.03 (b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1244, 5957, 1229])).
% 1.85/2.03 tff(5959,plain,
% 1.85/2.03 (~b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2569, 5958, 123, 1727, 5934, 5954])).
% 1.85/2.03 tff(5960,plain,
% 1.85/2.03 (r(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[348, 5959])).
% 1.85/2.03 tff(5961,plain,
% 1.85/2.03 (~r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[727, 5960, 354, 2311])).
% 1.85/2.03 tff(5962,plain,
% 1.85/2.03 (~(s(z) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3965, 5959, 5935])).
% 1.85/2.03 tff(5963,plain,
% 1.85/2.03 (~(elem!1 = s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[712, 5962])).
% 1.85/2.03 tff(5964,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[720, 5963, 5961, 708])).
% 1.85/2.03 tff(5965,plain,((~r(elem!1, s(elem!1))) | b(elem!1, s(z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5966,plain,
% 1.85/2.03 (~r(elem!1, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5965, 509, 354, 123, 1727, 51, 606, 1, 2310, 708])).
% 1.85/2.03 tff(5967,plain,
% 1.85/2.03 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[152, 134, 123, 133])).
% 1.85/2.03 tff(5968,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[121, 5967, 3396])).
% 1.85/2.03 tff(5969,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[555, 133, 3745, 1728])).
% 1.85/2.03 tff(5970,plain,
% 1.85/2.03 (~b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1732, 134, 1727, 902, 1725])).
% 1.85/2.03 tff(5971,plain,
% 1.85/2.03 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2946, 5970, 123])).
% 1.85/2.03 tff(5972,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[542, 5971, 5969])).
% 1.85/2.03 tff(5973,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2894, 5972, 5968, 670, 51])).
% 1.85/2.03 tff(5974,plain,((~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(5975,plain,
% 1.85/2.03 (~b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5974, 3923, 51, 453, 123, 670, 1727, 902, 1725])).
% 1.85/2.03 tff(5976,plain,
% 1.85/2.03 (s(z) = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[406, 5975, 2310])).
% 1.85/2.03 tff(5977,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3934, 5976, 123, 1728, 3923])).
% 1.85/2.03 tff(5978,plain,
% 1.85/2.03 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4578, 5977, 902, 1728, 3923, 51, 509, 670, 408])).
% 1.85/2.03 tff(5979,plain,
% 1.85/2.03 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5978, 175])).
% 1.85/2.03 tff(5980,plain,
% 1.85/2.03 (~r(s(s(s(z))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5824, 333, 670, 509, 1699])).
% 1.85/2.03 tff(5981,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[5835, 509, 1699, 670])).
% 1.85/2.03 tff(5982,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2899, 5978, 509])).
% 1.85/2.03 tff(5983,plain,
% 1.85/2.03 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3282, 5982, 670, 408])).
% 1.85/2.03 tff(5984,plain,
% 1.85/2.03 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[121, 5983, 453])).
% 1.85/2.03 tff(5985,plain,
% 1.85/2.03 (~b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4745, 5984, 51, 1728, 670, 1237, 5976, 5977, 606, 1368])).
% 1.85/2.03 tff(5986,plain,
% 1.85/2.03 (r(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[348, 5985])).
% 1.85/2.03 tff(5987,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[341, 5986, 51, 5982])).
% 1.85/2.03 tff(5988,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[319, 5987])).
% 1.85/2.03 tff(5989,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[927])).
% 1.85/2.03 tff(5990,plain,
% 1.85/2.03 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[5989])).
% 1.85/2.03 tff(5991,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[959, 5990])).
% 1.85/2.03 tff(5992,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[249, 5991])).
% 1.85/2.03 tff(5993,plain,
% 1.85/2.03 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[927])).
% 1.85/2.03 tff(5994,plain,
% 1.85/2.03 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[5993])).
% 1.85/2.03 tff(5995,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.85/2.03 tff(5996,plain,
% 1.85/2.03 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[5995, 5994])).
% 1.85/2.03 tff(5997,plain,
% 1.85/2.03 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1137, 5996])).
% 1.85/2.03 tff(5998,plain,
% 1.85/2.03 (~b(s(z), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2262, 5997, 123, 5992])).
% 1.85/2.03 tff(5999,plain,
% 1.85/2.03 (r(s(z), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[170, 44, 167, 5998])).
% 1.85/2.03 tff(6000,plain,
% 1.85/2.03 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6001,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6000])).
% 1.85/2.03 tff(6002,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6001, 1119])).
% 1.85/2.03 tff(6003,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6004,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6003, 6002])).
% 1.85/2.03 tff(6005,plain,
% 1.85/2.03 (~b(s(s(s(z))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6004, 144, 123, 5997, 304])).
% 1.85/2.03 tff(6006,plain,
% 1.85/2.03 (r(s(s(s(z))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2794, 6005])).
% 1.85/2.03 tff(6007,plain,
% 1.85/2.03 (((~![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(z))), z)) | (~r(s(s(s(z))), 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(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6008,plain,
% 1.85/2.03 (((~r(s(z), s(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6009,plain,
% 1.85/2.03 (((~![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(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6008])).
% 1.85/2.03 tff(6010,plain,
% 1.85/2.03 (((~![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(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6009, 6007])).
% 1.85/2.03 tff(6011,plain,
% 1.85/2.03 ((~![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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6012,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6011, 6010])).
% 1.85/2.03 tff(6013,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6012, 333, 354, 1699, 6006, 5999])).
% 1.85/2.03 tff(6014,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(z))), s(elem!1)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(6015,plain,
% 1.85/2.03 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6014, 5988, 1699, 123, 5981, 5980, 354])).
% 1.85/2.03 tff(6016,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6015, 5979])).
% 1.85/2.03 tff(6017,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | b(z, elem!1) | (elem!1 = z) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | r(s(z), elem!1) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6018,plain,
% 1.85/2.04 (~r(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6017, 114, 123, 354, 51, 2311, 1229, 606, 77, 509, 902, 2310, 1727, 1725, 5821])).
% 1.85/2.04 tff(6019,plain,
% 1.85/2.04 (b(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1380, 6018, 77])).
% 1.85/2.04 tff(6020,plain,
% 1.85/2.04 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[2691])).
% 1.85/2.04 tff(6021,plain,
% 1.85/2.04 ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6020])).
% 1.85/2.04 tff(6022,plain,
% 1.85/2.04 (b(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3965, 57, 624])).
% 1.85/2.04 tff(6023,plain,
% 1.85/2.04 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4789, 6022, 670, 509, 123, 451, 902, 51, 57])).
% 1.85/2.04 tff(6024,plain,
% 1.85/2.04 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4745, 6022, 51, 451, 670, 1237, 57, 6023, 606, 1368])).
% 1.85/2.04 tff(6025,plain,
% 1.85/2.04 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6024, 6021])).
% 1.85/2.04 tff(6026,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[123, 6025])).
% 1.85/2.04 tff(6027,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | b(z, elem!1) | (elem!1 = z) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6028,plain,
% 1.85/2.04 (~(s(z) = elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6027, 6019, 51, 1728, 2311, 1229, 606, 77, 509, 902, 123])).
% 1.85/2.04 tff(6029,plain,
% 1.85/2.04 (~(elem!1 = s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[712, 6028])).
% 1.85/2.04 tff(6030,plain,
% 1.85/2.04 (b(s(z), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[406, 6028, 2310])).
% 1.85/2.04 tff(6031,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4850, 6030, 6029, 1727, 902, 354, 123, 51, 606, 6019, 1, 114, 2310])).
% 1.85/2.04 tff(6032,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), elem!1) | (~r(s(elem!1), z)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6033,plain,
% 1.85/2.04 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6032, 5933, 1727, 354, 123, 51, 606, 1, 2310, 509, 5966])).
% 1.85/2.04 tff(6034,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[735, 6033, 708])).
% 1.85/2.04 tff(6035,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[319, 6034])).
% 1.85/2.04 tff(6036,plain,
% 1.85/2.04 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3868, 6033, 1727])).
% 1.85/2.04 tff(6037,plain,
% 1.85/2.04 (~(s(elem!1) = elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[906, 5933])).
% 1.85/2.04 tff(6038,plain,
% 1.85/2.04 (b(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[448, 6037, 1727])).
% 1.85/2.04 tff(6039,plain,
% 1.85/2.04 (~r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2319, 6035, 354, 51])).
% 1.85/2.04 tff(6040,plain,
% 1.85/2.04 (b(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1244, 6039, 1229])).
% 1.85/2.04 tff(6041,plain,
% 1.85/2.04 (~b(s(z), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1732, 6040, 1727, 5933, 5966])).
% 1.85/2.04 tff(6042,plain,
% 1.85/2.04 (s(z) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[406, 6041, 2310])).
% 1.85/2.04 tff(6043,plain,
% 1.85/2.04 (~b(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4789, 6042, 2311, 509, 123, 6038, 5933, 51, 6036])).
% 1.85/2.04 tff(6044,plain,
% 1.85/2.04 (r(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[348, 6043])).
% 1.85/2.04 tff(6045,plain,
% 1.85/2.04 (~b(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6027, 6042, 51, 6038, 2311, 1229, 606, 77, 509, 5933, 123])).
% 1.85/2.04 tff(6046,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[787, 6045, 6033])).
% 1.85/2.04 tff(6047,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[302, 6046])).
% 1.85/2.04 tff(6048,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[341, 6047, 6044, 51, 6035])).
% 1.85/2.04 tff(6049,plain,((~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(z), elem!1) | r(s(elem!1), elem!1) | (~r(z, s(z))) | b(elem!1, s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6050,plain,
% 1.85/2.04 (~r(s(elem!1), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6049, 708, 50, 606, 2310, 1727, 354, 51, 1])).
% 1.85/2.04 tff(6051,plain,
% 1.85/2.04 (b(s(elem!1), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[507, 6050])).
% 1.85/2.04 tff(6052,plain,
% 1.85/2.04 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[982])).
% 1.85/2.04 tff(6053,plain,
% 1.85/2.04 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.85/2.04 inference(symmetry,[status(thm)],[6052])).
% 1.85/2.04 tff(6054,plain,
% 1.85/2.04 ((~b(s(s(s(z))), z)) <=> (~b(s(elem!1), z))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6053])).
% 1.85/2.04 tff(6055,plain,
% 1.85/2.04 (~b(s(elem!1), z)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[1963, 6054])).
% 1.85/2.04 tff(6056,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[491, 6055])).
% 1.85/2.04 tff(6057,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(elem!1), z)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6058,plain,
% 1.85/2.04 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6057, 6051, 5774])).
% 1.85/2.04 tff(6059,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[130, 4919, 114])).
% 1.85/2.04 tff(6060,plain,
% 1.85/2.04 (b(s(z), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[406, 706, 2310])).
% 1.85/2.04 tff(6061,plain,
% 1.85/2.04 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[152, 6060, 123, 6059])).
% 1.85/2.04 tff(6062,plain,
% 1.85/2.04 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[121, 6061, 453])).
% 1.85/2.04 tff(6063,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3282, 6062, 2311, 408])).
% 1.85/2.04 tff(6064,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[302, 6063])).
% 1.85/2.04 tff(6065,plain,
% 1.85/2.04 (r(elem!1, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[720, 713, 708])).
% 1.85/2.04 tff(6066,plain,
% 1.85/2.04 (~r(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[727, 6065, 354, 2311])).
% 1.85/2.04 tff(6067,plain,
% 1.85/2.04 (b(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[348, 6066])).
% 1.85/2.04 tff(6068,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2894, 6062, 2311, 51])).
% 1.85/2.04 tff(6069,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2541, 6062, 2311, 51])).
% 1.85/2.04 tff(6070,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[319, 6069])).
% 1.85/2.04 tff(6071,plain,
% 1.85/2.04 (r(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[5974, 6060, 51, 453, 123, 2311, 1727, 902, 6059])).
% 1.85/2.04 tff(6072,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3762, 6064, 1728, 6060, 1, 2311, 6059, 6071, 6070])).
% 1.85/2.04 tff(6073,plain,
% 1.85/2.04 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[542, 6072, 6068])).
% 1.85/2.04 tff(6074,plain,
% 1.85/2.04 (b(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2946, 6073, 123])).
% 1.85/2.04 tff(6075,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3222, 6074, 6067, 123, 6064])).
% 1.85/2.04 tff(6076,plain,
% 1.85/2.04 (~r(s(elem!1), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6049, 708, 123, 606, 2310, 1727, 354, 51, 1])).
% 1.85/2.04 tff(6077,plain,
% 1.85/2.04 (b(s(elem!1), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[507, 6076])).
% 1.85/2.04 tff(6078,plain,
% 1.85/2.04 (~b(z, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2383, 6074, 6077, 6067])).
% 1.85/2.04 tff(6079,plain,
% 1.85/2.04 (r(z, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[583, 6078])).
% 1.85/2.04 tff(6080,plain,
% 1.85/2.04 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4052, 6079, 2311, 6071])).
% 1.85/2.04 tff(6081,plain,
% 1.85/2.04 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[472, 6080, 6075])).
% 1.85/2.04 tff(6082,plain,
% 1.85/2.04 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6081])).
% 1.85/2.04 tff(6083,plain,
% 1.85/2.04 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6082])).
% 1.85/2.04 tff(6084,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6083])).
% 1.85/2.04 tff(6085,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6084])).
% 1.85/2.04 tff(6086,plain,
% 1.85/2.04 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.04 inference(symmetry,[status(thm)],[6081])).
% 1.85/2.04 tff(6087,plain,
% 1.85/2.04 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6086])).
% 1.85/2.04 tff(6088,plain,
% 1.85/2.04 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6087, 2502])).
% 1.85/2.04 tff(6089,plain,
% 1.85/2.04 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6088])).
% 1.85/2.04 tff(6090,plain,
% 1.85/2.04 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6089])).
% 1.85/2.04 tff(6091,plain,
% 1.85/2.04 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[2727, 6090])).
% 1.85/2.04 tff(6092,plain,
% 1.85/2.04 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6081])).
% 1.85/2.04 tff(6093,plain,
% 1.85/2.04 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4957, 6060, 123, 1, 1727, 408, 51, 114, 354, 902, 606, 713])).
% 1.85/2.04 tff(6094,plain,
% 1.85/2.04 (~r(s(elem!1), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2393, 6079, 2311, 6071])).
% 1.85/2.04 tff(6095,plain,
% 1.85/2.04 (b(s(elem!1), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[486, 6094, 1])).
% 1.85/2.04 tff(6096,plain,
% 1.85/2.04 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6014, 123, 1699, 304, 354, 5995, 959])).
% 1.85/2.04 tff(6097,plain,
% 1.85/2.04 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[472, 6096, 466])).
% 1.85/2.04 tff(6098,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[869, 144, 488, 123, 304, 6097])).
% 1.85/2.04 tff(6099,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | r(s(s(s(z))), s(elem!1)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6100,plain,
% 1.85/2.04 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6099, 6095, 354, 5821, 6070, 123, 6080, 6093])).
% 1.85/2.04 tff(6101,plain,
% 1.85/2.04 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6100, 6092])).
% 1.85/2.04 tff(6102,plain,
% 1.85/2.04 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[927])).
% 1.85/2.04 tff(6103,plain,
% 1.85/2.04 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6102])).
% 1.85/2.04 tff(6104,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.04 tff(6105,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6104])).
% 1.85/2.04 tff(6106,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[3654, 6105])).
% 1.85/2.04 tff(6107,assumption,(r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.85/2.04 tff(6108,plain,
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% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6109,plain,
% 1.85/2.04 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6110,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6109])).
% 1.85/2.04 tff(6111,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6110, 6108])).
% 1.85/2.04 tff(6112,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6113,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6112, 6111])).
% 1.85/2.04 tff(6114,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6113, 333, 1699, 6107, 51])).
% 1.85/2.04 tff(6115,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6114, 6106])).
% 1.85/2.04 tff(6116,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6117,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6116, 6081, 5821, 6101, 51])).
% 1.85/2.04 tff(6118,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2758, 6117, 6091])).
% 1.85/2.04 tff(6119,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6118, 6085])).
% 1.85/2.04 tff(6120,plain,
% 1.85/2.04 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6081])).
% 1.85/2.04 tff(6121,plain,
% 1.85/2.04 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6120])).
% 1.85/2.04 tff(6122,plain,
% 1.85/2.04 (s(s(s(s(s(s(z)))))) = elem!1),
% 1.85/2.04 inference(transitivity,[status(thm)],[21, 6121, 850])).
% 1.85/2.04 tff(6123,plain,
% 1.85/2.04 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6122])).
% 1.85/2.04 tff(6124,plain,
% 1.85/2.04 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6123])).
% 1.85/2.04 tff(6125,plain,
% 1.85/2.04 (r(z, s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[2311, 6124])).
% 1.85/2.04 tff(6126,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(z)))))), z) <=> r(elem!1, z)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6122])).
% 1.85/2.04 tff(6127,plain,
% 1.85/2.04 (r(elem!1, z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.85/2.04 inference(symmetry,[status(thm)],[6126])).
% 1.85/2.04 tff(6128,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[408, 6127])).
% 1.85/2.04 tff(6129,plain,
% 1.85/2.04 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6083, 6122])).
% 1.85/2.04 tff(6130,plain,
% 1.85/2.04 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(elem!1)))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6129, 1218])).
% 1.85/2.04 tff(6131,plain,
% 1.85/2.04 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6130])).
% 1.85/2.04 tff(6132,plain,
% 1.85/2.04 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6131])).
% 1.85/2.04 tff(6133,plain,
% 1.85/2.04 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1216, 6073])).
% 1.85/2.04 tff(6134,plain,
% 1.85/2.04 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6133, 6132])).
% 1.85/2.04 tff(6135,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6122])).
% 1.85/2.04 tff(6136,plain,
% 1.85/2.04 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6135])).
% 1.85/2.04 tff(6137,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6060, 6136])).
% 1.85/2.04 tff(6138,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6081])).
% 1.85/2.04 tff(6139,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6138])).
% 1.85/2.04 tff(6140,plain,
% 1.85/2.04 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6139])).
% 1.85/2.04 tff(6141,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.04 tff(6142,plain,
% 1.85/2.04 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6141])).
% 1.85/2.04 tff(6143,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.04 tff(6144,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6143])).
% 1.85/2.04 tff(6145,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.04 tff(6146,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6145])).
% 1.85/2.04 tff(6147,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.85/2.04 tff(6148,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6147, 6146])).
% 1.85/2.04 tff(6149,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6150,plain,
% 1.85/2.04 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6151,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6150])).
% 1.85/2.04 tff(6152,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6151, 6149])).
% 1.85/2.04 tff(6153,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6154,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6153, 6152])).
% 1.85/2.04 tff(6155,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6154, 144, 123, 304])).
% 1.85/2.04 tff(6156,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6155, 6148])).
% 1.85/2.04 tff(6157,plain,
% 1.85/2.04 (~b(s(s(elem!1)), s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6156, 6144])).
% 1.85/2.04 tff(6158,plain,
% 1.85/2.04 (r(s(s(elem!1)), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4983, 6157])).
% 1.85/2.04 tff(6159,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6158, 6142])).
% 1.85/2.04 tff(6160,plain,
% 1.85/2.04 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6102])).
% 1.85/2.04 tff(6161,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.04 tff(6162,plain,
% 1.85/2.04 ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(z), s(s(elem!1))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6161])).
% 1.85/2.04 tff(6163,plain,
% 1.85/2.04 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[927])).
% 1.85/2.04 tff(6164,plain,
% 1.85/2.04 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6163])).
% 1.85/2.04 tff(6165,plain,
% 1.85/2.04 (s(s(s(s(s(s(z)))))) = elem!1),
% 1.85/2.04 inference(transitivity,[status(thm)],[21, 6164, 850])).
% 1.85/2.04 tff(6166,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6165])).
% 1.85/2.04 tff(6167,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6166])).
% 1.85/2.04 tff(6168,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[133, 6167])).
% 1.85/2.04 tff(6169,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.85/2.04 tff(6170,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6171,plain,
% 1.85/2.04 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6172,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6171])).
% 1.85/2.04 tff(6173,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6172, 6170])).
% 1.85/2.04 tff(6174,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6175,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6174, 6173])).
% 1.85/2.04 tff(6176,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6175, 144, 123, 6169])).
% 1.85/2.04 tff(6177,plain,
% 1.85/2.04 (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6176, 6148, 6168])).
% 1.85/2.04 tff(6178,plain,
% 1.85/2.04 (~b(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6177, 6162])).
% 1.85/2.05 tff(6179,plain,
% 1.85/2.05 (r(s(z), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5484, 6178])).
% 1.85/2.05 tff(6180,plain,
% 1.85/2.05 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6179, 6160])).
% 1.85/2.05 tff(6181,plain,
% 1.85/2.05 (((~![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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6182,plain,
% 1.85/2.05 (((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6183,plain,
% 1.85/2.05 (((~![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(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6182])).
% 1.85/2.05 tff(6184,plain,
% 1.85/2.05 (((~![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(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6183, 6181])).
% 1.85/2.05 tff(6185,plain,
% 1.85/2.05 ((~![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(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6186,plain,
% 1.85/2.05 ((~![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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.85/2.05 tff(6187,plain,
% 1.85/2.05 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6186, 333, 354, 6180, 6159])).
% 1.85/2.05 tff(6188,plain,
% 1.85/2.05 ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1320, 44, 6187])).
% 1.85/2.05 tff(6189,plain,
% 1.85/2.05 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6188, 1309])).
% 1.85/2.05 tff(6190,plain,
% 1.85/2.05 (((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(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(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6191,plain,
% 1.85/2.05 (((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6192,plain,
% 1.85/2.05 (((~![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(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6191])).
% 1.85/2.05 tff(6193,plain,
% 1.85/2.05 (((~![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(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6192, 6190])).
% 1.85/2.05 tff(6194,plain,
% 1.85/2.05 ((~![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(s(s(s(s(s(s(z)))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6195,plain,
% 1.85/2.05 ((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6194, 6193])).
% 1.85/2.05 tff(6196,plain,
% 1.85/2.05 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6195, 333, 354, 6180, 6159])).
% 1.85/2.05 tff(6197,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1333, 44, 1308, 6196])).
% 1.85/2.05 tff(6198,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.05 tff(6199,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6198])).
% 1.85/2.05 tff(6200,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[5659, 6199])).
% 1.85/2.05 tff(6201,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6202,plain,
% 1.85/2.05 (((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6203,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6202])).
% 1.85/2.05 tff(6204,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6203, 6201])).
% 1.85/2.05 tff(6205,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6206,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6205, 6204])).
% 1.85/2.05 tff(6207,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6206, 144, 286, 6200, 6197, 6189])).
% 1.85/2.05 tff(6208,plain,((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6209,plain,
% 1.85/2.05 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6208, 6064, 354, 6081, 123, 6070, 6137, 6118, 6059])).
% 1.85/2.05 tff(6210,plain,
% 1.85/2.05 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6209, 6140])).
% 1.85/2.05 tff(6211,plain,
% 1.85/2.05 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1283, 6210, 2727])).
% 1.85/2.05 tff(6212,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6165, 6103])).
% 1.85/2.05 tff(6213,plain,
% 1.85/2.05 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6212])).
% 1.85/2.05 tff(6214,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.85/2.05 tff(6215,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(elem!1, s(s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6165, 6103])).
% 1.85/2.05 tff(6216,plain,
% 1.85/2.05 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6215])).
% 1.85/2.05 tff(6217,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[2736, 6216])).
% 1.85/2.05 tff(6218,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(elem!1, s(z))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6165])).
% 1.85/2.05 tff(6219,plain,
% 1.85/2.05 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6218])).
% 1.85/2.05 tff(6220,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[722, 6219])).
% 1.85/2.05 tff(6221,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6103])).
% 1.85/2.05 tff(6222,plain,
% 1.85/2.05 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6221])).
% 1.85/2.05 tff(6223,plain,
% 1.85/2.05 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[927])).
% 1.85/2.05 tff(6224,plain,
% 1.85/2.05 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[2737, 6223])).
% 1.85/2.05 tff(6225,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6224, 6222])).
% 1.85/2.05 tff(6226,plain,
% 1.85/2.05 (((~![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(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6227,plain,
% 1.85/2.05 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6228,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6227])).
% 1.85/2.05 tff(6229,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6228, 6226])).
% 1.85/2.05 tff(6230,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6231,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6230, 6229])).
% 1.85/2.05 tff(6232,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6231, 333, 2737, 2736, 3654, 2323])).
% 1.85/2.05 tff(6233,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6234,plain,
% 1.85/2.05 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6233, 2736, 2323, 2737])).
% 1.85/2.05 tff(6235,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2758, 6234, 2725])).
% 1.85/2.05 tff(6236,plain,
% 1.85/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6235, 6199])).
% 1.85/2.05 tff(6237,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6238,plain,
% 1.85/2.05 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6239,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6238])).
% 1.85/2.05 tff(6240,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6239, 6237])).
% 1.85/2.05 tff(6241,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6242,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6241, 6240])).
% 1.85/2.05 tff(6243,plain,
% 1.85/2.05 ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6242, 144, 123, 6214, 6169])).
% 1.85/2.05 tff(6244,plain,
% 1.85/2.05 (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6243, 6236])).
% 1.85/2.05 tff(6245,plain,
% 1.85/2.05 (~b(s(z), s(s(elem!1)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6244, 6162])).
% 1.85/2.05 tff(6246,plain,
% 1.85/2.05 (r(s(z), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5484, 6245])).
% 1.85/2.05 tff(6247,plain,
% 1.85/2.05 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6246, 6160])).
% 1.85/2.05 tff(6248,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(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(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6249,plain,
% 1.85/2.06 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6250,plain,
% 1.85/2.06 (((~![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(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6249])).
% 1.85/2.06 tff(6251,plain,
% 1.85/2.06 (((~![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(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6250, 6248])).
% 1.85/2.06 tff(6252,plain,
% 1.85/2.06 ((~![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(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6253,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 1.85/2.06 tff(6254,plain,
% 1.85/2.06 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6253, 333, 6247])).
% 1.85/2.06 tff(6255,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6254, 6225, 6220, 6217])).
% 1.85/2.06 tff(6256,plain,((~r(elem!1, s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(6257,plain,
% 1.85/2.06 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6256, 6214, 722, 123, 2737, 6169, 2725, 2323, 927])).
% 1.85/2.06 tff(6258,plain,
% 1.85/2.06 (b(elem!1, s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2522, 6257, 1221])).
% 1.85/2.06 tff(6259,plain,
% 1.85/2.06 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6258, 6213])).
% 1.85/2.06 tff(6260,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6261,plain,
% 1.85/2.06 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6262,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6261])).
% 1.85/2.06 tff(6263,plain,
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% 1.85/2.06 tff(6267,plain,
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% 1.85/2.06 tff(6285,plain,
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% 1.85/2.06 tff(6297,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6206, 144, 6064, 6296, 6284, 6119])).
% 1.85/2.06 tff(6298,plain,((s(z) = elem!1) | (~r(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = s(elem!1)) | b(z, elem!1) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(6299,plain,
% 1.85/2.06 (s(z) = elem!1),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6298, 408, 123, 354, 51, 1, 1727, 114, 902, 606, 708, 2310])).
% 1.85/2.06 tff(6300,plain,
% 1.85/2.06 (s(s(z)) = s(elem!1)),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.06 tff(6301,plain,
% 1.85/2.06 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6300])).
% 1.85/2.06 tff(6302,plain,
% 1.85/2.06 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6301])).
% 1.85/2.06 tff(6303,plain,
% 1.85/2.06 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.06 tff(6304,plain,
% 1.85/2.06 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.85/2.06 inference(symmetry,[status(thm)],[6303])).
% 1.85/2.06 tff(6305,plain,
% 1.85/2.06 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6304])).
% 1.85/2.06 tff(6306,plain,
% 1.85/2.06 (((~![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(z))), 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6307,plain,
% 1.85/2.06 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6308,plain,
% 1.85/2.06 (((~![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(z))), z)) | (~r(elem!1, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6307])).
% 1.85/2.06 tff(6309,plain,
% 1.85/2.06 (((~![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(z))), z)) | (~r(elem!1, 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6308, 6306])).
% 1.85/2.06 tff(6310,plain,
% 1.85/2.06 ((~![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(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6311,plain,
% 1.85/2.07 ((~![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(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6310, 6309])).
% 1.85/2.07 tff(6312,plain,
% 1.85/2.07 (~r(elem!1, s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6311, 333, 2311, 408, 5821])).
% 1.85/2.07 tff(6313,plain,
% 1.85/2.07 (~r(s(z), s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6312, 6305])).
% 1.85/2.07 tff(6314,plain,
% 1.85/2.07 (b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[172, 6313])).
% 1.85/2.07 tff(6315,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.07 tff(6316,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6315])).
% 1.85/2.07 tff(6317,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6059, 6316])).
% 1.85/2.07 tff(6318,plain,
% 1.85/2.07 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.07 tff(6319,plain,
% 1.85/2.07 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6318])).
% 1.85/2.07 tff(6320,plain,
% 1.85/2.07 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6319])).
% 1.85/2.07 tff(6321,plain,
% 1.85/2.07 (~r(s(s(s(z))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2079, 408, 2311, 5821])).
% 1.85/2.07 tff(6322,plain,
% 1.85/2.07 (~r(s(s(s(z))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6321, 6320])).
% 1.85/2.07 tff(6323,plain,
% 1.85/2.07 (b(s(s(s(z))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2794, 6322])).
% 1.85/2.07 tff(6324,plain,
% 1.85/2.07 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.07 tff(6325,plain,
% 1.85/2.07 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6324])).
% 1.85/2.07 tff(6326,plain,
% 1.85/2.07 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6300])).
% 1.85/2.07 tff(6327,plain,
% 1.85/2.07 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.85/2.07 inference(symmetry,[status(thm)],[6326])).
% 1.85/2.07 tff(6328,plain,
% 1.85/2.07 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6327, 6325])).
% 1.85/2.07 tff(6329,plain,
% 1.85/2.07 (b(s(s(z)), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1728, 6328])).
% 1.85/2.07 tff(6330,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.85/2.07 tff(6331,plain,
% 1.85/2.07 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6332,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6331])).
% 1.85/2.07 tff(6333,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6332, 839])).
% 1.85/2.07 tff(6334,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6335,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6334, 6333])).
% 1.85/2.07 tff(6336,plain,
% 1.85/2.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6335, 144, 56, 838, 304])).
% 1.85/2.07 tff(6337,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[249, 6336])).
% 1.85/2.07 tff(6338,plain,
% 1.85/2.07 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6339,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6338])).
% 1.85/2.07 tff(6340,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6339, 1418])).
% 1.85/2.07 tff(6341,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6342,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6341, 6340])).
% 1.85/2.07 tff(6343,plain,
% 1.85/2.07 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6342, 144, 1417, 123, 304])).
% 1.85/2.07 tff(6344,plain,
% 1.85/2.07 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1451, 6343])).
% 1.85/2.07 tff(6345,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6346,plain,
% 1.85/2.07 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6347,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6346])).
% 1.85/2.07 tff(6348,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6347, 6345])).
% 1.85/2.07 tff(6349,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6350,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6349, 6348])).
% 1.85/2.07 tff(6351,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6350, 333, 1699, 6344, 6337, 6330])).
% 1.85/2.07 tff(6352,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6353,plain,
% 1.85/2.07 (~r(s(s(z)), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6352, 6329, 5821, 6323, 123, 6317, 6314])).
% 1.85/2.07 tff(6354,plain,
% 1.85/2.07 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6353, 6302])).
% 1.85/2.07 tff(6355,plain,
% 1.85/2.07 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6057, 6077, 5820])).
% 1.85/2.07 tff(6356,plain,
% 1.85/2.07 (s(s(s(z))) = s(s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6300])).
% 1.85/2.07 tff(6357,plain,
% 1.85/2.07 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6356])).
% 1.85/2.07 tff(6358,plain,
% 1.85/2.07 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6357])).
% 1.85/2.07 tff(6359,plain,
% 1.85/2.07 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6358])).
% 1.85/2.07 tff(6360,plain,
% 1.85/2.07 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6299])).
% 1.85/2.07 tff(6361,plain,
% 1.85/2.07 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6360, 1218])).
% 1.85/2.07 tff(6362,plain,
% 1.85/2.07 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.85/2.07 inference(transitivity,[status(thm)],[6361, 4572])).
% 1.85/2.07 tff(6363,plain,
% 1.85/2.07 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6362])).
% 1.85/2.07 tff(6364,plain,
% 1.85/2.07 (~(s(s(elem!1)) = elem!1)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[107, 6363])).
% 1.85/2.07 tff(6365,plain,
% 1.85/2.07 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6356])).
% 1.85/2.07 tff(6366,plain,
% 1.85/2.07 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6365])).
% 1.85/2.07 tff(6367,plain,
% 1.85/2.07 (~r(s(s(elem!1)), elem!1)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6321, 6366])).
% 1.85/2.07 tff(6368,plain,
% 1.85/2.07 (b(s(s(elem!1)), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1260, 44, 6367, 6364])).
% 1.85/2.07 tff(6369,plain,
% 1.85/2.07 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6361])).
% 1.85/2.07 tff(6370,plain,
% 1.85/2.07 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[107, 6369])).
% 1.85/2.07 tff(6371,plain,
% 1.85/2.07 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6356])).
% 1.85/2.07 tff(6372,plain,
% 1.85/2.07 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6371])).
% 1.85/2.07 tff(6373,plain,
% 1.85/2.07 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6312, 6372])).
% 1.85/2.07 tff(6374,plain,
% 1.85/2.07 (b(elem!1, s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2522, 6373, 6370])).
% 1.85/2.07 tff(6375,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6376,plain,
% 1.85/2.07 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6377,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6376])).
% 1.85/2.07 tff(6378,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6377, 6375])).
% 1.85/2.07 tff(6379,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6380,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6379, 6378])).
% 1.85/2.07 tff(6381,plain,
% 1.85/2.07 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6380, 144, 1728, 6374, 6368])).
% 1.85/2.07 tff(6382,plain,
% 1.85/2.07 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6381, 6359])).
% 1.85/2.07 tff(6383,plain,
% 1.85/2.07 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[965, 6382, 6355])).
% 1.85/2.07 tff(6384,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6383, 6354])).
% 1.85/2.07 tff(6385,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = s(elem!1)) | b(z, elem!1) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6386,plain,
% 1.85/2.07 (~r(elem!1, z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6385, 114, 354, 51, 1, 1727, 50, 902, 606, 708, 2310])).
% 1.85/2.07 tff(6387,plain,
% 1.85/2.07 (b(elem!1, z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1380, 6386, 77])).
% 1.85/2.07 tff(6388,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4850, 6060, 713, 1727, 902, 354, 123, 51, 606, 624, 1, 114, 2310])).
% 1.85/2.07 tff(6389,plain,((s(z) = elem!1) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~b(elem!1, z)) | (s(elem!1) = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6390,plain,
% 1.85/2.07 (s(z) = elem!1),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6389, 6387, 902, 354, 50, 51, 606, 1727, 1, 114, 2310])).
% 1.85/2.07 tff(6391,plain,
% 1.85/2.07 (s(s(z)) = s(elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6390])).
% 1.85/2.07 tff(6392,plain,
% 1.85/2.07 (s(s(s(z))) = s(s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6391])).
% 1.85/2.07 tff(6393,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6392])).
% 1.85/2.07 tff(6394,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6393])).
% 1.85/2.07 tff(6395,plain,
% 1.85/2.07 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6392])).
% 1.85/2.07 tff(6396,plain,
% 1.85/2.07 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6395])).
% 1.85/2.07 tff(6397,plain,
% 1.85/2.07 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6396])).
% 1.85/2.07 tff(6398,plain,
% 1.85/2.07 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6397])).
% 1.85/2.07 tff(6399,plain,
% 1.85/2.07 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[244, 6398])).
% 1.85/2.07 tff(6400,plain,
% 1.85/2.07 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6391])).
% 1.85/2.07 tff(6401,plain,
% 1.85/2.07 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6400, 174])).
% 1.85/2.07 tff(6402,plain,
% 1.85/2.07 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6401, 175])).
% 1.85/2.07 tff(6403,plain,
% 1.85/2.07 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6402])).
% 1.85/2.07 tff(6404,plain,
% 1.85/2.07 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1446, 6403])).
% 1.85/2.07 tff(6405,plain,
% 1.85/2.07 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6390])).
% 1.85/2.07 tff(6406,plain,
% 1.85/2.07 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[50, 6405])).
% 1.85/2.07 tff(6407,plain,
% 1.85/2.07 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6390])).
% 1.85/2.07 tff(6408,plain,
% 1.85/2.07 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6407])).
% 1.85/2.07 tff(6409,plain,
% 1.85/2.07 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[4, 6408])).
% 1.85/2.07 tff(6410,plain,
% 1.85/2.07 (b(s(z), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[3965, 6390, 6387])).
% 1.85/2.07 tff(6411,plain,
% 1.85/2.07 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4745, 6406, 51, 1728, 2311, 1229, 6390, 6410, 606, 77])).
% 1.85/2.07 tff(6412,plain,
% 1.85/2.07 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[472, 6411, 6404])).
% 1.85/2.07 tff(6413,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[464, 6412, 114, 1728, 6409])).
% 1.85/2.07 tff(6414,plain,
% 1.85/2.07 (~b(z, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[5289, 6413, 6406, 6404, 6387, 902, 606, 51, 77, 2311])).
% 1.85/2.07 tff(6415,plain,
% 1.85/2.07 (r(z, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[583, 6414])).
% 1.85/2.07 tff(6416,plain,
% 1.85/2.07 (r(s(s(s(z))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[396, 5774])).
% 1.85/2.07 tff(6417,plain,
% 1.85/2.07 (~r(elem!1, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2492, 6413, 2311, 51])).
% 1.85/2.07 tff(6418,plain,
% 1.85/2.07 (b(elem!1, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[560, 6417, 902])).
% 1.85/2.07 tff(6419,plain,
% 1.85/2.07 (b(s(z), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4682, 6418, 6390])).
% 1.85/2.07 tff(6420,plain,
% 1.85/2.07 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[3222, 6419, 6410, 50, 6412])).
% 1.85/2.07 tff(6421,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[302, 6420])).
% 1.85/2.07 tff(6422,plain,
% 1.85/2.07 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[2499])).
% 1.85/2.07 tff(6423,plain,
% 1.85/2.07 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 1.85/2.07 inference(symmetry,[status(thm)],[6422])).
% 1.85/2.07 tff(6424,plain,
% 1.85/2.07 (r(s(s(elem!1)), z)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1699, 6423])).
% 1.85/2.07 tff(6425,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6426,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6427,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6426, 6425])).
% 1.85/2.07 tff(6428,plain,
% 1.85/2.07 (~r(s(s(elem!1)), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6427, 333, 562, 3654, 321])).
% 1.85/2.07 tff(6429,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6428, 6424])).
% 1.85/2.07 tff(6430,plain,((~r(s(s(s(z))), z)) | (~(s(z) = elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6431,plain,
% 1.85/2.07 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6430, 6421, 6416, 6390, 6415])).
% 1.85/2.07 tff(6432,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2758, 6431, 6399])).
% 1.85/2.07 tff(6433,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6432, 6394])).
% 1.85/2.07 tff(6434,plain,
% 1.85/2.07 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6390])).
% 1.85/2.07 tff(6435,plain,
% 1.85/2.07 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6434])).
% 1.85/2.07 tff(6436,plain,
% 1.85/2.07 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6391])).
% 1.85/2.07 tff(6437,plain,
% 1.85/2.07 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.85/2.07 inference(symmetry,[status(thm)],[6436])).
% 1.85/2.07 tff(6438,plain,
% 1.85/2.07 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6437, 6435])).
% 1.85/2.07 tff(6439,plain,
% 1.85/2.07 (b(s(s(z)), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1728, 6438])).
% 1.85/2.07 tff(6440,plain,
% 1.85/2.07 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2674, 6411, 6390])).
% 1.85/2.07 tff(6441,plain,
% 1.85/2.07 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1451, 6440])).
% 1.85/2.07 tff(6442,plain,
% 1.85/2.07 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1425, 6441, 50, 6439])).
% 1.85/2.07 tff(6443,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[319, 6442])).
% 1.85/2.07 tff(6444,plain,
% 1.85/2.07 (~r(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[362, 6421, 6443, 354])).
% 1.85/2.07 tff(6445,plain,
% 1.85/2.07 (b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[172, 6444])).
% 1.85/2.07 tff(6446,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[5507, 6424])).
% 1.85/2.07 tff(6447,plain,(r(s(s(elem!1)), z) | (~r(s(s(s(z))), z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6448,plain,
% 1.85/2.07 (r(s(s(elem!1)), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6447, 6390, 6416])).
% 1.85/2.07 tff(6449,plain,
% 1.85/2.07 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[2499])).
% 1.85/2.07 tff(6450,plain,
% 1.85/2.07 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6449])).
% 1.85/2.07 tff(6451,plain,
% 1.85/2.07 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6107, 6450])).
% 1.85/2.07 tff(6452,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6453,plain,
% 1.85/2.07 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6454,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6453])).
% 1.85/2.08 tff(6455,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6454, 6452])).
% 1.85/2.08 tff(6456,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6457,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6456, 6455])).
% 1.85/2.08 tff(6458,plain,
% 1.85/2.08 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6457, 333, 562, 321, 5497])).
% 1.85/2.08 tff(6459,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6458, 6451])).
% 1.85/2.08 tff(6460,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6461,plain,
% 1.85/2.08 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6460, 6421, 6415, 6390, 6448])).
% 1.85/2.08 tff(6462,plain,
% 1.85/2.08 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1137, 6461])).
% 1.85/2.08 tff(6463,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2262, 6462, 50, 6445])).
% 1.85/2.08 tff(6464,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6463, 6433])).
% 1.85/2.08 tff(6465,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(z))) | (elem!1 = s(elem!1)) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6466,plain,
% 1.85/2.08 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6465, 902, 354, 606, 51, 4, 1727, 1, 2310, 708])).
% 1.85/2.08 tff(6467,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[735, 6466, 708])).
% 1.85/2.08 tff(6468,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[319, 6467])).
% 1.85/2.08 tff(6469,plain,
% 1.85/2.08 (~r(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2319, 6468, 354, 51])).
% 1.85/2.08 tff(6470,plain,
% 1.85/2.08 (b(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1244, 6469, 1229])).
% 1.85/2.08 tff(6471,plain,
% 1.85/2.08 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6466])).
% 1.85/2.08 tff(6472,plain,
% 1.85/2.08 (b(s(z), elem!1)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[50, 6471])).
% 1.85/2.08 tff(6473,plain,
% 1.85/2.08 (r(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1732, 6472, 1727, 902, 6470])).
% 1.85/2.08 tff(6474,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(elem!1, s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6466])).
% 1.85/2.08 tff(6475,plain,
% 1.85/2.08 (r(elem!1, s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6468, 6474])).
% 1.85/2.08 tff(6476,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[727, 6475, 354, 2311])).
% 1.85/2.08 tff(6477,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[348, 6476])).
% 1.85/2.08 tff(6478,plain,
% 1.85/2.08 (~b(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2383, 6477, 6051, 6470])).
% 1.85/2.08 tff(6479,plain,
% 1.85/2.08 (r(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[583, 6478])).
% 1.85/2.08 tff(6480,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5074, 6479, 2311, 6473])).
% 1.85/2.08 tff(6481,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[965, 6480, 6058])).
% 1.85/2.08 tff(6482,plain,
% 1.85/2.08 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6466])).
% 1.85/2.08 tff(6483,plain,
% 1.85/2.08 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6482])).
% 1.85/2.08 tff(6484,plain,
% 1.85/2.08 (~(elem!1 = s(s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[244, 6483])).
% 1.85/2.08 tff(6485,plain,
% 1.85/2.08 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3398, 6466])).
% 1.85/2.08 tff(6486,plain,
% 1.85/2.08 (r(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2569, 6477, 50, 1727, 6485, 6470])).
% 1.85/2.08 tff(6487,plain,
% 1.85/2.08 (~r(elem!1, s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6311, 333, 2311, 6486, 6416])).
% 1.85/2.08 tff(6488,plain,
% 1.85/2.08 (b(elem!1, s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1538, 6487, 6484])).
% 1.85/2.08 tff(6489,plain,
% 1.85/2.08 (~r(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2393, 6479, 2311, 6473])).
% 1.85/2.08 tff(6490,plain,
% 1.85/2.08 (b(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[486, 6489, 1])).
% 1.85/2.08 tff(6491,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6492,plain,
% 1.85/2.08 (((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6493,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6492])).
% 1.85/2.08 tff(6494,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6493, 6491])).
% 1.85/2.08 tff(6495,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6496,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6495, 6494])).
% 1.85/2.08 tff(6497,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6496, 144, 1728, 6472, 6490, 6488, 6481])).
% 1.85/2.08 tff(6498,plain,((elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(z)) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6499,plain,
% 1.85/2.08 (elem!1 = s(elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6498, 708, 1727, 354, 51, 1, 606, 4, 2310])).
% 1.85/2.08 tff(6500,plain,
% 1.85/2.08 (b(elem!1, z) <=> b(s(elem!1), z)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6499])).
% 1.85/2.08 tff(6501,plain,
% 1.85/2.08 (b(s(elem!1), z) <=> b(elem!1, z)),
% 1.85/2.08 inference(symmetry,[status(thm)],[6500])).
% 1.85/2.08 tff(6502,plain,
% 1.85/2.08 (b(elem!1, z)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6051, 6501])).
% 1.85/2.08 tff(6503,plain,
% 1.85/2.08 (s(s(s(elem!1))) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2482, 6499])).
% 1.85/2.08 tff(6504,plain,
% 1.85/2.08 (~(s(z) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2468, 6503])).
% 1.85/2.08 tff(6505,plain,
% 1.85/2.08 (~(elem!1 = s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[712, 6504])).
% 1.85/2.08 tff(6506,plain,
% 1.85/2.08 (r(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[720, 6505, 708])).
% 1.85/2.08 tff(6507,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[727, 6506, 354, 2311])).
% 1.85/2.08 tff(6508,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[348, 6507])).
% 1.85/2.08 tff(6509,plain,
% 1.85/2.08 (b(s(z), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[406, 6504, 2310])).
% 1.85/2.08 tff(6510,plain,
% 1.85/2.08 (s(elem!1) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1569, 6499])).
% 1.85/2.08 tff(6511,plain,
% 1.85/2.08 (elem!1 = s(s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5813, 6510])).
% 1.85/2.08 tff(6512,plain,
% 1.85/2.08 (s(s(elem!1)) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5603, 6511])).
% 1.85/2.08 tff(6513,plain,
% 1.85/2.08 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5010, 6512])).
% 1.85/2.08 tff(6514,plain,
% 1.85/2.08 (~b(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[890, 6499, 708])).
% 1.85/2.08 tff(6515,plain,
% 1.85/2.08 (r(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[486, 6514, 1])).
% 1.85/2.08 tff(6516,plain,
% 1.85/2.08 (b(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3262, 6509, 6510])).
% 1.85/2.08 tff(6517,plain,
% 1.85/2.08 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3363, 6516, 51, 606, 1727, 6509, 6515, 2311])).
% 1.85/2.08 tff(6518,plain,
% 1.85/2.08 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[130, 6517, 6513])).
% 1.85/2.08 tff(6519,plain,
% 1.85/2.08 (~b(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2297, 6518, 6509, 6508, 50])).
% 1.85/2.08 tff(6520,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6519, 6502])).
% 1.85/2.08 tff(6521,plain,(b(elem!1, s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(elem!1), elem!1) | (~r(z, s(z))) | r(s(z), elem!1) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6522,plain,
% 1.85/2.08 (b(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6521, 1727, 606, 51, 354, 2310, 1, 4])).
% 1.85/2.08 tff(6523,plain,
% 1.85/2.08 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[57])).
% 1.85/2.08 tff(6524,plain,
% 1.85/2.08 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[6523])).
% 1.85/2.08 tff(6525,plain,
% 1.85/2.08 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6524])).
% 1.85/2.08 tff(6526,plain,
% 1.85/2.08 (~b(elem!1, s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[5882, 6525])).
% 1.85/2.08 tff(6527,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[305, 6526])).
% 1.85/2.08 tff(6528,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6529,plain,
% 1.85/2.08 (~(s(z) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6528, 305])).
% 1.85/2.08 tff(6530,plain,
% 1.85/2.08 (b(s(z), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[406, 6529, 2310])).
% 1.85/2.08 tff(6531,plain,
% 1.85/2.08 (~b(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4344, 144, 1728, 6530, 305])).
% 1.85/2.08 tff(6532,plain,
% 1.85/2.08 (r(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[486, 6531, 1])).
% 1.85/2.08 tff(6533,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4423, 6060, 51, 305, 453, 123, 2311])).
% 1.85/2.08 tff(6534,plain,
% 1.85/2.08 (~b(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6389, 706, 902, 354, 123, 51, 606, 1727, 1, 114, 2310])).
% 1.85/2.08 tff(6535,plain,
% 1.85/2.08 (r(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[653, 6534, 77])).
% 1.85/2.08 tff(6536,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2938, 6535, 6533, 2311, 51])).
% 1.85/2.08 tff(6537,plain,((s(z) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | b(z, elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6538,plain,
% 1.85/2.08 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6537, 902, 305, 123, 6529, 354, 606, 1727, 1, 51, 2310])).
% 1.85/2.08 tff(6539,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3868, 6538, 1727])).
% 1.85/2.08 tff(6540,plain,
% 1.85/2.08 (~(s(s(s(z))) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[109, 6538])).
% 1.85/2.08 tff(6541,plain,
% 1.85/2.08 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6538])).
% 1.85/2.08 tff(6542,plain,
% 1.85/2.08 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[6541])).
% 1.85/2.08 tff(6543,plain,
% 1.85/2.08 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[305, 6542])).
% 1.85/2.08 tff(6544,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3713, 6538, 1728])).
% 1.85/2.08 tff(6545,plain,
% 1.85/2.08 (~b(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4344, 144, 1728, 134, 305])).
% 1.85/2.08 tff(6546,plain,
% 1.85/2.08 (r(s(elem!1), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[486, 6545, 1])).
% 1.85/2.08 tff(6547,plain,
% 1.85/2.08 (~r(s(s(s(z))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2079, 408, 670, 1699])).
% 1.85/2.08 tff(6548,plain,
% 1.85/2.08 (b(s(s(s(z))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[704, 6547, 698])).
% 1.85/2.08 tff(6549,plain,
% 1.85/2.08 (~b(s(s(s(z))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4375, 6548, 305, 134])).
% 1.85/2.08 tff(6550,plain,
% 1.85/2.08 (r(s(s(s(z))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2794, 6549])).
% 1.85/2.08 tff(6551,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6552,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6553,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6552, 6551])).
% 1.85/2.08 tff(6554,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6553, 333, 354, 323, 1699, 3193])).
% 1.85/2.08 tff(6555,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6556,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6555, 6550, 354, 1699])).
% 1.85/2.08 tff(6557,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[348, 6556])).
% 1.85/2.08 tff(6558,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6559,plain,
% 1.85/2.08 (((~r(s(z), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6560,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6559])).
% 1.85/2.08 tff(6561,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6560, 6558])).
% 1.85/2.08 tff(6562,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6563,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6562, 6561])).
% 1.85/2.08 tff(6564,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6563, 333, 354, 1699, 1230, 3193])).
% 1.85/2.08 tff(6565,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6566,plain,
% 1.85/2.08 (~r(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6565, 6550, 354, 1699])).
% 1.85/2.08 tff(6567,plain,
% 1.85/2.08 (b(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1244, 6566, 1229])).
% 1.85/2.08 tff(6568,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3372, 6567, 6557, 1727, 670, 902, 1, 450, 134, 354, 304, 6546, 408])).
% 1.85/2.08 tff(6569,plain,((~r(elem!1, z)) | r(s(elem!1), elem!1) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6570,plain,
% 1.85/2.08 (~r(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6569, 902, 2311, 1727, 1, 6544, 6530, 354, 6543, 5821, 305, 6540])).
% 1.85/2.08 tff(6571,plain,
% 1.85/2.08 (b(elem!1, z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1380, 6570, 77])).
% 1.85/2.08 tff(6572,plain,
% 1.85/2.08 (r(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3973, 6571, 51, 354, 1, 123, 1727, 902, 6530, 6539])).
% 1.85/2.08 tff(6573,plain,
% 1.85/2.08 (~r(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2393, 6572, 2311, 6532])).
% 1.85/2.08 tff(6574,plain,
% 1.85/2.08 (b(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[583, 6573])).
% 1.85/2.08 tff(6575,plain,
% 1.85/2.08 (~(elem!1 = s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[712, 6529])).
% 1.85/2.08 tff(6576,plain,
% 1.85/2.08 (~r(s(elem!1), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4871, 6570, 1727, 1, 1728, 354, 2311, 123, 6530, 6538, 6575, 51])).
% 1.85/2.08 tff(6577,plain,
% 1.85/2.08 (b(s(elem!1), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[507, 6576])).
% 1.85/2.08 tff(6578,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6579,plain,
% 1.85/2.08 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6580,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6579])).
% 1.85/2.08 tff(6581,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6580, 6578])).
% 1.85/2.08 tff(6582,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6583,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 1.85/2.08 tff(6584,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6583, 333, 563, 670, 1699, 707])).
% 1.85/2.08 tff(6585,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6586,plain,
% 1.85/2.08 (~r(s(s(s(z))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6585, 6572, 2311, 5821])).
% 1.85/2.08 tff(6587,plain,
% 1.85/2.08 (b(s(s(s(z))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[704, 6586, 6540])).
% 1.85/2.08 tff(6588,plain,
% 1.85/2.08 (~b(s(s(s(z))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4375, 6587, 305, 6530])).
% 1.85/2.08 tff(6589,plain,
% 1.85/2.08 (r(s(s(s(z))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2794, 6588])).
% 1.85/2.08 tff(6590,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6555, 6589, 354, 5821])).
% 1.85/2.08 tff(6591,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[348, 6590])).
% 1.85/2.08 tff(6592,plain,
% 1.85/2.08 (~r(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6565, 6589, 354, 5821])).
% 1.85/2.08 tff(6593,plain,
% 1.85/2.08 (b(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1244, 6592, 1229])).
% 1.85/2.08 tff(6594,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2383, 6593, 6591, 6577, 6574])).
% 1.85/2.08 tff(6595,plain,((elem!1 = s(elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6596,plain,
% 1.85/2.08 (elem!1 = s(elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6595, 6522, 354, 51, 1, 50, 1727, 606, 2310])).
% 1.85/2.08 tff(6597,plain,
% 1.85/2.08 (s(elem!1) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1569, 6596])).
% 1.85/2.08 tff(6598,plain,
% 1.85/2.08 (elem!1 = s(s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5813, 6597])).
% 1.85/2.08 tff(6599,plain,
% 1.85/2.08 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1216, 6598])).
% 1.85/2.08 tff(6600,plain,
% 1.85/2.08 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[930, 6599])).
% 1.85/2.08 tff(6601,plain,
% 1.85/2.08 (~(s(z) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6528, 6522])).
% 1.85/2.08 tff(6602,plain,
% 1.85/2.08 (b(s(z), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[406, 6601, 2310])).
% 1.85/2.08 tff(6603,plain,
% 1.85/2.08 (s(s(elem!1)) = elem!1),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5603, 6598])).
% 1.85/2.08 tff(6604,plain,
% 1.85/2.08 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5010, 6603])).
% 1.85/2.08 tff(6605,plain,
% 1.85/2.08 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[116, 6604])).
% 1.85/2.08 tff(6606,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4423, 6605, 51, 6522, 6602, 50, 2311])).
% 1.85/2.08 tff(6607,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4003, 6606, 606, 51, 77, 2311])).
% 1.85/2.08 tff(6608,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[472, 6607, 6600])).
% 1.85/2.08 tff(6609,plain,
% 1.85/2.08 (b(s(z), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3262, 6597, 6602])).
% 1.85/2.08 tff(6610,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4150, 6608, 50, 1727, 6596, 51, 6602, 1, 606, 6604])).
% 1.85/2.08 tff(6611,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[348, 6610])).
% 1.85/2.08 tff(6612,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3222, 6611, 6609, 50, 6608])).
% 1.85/2.08 tff(6613,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[302, 6612])).
% 1.85/2.08 tff(6614,plain,
% 1.85/2.08 (~b(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2974, 6596, 606])).
% 1.85/2.08 tff(6615,plain,
% 1.85/2.08 (r(z, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[583, 6614])).
% 1.85/2.08 tff(6616,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6617,plain,
% 1.85/2.09 ((~![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(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6618,plain,
% 1.85/2.09 ((~![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(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6617, 6616])).
% 1.85/2.09 tff(6619,plain,
% 1.85/2.09 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6618, 333, 6615, 6416, 6613])).
% 1.85/2.09 tff(6620,plain,
% 1.85/2.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[249, 6619])).
% 1.85/2.09 tff(6621,plain,
% 1.85/2.09 (((~![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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6622,plain,
% 1.85/2.09 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6623,plain,
% 1.85/2.09 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6622])).
% 1.85/2.09 tff(6624,plain,
% 1.85/2.09 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6623, 6621])).
% 1.85/2.09 tff(6625,plain,
% 1.85/2.09 ((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6626,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6625, 6624])).
% 1.85/2.09 tff(6627,plain,
% 1.85/2.09 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6626, 333, 6615, 6416, 6613])).
% 1.85/2.09 tff(6628,plain,
% 1.85/2.09 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1137, 6627])).
% 1.85/2.09 tff(6629,plain,
% 1.85/2.09 (~b(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2262, 6628, 50, 6620])).
% 1.85/2.09 tff(6630,plain,
% 1.85/2.09 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6596])).
% 1.85/2.09 tff(6631,plain,
% 1.85/2.09 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[6630])).
% 1.85/2.09 tff(6632,plain,
% 1.85/2.09 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6608, 6631])).
% 1.85/2.09 tff(6633,plain,
% 1.85/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[313, 6632, 50, 6522])).
% 1.85/2.09 tff(6634,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[319, 6633])).
% 1.85/2.09 tff(6635,plain,
% 1.85/2.09 (~r(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[362, 6634, 6613, 354])).
% 1.85/2.09 tff(6636,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[172, 6635, 6629])).
% 1.85/2.09 tff(6637,plain,(r(s(elem!1), elem!1) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6638,plain,
% 1.85/2.09 (r(s(elem!1), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6637, 51, 354, 1, 606, 2310, 4])).
% 1.85/2.09 tff(6639,plain,
% 1.85/2.09 (~b(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5440, 713, 2311, 435, 51, 114, 123, 6060, 1, 354, 902])).
% 1.85/2.09 tff(6640,plain,
% 1.85/2.09 (r(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[583, 6639])).
% 1.85/2.09 tff(6641,plain,
% 1.85/2.09 (~r(elem!1, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1863, 6640, 2311, 435])).
% 1.85/2.09 tff(6642,plain,
% 1.85/2.09 (b(elem!1, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[720, 6641, 713])).
% 1.85/2.09 tff(6643,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4423, 6642, 51, 453, 6060, 123, 2311])).
% 1.85/2.09 tff(6644,plain,
% 1.85/2.09 (~r(elem!1, z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2938, 6643, 2311, 51])).
% 1.85/2.09 tff(6645,plain,
% 1.85/2.09 (b(elem!1, z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1380, 6644, 77])).
% 1.85/2.09 tff(6646,plain,
% 1.85/2.09 (~r(elem!1, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2492, 6643, 2311, 51])).
% 1.85/2.09 tff(6647,plain,
% 1.85/2.09 (b(elem!1, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[560, 6646, 902])).
% 1.85/2.09 tff(6648,plain,
% 1.85/2.09 (~r(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5456, 6647, 1, 2311, 6642, 354, 706, 435, 902, 6645])).
% 1.85/2.09 tff(6649,plain,
% 1.85/2.09 (b(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[348, 6648])).
% 1.85/2.09 tff(6650,plain,
% 1.85/2.09 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4003, 6643, 606, 51, 77, 2311])).
% 1.85/2.09 tff(6651,plain,
% 1.85/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3424, 6649, 123, 435, 2311, 902, 713, 51, 6645, 354, 1, 6060, 6650])).
% 1.85/2.09 tff(6652,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[319, 6651])).
% 1.85/2.09 tff(6653,plain,
% 1.85/2.09 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2541, 6652, 2311, 51])).
% 1.85/2.09 tff(6654,plain,
% 1.85/2.09 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[121, 6653, 453])).
% 1.85/2.09 tff(6655,plain,
% 1.85/2.09 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2105, 6654, 6060, 123, 6649])).
% 1.85/2.09 tff(6656,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[302, 6655])).
% 1.85/2.09 tff(6657,plain,
% 1.85/2.09 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5359, 6640, 2311, 435])).
% 1.85/2.09 tff(6658,plain,
% 1.85/2.09 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2655, 6640, 51, 435])).
% 1.85/2.09 tff(6659,plain,
% 1.85/2.09 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5467, 6654, 6658, 6647, 6650])).
% 1.85/2.09 tff(6660,plain,
% 1.85/2.09 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1216, 6659])).
% 1.85/2.09 tff(6661,plain,
% 1.85/2.09 (b(elem!1, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2522, 6660, 6657])).
% 1.85/2.09 tff(6662,plain,
% 1.85/2.09 (~r(s(s(elem!1)), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5640, 6661, 435, 6645, 6640])).
% 1.85/2.09 tff(6663,plain,
% 1.85/2.09 (b(s(s(elem!1)), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1283, 6662, 2727])).
% 1.85/2.09 tff(6664,plain,
% 1.85/2.09 (~b(s(z), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5494, 6663, 6642, 6647, 6661])).
% 1.85/2.09 tff(6665,plain,
% 1.85/2.09 (r(s(z), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5484, 6664])).
% 1.85/2.09 tff(6666,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6667,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6668,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6667, 6666])).
% 1.85/2.09 tff(6669,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6668, 333, 354, 6665, 6652, 6656])).
% 1.85/2.09 tff(6670,plain,((s(z) = elem!1) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | b(z, elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6671,plain,
% 1.85/2.09 (s(z) = elem!1),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6670, 114, 435, 123, 51, 902, 1, 606, 354, 2310])).
% 1.85/2.09 tff(6672,plain,
% 1.85/2.09 (s(s(z)) = s(elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.09 tff(6673,plain,
% 1.85/2.09 (s(s(s(z))) = s(s(elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6672])).
% 1.85/2.09 tff(6674,plain,
% 1.85/2.09 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.09 inference(symmetry,[status(thm)],[6673])).
% 1.85/2.09 tff(6675,plain,
% 1.85/2.09 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6674])).
% 1.85/2.09 tff(6676,plain,
% 1.85/2.09 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(symmetry,[status(thm)],[6675])).
% 1.85/2.09 tff(6677,plain,
% 1.85/2.09 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6673])).
% 1.85/2.09 tff(6678,plain,
% 1.85/2.09 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6677, 2502])).
% 1.85/2.09 tff(6679,plain,
% 1.85/2.09 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[6678])).
% 1.85/2.09 tff(6680,plain,
% 1.85/2.09 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6679])).
% 1.85/2.09 tff(6681,plain,
% 1.85/2.09 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[2727, 6680])).
% 1.85/2.09 tff(6682,plain,
% 1.85/2.09 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6673])).
% 1.85/2.09 tff(6683,plain,
% 1.85/2.09 ((~b(s(s(s(z))), z)) <=> (~b(s(s(elem!1)), z))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6682])).
% 1.85/2.09 tff(6684,plain,
% 1.85/2.09 (~b(s(s(elem!1)), z)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[5820, 6683])).
% 1.85/2.09 tff(6685,plain,
% 1.85/2.09 (r(s(s(elem!1)), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6447, 6671, 5821])).
% 1.85/2.09 tff(6686,plain,
% 1.85/2.09 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.09 tff(6687,plain,
% 1.85/2.09 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[123, 6686])).
% 1.85/2.09 tff(6688,plain,
% 1.85/2.09 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6674])).
% 1.85/2.09 tff(6689,plain,
% 1.85/2.09 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6688, 972])).
% 1.85/2.09 tff(6690,plain,
% 1.85/2.09 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6689])).
% 1.85/2.09 tff(6691,plain,
% 1.85/2.09 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4281, 2727])).
% 1.85/2.09 tff(6692,plain,
% 1.85/2.09 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6691, 6690])).
% 1.85/2.09 tff(6693,plain,
% 1.85/2.09 (r(s(elem!1), s(z))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[435, 4192])).
% 1.85/2.09 tff(6694,plain,
% 1.85/2.09 (~r(s(elem!1), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1365, 3922, 354, 6693])).
% 1.85/2.09 tff(6695,plain,
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% 1.85/2.09 inference(unit_resolution,[status(thm)],[507, 6694])).
% 1.85/2.09 tff(6696,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4215, 5223, 670, 6693, 3523, 3922, 6695])).
% 1.85/2.09 tff(6697,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1101, 6696])).
% 1.85/2.09 tff(6698,plain,
% 1.85/2.09 (b(s(s(s(s(z)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3588, 6697, 57])).
% 1.85/2.09 tff(6699,plain,
% 1.85/2.09 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3552, 144, 6698, 5229, 132])).
% 1.85/2.09 tff(6700,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3556, 44, 196, 6699])).
% 1.85/2.09 tff(6701,plain,
% 1.85/2.09 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[4584])).
% 1.85/2.09 tff(6702,plain,
% 1.85/2.09 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6701])).
% 1.85/2.09 tff(6703,plain,
% 1.85/2.09 (~r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5047, 5221, 5038, 670])).
% 1.85/2.09 tff(6704,plain,
% 1.85/2.09 (b(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1260, 44, 6703, 4575])).
% 1.85/2.09 tff(6705,plain,
% 1.85/2.09 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6706,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6705])).
% 1.85/2.09 tff(6707,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6706, 4601])).
% 1.85/2.09 tff(6708,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6709,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6708, 6707])).
% 1.85/2.09 tff(6710,plain,
% 1.85/2.09 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6709, 144, 5229, 132, 6704])).
% 1.85/2.09 tff(6711,plain,
% 1.85/2.09 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6710, 6702])).
% 1.85/2.09 tff(6712,plain,
% 1.85/2.09 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1137, 6711])).
% 1.85/2.09 tff(6713,plain,
% 1.85/2.09 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6712, 2767])).
% 1.85/2.09 tff(6714,plain,
% 1.85/2.09 (((~![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)), z)) | (~r(z, elem!1)) | (~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, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6715,plain,
% 1.85/2.09 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6716,plain,
% 1.85/2.09 (((~![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(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6715])).
% 1.85/2.09 tff(6717,plain,
% 1.85/2.09 (((~![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(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6716, 6714])).
% 1.85/2.09 tff(6718,plain,
% 1.85/2.09 ((~![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(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6719,plain,
% 1.85/2.09 ((~![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)), z)) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6718, 6717])).
% 1.85/2.09 tff(6720,plain,
% 1.85/2.09 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6719, 333, 670, 5221, 5497])).
% 1.85/2.09 tff(6721,plain,
% 1.85/2.09 (b(elem!1, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2522, 6720, 2462])).
% 1.85/2.09 tff(6722,plain,
% 1.85/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4728, 144, 6721, 5229, 6704])).
% 1.85/2.09 tff(6723,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2758, 6722, 2704])).
% 1.85/2.09 tff(6724,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.85/2.09 tff(6725,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6726,plain,
% 1.85/2.09 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6727,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6726])).
% 1.85/2.09 tff(6728,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6727, 6725])).
% 1.85/2.09 tff(6729,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6730,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6729, 6728])).
% 1.85/2.09 tff(6731,plain,
% 1.85/2.09 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6730, 144, 6721, 6698, 6704])).
% 1.85/2.09 tff(6732,plain,
% 1.85/2.09 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6731, 4285])).
% 1.85/2.09 tff(6733,plain,
% 1.85/2.09 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1116, 6732, 6724])).
% 1.85/2.09 tff(6734,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6733, 4272])).
% 1.85/2.09 tff(6735,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6736,plain,
% 1.85/2.09 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6737,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6736])).
% 1.85/2.09 tff(6738,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6737, 6735])).
% 1.85/2.09 tff(6739,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6740,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6739, 6738])).
% 1.85/2.09 tff(6741,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6740, 333, 6734, 6723, 6713, 6700])).
% 1.85/2.09 tff(6742,plain,(b(s(z), z) | (~(s(z) = elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(elem!1)), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6743,plain,
% 1.85/2.09 (b(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6742, 6671, 6692, 6687, 2311, 435, 6685, 114, 6684, 51, 77, 354])).
% 1.85/2.09 tff(6744,plain,
% 1.85/2.09 (b(s(z), z) <=> b(elem!1, z)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.09 tff(6745,plain,
% 1.85/2.09 (b(elem!1, z)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6743, 6744])).
% 1.85/2.09 tff(6746,plain,
% 1.85/2.09 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6672])).
% 1.85/2.09 tff(6747,plain,
% 1.85/2.09 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6746, 174])).
% 1.85/2.09 tff(6748,plain,
% 1.85/2.09 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6747, 175])).
% 1.85/2.09 tff(6749,plain,
% 1.85/2.09 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6748])).
% 1.85/2.09 tff(6750,plain,
% 1.85/2.09 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[1446, 6749])).
% 1.85/2.09 tff(6751,plain,
% 1.85/2.09 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6747])).
% 1.85/2.09 tff(6752,plain,
% 1.85/2.09 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[1446, 6751])).
% 1.85/2.09 tff(6753,plain,
% 1.85/2.09 (~b(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5289, 2484, 132, 432, 624, 902, 606, 51, 1368, 670])).
% 1.85/2.09 tff(6754,plain,
% 1.85/2.09 (r(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[583, 6753])).
% 1.85/2.09 tff(6755,plain,
% 1.85/2.09 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5467, 5281, 132, 537, 5279])).
% 1.85/2.09 tff(6756,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2655, 6755, 6754, 51, 435])).
% 1.85/2.09 tff(6757,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | b(z, elem!1) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6758,plain,
% 1.85/2.09 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6757, 6687, 435, 51, 6752, 902, 6750, 6745, 606, 77, 2311])).
% 1.85/2.09 tff(6759,plain,
% 1.85/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[130, 6758, 114])).
% 1.85/2.10 tff(6760,plain,
% 1.85/2.10 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.85/2.10 inference(monotonicity,[status(thm)],[2496])).
% 1.85/2.10 tff(6761,plain,
% 1.85/2.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(symmetry,[status(thm)],[6760])).
% 1.85/2.10 tff(6762,plain,
% 1.85/2.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6761, 59])).
% 1.85/2.10 tff(6763,plain,
% 1.85/2.10 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(z))), s(z)))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6762])).
% 1.85/2.10 tff(6764,plain,
% 1.85/2.10 (r(s(s(elem!1)), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6447, 57, 1699])).
% 1.85/2.10 tff(6765,plain,
% 1.85/2.10 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[2854, 2506])).
% 1.85/2.10 tff(6766,plain,
% 1.85/2.10 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[5835, 3889, 1699, 670])).
% 1.85/2.10 tff(6767,plain,
% 1.85/2.10 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[965, 6766, 6765])).
% 1.85/2.10 tff(6768,plain,
% 1.85/2.10 (b(s(elem!1), s(s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6767, 2501])).
% 1.85/2.10 tff(6769,plain,
% 1.85/2.10 (((~![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(s(elem!1)), z)) | (~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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6770,plain,
% 1.85/2.10 ((~![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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6771,plain,
% 1.85/2.10 ((~![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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6770, 6769])).
% 1.85/2.10 tff(6772,plain,
% 1.85/2.10 (~r(s(s(elem!1)), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6771, 333, 670, 3889, 6764])).
% 1.85/2.10 tff(6773,plain,
% 1.85/2.10 (b(s(s(elem!1)), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1283, 6772, 2854])).
% 1.85/2.10 tff(6774,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6775,plain,
% 1.85/2.10 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6776,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6775])).
% 1.85/2.10 tff(6777,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6776, 6774])).
% 1.85/2.10 tff(6778,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6779,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6778, 6777])).
% 1.85/2.10 tff(6780,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6779, 144, 585, 1249, 2811, 3627])).
% 1.85/2.10 tff(6781,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6782,plain,
% 1.85/2.10 (~b(z, s(s(elem!1)))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6781, 6773, 585, 6768])).
% 1.85/2.10 tff(6783,plain,
% 1.85/2.10 (~b(z, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2828, 6782, 57])).
% 1.85/2.10 tff(6784,plain,
% 1.85/2.10 (r(z, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[619, 6783])).
% 1.85/2.10 tff(6785,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6786,plain,
% 1.85/2.10 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6787,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6786])).
% 1.85/2.10 tff(6788,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6787, 6785])).
% 1.85/2.10 tff(6789,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6790,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6789, 6788])).
% 1.85/2.10 tff(6791,plain,
% 1.85/2.10 ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6790, 333, 3654])).
% 1.85/2.10 tff(6792,plain,
% 1.85/2.10 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6791, 6424, 2833])).
% 1.85/2.10 tff(6793,plain,
% 1.85/2.10 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[277, 44, 6792])).
% 1.85/2.10 tff(6794,plain,
% 1.85/2.10 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6793, 274])).
% 1.85/2.10 tff(6795,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6796,plain,
% 1.85/2.10 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6797,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6796])).
% 1.85/2.10 tff(6798,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6797, 6795])).
% 1.85/2.10 tff(6799,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6800,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6799, 6798])).
% 1.85/2.10 tff(6801,plain,
% 1.85/2.10 ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6800, 333, 3654])).
% 1.85/2.10 tff(6802,plain,
% 1.85/2.10 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6801, 6424, 2833])).
% 1.85/2.10 tff(6803,plain,
% 1.85/2.10 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[300, 44, 273, 6802])).
% 1.85/2.10 tff(6804,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6805,plain,
% 1.85/2.10 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6806,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6805])).
% 1.85/2.10 tff(6807,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6806, 6804])).
% 1.85/2.10 tff(6808,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6809,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6808, 6807])).
% 1.85/2.10 tff(6810,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6809, 144, 624, 132, 6803, 6794])).
% 1.85/2.10 tff(6811,plain,((~r(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6812,plain,
% 1.85/2.10 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6811, 6784, 1699, 57, 624, 132])).
% 1.85/2.10 tff(6813,plain,
% 1.85/2.10 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2758, 6812, 2704])).
% 1.85/2.10 tff(6814,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6815,plain,
% 1.85/2.10 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6816,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6815])).
% 1.85/2.10 tff(6817,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6816, 6814])).
% 1.85/2.10 tff(6818,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6819,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 1.85/2.10 tff(6820,plain,
% 1.85/2.10 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6819, 144, 6773, 6813, 6768])).
% 1.85/2.10 tff(6821,plain,
% 1.85/2.10 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[542, 6820, 2698])).
% 1.85/2.10 tff(6822,plain,
% 1.85/2.10 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[533, 6821, 51, 3889])).
% 1.85/2.10 tff(6823,plain,
% 1.85/2.10 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[472, 6822, 4762])).
% 1.85/2.10 tff(6824,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[5287, 144, 547, 624, 585, 132, 6823])).
% 1.85/2.10 tff(6825,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6826,plain,
% 1.85/2.10 (~b(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6825, 585, 2694, 132, 51, 1699, 57, 2727, 670])).
% 1.85/2.10 tff(6827,plain,
% 1.85/2.10 (r(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[560, 6826, 902])).
% 1.85/2.10 tff(6828,plain,
% 1.85/2.10 (~r(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3624, 6827, 670, 435])).
% 1.85/2.10 tff(6829,plain,
% 1.85/2.10 (b(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[507, 6828])).
% 1.85/2.10 tff(6830,plain,
% 1.85/2.10 (~b(s(z), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2383, 6829, 489, 585])).
% 1.85/2.10 tff(6831,plain,
% 1.85/2.10 (r(s(z), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1244, 6830, 1237])).
% 1.85/2.10 tff(6832,plain,
% 1.85/2.10 (~r(s(s(s(elem!1))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3139, 6831, 354, 6693, 3523, 6829, 585])).
% 1.85/2.10 tff(6833,plain,
% 1.85/2.10 (b(s(s(s(elem!1))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1101, 6832])).
% 1.85/2.10 tff(6834,plain,
% 1.85/2.10 (b(s(s(s(s(z)))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3588, 6833, 57])).
% 1.85/2.10 tff(6835,plain,
% 1.85/2.10 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3552, 144, 6834, 133, 132])).
% 1.85/2.10 tff(6836,plain,
% 1.85/2.10 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3556, 44, 196, 6835])).
% 1.85/2.10 tff(6837,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6838,plain,
% 1.85/2.11 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6839,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6838])).
% 1.85/2.11 tff(6840,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6839, 6837])).
% 1.85/2.11 tff(6841,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6842,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6841, 6840])).
% 1.85/2.11 tff(6843,plain,
% 1.85/2.11 (~r(s(s(s(s(z)))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6842, 333, 51, 524, 3559])).
% 1.85/2.11 tff(6844,plain,
% 1.85/2.11 (b(s(s(s(s(z)))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4243, 44, 242, 6843])).
% 1.85/2.11 tff(6845,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6846,plain,
% 1.85/2.11 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6847,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6846])).
% 1.85/2.11 tff(6848,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6847, 6845])).
% 1.85/2.11 tff(6849,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6850,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6849, 6848])).
% 1.85/2.11 tff(6851,plain,
% 1.85/2.11 (~r(z, s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6850, 333, 51, 524, 3559])).
% 1.85/2.11 tff(6852,plain,
% 1.85/2.11 (b(z, s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4260, 6851])).
% 1.85/2.11 tff(6853,plain,
% 1.85/2.11 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4267, 144, 491, 6852, 6844])).
% 1.85/2.11 tff(6854,plain,
% 1.85/2.11 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6853, 3528])).
% 1.85/2.11 tff(6855,plain,
% 1.85/2.11 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1067, 6854, 3524])).
% 1.85/2.11 tff(6856,plain,
% 1.85/2.11 (r(s(elem!1), s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[3545, 6855, 57])).
% 1.85/2.11 tff(6857,plain,
% 1.85/2.11 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.85/2.11 inference(commutativity,[status(thm)],[])).
% 1.85/2.11 tff(6858,plain,
% 1.85/2.11 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[3526])).
% 1.85/2.11 tff(6859,plain,
% 1.85/2.11 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.85/2.11 inference(transitivity,[status(thm)],[6858, 6857])).
% 1.85/2.11 tff(6860,plain,
% 1.85/2.11 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[6859])).
% 1.85/2.11 tff(6861,plain,
% 1.85/2.11 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6860])).
% 1.85/2.11 tff(6862,plain,
% 1.85/2.11 (~(elem!1 = s(s(s(s(z)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[2469, 6861])).
% 1.85/2.11 tff(6863,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6864,plain,
% 1.85/2.11 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6865,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6864])).
% 1.85/2.11 tff(6866,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6865, 6863])).
% 1.85/2.11 tff(6867,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6868,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6867, 6866])).
% 1.85/2.11 tff(6869,plain,
% 1.85/2.11 (~b(elem!1, s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6868, 144, 624, 6852, 6844])).
% 1.85/2.11 tff(6870,plain,
% 1.85/2.11 (((~![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))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6871,plain,
% 1.85/2.11 ((~![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))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6872,plain,
% 1.85/2.11 ((~![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)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6871, 6870])).
% 1.85/2.11 tff(6873,plain,
% 1.85/2.11 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6872, 44])).
% 1.85/2.11 tff(6874,plain,
% 1.85/2.11 (r(elem!1, s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6873, 6869, 6862])).
% 1.85/2.11 tff(6875,plain,
% 1.85/2.11 (((~![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(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), 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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6876,plain,
% 1.85/2.11 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6877,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6876])).
% 1.85/2.11 tff(6878,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6877, 6875])).
% 1.85/2.11 tff(6879,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6880,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6879, 6878])).
% 1.85/2.11 tff(6881,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6880, 333, 435, 6874, 6856, 3559])).
% 1.85/2.11 tff(6882,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(6883,plain,
% 1.85/2.11 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6882, 6836, 435, 57, 6829, 2694, 51])).
% 1.85/2.11 tff(6884,plain,
% 1.85/2.11 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[542, 6883, 2698])).
% 1.85/2.11 tff(6885,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6886,plain,
% 1.85/2.11 (((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6887,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6886])).
% 1.85/2.11 tff(6888,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6887, 6885])).
% 1.85/2.11 tff(6889,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6890,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 1.85/2.11 tff(6891,plain,
% 1.85/2.11 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6890, 144, 2694, 585, 133, 6884])).
% 1.85/2.11 tff(6892,plain,
% 1.85/2.11 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[302, 6891])).
% 1.85/2.11 tff(6893,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6894,plain,
% 1.85/2.11 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6895,plain,
% 1.85/2.11 (((~![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(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6894])).
% 1.85/2.11 tff(6896,plain,
% 1.85/2.11 (((~![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(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6895, 6893])).
% 1.85/2.11 tff(6897,plain,
% 1.85/2.11 ((~![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(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6898,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6897, 6896])).
% 1.85/2.11 tff(6899,plain,
% 1.85/2.11 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6898, 333, 670, 6892, 6764])).
% 1.85/2.11 tff(6900,plain,
% 1.85/2.11 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6899, 4024])).
% 1.85/2.11 tff(6901,plain,
% 1.85/2.11 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1137, 6900])).
% 1.85/2.11 tff(6902,plain,
% 1.85/2.11 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6901, 4584])).
% 1.85/2.11 tff(6903,plain,
% 1.85/2.11 (~b(s(s(elem!1)), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4606, 144, 133, 132, 6902])).
% 1.85/2.11 tff(6904,plain,
% 1.85/2.11 (~b(s(s(s(z))), s(z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6903, 6763])).
% 1.85/2.11 tff(6905,plain,
% 1.85/2.11 (~r(s(s(s(z))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6565, 6831, 354, 1699])).
% 1.85/2.11 tff(6906,plain,
% 1.85/2.11 (b(s(s(s(z))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2794, 6905])).
% 1.85/2.11 tff(6907,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6906, 6904])).
% 1.85/2.11 tff(6908,plain,((~b(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(6909,plain,
% 1.85/2.11 (~b(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6908, 6671, 6759, 6687, 2311, 435, 51, 354, 5821, 1229, 6743, 902])).
% 1.85/2.11 tff(6910,plain,
% 1.85/2.11 (r(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[583, 6909])).
% 1.85/2.11 tff(6911,plain,
% 1.85/2.11 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.11 tff(6912,plain,
% 1.85/2.11 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.85/2.11 inference(symmetry,[status(thm)],[6911])).
% 1.85/2.11 tff(6913,plain,
% 1.85/2.11 (r(s(elem!1), s(z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[435, 6912])).
% 1.85/2.11 tff(6914,plain,
% 1.85/2.11 (~r(elem!1, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2393, 6910, 2311, 6913])).
% 1.85/2.11 tff(6915,plain,
% 1.85/2.11 (b(elem!1, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[560, 6914, 902])).
% 1.85/2.11 tff(6916,plain,
% 1.85/2.11 (~r(s(s(elem!1)), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[5505, 6910, 435, 6685])).
% 1.85/2.11 tff(6917,plain,
% 1.85/2.11 (b(s(s(elem!1)), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1283, 6916, 2727])).
% 1.85/2.11 tff(6918,plain,
% 1.85/2.11 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.11 tff(6919,plain,
% 1.85/2.11 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6918, 1218])).
% 1.85/2.11 tff(6920,plain,
% 1.85/2.11 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6919])).
% 1.85/2.11 tff(6921,plain,
% 1.85/2.11 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[107, 6920])).
% 1.85/2.11 tff(6922,plain,
% 1.85/2.11 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[5359, 6910, 2311, 435])).
% 1.85/2.11 tff(6923,plain,
% 1.85/2.11 (b(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2522, 6922, 6921])).
% 1.85/2.11 tff(6924,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6925,plain,
% 1.85/2.11 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6926,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6925])).
% 1.85/2.11 tff(6927,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6926, 6924])).
% 1.85/2.11 tff(6928,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(6929,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[6928, 6927])).
% 1.85/2.12 tff(6930,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6929, 144, 547, 624, 1249, 2812, 2811])).
% 1.85/2.12 tff(6931,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6932,plain,
% 1.85/2.12 (~b(z, s(s(elem!1)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6931, 6923, 6917, 6915, 6745])).
% 1.85/2.12 tff(6933,plain,
% 1.85/2.12 (~b(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2828, 6932, 6671])).
% 1.85/2.12 tff(6934,plain,
% 1.85/2.12 (r(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[619, 6933])).
% 1.85/2.12 tff(6935,plain,
% 1.85/2.12 (~r(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1972, 6934, 5821, 6910])).
% 1.85/2.12 tff(6936,plain,
% 1.85/2.12 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[965, 6935, 6681])).
% 1.85/2.12 tff(6937,plain,
% 1.85/2.12 (b(s(elem!1), s(s(elem!1)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[6936, 6676])).
% 1.85/2.12 tff(6938,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(6939,plain,
% 1.85/2.12 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(6940,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[6939])).
% 1.85/2.12 tff(6941,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[6940, 6938])).
% 1.85/2.12 tff(6942,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(6943,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[6942, 6941])).
% 1.85/2.12 tff(6944,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6943, 144, 6915, 6917, 6923, 6937])).
% 1.85/2.12 tff(6945,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | b(z, elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6946,plain,
% 1.85/2.12 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6945, 902, 435, 51, 354, 606, 123, 1, 2310])).
% 1.85/2.12 tff(6947,plain,
% 1.85/2.12 (~b(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5674, 562, 1, 354, 435, 2727, 81, 51, 670])).
% 1.85/2.12 tff(6948,plain,
% 1.85/2.12 (~r(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4052, 562, 670, 5612])).
% 1.85/2.12 tff(6949,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[560, 6948, 6947, 902])).
% 1.85/2.12 tff(6950,plain,((~r(z, s(elem!1))) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6951,plain,
% 1.85/2.12 (~r(z, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6950, 902, 2311, 1, 354, 435, 6946, 51])).
% 1.85/2.12 tff(6952,plain,
% 1.85/2.12 (b(z, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[583, 6951])).
% 1.85/2.12 tff(6953,plain,
% 1.85/2.12 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = elem!1)),
% 1.85/2.12 inference(monotonicity,[status(thm)],[6946])).
% 1.85/2.12 tff(6954,plain,
% 1.85/2.12 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(z))),
% 1.85/2.12 inference(transitivity,[status(thm)],[6953, 53])).
% 1.85/2.12 tff(6955,plain,
% 1.85/2.12 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(z)))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[6954])).
% 1.85/2.12 tff(6956,plain,
% 1.85/2.12 (~(elem!1 = s(z))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[34, 6955])).
% 1.85/2.12 tff(6957,plain,
% 1.85/2.12 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 1.85/2.12 inference(monotonicity,[status(thm)],[6946])).
% 1.85/2.12 tff(6958,plain,
% 1.85/2.12 (b(s(z), elem!1)),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[123, 6957])).
% 1.85/2.12 tff(6959,plain,
% 1.85/2.12 (~r(z, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[940, 4356, 51, 5612])).
% 1.85/2.12 tff(6960,plain,
% 1.85/2.12 (b(z, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[583, 6959])).
% 1.85/2.12 tff(6961,plain,
% 1.85/2.12 (~r(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2079, 4414, 670, 1699])).
% 1.85/2.12 tff(6962,plain,
% 1.85/2.12 (b(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[704, 6961, 4363])).
% 1.85/2.12 tff(6963,plain,
% 1.85/2.12 (b(elem!1, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5692, 4436, 435, 81, 670, 1237, 354, 51])).
% 1.85/2.12 tff(6964,plain,
% 1.85/2.12 (~b(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4375, 6963, 6962, 134])).
% 1.85/2.12 tff(6965,plain,
% 1.85/2.12 (r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2794, 6964])).
% 1.85/2.12 tff(6966,plain,
% 1.85/2.12 (~r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6555, 6965, 354, 1699])).
% 1.85/2.12 tff(6967,plain,
% 1.85/2.12 (b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[348, 6966])).
% 1.85/2.12 tff(6968,plain,
% 1.85/2.12 (~r(s(z), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6565, 6965, 354, 1699])).
% 1.85/2.12 tff(6969,plain,
% 1.85/2.12 (b(s(z), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1244, 6968, 1237])).
% 1.85/2.12 tff(6970,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2383, 6969, 6967, 4436, 6960])).
% 1.85/2.12 tff(6971,plain,(b(elem!1, z) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6972,plain,
% 1.85/2.12 (b(elem!1, z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6971, 6958, 354, 5821, 1229, 435, 6946, 2311, 51, 77])).
% 1.85/2.12 tff(6973,plain,
% 1.85/2.12 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(z) = elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[6953])).
% 1.85/2.12 tff(6974,plain,
% 1.85/2.12 (~(s(z) = elem!1)),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[34, 6973])).
% 1.85/2.12 tff(6975,plain,
% 1.85/2.12 (~(s(s(s(z))) = elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[109, 6946])).
% 1.85/2.12 tff(6976,plain,
% 1.85/2.12 (~b(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5456, 5398, 1, 670, 323, 354, 706, 435, 902, 624])).
% 1.85/2.12 tff(6977,plain,
% 1.85/2.12 (r(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[560, 6976, 902])).
% 1.85/2.12 tff(6978,plain,
% 1.85/2.12 (~r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6555, 323, 354, 1699])).
% 1.85/2.12 tff(6979,plain,
% 1.85/2.12 (b(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2794, 6978])).
% 1.85/2.12 tff(6980,plain,
% 1.85/2.12 (~b(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4375, 6979, 5398, 134])).
% 1.85/2.12 tff(6981,plain,
% 1.85/2.12 (r(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[704, 6980, 698])).
% 1.85/2.12 tff(6982,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6585, 6981, 6977, 670, 1699])).
% 1.85/2.12 tff(6983,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6984,plain,
% 1.85/2.12 (~r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6983, 6975, 5821, 2311, 902, 6958, 1, 354, 6974, 435, 6972, 6956])).
% 1.85/2.12 tff(6985,plain,
% 1.85/2.12 (b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[348, 6984])).
% 1.85/2.12 tff(6986,plain,
% 1.85/2.12 (~b(s(elem!1), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5692, 708, 435, 81, 670, 1237, 354, 51])).
% 1.85/2.12 tff(6987,plain,
% 1.85/2.12 (r(s(elem!1), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[507, 6986])).
% 1.85/2.12 tff(6988,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5438, 333, 435, 670, 6987, 5681])).
% 1.85/2.12 tff(6989,plain,(b(elem!1, s(z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6990,plain,
% 1.85/2.12 (b(elem!1, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6989, 6946, 2311, 435, 1229, 354, 51])).
% 1.85/2.12 tff(6991,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5427, 144, 547, 624, 585, 489, 305])).
% 1.85/2.12 tff(6992,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(6993,plain,
% 1.85/2.12 (~b(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6992, 6972, 6952, 6985, 6990])).
% 1.85/2.12 tff(6994,plain,
% 1.85/2.12 (r(elem!1, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[560, 6993, 902])).
% 1.85/2.12 tff(6995,plain,
% 1.85/2.12 (~r(s(elem!1), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[3624, 6994, 2311, 435])).
% 1.85/2.12 tff(6996,plain,
% 1.85/2.12 (b(s(elem!1), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[507, 6995])).
% 1.85/2.12 tff(6997,plain,
% 1.85/2.12 (~b(s(z), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2383, 6996, 6985, 6952])).
% 1.85/2.12 tff(6998,plain,
% 1.85/2.12 (r(s(z), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1244, 6997, 1229])).
% 1.85/2.12 tff(6999,plain,
% 1.85/2.12 (~r(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6585, 6994, 2311, 5821])).
% 1.85/2.12 tff(7000,plain,
% 1.85/2.12 (b(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[704, 6999, 6975])).
% 1.85/2.12 tff(7001,plain,
% 1.85/2.12 (~b(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4375, 7000, 6990, 6958])).
% 1.85/2.12 tff(7002,plain,
% 1.85/2.12 (r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2794, 7001])).
% 1.85/2.12 tff(7003,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6565, 7002, 6998, 354, 5821])).
% 1.85/2.12 tff(7004,plain,((elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7005,plain,
% 1.85/2.12 (elem!1 = s(elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7004, 6638, 354, 1, 51, 50, 606, 2310])).
% 1.85/2.12 tff(7006,plain,
% 1.85/2.12 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[7005])).
% 1.85/2.12 tff(7007,plain,
% 1.85/2.12 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), elem!1)),
% 1.85/2.12 inference(symmetry,[status(thm)],[7006])).
% 1.85/2.12 tff(7008,plain,
% 1.85/2.12 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[7007])).
% 1.85/2.12 tff(7009,plain,
% 1.85/2.12 (~r(s(elem!1), elem!1)),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[3482, 7008])).
% 1.85/2.12 tff(7010,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6638, 7009])).
% 1.85/2.12 tff(7011,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7012,plain,
% 1.85/2.12 (~r(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7011, 2309, 1, 2286, 2306, 4])).
% 1.85/2.12 tff(7013,plain,
% 1.85/2.12 (b(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[372, 7012])).
% 1.85/2.12 tff(7014,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2273, 7013, 2289, 2029, 56])).
% 1.85/2.12 tff(7015,plain,(b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7016,plain,
% 1.85/2.12 (b(elem!1, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7015, 56, 1, 4, 705, 54, 3, 64])).
% 1.85/2.12 tff(7017,plain,
% 1.85/2.12 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[313, 454, 123, 305])).
% 1.85/2.12 tff(7018,plain,
% 1.85/2.12 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[319, 7017])).
% 1.85/2.12 tff(7019,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(7020,plain,
% 1.85/2.12 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(7021,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[7020])).
% 1.85/2.12 tff(7022,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[7021, 7019])).
% 1.85/2.12 tff(7023,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(7024,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[7023, 7022])).
% 1.85/2.12 tff(7025,plain,
% 1.85/2.12 (~b(elem!1, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7024, 144, 305, 56, 123, 454])).
% 1.85/2.12 tff(7026,plain,
% 1.85/2.12 (r(elem!1, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1538, 7025, 1524])).
% 1.85/2.12 tff(7027,plain,
% 1.85/2.12 (((~![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))), elem!1)) | (~r(elem!1, 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), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(7028,plain,
% 1.85/2.12 (((~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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(7029,plain,
% 1.85/2.12 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[7028])).
% 1.85/2.12 tff(7030,plain,
% 1.85/2.12 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[7029, 7027])).
% 1.85/2.12 tff(7031,plain,
% 1.85/2.12 ((~![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(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(7032,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[7031, 7030])).
% 1.85/2.12 tff(7033,plain,
% 1.85/2.12 (~r(s(z), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7032, 333, 1759, 7026, 707])).
% 1.85/2.12 tff(7034,plain,
% 1.85/2.12 (b(s(z), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[172, 7033])).
% 1.85/2.12 tff(7035,plain,
% 1.85/2.12 (~r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1376, 354, 408, 409])).
% 1.85/2.12 tff(7036,plain,
% 1.85/2.12 (b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[348, 7035])).
% 1.85/2.12 tff(7037,plain,
% 1.85/2.12 (~b(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2156, 2128, 838, 7036])).
% 1.85/2.12 tff(7038,plain,
% 1.85/2.12 (r(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[619, 7037])).
% 1.85/2.12 tff(7039,plain,
% 1.85/2.12 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[429, 354, 322, 409])).
% 1.85/2.12 tff(7040,plain,
% 1.85/2.12 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[279, 7039])).
% 1.85/2.12 tff(7041,plain,
% 1.85/2.12 (~b(z, elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[267, 7040, 133, 132])).
% 1.85/2.12 tff(7042,plain,
% 1.85/2.12 (r(z, elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[658, 7041, 74])).
% 1.85/2.12 tff(7043,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2136, 7042, 7038, 707, 408])).
% 1.85/2.12 tff(7044,plain,((~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7045,plain,
% 1.85/2.12 (~r(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7044, 408, 707, 74, 133, 132, 838, 322, 409])).
% 1.85/2.12 tff(7046,plain,
% 1.85/2.12 (b(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[372, 7045])).
% 1.85/2.12 tff(7047,plain,
% 1.85/2.12 (~b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2055, 7046, 707, 408, 56, 838])).
% 1.85/2.12 tff(7048,plain,
% 1.85/2.12 (r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[348, 7047])).
% 1.85/2.12 tff(7049,plain,
% 1.85/2.12 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[417, 7048, 408, 409])).
% 1.85/2.12 tff(7050,plain,
% 1.85/2.12 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[279, 7049])).
% 1.85/2.12 tff(7051,plain,
% 1.85/2.12 (~b(z, elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[267, 7050, 133, 132])).
% 1.85/2.12 tff(7052,plain,
% 1.85/2.12 (r(z, elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[658, 7051, 74])).
% 1.85/2.12 tff(7053,plain,
% 1.85/2.12 (~r(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2136, 7052, 707, 408])).
% 1.85/2.12 tff(7054,plain,
% 1.85/2.12 (b(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[619, 7053])).
% 1.85/2.12 tff(7055,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2025, 144, 7046, 7054, 56, 838])).
% 1.85/2.12 tff(7056,plain,((~r(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7057,plain,
% 1.85/2.12 (~r(elem!1, z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7056, 7034, 56, 707, 74, 452, 454, 1759, 7018])).
% 1.85/2.12 tff(7058,plain,
% 1.85/2.12 (b(elem!1, z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1380, 7057, 730])).
% 1.85/2.12 tff(7059,plain,
% 1.85/2.12 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[632, 7058, 305, 123, 454])).
% 1.85/2.12 tff(7060,plain,
% 1.85/2.12 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[302, 7059])).
% 1.85/2.12 tff(7061,plain,
% 1.85/2.12 (~r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[779, 490, 56, 123, 322, 321])).
% 1.85/2.12 tff(7062,plain,
% 1.85/2.12 (b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[348, 7061])).
% 1.85/2.12 tff(7063,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[387, 144, 624, 490, 7062, 305])).
% 1.85/2.12 tff(7064,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7065,plain,
% 1.85/2.12 (~b(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7064, 7058, 305, 56, 123, 7018, 7060])).
% 1.85/2.12 tff(7066,plain,
% 1.85/2.12 (r(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[372, 7065])).
% 1.85/2.12 tff(7067,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2209, 333, 1759, 7066, 7018, 7060])).
% 1.85/2.12 tff(7068,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (z = elem!1) | (elem!1 = s(s(s(z)))) | (s(z) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(7069,plain,
% 1.85/2.12 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7068, 7016, 56, 50, 705, 71, 697, 64, 3, 54])).
% 1.85/2.12 tff(7070,plain,
% 1.85/2.12 (~(s(s(z)) = s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[855, 64])).
% 1.85/2.12 tff(7071,plain,
% 1.85/2.12 (b(s(z), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2235, 81, 123])).
% 1.85/2.12 tff(7072,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7073,plain,
% 1.95/2.12 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7074,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7073])).
% 1.95/2.12 tff(7075,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7074, 7072])).
% 1.95/2.13 tff(7076,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7077,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 1.95/2.13 tff(7078,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7077, 144, 251, 134, 490, 305])).
% 1.95/2.13 tff(7079,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7080,plain,
% 1.95/2.13 (~b(z, elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7079, 490, 305, 7071])).
% 1.95/2.13 tff(7081,plain,
% 1.95/2.13 (r(z, elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[658, 7080, 71])).
% 1.95/2.13 tff(7082,plain,
% 1.95/2.13 (~(s(elem!1) = elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1565, 81, 1524])).
% 1.95/2.13 tff(7083,plain,
% 1.95/2.13 (~(elem!1 = s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1569, 7082])).
% 1.95/2.13 tff(7084,plain,
% 1.95/2.13 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.13 inference(symmetry,[status(thm)],[732])).
% 1.95/2.13 tff(7085,plain,
% 1.95/2.13 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[305, 7084])).
% 1.95/2.13 tff(7086,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7087,plain,
% 1.95/2.13 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7088,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7087])).
% 1.95/2.13 tff(7089,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7088, 7086])).
% 1.95/2.13 tff(7090,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7091,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7090, 7089])).
% 1.95/2.13 tff(7092,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7091, 144, 490, 489, 304, 286])).
% 1.95/2.13 tff(7093,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7094,plain,
% 1.95/2.13 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7093, 489, 304, 490])).
% 1.95/2.13 tff(7095,plain,
% 1.95/2.13 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[302, 7094])).
% 1.95/2.13 tff(7096,plain,
% 1.95/2.13 (~b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2273, 489, 490, 56])).
% 1.95/2.13 tff(7097,plain,
% 1.95/2.13 (r(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[396, 7096])).
% 1.95/2.13 tff(7098,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2079, 7097, 707, 670])).
% 1.95/2.13 tff(7099,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2558, 7098, 7095, 81])).
% 1.95/2.13 tff(7100,plain,((~b(s(z), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7101,plain,
% 1.95/2.13 (~b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7100, 7081, 707, 81, 7085, 490, 56])).
% 1.95/2.13 tff(7102,plain,
% 1.95/2.13 (r(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[348, 7101])).
% 1.95/2.13 tff(7103,plain,
% 1.95/2.13 (~r(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1843, 333, 670, 323, 509])).
% 1.95/2.13 tff(7104,plain,
% 1.95/2.13 (b(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[486, 7103, 1])).
% 1.95/2.13 tff(7105,plain,
% 1.95/2.13 (~r(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1835, 333, 670, 323, 509])).
% 1.95/2.13 tff(7106,plain,
% 1.95/2.13 (b(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1244, 7105, 1229])).
% 1.95/2.13 tff(7107,plain,
% 1.95/2.13 (~b(z, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1853, 7106, 490, 7104])).
% 1.95/2.13 tff(7108,plain,
% 1.95/2.13 (r(z, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[583, 7107])).
% 1.95/2.13 tff(7109,plain,
% 1.95/2.13 (~b(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4409, 7106, 305, 7104])).
% 1.95/2.13 tff(7110,plain,
% 1.95/2.13 (r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[560, 7109, 902])).
% 1.95/2.13 tff(7111,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1871, 333, 7110, 670, 509, 7108])).
% 1.95/2.13 tff(7112,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7113,plain,
% 1.95/2.13 (~r(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7112, 7081, 7083, 490, 305, 1, 7102])).
% 1.95/2.13 tff(7114,plain,
% 1.95/2.13 (b(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[507, 7113])).
% 1.95/2.13 tff(7115,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2079, 1699, 707, 670])).
% 1.95/2.13 tff(7116,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1380, 7115, 1368])).
% 1.95/2.13 tff(7117,plain,
% 1.95/2.13 (~r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6585, 1699, 707, 670])).
% 1.95/2.13 tff(7118,plain,
% 1.95/2.13 (b(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[560, 7117, 902])).
% 1.95/2.13 tff(7119,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7120,plain,
% 1.95/2.13 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7121,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7120])).
% 1.95/2.13 tff(7122,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7121, 7119])).
% 1.95/2.13 tff(7123,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7124,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7123, 7122])).
% 1.95/2.13 tff(7125,plain,
% 1.95/2.13 ((~b(elem!1, z)) | (~b(elem!1, s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7124, 144, 491, 490, 305])).
% 1.95/2.13 tff(7126,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7125, 7118, 7116])).
% 1.95/2.13 tff(7127,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (elem!1 = s(elem!1)) | (elem!1 = z) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7128,plain,
% 1.95/2.13 (~r(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7127, 7114, 490, 305, 7083, 77, 707, 7081])).
% 1.95/2.13 tff(7129,plain,
% 1.95/2.13 (b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[396, 7128])).
% 1.95/2.13 tff(7130,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2136, 408, 707, 7081])).
% 1.95/2.13 tff(7131,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[619, 7130])).
% 1.95/2.13 tff(7132,plain,
% 1.95/2.13 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[757, 490, 123, 7085])).
% 1.95/2.13 tff(7133,plain,
% 1.95/2.13 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[279, 7132])).
% 1.95/2.13 tff(7134,plain,
% 1.95/2.13 (~r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[678, 509, 408, 670])).
% 1.95/2.13 tff(7135,plain,
% 1.95/2.13 (~r(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[517, 509, 51, 408])).
% 1.95/2.13 tff(7136,plain,
% 1.95/2.13 (~b(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1732, 7135, 134, 902, 7134])).
% 1.95/2.13 tff(7137,plain,
% 1.95/2.13 (r(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1244, 7136, 1237])).
% 1.95/2.13 tff(7138,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1835, 333, 670, 323, 509, 7137])).
% 1.95/2.13 tff(7139,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7140,plain,
% 1.95/2.13 (~r(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7139, 408, 7102, 1229, 7071, 7083, 7081, 7133])).
% 1.95/2.13 tff(7141,plain,
% 1.95/2.13 (b(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[507, 7140])).
% 1.95/2.13 tff(7142,plain,
% 1.95/2.13 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1802, 7141, 7131, 285])).
% 1.95/2.13 tff(7143,plain,
% 1.95/2.13 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[965, 7142, 1682])).
% 1.95/2.13 tff(7144,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2136, 408, 707, 670])).
% 1.95/2.13 tff(7145,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[619, 7144])).
% 1.95/2.13 tff(7146,plain,
% 1.95/2.13 (~r(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[678, 563, 408, 670])).
% 1.95/2.13 tff(7147,plain,
% 1.95/2.13 (b(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[507, 7146])).
% 1.95/2.13 tff(7148,plain,
% 1.95/2.13 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1802, 7147, 7145, 285])).
% 1.95/2.13 tff(7149,plain,
% 1.95/2.13 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[965, 7148, 960])).
% 1.95/2.13 tff(7150,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1739, 333, 563, 1525, 707, 7149])).
% 1.95/2.13 tff(7151,plain,((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7152,plain,
% 1.95/2.13 (~r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7151, 1525, 707, 1682, 285, 408, 7081])).
% 1.95/2.13 tff(7153,plain,
% 1.95/2.13 (b(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[560, 7152, 1722])).
% 1.95/2.13 tff(7154,plain,
% 1.95/2.13 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[5657, 7153, 81])).
% 1.95/2.13 tff(7155,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.95/2.13 tff(7156,plain,
% 1.95/2.13 (((~![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(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, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7157,plain,
% 1.95/2.13 ((~![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(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7158,plain,
% 1.95/2.13 ((~![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(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7157, 7156])).
% 1.95/2.13 tff(7159,plain,
% 1.95/2.13 (~r(s(s(z)), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7158, 333, 670, 408, 7155])).
% 1.95/2.13 tff(7160,plain,
% 1.95/2.13 (b(s(s(z)), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1462, 44, 164, 7159])).
% 1.95/2.13 tff(7161,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7162,plain,
% 1.95/2.13 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7163,plain,
% 1.95/2.13 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7162])).
% 1.95/2.13 tff(7164,plain,
% 1.95/2.13 (((~![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(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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7163, 7161])).
% 1.95/2.13 tff(7165,plain,
% 1.95/2.13 ((~![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(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7166,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7165, 7164])).
% 1.95/2.13 tff(7167,plain,
% 1.95/2.13 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7166, 333, 408, 707, 7155])).
% 1.95/2.13 tff(7168,plain,
% 1.95/2.13 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1473, 44, 7167, 217])).
% 1.95/2.13 tff(7169,plain,
% 1.95/2.13 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7170,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7169])).
% 1.95/2.13 tff(7171,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7170, 1485])).
% 1.95/2.13 tff(7172,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7173,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7172, 7171])).
% 1.95/2.13 tff(7174,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7173, 144, 285, 7145, 7168, 7160])).
% 1.95/2.13 tff(7175,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7176,plain,
% 1.95/2.13 (~r(s(s(z)), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7175, 408, 285, 707, 7081])).
% 1.95/2.13 tff(7177,plain,
% 1.95/2.13 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), elem!1)),
% 1.95/2.13 inference(monotonicity,[status(thm)],[81])).
% 1.95/2.13 tff(7178,plain,
% 1.95/2.13 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(symmetry,[status(thm)],[7177])).
% 1.95/2.13 tff(7179,plain,
% 1.95/2.13 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7178])).
% 1.95/2.13 tff(7180,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.95/2.13 tff(7181,plain,
% 1.95/2.13 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7180, 7179])).
% 1.95/2.13 tff(7182,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2671, 7181])).
% 1.95/2.13 tff(7183,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7184,plain,
% 1.95/2.13 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7183, 7176, 81])).
% 1.95/2.13 tff(7185,plain,
% 1.95/2.13 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1451, 7184])).
% 1.95/2.13 tff(7186,plain,
% 1.95/2.13 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.95/2.13 inference(symmetry,[status(thm)],[3287])).
% 1.95/2.13 tff(7187,plain,
% 1.95/2.13 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7186, 175])).
% 1.95/2.13 tff(7188,plain,
% 1.95/2.13 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7187])).
% 1.95/2.13 tff(7189,plain,
% 1.95/2.13 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1722, 7188])).
% 1.95/2.13 tff(7190,plain,
% 1.95/2.13 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[965, 1803, 1682])).
% 1.95/2.13 tff(7191,plain,
% 1.95/2.13 (((~![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(s(s(s(z))), elem!1)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7192,plain,
% 1.95/2.13 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7193,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7192])).
% 1.95/2.13 tff(7194,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7193, 7191])).
% 1.95/2.13 tff(7195,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7196,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7195, 7194])).
% 1.95/2.13 tff(7197,plain,
% 1.95/2.13 (~r(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7196, 333, 1525, 707, 7190])).
% 1.95/2.13 tff(7198,plain,
% 1.95/2.13 (b(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[448, 7197, 433])).
% 1.95/2.13 tff(7199,plain,
% 1.95/2.13 (~b(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1820, 7198, 7071, 490, 491])).
% 1.95/2.13 tff(7200,plain,
% 1.95/2.13 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3868, 7197, 81])).
% 1.95/2.13 tff(7201,plain,
% 1.95/2.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[472, 7200, 7189])).
% 1.95/2.13 tff(7202,plain,
% 1.95/2.13 (~r(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1435, 7201, 323, 860, 304, 1398, 123, 546])).
% 1.95/2.13 tff(7203,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[486, 7202, 7199, 1])).
% 1.95/2.13 tff(7204,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7205,plain,
% 1.95/2.13 (~b(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7204, 7154, 323, 860, 7085, 7185, 123, 1, 490, 433, 81, 1525, 707, 7131, 285])).
% 1.95/2.13 tff(7206,plain,
% 1.95/2.13 (r(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[507, 7205])).
% 1.95/2.13 tff(7207,plain,
% 1.95/2.13 (~r(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[517, 7206, 7133, 408])).
% 1.95/2.13 tff(7208,plain,
% 1.95/2.13 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3868, 7207, 81])).
% 1.95/2.13 tff(7209,plain,
% 1.95/2.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[472, 7208, 7189])).
% 1.95/2.13 tff(7210,plain,
% 1.95/2.13 (~r(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1435, 7209, 323, 860, 7085, 7185, 123, 7154])).
% 1.95/2.13 tff(7211,plain,
% 1.95/2.13 (b(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[486, 7210, 1])).
% 1.95/2.13 tff(7212,plain,
% 1.95/2.13 (b(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[448, 7207, 433])).
% 1.95/2.13 tff(7213,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4344, 144, 7212, 7071, 7211, 305])).
% 1.95/2.13 tff(7214,plain,((~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (s(s(z)) = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(elem!1, z)) | (~b(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7215,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7214, 408, 1, 7102, 860, 123, 7082, 81, 305, 490, 707, 285])).
% 1.95/2.14 tff(7216,plain,
% 1.95/2.14 (b(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1538, 7215, 1524])).
% 1.95/2.14 tff(7217,plain,
% 1.95/2.14 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7216, 1523])).
% 1.95/2.14 tff(7218,plain,
% 1.95/2.14 (~b(s(z), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[846, 7217, 56, 7085])).
% 1.95/2.14 tff(7219,plain,
% 1.95/2.14 (r(s(z), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[172, 7218])).
% 1.95/2.14 tff(7220,plain,
% 1.95/2.14 (((~![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(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), 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(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7221,plain,
% 1.95/2.14 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7222,plain,
% 1.95/2.14 (((~![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(z), s(s(s(z))))) | (~r(s(elem!1), s(s(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), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7221])).
% 1.95/2.14 tff(7223,plain,
% 1.95/2.14 (((~![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(z), s(s(s(z))))) | (~r(s(elem!1), s(s(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), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7222, 7220])).
% 1.95/2.14 tff(7224,plain,
% 1.95/2.14 ((~![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(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7225,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7224, 7223])).
% 1.95/2.14 tff(7226,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7225, 333, 434, 707, 1686, 353])).
% 1.95/2.14 tff(7227,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7228,plain,
% 1.95/2.14 (~r(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7227, 7143, 707, 7219])).
% 1.95/2.14 tff(7229,plain,
% 1.95/2.14 (b(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[486, 7228, 1])).
% 1.95/2.14 tff(7230,plain,
% 1.95/2.14 (~b(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1820, 7229, 7071, 490, 7141])).
% 1.95/2.14 tff(7231,plain,
% 1.95/2.14 (r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[448, 7230, 7082])).
% 1.95/2.14 tff(7232,plain,
% 1.95/2.14 (((~![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(s(s(s(z))), elem!1)) | (~r(s(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(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7233,plain,
% 1.95/2.14 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7234,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7233])).
% 1.95/2.14 tff(7235,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7234, 7232])).
% 1.95/2.14 tff(7236,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7237,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, z))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7236, 7235])).
% 1.95/2.14 tff(7238,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7237, 333, 7231, 408, 707, 7143])).
% 1.95/2.14 tff(7239,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7240,plain,
% 1.95/2.14 (~r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7239, 7129, 490, 1, 707, 56, 81, 1524, 860, 123, 305])).
% 1.95/2.14 tff(7241,plain,
% 1.95/2.14 (b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1380, 7240, 77])).
% 1.95/2.14 tff(7242,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7243,plain,
% 1.95/2.14 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7244,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7243])).
% 1.95/2.14 tff(7245,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7244, 7242])).
% 1.95/2.14 tff(7246,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7247,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7246, 7245])).
% 1.95/2.14 tff(7248,plain,
% 1.95/2.14 (~b(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7247, 144, 7241, 490, 305, 7129])).
% 1.95/2.14 tff(7249,plain,
% 1.95/2.14 (r(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1538, 7248, 1524])).
% 1.95/2.14 tff(7250,plain,
% 1.95/2.14 ((~b(elem!1, z)) | (~b(elem!1, s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7124, 144, 7114, 490, 305])).
% 1.95/2.14 tff(7251,plain,
% 1.95/2.14 (~b(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7250, 7241])).
% 1.95/2.14 tff(7252,plain,
% 1.95/2.14 (r(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[560, 7251, 7083])).
% 1.95/2.14 tff(7253,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(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, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7254,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7255,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7254, 7253])).
% 1.95/2.14 tff(7256,plain,
% 1.95/2.14 (~r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7255, 333, 7252, 7081, 707])).
% 1.95/2.14 tff(7257,plain,
% 1.95/2.14 (b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[619, 7256])).
% 1.95/2.14 tff(7258,plain,
% 1.95/2.14 (~b(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7124, 144, 624, 491, 490, 305])).
% 1.95/2.14 tff(7259,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[560, 1806, 7258, 902])).
% 1.95/2.14 tff(7260,plain,((~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7261,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7260, 7257, 7249, 7083, 707, 7114, 490, 305, 1682, 7241, 7129])).
% 1.95/2.14 tff(7262,plain,((~b(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(s(z)) = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7263,plain,
% 1.95/2.14 (~b(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7262, 705, 7016, 697, 1, 56, 7069, 7070, 50])).
% 1.95/2.14 tff(7264,plain,
% 1.95/2.14 (r(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[372, 7263])).
% 1.95/2.14 tff(7265,plain,
% 1.95/2.14 (r(z, elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[658, 606, 71])).
% 1.95/2.14 tff(7266,plain,
% 1.95/2.14 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), elem!1)),
% 1.95/2.14 inference(monotonicity,[status(thm)],[81])).
% 1.95/2.14 tff(7267,plain,
% 1.95/2.14 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(z), elem!1))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7266])).
% 1.95/2.14 tff(7268,plain,
% 1.95/2.14 (~r(s(z), elem!1)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[4, 7267])).
% 1.95/2.14 tff(7269,plain,
% 1.95/2.14 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7011, 606, 1, 7268, 354, 4])).
% 1.95/2.14 tff(7270,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2305, 7269, 7265, 81])).
% 1.95/2.14 tff(7271,plain,(b(z, elem!1) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7272,plain,
% 1.95/2.14 (b(z, elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7271, 7264, 1, 7069, 4])).
% 1.95/2.14 tff(7273,plain,
% 1.95/2.14 (b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2235, 7069, 50])).
% 1.95/2.14 tff(7274,plain,
% 1.95/2.14 (~r(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2122, 408, 707, 354])).
% 1.95/2.14 tff(7275,plain,
% 1.95/2.14 (b(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[396, 7274])).
% 1.95/2.14 tff(7276,plain,
% 1.95/2.14 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[902, 7188])).
% 1.95/2.14 tff(7277,plain,
% 1.95/2.14 (~r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1610, 333, 354, 408, 509])).
% 1.95/2.14 tff(7278,plain,
% 1.95/2.14 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3868, 7277, 81])).
% 1.95/2.14 tff(7279,plain,
% 1.95/2.14 (~r(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1620, 509, 408, 354])).
% 1.95/2.14 tff(7280,plain,
% 1.95/2.14 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2920, 7277, 1, 902, 304, 134, 354, 7279, 509])).
% 1.95/2.14 tff(7281,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[472, 7280, 7278, 7276])).
% 1.95/2.14 tff(7282,plain,((~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7283,plain,
% 1.95/2.14 (~r(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7282, 408, 1722, 7085, 134, 354, 81, 1])).
% 1.95/2.14 tff(7284,plain,
% 1.95/2.14 (b(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[507, 7283])).
% 1.95/2.14 tff(7285,plain,
% 1.95/2.14 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1802, 7284, 1521, 7275])).
% 1.95/2.14 tff(7286,plain,
% 1.95/2.14 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[965, 7285, 1682])).
% 1.95/2.14 tff(7287,plain,
% 1.95/2.14 (~r(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7227, 7286, 707, 353])).
% 1.95/2.14 tff(7288,plain,
% 1.95/2.14 (b(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[486, 7287, 1])).
% 1.95/2.14 tff(7289,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7290,plain,
% 1.95/2.14 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7291,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7290])).
% 1.95/2.14 tff(7292,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7291, 7289])).
% 1.95/2.14 tff(7293,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7294,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 1.95/2.14 tff(7295,plain,
% 1.95/2.14 (~b(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7294, 144, 251, 7284, 7288, 305])).
% 1.95/2.14 tff(7296,plain,
% 1.95/2.14 (r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[448, 7295, 433])).
% 1.95/2.14 tff(7297,plain,
% 1.95/2.14 (((~![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(elem!1), s(s(s(z))))) | (~r(s(z), s(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(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7298,plain,
% 1.95/2.14 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7299,plain,
% 1.95/2.14 (((~![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(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7298])).
% 1.95/2.14 tff(7300,plain,
% 1.95/2.14 (((~![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(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7299, 7297])).
% 1.95/2.14 tff(7301,plain,
% 1.95/2.14 ((~![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(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7302,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7301, 7300])).
% 1.95/2.14 tff(7303,plain,
% 1.95/2.14 (~r(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7302, 333, 707, 7286, 353])).
% 1.95/2.14 tff(7304,plain,
% 1.95/2.14 (b(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1244, 7303, 1229])).
% 1.95/2.14 tff(7305,plain,
% 1.95/2.14 (~b(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4409, 7304, 305, 7288])).
% 1.95/2.14 tff(7306,plain,
% 1.95/2.14 (r(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[560, 7305, 1722])).
% 1.95/2.14 tff(7307,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[957, 333, 7306, 7296, 707, 7286])).
% 1.95/2.14 tff(7308,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7309,plain,
% 1.95/2.14 (~r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7308, 353, 305, 7082, 251, 707, 1, 134, 354, 81])).
% 1.95/2.14 tff(7310,plain,
% 1.95/2.14 (b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1380, 7309, 77])).
% 1.95/2.14 tff(7311,plain,
% 1.95/2.14 (~b(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1602, 7310, 134, 251])).
% 1.95/2.14 tff(7312,plain,
% 1.95/2.14 (r(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[348, 7311])).
% 1.95/2.14 tff(7313,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1548, 333, 354, 323, 1699, 353])).
% 1.95/2.14 tff(7314,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7315,plain,
% 1.95/2.14 (~r(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7314, 7312, 354, 353])).
% 1.95/2.14 tff(7316,plain,
% 1.95/2.14 (b(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[396, 7315])).
% 1.95/2.15 tff(7317,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7318,plain,
% 1.95/2.15 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7319,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7318])).
% 1.95/2.15 tff(7320,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7319, 7317])).
% 1.95/2.15 tff(7321,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7322,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 1.95/2.15 tff(7323,plain,
% 1.95/2.15 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7322, 144, 305, 1521, 56])).
% 1.95/2.15 tff(7324,plain,
% 1.95/2.15 (~b(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7323, 7310])).
% 1.95/2.15 tff(7325,plain,
% 1.95/2.15 (r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1538, 7324, 1524])).
% 1.95/2.15 tff(7326,plain,
% 1.95/2.15 (~b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[916, 491, 624, 251])).
% 1.95/2.15 tff(7327,plain,
% 1.95/2.15 (r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[448, 7326, 433])).
% 1.95/2.15 tff(7328,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7196, 333, 7327, 1525, 707, 1804])).
% 1.95/2.15 tff(7329,plain,((~b(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(s(z)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7330,plain,
% 1.95/2.15 (~b(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7329, 7325, 707, 7082, 1682, 7310, 251, 1521, 7316])).
% 1.95/2.15 tff(7331,plain,
% 1.95/2.15 (r(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[507, 7330])).
% 1.95/2.15 tff(7332,plain,
% 1.95/2.15 (~r(s(elem!1), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1365, 7331, 354, 7312])).
% 1.95/2.15 tff(7333,plain,
% 1.95/2.15 (b(s(elem!1), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[486, 7332, 1])).
% 1.95/2.15 tff(7334,plain,
% 1.95/2.15 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7335,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7334])).
% 1.95/2.15 tff(7336,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7335, 4339])).
% 1.95/2.15 tff(7337,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7338,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7337, 7336])).
% 1.95/2.15 tff(7339,plain,
% 1.95/2.15 (~b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7338, 144, 134, 7333, 305])).
% 1.95/2.15 tff(7340,plain,
% 1.95/2.15 (r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[448, 7339, 7082])).
% 1.95/2.15 tff(7341,plain,
% 1.95/2.15 (~r(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1235, 7331, 354, 7312])).
% 1.95/2.15 tff(7342,plain,
% 1.95/2.15 (b(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1244, 7341, 1229])).
% 1.95/2.15 tff(7343,plain,
% 1.95/2.15 (~b(elem!1, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4409, 7342, 305, 7333])).
% 1.95/2.15 tff(7344,plain,
% 1.95/2.15 (r(elem!1, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[560, 7343, 7083])).
% 1.95/2.15 tff(7345,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7346,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7345, 3905])).
% 1.95/2.15 tff(7347,plain,
% 1.95/2.15 (~r(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7346, 333, 7344, 7340, 707])).
% 1.95/2.15 tff(7348,plain,
% 1.95/2.15 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1946, 144, 7333, 7342, 56])).
% 1.95/2.15 tff(7349,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 7348, 7347])).
% 1.95/2.15 tff(7350,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7351,plain,
% 1.95/2.15 (~r(s(z), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7350, 7264, 705, 7273, 7016, 1, 56, 7272, 697, 7069])).
% 1.95/2.15 tff(7352,plain,
% 1.95/2.15 (b(s(z), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[172, 7351])).
% 1.95/2.15 tff(7353,plain,
% 1.95/2.15 (~(s(elem!1) = elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1565, 7069, 697])).
% 1.95/2.15 tff(7354,plain,
% 1.95/2.15 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[846, 838, 56, 7085])).
% 1.95/2.15 tff(7355,plain,
% 1.95/2.15 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[249, 7354])).
% 1.95/2.15 tff(7356,plain,
% 1.95/2.15 (~r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2122, 1699, 707, 354])).
% 1.95/2.15 tff(7357,plain,
% 1.95/2.15 (b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1380, 7356, 77])).
% 1.95/2.15 tff(7358,plain,
% 1.95/2.15 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 1.95/2.15 inference(monotonicity,[status(thm)],[81])).
% 1.95/2.15 tff(7359,plain,
% 1.95/2.15 (b(s(s(z)), elem!1)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1398, 7358])).
% 1.95/2.15 tff(7360,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7361,plain,
% 1.95/2.15 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7362,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7361])).
% 1.95/2.15 tff(7363,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7362, 7360])).
% 1.95/2.15 tff(7364,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7365,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7364, 7363])).
% 1.95/2.15 tff(7366,plain,
% 1.95/2.15 (~b(s(s(z)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7365, 144, 251, 624, 7359])).
% 1.95/2.15 tff(7367,plain,
% 1.95/2.15 (r(s(s(z)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1462, 44, 164, 7366])).
% 1.95/2.15 tff(7368,plain,
% 1.95/2.15 (~b(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1602, 624, 7071, 251])).
% 1.95/2.15 tff(7369,plain,
% 1.95/2.15 (r(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[348, 7368])).
% 1.95/2.15 tff(7370,plain,
% 1.95/2.15 (((~![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(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(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7371,plain,
% 1.95/2.15 ((~![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(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7372,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7371, 7370])).
% 1.95/2.15 tff(7373,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7372, 333, 354, 7369, 7367, 1430])).
% 1.95/2.15 tff(7374,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7375,plain,
% 1.95/2.15 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7374, 7357, 251, 354, 81, 123, 304])).
% 1.95/2.15 tff(7376,plain,
% 1.95/2.15 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1451, 7375])).
% 1.95/2.15 tff(7377,plain,
% 1.95/2.15 (r(s(s(z)), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7183, 7376, 81])).
% 1.95/2.15 tff(7378,plain,
% 1.95/2.15 (r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[224, 1685])).
% 1.95/2.15 tff(7379,plain,
% 1.95/2.15 (~b(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1602, 7357, 7071, 251])).
% 1.95/2.15 tff(7380,plain,
% 1.95/2.15 (r(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[348, 7379])).
% 1.95/2.15 tff(7381,plain,
% 1.95/2.15 (~b(s(elem!1), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1716, 509, 960, 354, 1699, 56, 323])).
% 1.95/2.15 tff(7382,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1653, 7381, 509, 354, 706, 1575, 1, 902])).
% 1.95/2.15 tff(7383,plain,((~r(s(elem!1), z)) | (~r(z, s(z))) | (s(z) = elem!1) | r(z, elem!1) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7384,plain,
% 1.95/2.15 (~r(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7383, 7380, 706, 354, 1, 1722, 1682, 1575, 56, 1699])).
% 1.95/2.15 tff(7385,plain,
% 1.95/2.15 (b(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[507, 7384])).
% 1.95/2.15 tff(7386,plain,
% 1.95/2.15 (~b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[916, 7385, 251, 7357])).
% 1.95/2.15 tff(7387,plain,
% 1.95/2.15 (r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[448, 7386, 433])).
% 1.95/2.15 tff(7388,plain,
% 1.95/2.15 (((~![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(s(s(z)), elem!1)) | (~r(elem!1, s(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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7389,plain,
% 1.95/2.15 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7390,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7389])).
% 1.95/2.15 tff(7391,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7390, 7388])).
% 1.95/2.15 tff(7392,plain,
% 1.95/2.15 ((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7393,plain,
% 1.95/2.15 ((~![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(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7392, 7391])).
% 1.95/2.15 tff(7394,plain,
% 1.95/2.15 (~r(s(s(z)), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7393, 333, 7387, 7378, 7377])).
% 1.95/2.15 tff(7395,plain,
% 1.95/2.15 (b(s(s(z)), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1408, 44, 856, 7394])).
% 1.95/2.15 tff(7396,plain,
% 1.95/2.15 (((~![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(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7397,plain,
% 1.95/2.15 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7398,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7397])).
% 1.95/2.15 tff(7399,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7398, 7396])).
% 1.95/2.15 tff(7400,plain,
% 1.95/2.15 ((~![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(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7401,plain,
% 1.95/2.15 ((~![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(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 1.95/2.15 tff(7402,plain,
% 1.95/2.15 (~r(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7401, 333, 7387, 7378, 707])).
% 1.95/2.15 tff(7403,plain,
% 1.95/2.15 (b(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 7402])).
% 1.95/2.15 tff(7404,plain,
% 1.95/2.15 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7405,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7404])).
% 1.95/2.15 tff(7406,plain,
% 1.95/2.15 (((~![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(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7405, 7191])).
% 1.95/2.15 tff(7407,plain,
% 1.95/2.15 ((~![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(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7408,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7407, 7406])).
% 1.95/2.15 tff(7409,plain,
% 1.95/2.15 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7408, 333, 7387, 7378, 707])).
% 1.95/2.15 tff(7410,plain,
% 1.95/2.15 (b(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[965, 7409, 1682])).
% 1.95/2.15 tff(7411,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6350, 333, 1699, 2671, 224, 6330])).
% 1.95/2.15 tff(7412,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7413,plain,
% 1.95/2.15 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7412, 7376, 1699, 224])).
% 1.95/2.15 tff(7414,plain,
% 1.95/2.15 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1473, 44, 7413, 217])).
% 1.95/2.15 tff(7415,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7416,plain,
% 1.95/2.15 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7417,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7416])).
% 1.95/2.15 tff(7418,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7417, 7415])).
% 1.95/2.15 tff(7419,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7420,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7419, 7418])).
% 1.95/2.16 tff(7421,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7420, 144, 7414, 7410, 7403, 7395])).
% 1.95/2.16 tff(7422,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(z) = elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | r(z, elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7423,plain,
% 1.95/2.16 (~r(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7422, 1575, 433, 251, 7355, 81, 706, 354, 1, 707, 56, 123, 7085])).
% 1.95/2.16 tff(7424,plain,
% 1.95/2.16 (b(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[396, 7423])).
% 1.95/2.16 tff(7425,plain,
% 1.95/2.16 (~b(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2144, 144, 251, 7071, 7424, 838])).
% 1.95/2.16 tff(7426,plain,
% 1.95/2.16 (r(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[348, 7425])).
% 1.95/2.16 tff(7427,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7355, 1685])).
% 1.95/2.16 tff(7428,plain,
% 1.95/2.16 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7374, 624, 251, 354, 81, 123, 7085])).
% 1.95/2.16 tff(7429,plain,
% 1.95/2.16 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1451, 7428])).
% 1.95/2.16 tff(7430,plain,
% 1.95/2.16 (r(s(s(z)), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7183, 7429, 81])).
% 1.95/2.16 tff(7431,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 1.95/2.16 tff(7432,plain,
% 1.95/2.16 (s(s(z)) = s(elem!1)),
% 1.95/2.16 inference(symmetry,[status(thm)],[7431])).
% 1.95/2.16 tff(7433,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[860, 7432])).
% 1.95/2.16 tff(7434,plain,((~(s(elem!1) = s(s(z)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7435,plain,
% 1.95/2.16 (~(s(elem!1) = s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7434, 856])).
% 1.95/2.16 tff(7436,plain,
% 1.95/2.16 (~b(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[916, 491, 251, 624])).
% 1.95/2.16 tff(7437,plain,
% 1.95/2.16 (r(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[448, 7436, 433])).
% 1.95/2.16 tff(7438,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7408, 333, 7437, 1525, 707])).
% 1.95/2.16 tff(7439,plain,
% 1.95/2.16 (b(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[965, 7438, 960])).
% 1.95/2.16 tff(7440,plain,
% 1.95/2.16 (((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, 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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7441,plain,
% 1.95/2.16 (((~r(elem!1, s(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(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7442,plain,
% 1.95/2.16 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7441])).
% 1.95/2.16 tff(7443,plain,
% 1.95/2.16 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7442, 7440])).
% 1.95/2.16 tff(7444,plain,
% 1.95/2.16 ((~![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(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7445,plain,
% 1.95/2.16 ((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7444, 7443])).
% 1.95/2.16 tff(7446,plain,
% 1.95/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7445, 333, 1525, 707, 7155])).
% 1.95/2.16 tff(7447,plain,
% 1.95/2.16 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1473, 44, 7446, 217])).
% 1.95/2.16 tff(7448,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7449,plain,
% 1.95/2.16 (((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7450,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7449])).
% 1.95/2.16 tff(7451,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7450, 7448])).
% 1.95/2.16 tff(7452,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7453,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7452, 7451])).
% 1.95/2.16 tff(7454,plain,
% 1.95/2.16 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7453, 144, 491, 285, 7447])).
% 1.95/2.16 tff(7455,plain,
% 1.95/2.16 (~b(s(elem!1), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7454, 7439])).
% 1.95/2.16 tff(7456,plain,
% 1.95/2.16 (((~![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(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7457,plain,
% 1.95/2.16 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7458,plain,
% 1.95/2.16 (((~![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(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(z))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7457])).
% 1.95/2.16 tff(7459,plain,
% 1.95/2.16 (((~![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(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7458, 7456])).
% 1.95/2.16 tff(7460,plain,
% 1.95/2.16 ((~![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(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7461,plain,
% 1.95/2.16 ((~![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(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7460, 7459])).
% 1.95/2.16 tff(7462,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7461, 333, 7437, 1525, 7155])).
% 1.95/2.16 tff(7463,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 1.95/2.16 tff(7464,plain,
% 1.95/2.16 (((~![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))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7465,plain,
% 1.95/2.16 ((~![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))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7466,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7465, 7464])).
% 1.95/2.16 tff(7467,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7466, 44, 7463, 7462, 7455])).
% 1.95/2.16 tff(7468,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(s(z))) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7469,plain,
% 1.95/2.16 (~b(s(elem!1), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7468, 7430, 285, 1682, 1525, 7435, 707, 433, 251, 624])).
% 1.95/2.16 tff(7470,plain,
% 1.95/2.16 (r(s(elem!1), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[507, 7469])).
% 1.95/2.16 tff(7471,plain,
% 1.95/2.16 (b(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1653, 7470, 354, 706, 1575, 1, 1722])).
% 1.95/2.16 tff(7472,plain,
% 1.95/2.16 (~b(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7338, 144, 7071, 7471, 305])).
% 1.95/2.16 tff(7473,plain,
% 1.95/2.16 (r(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[448, 7472, 433])).
% 1.95/2.16 tff(7474,plain,
% 1.95/2.16 (~r(s(z), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1235, 7470, 354, 323])).
% 1.95/2.16 tff(7475,plain,
% 1.95/2.16 (b(s(z), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1244, 7474, 1229])).
% 1.95/2.16 tff(7476,plain,
% 1.95/2.16 (~b(elem!1, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4409, 7475, 305, 7471])).
% 1.95/2.16 tff(7477,plain,
% 1.95/2.16 (r(elem!1, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[560, 7476, 1722])).
% 1.95/2.16 tff(7478,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7479,plain,
% 1.95/2.16 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7480,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7479])).
% 1.95/2.16 tff(7481,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7480, 7478])).
% 1.95/2.16 tff(7482,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7483,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7482, 7481])).
% 1.95/2.16 tff(7484,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7483, 333, 7477, 7473, 7430])).
% 1.95/2.16 tff(7485,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[957, 333, 7477, 7473, 707])).
% 1.95/2.16 tff(7486,plain,
% 1.95/2.16 (b(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[965, 7485, 1682])).
% 1.95/2.16 tff(7487,plain,
% 1.95/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7445, 333, 1525, 707, 7430])).
% 1.95/2.16 tff(7488,plain,
% 1.95/2.16 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1473, 44, 7487, 217])).
% 1.95/2.16 tff(7489,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7490,plain,
% 1.95/2.16 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7491,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7490])).
% 1.95/2.16 tff(7492,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7491, 7489])).
% 1.95/2.16 tff(7493,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7494,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 1.95/2.16 tff(7495,plain,
% 1.95/2.16 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7494, 144, 7471, 56, 7488])).
% 1.95/2.16 tff(7496,plain,
% 1.95/2.16 (~b(s(elem!1), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7495, 7486])).
% 1.95/2.16 tff(7497,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7466, 44, 7435, 7496, 7484])).
% 1.95/2.16 tff(7498,plain,((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (s(z) = elem!1) | r(z, elem!1) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7499,plain,
% 1.95/2.16 (~b(elem!1, z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7498, 7426, 707, 433, 305, 354, 56, 706, 1575, 1, 7424, 7427, 251, 81, 123])).
% 1.95/2.16 tff(7500,plain,
% 1.95/2.16 (r(elem!1, z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[653, 7499, 77])).
% 1.95/2.16 tff(7501,plain,
% 1.95/2.16 (~r(s(elem!1), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7282, 7500, 1722, 7085, 7071, 354, 81, 1])).
% 1.95/2.16 tff(7502,plain,
% 1.95/2.16 (b(s(elem!1), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[507, 7501])).
% 1.95/2.16 tff(7503,plain,
% 1.95/2.16 (((~![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))), elem!1)) | (~r(elem!1, z)) | (~r(z, 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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7504,plain,
% 1.95/2.16 (((~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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7505,plain,
% 1.95/2.16 (((~![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))), 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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7504])).
% 1.95/2.16 tff(7506,plain,
% 1.95/2.16 (((~![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))), 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(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7505, 7503])).
% 1.95/2.16 tff(7507,plain,
% 1.95/2.16 ((~![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))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7508,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 1.95/2.16 tff(7509,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7508, 333, 408, 1525, 623, 707])).
% 1.95/2.16 tff(7510,plain,((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7511,plain,
% 1.95/2.16 (~r(z, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7510, 7500, 7427, 707])).
% 1.95/2.16 tff(7512,plain,
% 1.95/2.16 (b(z, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[619, 7511])).
% 1.95/2.16 tff(7513,plain,
% 1.95/2.16 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1802, 7512, 7424, 7502])).
% 1.95/2.16 tff(7514,plain,
% 1.95/2.16 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[965, 7513, 1682])).
% 1.95/2.16 tff(7515,plain,
% 1.95/2.16 (~r(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7196, 333, 7427, 707, 7514])).
% 1.95/2.16 tff(7516,plain,
% 1.95/2.16 (b(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[448, 7515, 433])).
% 1.95/2.16 tff(7517,plain,
% 1.95/2.16 (~r(elem!1, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1739, 333, 7427, 707, 7514])).
% 1.95/2.16 tff(7518,plain,
% 1.95/2.16 (b(elem!1, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[560, 7517, 1722])).
% 1.95/2.16 tff(7519,plain,
% 1.95/2.16 (~b(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1642, 451, 251, 547])).
% 1.95/2.16 tff(7520,plain,
% 1.95/2.16 (r(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[583, 7519])).
% 1.95/2.16 tff(7521,plain,
% 1.95/2.16 (~b(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4344, 144, 451, 134, 305])).
% 1.95/2.16 tff(7522,plain,
% 1.95/2.16 (r(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[486, 7521, 1])).
% 1.95/2.16 tff(7523,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1355, 333, 354, 323, 7522, 7520])).
% 1.95/2.16 tff(7524,plain,((~b(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7525,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7524, 7518, 7516, 7426, 1, 7071, 305, 251, 354])).
% 1.95/2.16 tff(7526,plain,(r(z, elem!1) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(z, s(z))) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(z))), s(z))) | (s(z) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7527,plain,
% 1.95/2.16 (r(z, elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7526, 7016, 1, 7272, 7264, 7353, 705, 7069, 56, 64, 50, 7352])).
% 1.95/2.16 tff(7528,plain,
% 1.95/2.16 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2305, 7527, 7069])).
% 1.95/2.16 tff(7529,plain,
% 1.95/2.16 (~(elem!1 = s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1569, 7353])).
% 1.95/2.16 tff(7530,plain,
% 1.95/2.16 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7069])).
% 1.95/2.17 tff(7531,plain,
% 1.95/2.17 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7069])).
% 1.95/2.17 tff(7532,plain,
% 1.95/2.17 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(symmetry,[status(thm)],[7531])).
% 1.95/2.17 tff(7533,plain,
% 1.95/2.17 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7016, 7532])).
% 1.95/2.17 tff(7534,plain,
% 1.95/2.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[846, 7352, 56, 7533])).
% 1.95/2.17 tff(7535,plain,
% 1.95/2.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[249, 7534])).
% 1.95/2.17 tff(7536,plain,
% 1.95/2.17 (r(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7535, 7530])).
% 1.95/2.17 tff(7537,plain,
% 1.95/2.17 (~b(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1602, 489, 134, 251])).
% 1.95/2.17 tff(7538,plain,
% 1.95/2.17 (r(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[653, 7537, 1368])).
% 1.95/2.17 tff(7539,plain,
% 1.95/2.17 (~r(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2122, 7538, 707, 354])).
% 1.95/2.17 tff(7540,plain,
% 1.95/2.17 (b(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[396, 7539])).
% 1.95/2.17 tff(7541,plain,
% 1.95/2.17 (~r(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7510, 7538, 1525, 707])).
% 1.95/2.17 tff(7542,plain,
% 1.95/2.17 (b(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[619, 7541])).
% 1.95/2.17 tff(7543,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2156, 7542, 7540, 838, 489])).
% 1.95/2.17 tff(7544,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (elem!1 = z) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7545,plain,
% 1.95/2.17 (~b(s(z), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7544, 7352, 7536, 705, 7264, 77, 7273, 7272])).
% 1.95/2.17 tff(7546,plain,
% 1.95/2.17 (r(s(z), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[348, 7545])).
% 1.95/2.17 tff(7547,plain,
% 1.95/2.17 (~r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6983, 7357, 698, 706, 1722, 354, 1, 134, 670, 323, 1699, 713])).
% 1.95/2.17 tff(7548,plain,
% 1.95/2.17 (b(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[560, 7117, 1722])).
% 1.95/2.17 tff(7549,plain,
% 1.95/2.17 (~b(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7524, 7548, 323, 1, 134, 305, 251, 354])).
% 1.95/2.17 tff(7550,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[448, 7549, 7547, 433])).
% 1.95/2.17 tff(7551,plain,((~r(s(s(s(z))), z)) | (s(elem!1) = elem!1) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(z, s(z))) | (s(s(s(z))) = elem!1) | (s(z) = elem!1) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7552,plain,
% 1.95/2.17 (~r(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7551, 7353, 7546, 1, 7273, 7016, 7272, 7264, 696, 64, 7527, 705])).
% 1.95/2.17 tff(7553,plain,
% 1.95/2.17 (b(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[396, 7552])).
% 1.95/2.17 tff(7554,plain,
% 1.95/2.17 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7069])).
% 1.95/2.17 tff(7555,plain,
% 1.95/2.17 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7554])).
% 1.95/2.17 tff(7556,plain,
% 1.95/2.17 (~(s(s(z)) = elem!1)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1446, 7555])).
% 1.95/2.17 tff(7557,plain,
% 1.95/2.17 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1508, 7556])).
% 1.95/2.17 tff(7558,plain,
% 1.95/2.17 (~(s(elem!1) = s(s(z)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7434, 7070])).
% 1.95/2.17 tff(7559,plain,
% 1.95/2.17 (~(elem!1 = s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[712, 64])).
% 1.95/2.17 tff(7560,plain,
% 1.95/2.17 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2305, 670, 81])).
% 1.95/2.17 tff(7561,plain,
% 1.95/2.17 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7374, 4833, 251, 354, 81, 123, 7085])).
% 1.95/2.17 tff(7562,plain,
% 1.95/2.17 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1451, 7561])).
% 1.95/2.17 tff(7563,plain,
% 1.95/2.17 (r(s(s(z)), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7183, 7562, 81])).
% 1.95/2.17 tff(7564,plain,
% 1.95/2.17 (~b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7468, 7563, 285, 1682, 1525, 7463, 707, 433, 251, 4833])).
% 1.95/2.17 tff(7565,plain,
% 1.95/2.17 (r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[507, 7564])).
% 1.95/2.17 tff(7566,plain,
% 1.95/2.17 (~r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4411, 7565, 1, 305, 1722, 354, 670, 323])).
% 1.95/2.17 tff(7567,plain,
% 1.95/2.17 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3868, 7566, 81])).
% 1.95/2.17 tff(7568,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4908, 7567, 7566, 123, 354, 670, 7560, 1, 1722, 714, 7071, 285, 1378, 81])).
% 1.95/2.17 tff(7569,plain,(r(elem!1, z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~b(s(s(s(z))), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7570,plain,
% 1.95/2.17 (r(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7569, 7264, 50, 7527, 1, 7559, 7553, 7069, 7016, 7546, 7536, 7558, 705, 7353, 7272])).
% 1.95/2.17 tff(7571,plain,
% 1.95/2.17 (~r(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7151, 7570, 705, 7557, 7527, 7536, 7553])).
% 1.95/2.17 tff(7572,plain,
% 1.95/2.17 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[862, 7070])).
% 1.95/2.17 tff(7573,plain,
% 1.95/2.17 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4917, 7572])).
% 1.95/2.17 tff(7574,plain,
% 1.95/2.17 (~r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7282, 7570, 7529, 7533, 7273, 7264, 7069, 1])).
% 1.95/2.17 tff(7575,plain,
% 1.95/2.17 (b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[507, 7574])).
% 1.95/2.17 tff(7576,plain,
% 1.95/2.17 (r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[5065, 7575, 7529, 7273, 7573, 7264, 7527, 7570, 1, 7069, 7528, 7571, 7553])).
% 1.95/2.17 tff(7577,plain,
% 1.95/2.17 (~r(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6950, 7576, 7069, 1, 7264, 7529, 7527, 7528])).
% 1.95/2.17 tff(7578,plain,
% 1.95/2.17 (~(s(s(elem!1)) = s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1196, 7529])).
% 1.95/2.17 tff(7579,plain,
% 1.95/2.17 (~b(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[5751, 7576, 7069, 7264, 1229, 7528, 7527, 7570, 7553, 7273, 7578])).
% 1.95/2.17 tff(7580,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[583, 7579, 7577])).
% 1.95/2.17 tff(7581,plain,((~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7582,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7581, 55, 4, 3, 54, 1])).
% 1.95/2.17 tff(7583,plain,
% 1.95/2.17 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[281])).
% 1.95/2.17 tff(7584,plain,
% 1.95/2.17 (~b(elem!1, s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2789, 7583])).
% 1.95/2.17 tff(7585,plain,
% 1.95/2.17 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[78])).
% 1.95/2.17 tff(7586,plain,
% 1.95/2.17 (r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2794, 2789])).
% 1.95/2.17 tff(7587,plain,
% 1.95/2.17 (r(elem!1, s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7586, 7585])).
% 1.95/2.17 tff(7588,plain,
% 1.95/2.17 (~(s(s(z)) = s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[855, 402])).
% 1.95/2.17 tff(7589,plain,
% 1.95/2.17 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[862, 7588])).
% 1.95/2.17 tff(7590,plain,
% 1.95/2.17 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[78])).
% 1.95/2.17 tff(7591,plain,
% 1.95/2.17 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.95/2.17 inference(symmetry,[status(thm)],[7590])).
% 1.95/2.17 tff(7592,plain,
% 1.95/2.17 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1218, 7591])).
% 1.95/2.17 tff(7593,plain,
% 1.95/2.17 (s(s(s(z))) = s(s(elem!1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1219, 7592])).
% 1.95/2.17 tff(7594,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1184, 7593])).
% 1.95/2.17 tff(7595,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7596,plain,
% 1.95/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7595, 7589, 78])).
% 1.95/2.17 tff(7597,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))), introduced(assumption)).
% 1.95/2.17 tff(7598,plain,
% 1.95/2.17 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7597])).
% 1.95/2.17 tff(7599,plain,
% 1.95/2.17 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.95/2.17 inference(transitivity,[status(thm)],[21, 7598, 101])).
% 1.95/2.17 tff(7600,plain,
% 1.95/2.17 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7599])).
% 1.95/2.17 tff(7601,plain,
% 1.95/2.17 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.95/2.17 inference(symmetry,[status(thm)],[7600])).
% 1.95/2.17 tff(7602,plain,
% 1.95/2.17 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[78, 1193, 7601, 92])).
% 1.95/2.17 tff(7603,plain,
% 1.95/2.17 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7602])).
% 1.95/2.17 tff(7604,plain,
% 1.95/2.17 (s(s(z)) = s(s(s(s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[87, 7603, 238])).
% 1.95/2.17 tff(7605,plain,
% 1.95/2.17 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7604])).
% 1.95/2.17 tff(7606,plain,
% 1.95/2.17 (s(z) = elem!1),
% 1.95/2.17 inference(transitivity,[status(thm)],[193, 7605, 183, 78])).
% 1.95/2.17 tff(7607,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[706, 7606])).
% 1.95/2.17 tff(7608,plain,((~(s(s(s(z))) = elem!1)) | (s(z) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7609,plain,
% 1.95/2.17 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7608, 402, 78])).
% 1.95/2.17 tff(7610,plain,
% 1.95/2.17 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[267, 251, 452, 454])).
% 1.95/2.17 tff(7611,plain,
% 1.95/2.17 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[279, 7610])).
% 1.95/2.17 tff(7612,plain,
% 1.95/2.17 (r(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[406, 706, 1758])).
% 1.95/2.17 tff(7613,plain,
% 1.95/2.17 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[464, 451, 54, 114, 3])).
% 1.95/2.17 tff(7614,plain,
% 1.95/2.17 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[472, 7613, 432])).
% 1.95/2.17 tff(7615,plain,
% 1.95/2.17 (~b(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[555, 4576, 133, 451])).
% 1.95/2.17 tff(7616,plain,
% 1.95/2.17 (r(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[560, 7615, 902])).
% 1.95/2.17 tff(7617,plain,
% 1.95/2.17 (~r(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[571, 7616, 408, 509])).
% 1.95/2.17 tff(7618,plain,
% 1.95/2.17 (b(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[583, 7617])).
% 1.95/2.17 tff(7619,plain,
% 1.95/2.17 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[593, 7618, 133, 4576, 451])).
% 1.95/2.17 tff(7620,plain,
% 1.95/2.17 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[302, 7619])).
% 1.95/2.17 tff(7621,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[601, 333, 509, 7620, 51, 525])).
% 1.95/2.17 tff(7622,plain,((~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7623,plain,
% 1.95/2.17 (~r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7622, 7614, 7611, 452, 451, 408, 902, 537])).
% 1.95/2.17 tff(7624,plain,
% 1.95/2.17 (b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[507, 7623])).
% 1.95/2.17 tff(7625,plain,
% 1.95/2.17 (~b(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[499, 7624, 489, 490])).
% 1.95/2.17 tff(7626,plain,
% 1.95/2.17 (r(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[486, 7625, 1])).
% 1.95/2.17 tff(7627,plain,
% 1.95/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[481, 7626, 433, 409, 54, 114, 3, 408, 432])).
% 1.95/2.17 tff(7628,plain,
% 1.95/2.17 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[319, 7627])).
% 1.95/2.17 tff(7629,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7630,plain,
% 1.95/2.17 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7631,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7630])).
% 1.95/2.17 tff(7632,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7631, 7629])).
% 1.95/2.17 tff(7633,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7634,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7633, 7632])).
% 1.95/2.17 tff(7635,plain,
% 1.95/2.17 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7634, 144, 251, 489, 452])).
% 1.95/2.17 tff(7636,plain,
% 1.95/2.17 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7635, 7628])).
% 1.95/2.17 tff(7637,plain,
% 1.95/2.17 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[302, 7636])).
% 1.95/2.17 tff(7638,plain,
% 1.95/2.17 (~r(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[940, 7637, 7611, 7614])).
% 1.95/2.17 tff(7639,plain,
% 1.95/2.17 (b(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[583, 7638])).
% 1.95/2.17 tff(7640,plain,
% 1.95/2.17 (~b(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1642, 7639, 251, 451])).
% 1.95/2.17 tff(7641,plain,
% 1.95/2.17 (r(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[560, 7640, 902])).
% 1.95/2.17 tff(7642,plain,
% 1.95/2.17 (~b(s(z), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2383, 7639, 489, 7624])).
% 1.95/2.17 tff(7643,plain,
% 1.95/2.17 (r(s(z), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1244, 7642, 1229])).
% 1.95/2.17 tff(7644,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(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(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7645,plain,
% 1.95/2.17 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7646,plain,
% 1.95/2.17 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(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(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7645])).
% 1.95/2.17 tff(7647,plain,
% 1.95/2.17 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(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(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7646, 7644])).
% 1.95/2.17 tff(7648,plain,
% 1.95/2.17 ((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7649,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 1.95/2.17 tff(7650,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7649, 333, 563, 409, 434, 1230])).
% 1.95/2.17 tff(7651,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7652,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7651, 7643, 7641, 409, 7626])).
% 1.95/2.17 tff(7653,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7654,plain,
% 1.95/2.17 (~b(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7653, 490, 902, 489, 251, 433, 54, 114, 3, 408, 432, 1, 409, 537])).
% 1.95/2.17 tff(7655,plain,
% 1.95/2.17 (r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[448, 7654, 433])).
% 1.95/2.17 tff(7656,plain,
% 1.95/2.17 (~r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[517, 7655, 7611, 408])).
% 1.95/2.17 tff(7657,plain,
% 1.95/2.17 (b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[507, 7656])).
% 1.95/2.17 tff(7658,plain,
% 1.95/2.17 (~r(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[443, 7655, 409, 408])).
% 1.95/2.17 tff(7659,plain,
% 1.95/2.17 (b(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[486, 7658, 1])).
% 1.95/2.17 tff(7660,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[499, 7659, 7657, 489, 490])).
% 1.95/2.17 tff(7661,plain,((~b(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7662,plain,
% 1.95/2.17 (~b(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7661, 408, 1, 409, 489, 433, 902, 251, 54, 114, 3, 432, 537])).
% 1.95/2.17 tff(7663,plain,
% 1.95/2.17 (r(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[372, 7662])).
% 1.95/2.17 tff(7664,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2063, 333, 409, 7663, 408, 722])).
% 1.95/2.17 tff(7665,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7666,plain,
% 1.95/2.17 (~r(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7665, 251, 722, 1, 489, 433, 902, 7612, 54, 114, 3, 432, 537])).
% 1.95/2.17 tff(7667,plain,
% 1.95/2.17 (b(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1380, 7666, 77])).
% 1.95/2.17 tff(7668,plain,
% 1.95/2.17 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[880, 7667, 452, 251])).
% 1.95/2.17 tff(7669,plain,
% 1.95/2.17 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[302, 7668])).
% 1.95/2.17 tff(7670,plain,
% 1.95/2.17 (r(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[406, 706, 350])).
% 1.95/2.17 tff(7671,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~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(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7672,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7673,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 1.95/2.17 tff(7674,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7673, 333, 435, 7670, 6065, 1230])).
% 1.95/2.17 tff(7675,plain,((s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7676,plain,
% 1.95/2.17 (~r(s(z), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7675, 7437, 706, 708, 350])).
% 1.95/2.17 tff(7677,plain,
% 1.95/2.17 (b(s(z), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1244, 7676, 1229])).
% 1.95/2.17 tff(7678,plain,
% 1.95/2.17 (~b(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2383, 7677, 489, 491])).
% 1.95/2.17 tff(7679,plain,
% 1.95/2.17 (r(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[583, 7678])).
% 1.95/2.17 tff(7680,plain,
% 1.95/2.17 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[940, 7679, 51, 321])).
% 1.95/2.17 tff(7681,plain,
% 1.95/2.17 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[472, 7680, 432])).
% 1.95/2.17 tff(7682,plain,
% 1.95/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2655, 7679, 51, 7437])).
% 1.95/2.17 tff(7683,plain,
% 1.95/2.17 (~b(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[5467, 7680, 132, 537, 7682])).
% 1.95/2.17 tff(7684,plain,
% 1.95/2.17 (r(elem!1, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[560, 7683, 902])).
% 1.95/2.17 tff(7685,plain,
% 1.95/2.17 (~r(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1390, 7684, 7670, 7437])).
% 1.95/2.17 tff(7686,plain,
% 1.95/2.17 (b(s(elem!1), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[486, 7685, 1])).
% 1.95/2.17 tff(7687,plain,
% 1.95/2.17 (~b(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[499, 7686, 489, 491])).
% 1.95/2.17 tff(7688,plain,
% 1.95/2.17 (r(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[372, 7687])).
% 1.95/2.17 tff(7689,plain,
% 1.95/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[429, 7688, 7670, 51])).
% 1.95/2.17 tff(7690,plain,
% 1.95/2.17 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[319, 7689])).
% 1.95/2.17 tff(7691,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2958, 144, 491, 489, 7686, 7690, 7681])).
% 1.95/2.17 tff(7692,plain,((~b(s(elem!1), z)) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1) | b(elem!1, s(z)) | b(s(z), elem!1) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7693,plain,
% 1.95/2.17 (~b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7692, 7611, 489, 1, 902, 454, 537, 432, 7669, 706, 708, 1758, 433, 251, 7667])).
% 1.95/2.17 tff(7694,plain,
% 1.95/2.17 (r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[507, 7693])).
% 1.95/2.17 tff(7695,plain,
% 1.95/2.17 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[601, 333, 7694, 7669, 7611])).
% 1.95/2.17 tff(7696,plain,
% 1.95/2.17 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[472, 7695, 432])).
% 1.95/2.17 tff(7697,plain,
% 1.95/2.17 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7698,plain,
% 1.95/2.17 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7699,plain,
% 1.95/2.17 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7698])).
% 1.95/2.17 tff(7700,plain,
% 1.95/2.17 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7699, 7697])).
% 1.95/2.17 tff(7701,plain,
% 1.95/2.17 ((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7702,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7701, 7700])).
% 1.95/2.17 tff(7703,plain,
% 1.95/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7702, 333, 7694, 7669, 7611])).
% 1.95/2.17 tff(7704,plain,
% 1.95/2.17 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[542, 7703, 537])).
% 1.95/2.18 tff(7705,plain,
% 1.95/2.18 (~b(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[464, 7696, 54, 114, 3])).
% 1.95/2.18 tff(7706,plain,
% 1.95/2.18 (r(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[448, 7705, 433])).
% 1.95/2.18 tff(7707,plain,
% 1.95/2.18 (~r(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7675, 7706, 706, 708, 1758])).
% 1.95/2.18 tff(7708,plain,
% 1.95/2.18 (b(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1244, 7707, 1229])).
% 1.95/2.18 tff(7709,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3388, 144, 7708, 123, 7704, 7696])).
% 1.95/2.18 tff(7710,plain,((~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | b(elem!1, s(z)) | (s(elem!1) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7711,plain,
% 1.95/2.18 (~b(z, elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7710, 489, 706, 708, 433, 54, 114, 3, 537, 432, 123, 1, 902, 722])).
% 1.95/2.18 tff(7712,plain,
% 1.95/2.18 (r(z, elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[658, 7711, 71])).
% 1.95/2.18 tff(7713,plain,
% 1.95/2.18 (((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7714,plain,
% 1.95/2.18 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7713])).
% 1.95/2.18 tff(7715,plain,
% 1.95/2.18 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7714, 2179])).
% 1.95/2.18 tff(7716,plain,
% 1.95/2.18 ((~![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(z, elem!1)) | (~r(z, s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7717,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7716, 7715])).
% 1.95/2.18 tff(7718,plain,
% 1.95/2.18 (~r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7717, 333, 7712, 7612, 722])).
% 1.95/2.18 tff(7719,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[372, 7718])).
% 1.95/2.18 tff(7720,plain,
% 1.95/2.18 (~r(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5438, 333, 435, 670, 722])).
% 1.95/2.18 tff(7721,plain,
% 1.95/2.18 (b(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[507, 7720])).
% 1.95/2.18 tff(7722,plain,
% 1.95/2.18 (~b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[499, 7721, 490, 489])).
% 1.95/2.18 tff(7723,plain,
% 1.95/2.18 (r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[486, 7722, 1])).
% 1.95/2.18 tff(7724,plain,
% 1.95/2.18 (((~![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(elem!1, s(z))) | (~r(s(elem!1), 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(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7725,plain,
% 1.95/2.18 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7726,plain,
% 1.95/2.18 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7725])).
% 1.95/2.18 tff(7727,plain,
% 1.95/2.18 (((~![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(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(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7726, 7724])).
% 1.95/2.18 tff(7728,plain,
% 1.95/2.18 ((~![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(z))))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7729,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7728, 7727])).
% 1.95/2.18 tff(7730,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7729, 333, 435, 7723, 722, 353])).
% 1.95/2.18 tff(7731,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7732,plain,
% 1.95/2.18 (~r(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7731, 7719, 722, 1, 353, 489, 7712])).
% 1.95/2.18 tff(7733,plain,
% 1.95/2.18 (b(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[448, 7732, 433])).
% 1.95/2.18 tff(7734,plain,
% 1.95/2.18 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[464, 7733, 54, 114, 3])).
% 1.95/2.18 tff(7735,plain,
% 1.95/2.18 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[472, 7734, 432])).
% 1.95/2.18 tff(7736,plain,
% 1.95/2.18 (~r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7717, 333, 670, 409, 722])).
% 1.95/2.18 tff(7737,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[372, 7736])).
% 1.95/2.18 tff(7738,plain,
% 1.95/2.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3510, 509, 133, 451, 537, 670, 525, 624])).
% 1.95/2.18 tff(7739,plain,
% 1.95/2.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[279, 7738])).
% 1.95/2.18 tff(7740,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2217, 144, 489, 123, 286, 259])).
% 1.95/2.18 tff(7741,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7742,plain,
% 1.95/2.18 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7741, 7739, 123, 489])).
% 1.95/2.18 tff(7743,plain,
% 1.95/2.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[302, 7742])).
% 1.95/2.18 tff(7744,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3508, 333, 670, 509, 7743, 525])).
% 1.95/2.18 tff(7745,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7746,plain,
% 1.95/2.18 (~r(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7745, 624, 525, 123, 489, 133, 451, 537, 670])).
% 1.95/2.18 tff(7747,plain,
% 1.95/2.18 (b(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[507, 7746])).
% 1.95/2.18 tff(7748,plain,
% 1.95/2.18 (~b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[499, 7747, 489, 7737])).
% 1.95/2.18 tff(7749,plain,
% 1.95/2.18 (r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[486, 7748, 1])).
% 1.95/2.18 tff(7750,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7751,plain,
% 1.95/2.18 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7752,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7751])).
% 1.95/2.18 tff(7753,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7752, 7750])).
% 1.95/2.18 tff(7754,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7755,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 1.95/2.18 tff(7756,plain,
% 1.95/2.18 (~r(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7755, 333, 409, 7749, 722])).
% 1.95/2.18 tff(7757,plain,
% 1.95/2.18 (b(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[560, 7756, 902])).
% 1.95/2.18 tff(7758,plain,
% 1.95/2.18 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[555, 7757, 133, 451])).
% 1.95/2.18 tff(7759,plain,
% 1.95/2.18 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[542, 7758, 537])).
% 1.95/2.18 tff(7760,plain,
% 1.95/2.18 (~b(z, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[949, 7757, 624, 7747])).
% 1.95/2.18 tff(7761,plain,
% 1.95/2.18 (r(z, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[583, 7760])).
% 1.95/2.18 tff(7762,plain,
% 1.95/2.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3607, 7761, 7759, 525])).
% 1.95/2.18 tff(7763,plain,
% 1.95/2.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[279, 7762])).
% 1.95/2.18 tff(7764,plain,
% 1.95/2.18 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[757, 7763, 123, 7737])).
% 1.95/2.18 tff(7765,plain,
% 1.95/2.18 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[319, 7764])).
% 1.95/2.18 tff(7766,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(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(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7767,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7768,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7767, 7766])).
% 1.95/2.18 tff(7769,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7768, 333, 409, 7749, 7765, 7759])).
% 1.95/2.18 tff(7770,plain,((~b(elem!1, z)) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7771,plain,
% 1.95/2.18 (~b(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7770, 7735, 123, 7612, 537, 452, 7733, 902, 722, 1, 489, 7712])).
% 1.95/2.18 tff(7772,plain,
% 1.95/2.18 (r(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[653, 7771, 77])).
% 1.95/2.18 tff(7773,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.95/2.18 tff(7774,plain,
% 1.95/2.18 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.95/2.18 inference(symmetry,[status(thm)],[7773])).
% 1.95/2.18 tff(7775,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2725, 7774])).
% 1.95/2.18 tff(7776,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7777,plain,
% 1.95/2.18 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7776, 2725])).
% 1.95/2.18 tff(7778,plain,
% 1.95/2.18 (~b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[499, 491, 489, 7737])).
% 1.95/2.18 tff(7779,plain,
% 1.95/2.18 (r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[486, 7778, 1])).
% 1.95/2.18 tff(7780,plain,
% 1.95/2.18 (~b(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7770, 7614, 123, 409, 537, 452, 451, 902, 722, 1, 489, 670])).
% 1.95/2.18 tff(7781,plain,
% 1.95/2.18 (r(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[653, 7780, 77])).
% 1.95/2.18 tff(7782,plain,
% 1.95/2.18 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[481, 7779, 433, 409, 54, 114, 3, 7781, 432])).
% 1.95/2.18 tff(7783,plain,
% 1.95/2.18 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[319, 7782])).
% 1.95/2.18 tff(7784,plain,
% 1.95/2.18 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7093, 7783, 7737, 489])).
% 1.95/2.18 tff(7785,plain,
% 1.95/2.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[302, 7784])).
% 1.95/2.18 tff(7786,plain,
% 1.95/2.18 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[757, 7783, 123, 7737])).
% 1.95/2.18 tff(7787,plain,
% 1.95/2.18 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[279, 7786])).
% 1.95/2.18 tff(7788,plain,
% 1.95/2.18 (~r(z, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[940, 7787, 7614, 7785])).
% 1.95/2.18 tff(7789,plain,
% 1.95/2.18 (b(z, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[583, 7788])).
% 1.95/2.18 tff(7790,plain,
% 1.95/2.18 (~b(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2383, 7789, 489, 491])).
% 1.95/2.18 tff(7791,plain,
% 1.95/2.18 (r(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1244, 7790, 1229])).
% 1.95/2.18 tff(7792,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(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(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7793,plain,
% 1.95/2.18 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7794,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7793])).
% 1.95/2.18 tff(7795,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7794, 7792])).
% 1.95/2.18 tff(7796,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7797,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7796, 7795])).
% 1.95/2.18 tff(7798,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7797, 333, 563, 434, 722, 1230])).
% 1.95/2.18 tff(7799,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7800,plain,
% 1.95/2.18 (~r(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7799, 7791, 722, 7779])).
% 1.95/2.18 tff(7801,plain,
% 1.95/2.18 (b(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[560, 7800, 902])).
% 1.95/2.18 tff(7802,plain,
% 1.95/2.18 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[555, 7801, 452, 451])).
% 1.95/2.18 tff(7803,plain,
% 1.95/2.18 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[542, 7802, 537])).
% 1.95/2.18 tff(7804,plain,
% 1.95/2.18 (~b(s(s(elem!1)), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5572, 1249, 585, 491])).
% 1.95/2.18 tff(7805,plain,
% 1.95/2.18 (~r(s(s(elem!1)), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5047, 7804, 408, 670])).
% 1.95/2.18 tff(7806,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1260, 44, 7805, 1257, 1256])).
% 1.95/2.18 tff(7807,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7808,plain,
% 1.95/2.18 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7807, 7801, 670, 1257, 451, 7781, 7789, 491])).
% 1.95/2.18 tff(7809,plain,
% 1.95/2.18 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1283, 7808, 2727])).
% 1.95/2.18 tff(7810,plain,
% 1.95/2.18 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7811,plain,
% 1.95/2.18 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7812,plain,
% 1.95/2.18 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7811])).
% 1.95/2.18 tff(7813,plain,
% 1.95/2.18 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7812, 7810])).
% 1.95/2.18 tff(7814,plain,
% 1.95/2.18 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7815,plain,
% 1.95/2.18 ((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7814, 7813])).
% 1.95/2.18 tff(7816,plain,
% 1.95/2.18 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7815, 333, 7809, 7779, 7803])).
% 1.95/2.18 tff(7817,plain,
% 1.95/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7818,plain,
% 1.95/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7819,plain,
% 1.95/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7818, 7817])).
% 1.95/2.18 tff(7820,plain,
% 1.95/2.18 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7819, 44, 7816, 7777])).
% 1.95/2.18 tff(7821,plain,
% 1.95/2.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3662, 7809, 7803, 7614])).
% 1.95/2.18 tff(7822,plain,
% 1.95/2.18 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2758, 7821, 2725])).
% 1.95/2.18 tff(7823,plain,
% 1.95/2.18 (((~![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(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7824,plain,
% 1.95/2.18 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7825,plain,
% 1.95/2.18 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~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), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7824])).
% 1.95/2.19 tff(7826,plain,
% 1.95/2.19 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~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), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7825, 7823])).
% 1.95/2.19 tff(7827,plain,
% 1.95/2.19 ((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7828,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7827, 7826])).
% 1.95/2.19 tff(7829,plain,
% 1.95/2.19 (~r(s(z), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7828, 333, 7809, 7779, 7791])).
% 1.95/2.19 tff(7830,plain,
% 1.95/2.19 (b(s(z), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5484, 7829])).
% 1.95/2.19 tff(7831,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7832,plain,
% 1.95/2.19 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7833,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7832])).
% 1.95/2.19 tff(7834,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7833, 7831])).
% 1.95/2.19 tff(7835,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7836,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7835, 7834])).
% 1.95/2.19 tff(7837,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7836, 144, 7830, 7822, 123, 7820])).
% 1.95/2.19 tff(7838,plain,((~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (~r(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7839,plain,
% 1.95/2.19 (~b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7838, 7712, 2725, 537, 123, 1257, 7733, 902, 722, 489, 433, 7612, 54, 114, 3, 432, 1])).
% 1.95/2.19 tff(7840,plain,
% 1.95/2.19 (r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[507, 7839])).
% 1.95/2.19 tff(7841,plain,
% 1.95/2.19 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7622, 7840, 7733, 452, 7735, 7772, 902, 537])).
% 1.95/2.19 tff(7842,plain,
% 1.95/2.19 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[279, 7841])).
% 1.95/2.19 tff(7843,plain,
% 1.95/2.19 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7741, 7842, 123, 489])).
% 1.95/2.19 tff(7844,plain,
% 1.95/2.19 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[302, 7843])).
% 1.95/2.19 tff(7845,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3508, 333, 7712, 7840, 7844, 7735])).
% 1.95/2.19 tff(7846,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(z))) | (s(elem!1) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7847,plain,
% 1.95/2.19 (~b(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7846, 545, 123, 523, 7609, 7596, 7587, 221, 54, 110, 3, 197, 1, 173, 402, 7584])).
% 1.95/2.19 tff(7848,plain,
% 1.95/2.19 (r(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[348, 7847])).
% 1.95/2.19 tff(7849,plain,
% 1.95/2.19 (~b(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7846, 545, 123, 523, 7609, 7596, 722, 221, 54, 110, 3, 197, 1, 173, 402, 708])).
% 1.95/2.19 tff(7850,plain,
% 1.95/2.19 (r(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[348, 7849])).
% 1.95/2.19 tff(7851,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[78])).
% 1.95/2.19 tff(7852,plain,
% 1.95/2.19 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[7851])).
% 1.95/2.19 tff(7853,plain,
% 1.95/2.19 ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7852])).
% 1.95/2.19 tff(7854,plain,
% 1.95/2.19 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[3, 7853])).
% 1.95/2.19 tff(7855,plain,
% 1.95/2.19 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1769, 624, 110, 402, 71, 123, 722, 7850, 3, 54])).
% 1.95/2.19 tff(7856,plain,
% 1.95/2.19 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[302, 7855])).
% 1.95/2.19 tff(7857,plain,
% 1.95/2.19 (~b(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[152, 132, 123, 133])).
% 1.95/2.19 tff(7858,plain,
% 1.95/2.19 (r(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[406, 402, 7857])).
% 1.95/2.19 tff(7859,plain,
% 1.95/2.19 (((~![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(elem!1), elem!1)) | (~r(elem!1, 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7860,plain,
% 1.95/2.19 (((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7861,plain,
% 1.95/2.19 (((~![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(s(elem!1), 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7860])).
% 1.95/2.19 tff(7862,plain,
% 1.95/2.19 (((~![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(s(elem!1), 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7861, 7859])).
% 1.95/2.19 tff(7863,plain,
% 1.95/2.19 ((~![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(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7864,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7863, 7862])).
% 1.95/2.19 tff(7865,plain,
% 1.95/2.19 (~r(s(elem!1), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7864, 333, 435, 7858, 722])).
% 1.95/2.19 tff(7866,plain,
% 1.95/2.19 (b(s(elem!1), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[486, 7865, 1])).
% 1.95/2.19 tff(7867,plain,
% 1.95/2.19 (~r(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7675, 435, 402, 708, 7857])).
% 1.95/2.19 tff(7868,plain,
% 1.95/2.19 (b(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1244, 7867, 1229])).
% 1.95/2.19 tff(7869,plain,
% 1.95/2.19 (~r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[727, 670, 722, 323])).
% 1.95/2.19 tff(7870,plain,
% 1.95/2.19 (b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[372, 7869])).
% 1.95/2.19 tff(7871,plain,
% 1.95/2.19 (~r(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1863, 670, 722, 435])).
% 1.95/2.19 tff(7872,plain,
% 1.95/2.19 (b(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[583, 7871])).
% 1.95/2.19 tff(7873,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1853, 7872, 7870, 1262, 488])).
% 1.95/2.19 tff(7874,plain,((~r(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7875,plain,
% 1.95/2.19 (~r(z, elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7874, 7868, 7866, 722, 435, 323])).
% 1.95/2.19 tff(7876,plain,
% 1.95/2.19 (b(z, elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[658, 7875, 71])).
% 1.95/2.19 tff(7877,plain,
% 1.95/2.19 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[267, 7876, 133, 132])).
% 1.95/2.19 tff(7878,plain,
% 1.95/2.19 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[279, 7877])).
% 1.95/2.19 tff(7879,plain,
% 1.95/2.19 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[341, 7878, 323, 321])).
% 1.95/2.19 tff(7880,plain,
% 1.95/2.19 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[319, 7879])).
% 1.95/2.19 tff(7881,plain,
% 1.95/2.19 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[869, 144, 7866, 123, 7880])).
% 1.95/2.19 tff(7882,plain,
% 1.95/2.19 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[472, 7881, 197])).
% 1.95/2.19 tff(7883,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7884,plain,
% 1.95/2.19 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7885,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7884])).
% 1.95/2.19 tff(7886,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7885, 7883])).
% 1.95/2.19 tff(7887,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7888,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7887, 7886])).
% 1.95/2.19 tff(7889,plain,
% 1.95/2.19 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7888, 144, 7866, 7868, 7880])).
% 1.95/2.19 tff(7890,plain,
% 1.95/2.19 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[542, 7889, 523])).
% 1.95/2.19 tff(7891,plain,
% 1.95/2.19 (~r(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2655, 7890, 435, 7878])).
% 1.95/2.19 tff(7892,plain,
% 1.95/2.19 (b(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[583, 7891])).
% 1.95/2.19 tff(7893,plain,
% 1.95/2.19 (~r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[533, 7882, 7878, 7890])).
% 1.95/2.19 tff(7894,plain,
% 1.95/2.19 (b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[507, 7893])).
% 1.95/2.19 tff(7895,plain,
% 1.95/2.19 (((~![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(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7896,plain,
% 1.95/2.19 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7897,plain,
% 1.95/2.19 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), 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)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7896])).
% 1.95/2.19 tff(7898,plain,
% 1.95/2.19 (((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), 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)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7897, 7895])).
% 1.95/2.19 tff(7899,plain,
% 1.95/2.19 ((~![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(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(elem!1))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7900,plain,
% 1.95/2.19 ((~![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(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7899, 7898])).
% 1.95/2.19 tff(7901,plain,
% 1.95/2.19 (~r(s(s(z)), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7900, 333, 2671, 321, 525])).
% 1.95/2.19 tff(7902,plain,
% 1.95/2.19 (b(s(s(z)), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1408, 44, 860, 7901])).
% 1.95/2.19 tff(7903,plain,
% 1.95/2.19 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7904,plain,
% 1.95/2.19 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7905,plain,
% 1.95/2.19 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7904])).
% 1.95/2.19 tff(7906,plain,
% 1.95/2.19 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7905, 7903])).
% 1.95/2.19 tff(7907,plain,
% 1.95/2.19 ((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7908,plain,
% 1.95/2.19 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7907, 7906])).
% 1.95/2.19 tff(7909,plain,
% 1.95/2.19 (~r(s(s(z)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7908, 333, 2671, 321, 51])).
% 1.95/2.19 tff(7910,plain,
% 1.95/2.19 (b(s(s(z)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1462, 44, 164, 7909])).
% 1.95/2.19 tff(7911,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7912,plain,
% 1.95/2.19 (((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7913,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7912])).
% 1.95/2.19 tff(7914,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7913, 7911])).
% 1.95/2.19 tff(7915,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7916,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 1.95/2.19 tff(7917,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7916, 144, 491, 585, 7910, 7902])).
% 1.95/2.19 tff(7918,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7919,plain,
% 1.95/2.19 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7918, 7894, 7892, 7588, 321, 7882, 7878])).
% 1.95/2.20 tff(7920,plain,
% 1.95/2.20 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1451, 7919])).
% 1.95/2.20 tff(7921,plain,
% 1.95/2.20 (~b(s(s(z)), s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1425, 7920, 123, 7880])).
% 1.95/2.20 tff(7922,plain,
% 1.95/2.20 (r(s(s(z)), s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1429, 44, 7921, 1416])).
% 1.95/2.20 tff(7923,plain,
% 1.95/2.20 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.95/2.20 inference(monotonicity,[status(thm)],[78])).
% 1.95/2.20 tff(7924,plain,
% 1.95/2.20 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[7923])).
% 1.95/2.20 tff(7925,plain,
% 1.95/2.20 (~(s(s(z)) = elem!1)),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[217, 7924])).
% 1.95/2.20 tff(7926,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 1.95/2.20 tff(7927,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.95/2.20 tff(7928,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.95/2.20 tff(7929,plain,
% 1.95/2.20 (elem!1 = s(s(s(z)))),
% 1.95/2.20 inference(symmetry,[status(thm)],[78])).
% 1.95/2.20 tff(7930,plain,
% 1.95/2.20 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[7929])).
% 1.95/2.20 tff(7931,plain,
% 1.95/2.20 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.95/2.20 inference(symmetry,[status(thm)],[7930])).
% 1.95/2.20 tff(7932,plain,
% 1.95/2.20 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[7931])).
% 1.95/2.20 tff(7933,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.95/2.20 tff(7934,plain,
% 1.95/2.20 (~b(s(s(z)), elem!1)),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[7933, 7932])).
% 1.95/2.20 tff(7935,plain,
% 1.95/2.20 ($false),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[7928, 7934])).
% 1.95/2.20 tff(7936,plain,((~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(z)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.20 tff(7937,plain,
% 1.95/2.20 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[7936, 7928, 78])).
% 1.95/2.20 tff(7938,plain,
% 1.95/2.20 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.20 inference(symmetry,[status(thm)],[1126])).
% 1.95/2.20 tff(7939,plain,
% 1.95/2.20 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[7938])).
% 1.95/2.20 tff(7940,plain,
% 1.95/2.20 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[1129, 7939])).
% 1.95/2.20 tff(7941,plain,
% 1.95/2.20 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1136, 7940, 7927])).
% 1.95/2.20 tff(7942,plain,
% 1.95/2.20 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[248, 1129, 7926])).
% 1.95/2.20 tff(7943,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.95/2.20 tff(7944,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(7945,plain,
% 1.95/2.20 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(7946,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7945])).
% 2.02/2.20 tff(7947,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7946, 7944])).
% 2.02/2.20 tff(7948,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7949,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7948, 7947])).
% 2.02/2.20 tff(7950,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7949, 144, 7943, 1398, 7942, 7941])).
% 2.02/2.20 tff(7951,plain,((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7952,plain,
% 2.02/2.20 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7951, 244])).
% 2.02/2.20 tff(7953,plain,
% 2.02/2.20 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7952, 7937, 7927, 7926])).
% 2.02/2.20 tff(7954,plain,
% 2.02/2.20 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1451, 7953])).
% 2.02/2.20 tff(7955,plain,
% 2.02/2.20 (~r(s(s(z)), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7908, 333, 7954, 321, 51])).
% 2.02/2.20 tff(7956,plain,
% 2.02/2.20 (b(s(s(z)), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1462, 44, 164, 7955])).
% 2.02/2.20 tff(7957,plain,
% 2.02/2.20 (((~b(elem!1, z)) | (~b(s(s(z)), 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)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7958,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7957])).
% 2.02/2.20 tff(7959,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7958, 7360])).
% 2.02/2.20 tff(7960,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), elem!1)) | (~b(s(s(z)), z)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7961,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7960, 7959])).
% 2.02/2.20 tff(7962,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7961, 144, 251, 624, 7928, 7956])).
% 2.02/2.20 tff(7963,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7964,plain,
% 2.02/2.20 (~b(s(s(z)), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7963, 7876, 624, 321, 7878, 7927, 7926, 78])).
% 2.02/2.20 tff(7965,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 2.02/2.20 tff(7966,plain,
% 2.02/2.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7967,plain,
% 2.02/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7968,plain,
% 2.02/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7967, 7966])).
% 2.02/2.20 tff(7969,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7968, 44, 1506, 7965, 7180])).
% 2.02/2.20 tff(7970,plain,(b(s(s(z)), elem!1) | (s(s(z)) = elem!1) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7971,plain,
% 2.02/2.20 (r(s(s(z)), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7970, 7964, 7925])).
% 2.02/2.20 tff(7972,plain,
% 2.02/2.20 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7973,plain,
% 2.02/2.20 ((~![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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7974,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7973, 7972])).
% 2.02/2.20 tff(7975,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7974, 333, 7858, 722, 7971, 7922])).
% 2.02/2.20 tff(7976,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7977,plain,
% 2.02/2.20 (~r(s(elem!1), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7976, 7856, 123, 722, 624, 7854, 228, 78, 7850, 131, 122, 1, 708])).
% 2.02/2.20 tff(7978,plain,
% 2.02/2.20 (b(s(elem!1), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[448, 7977, 221])).
% 2.02/2.20 tff(7979,plain,
% 2.02/2.20 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[464, 7978, 54, 110, 3])).
% 2.02/2.20 tff(7980,plain,
% 2.02/2.20 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[472, 7979, 197])).
% 2.02/2.20 tff(7981,plain,
% 2.02/2.20 (~b(z, elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[267, 259, 133, 132])).
% 2.02/2.20 tff(7982,plain,
% 2.02/2.20 (~b(z, s(s(s(z))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[609, 7981, 78])).
% 2.02/2.20 tff(7983,plain,
% 2.02/2.20 (r(z, s(s(s(z))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[619, 7982])).
% 2.02/2.20 tff(7984,plain,
% 2.02/2.20 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[642, 7983, 323, 321])).
% 2.02/2.20 tff(7985,plain,
% 2.02/2.20 (r(z, elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[658, 7981, 74])).
% 2.02/2.20 tff(7986,plain,
% 2.02/2.20 (~r(z, s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[727, 7985, 722, 323])).
% 2.02/2.20 tff(7987,plain,
% 2.02/2.20 (b(z, s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[372, 7986])).
% 2.02/2.20 tff(7988,plain,
% 2.02/2.20 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[757, 7987, 123, 259])).
% 2.02/2.20 tff(7989,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[319, 7988, 7984])).
% 2.02/2.20 tff(7990,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7991,plain,
% 2.02/2.20 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7990, 7856, 7850, 123, 722, 78, 71, 131, 122])).
% 2.02/2.20 tff(7992,plain,
% 2.02/2.20 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[279, 7991])).
% 2.02/2.20 tff(7993,plain,
% 2.02/2.20 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7994,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7993])).
% 2.02/2.20 tff(7995,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7994, 596])).
% 2.02/2.20 tff(7996,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7997,plain,
% 2.02/2.20 ((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7996, 7995])).
% 2.02/2.20 tff(7998,plain,
% 2.02/2.20 (~r(s(elem!1), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7997, 333, 7856, 7992, 7980])).
% 2.02/2.20 tff(7999,plain,
% 2.02/2.20 (b(s(elem!1), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[507, 7998])).
% 2.02/2.20 tff(8000,plain,
% 2.02/2.20 (~b(z, elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[916, 7999, 7978, 624])).
% 2.02/2.20 tff(8001,plain,
% 2.02/2.20 (r(z, elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[658, 8000, 71])).
% 2.02/2.20 tff(8002,plain,
% 2.02/2.20 (~r(z, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[940, 7992, 7980, 7856])).
% 2.02/2.20 tff(8003,plain,
% 2.02/2.20 (b(z, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[583, 8002])).
% 2.02/2.20 tff(8004,plain,
% 2.02/2.20 (~b(elem!1, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[949, 7999, 624, 8003])).
% 2.02/2.20 tff(8005,plain,
% 2.02/2.20 (r(elem!1, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[560, 8004, 545])).
% 2.02/2.20 tff(8006,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), 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(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(8007,plain,
% 2.02/2.20 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(8008,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.02/2.20 tff(8009,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 2.02/2.20 inference(transitivity,[status(thm)],[8008, 8006])).
% 2.02/2.20 tff(8010,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(8011,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 2.02/2.20 tff(8012,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[8011, 333, 8005, 8001, 407, 7850])).
% 2.02/2.20 tff(8013,plain,((~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(8014,plain,
% 2.02/2.20 (~b(elem!1, z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[8013, 7587, 123, 78, 54, 3, 1, 7584])).
% 2.02/2.20 tff(8015,plain,
% 2.02/2.20 (r(elem!1, z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[653, 8014, 77])).
% 2.02/2.20 tff(8016,plain,
% 2.02/2.20 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[417, 8015, 407, 7848])).
% 2.02/2.20 tff(8017,plain,
% 2.02/2.20 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[279, 8016])).
% 2.02/2.20 tff(8018,plain,
% 2.02/2.20 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[763, 8015, 402, 3, 7584, 123, 54, 7848])).
% 2.02/2.20 tff(8019,plain,
% 2.02/2.20 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[319, 8018])).
% 2.02/2.20 tff(8020,plain,
% 2.02/2.20 (~r(s(elem!1), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[481, 8019, 221, 407, 54, 110, 3, 8015, 197])).
% 2.02/2.20 tff(8021,plain,
% 2.02/2.20 (b(s(elem!1), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[486, 8020, 1])).
% 2.02/2.20 tff(8022,plain,
% 2.02/2.20 (~r(z, s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1376, 8015, 407, 7848])).
% 2.02/2.20 tff(8023,plain,
% 2.02/2.20 (b(z, s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[372, 8022])).
% 2.02/2.20 tff(8024,plain,
% 2.02/2.20 (~b(s(s(s(z))), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[380, 8014, 78])).
% 2.02/2.20 tff(8025,plain,
% 2.02/2.20 (r(s(s(s(z))), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[396, 8024])).
% 2.02/2.20 tff(8026,plain,
% 2.02/2.20 (((~![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(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(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(8027,plain,
% 2.02/2.20 ((~![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(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(8028,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 2.02/2.20 tff(8029,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[8028, 333, 323, 562, 1699, 3193])).
% 2.02/2.20 tff(8030,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(8031,plain,
% 2.02/2.20 (~r(z, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[8030, 8025, 7586, 7848])).
% 2.02/2.20 tff(8032,plain,
% 2.02/2.20 (b(z, s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[583, 8031])).
% 2.02/2.20 tff(8033,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(8034,plain,
% 2.02/2.20 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(8035,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[8034])).
% 2.02/2.20 tff(8036,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[8035, 8033])).
% 2.02/2.20 tff(8037,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(8038,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[8037, 8036])).
% 2.02/2.20 tff(8039,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[8038, 144, 8032, 8023, 8021, 123, 8017])).
% 2.02/2.21 tff(8040,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8041,plain,
% 2.02/2.21 (~(s(s(s(z))) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8040, 7582, 1, 54, 3, 50])).
% 2.02/2.21 tff(8042,plain,
% 2.02/2.21 (r(s(s(s(z))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[704, 8041, 55])).
% 2.02/2.21 tff(8043,plain,
% 2.02/2.21 (~(elem!1 = s(s(s(z))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8041, 65])).
% 2.02/2.21 tff(8044,plain,
% 2.02/2.21 (r(s(s(s(z))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2794, 7582])).
% 2.02/2.21 tff(8045,plain,
% 2.02/2.21 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[279, 2303])).
% 2.02/2.21 tff(8046,plain,
% 2.02/2.21 (~(s(s(s(z))) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8040, 2789, 1, 54, 3, 123])).
% 2.02/2.21 tff(8047,plain,
% 2.02/2.21 (~(elem!1 = s(s(s(z))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8046, 65])).
% 2.02/2.21 tff(8048,plain,
% 2.02/2.21 (r(s(s(s(z))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[704, 8046, 55])).
% 2.02/2.21 tff(8049,plain,
% 2.02/2.21 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2305, 7265, 2303])).
% 2.02/2.21 tff(8050,plain,
% 2.02/2.21 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[130, 8049, 54])).
% 2.02/2.21 tff(8051,plain,
% 2.02/2.21 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[116, 8049])).
% 2.02/2.21 tff(8052,plain,
% 2.02/2.21 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[121, 8051, 3])).
% 2.02/2.21 tff(8053,plain,
% 2.02/2.21 (~b(s(z), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[152, 8052, 123, 8050])).
% 2.02/2.21 tff(8054,plain,
% 2.02/2.21 (~r(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2079, 408, 707, 7265])).
% 2.02/2.21 tff(8055,plain,
% 2.02/2.21 (b(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[396, 8054])).
% 2.02/2.21 tff(8056,plain,
% 2.02/2.21 (~r(z, s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2136, 408, 707, 7265])).
% 2.02/2.21 tff(8057,plain,
% 2.02/2.21 (b(z, s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[619, 8056])).
% 2.02/2.21 tff(8058,plain,
% 2.02/2.21 (((~![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, elem!1)) | (~r(elem!1, 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), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8059,plain,
% 2.02/2.21 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8060,plain,
% 2.02/2.21 (((~![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(elem!1), 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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8059])).
% 2.02/2.21 tff(8061,plain,
% 2.02/2.21 (((~![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(elem!1), 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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8060, 8058])).
% 2.02/2.21 tff(8062,plain,
% 2.02/2.21 ((~![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(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8063,plain,
% 2.02/2.21 ((~![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, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8062, 8061])).
% 2.02/2.21 tff(8064,plain,
% 2.02/2.21 (~r(s(elem!1), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8063, 333, 670, 408, 509])).
% 2.02/2.21 tff(8065,plain,
% 2.02/2.21 (b(s(elem!1), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[448, 8064, 433])).
% 2.02/2.21 tff(8066,plain,
% 2.02/2.21 (~r(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2079, 408, 707, 670])).
% 2.02/2.21 tff(8067,plain,
% 2.02/2.21 (b(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[396, 8066])).
% 2.02/2.21 tff(8068,plain,
% 2.02/2.21 (~b(s(z), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2156, 489, 7145, 8067])).
% 2.02/2.21 tff(8069,plain,
% 2.02/2.21 (r(s(z), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[172, 8068])).
% 2.02/2.21 tff(8070,plain,
% 2.02/2.21 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7741, 489, 123, 259])).
% 2.02/2.21 tff(8071,plain,
% 2.02/2.21 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[302, 8070])).
% 2.02/2.21 tff(8072,plain,
% 2.02/2.21 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3508, 333, 670, 509, 321])).
% 2.02/2.21 tff(8073,plain,
% 2.02/2.21 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3934, 8072, 123, 57, 451])).
% 2.02/2.21 tff(8074,plain,
% 2.02/2.21 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[130, 8073, 114])).
% 2.02/2.21 tff(8075,plain,
% 2.02/2.21 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[4779, 333, 670, 509, 321])).
% 2.02/2.21 tff(8076,plain,
% 2.02/2.21 (~b(elem!1, s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[5467, 8075, 2692, 2698, 8072])).
% 2.02/2.21 tff(8077,plain,
% 2.02/2.21 (r(elem!1, s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[560, 8076, 2483])).
% 2.02/2.21 tff(8078,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8079,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8080,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8079, 8078])).
% 2.02/2.21 tff(8081,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8080, 333, 8077, 670, 8074, 321])).
% 2.02/2.21 tff(8082,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8083,plain,
% 2.02/2.21 (~(s(z) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8082, 8071, 509, 670, 123, 114, 451])).
% 2.02/2.21 tff(8084,plain,
% 2.02/2.21 (r(s(z), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[406, 8083, 350])).
% 2.02/2.21 tff(8085,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2035, 333, 8084, 408, 707, 8069])).
% 2.02/2.21 tff(8086,plain,((~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | b(s(z), elem!1) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8087,plain,
% 2.02/2.21 (~b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8086, 509, 707, 350, 408, 670, 123, 114, 8065, 259])).
% 2.02/2.21 tff(8088,plain,
% 2.02/2.21 (r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[348, 8087])).
% 2.02/2.21 tff(8089,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8090,plain,
% 2.02/2.21 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8091,plain,
% 2.02/2.21 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8090])).
% 2.02/2.21 tff(8092,plain,
% 2.02/2.21 (((~![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(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8091, 8089])).
% 2.02/2.21 tff(8093,plain,
% 2.02/2.21 ((~![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)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8094,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 2.02/2.21 tff(8095,plain,
% 2.02/2.21 (~r(s(z), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8094, 333, 670, 8088, 408])).
% 2.02/2.21 tff(8096,plain,
% 2.02/2.21 (s(z) = elem!1),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[406, 8095, 350])).
% 2.02/2.21 tff(8097,plain,
% 2.02/2.21 (b(z, s(z)) <=> b(z, elem!1)),
% 2.02/2.21 inference(monotonicity,[status(thm)],[57])).
% 2.02/2.21 tff(8098,plain,
% 2.02/2.21 (b(z, elem!1) <=> b(z, s(z))),
% 2.02/2.21 inference(symmetry,[status(thm)],[8097])).
% 2.02/2.21 tff(8099,plain,
% 2.02/2.21 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8098])).
% 2.02/2.21 tff(8100,plain,
% 2.02/2.21 (~b(z, s(z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[606, 8099])).
% 2.02/2.21 tff(8101,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[490, 8100])).
% 2.02/2.21 tff(8102,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8103,plain,
% 2.02/2.21 (~b(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8102, 8096, 606])).
% 2.02/2.21 tff(8104,plain,
% 2.02/2.21 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7776, 2704])).
% 2.02/2.21 tff(8105,plain,
% 2.02/2.21 (~r(s(elem!1), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8082, 8071, 670, 114, 123, 57, 451])).
% 2.02/2.21 tff(8106,plain,
% 2.02/2.21 (b(s(elem!1), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[507, 8105])).
% 2.02/2.21 tff(8107,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8108,plain,
% 2.02/2.21 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8109,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8108])).
% 2.02/2.21 tff(8110,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8109, 8107])).
% 2.02/2.21 tff(8111,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8112,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8111, 8110])).
% 2.02/2.21 tff(8113,plain,
% 2.02/2.21 (~b(elem!1, s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8112, 144, 2694, 8106, 2692, 259])).
% 2.02/2.21 tff(8114,plain,
% 2.02/2.21 (r(elem!1, s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[560, 8113, 2483])).
% 2.02/2.21 tff(8115,plain,
% 2.02/2.21 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[4052, 8114, 670, 562])).
% 2.02/2.21 tff(8116,plain,
% 2.02/2.21 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[472, 8115, 4762])).
% 2.02/2.21 tff(8117,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8118,plain,
% 2.02/2.21 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8119,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8118])).
% 2.02/2.21 tff(8120,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8119, 8117])).
% 2.02/2.21 tff(8121,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8122,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8121, 8120])).
% 2.02/2.21 tff(8123,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8122, 144, 451, 2694, 8106, 8116, 259])).
% 2.02/2.21 tff(8124,plain,((~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8125,plain,
% 2.02/2.21 (~b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8124, 562, 259, 670, 451, 114, 123, 57])).
% 2.02/2.21 tff(8126,plain,
% 2.02/2.21 (r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[348, 8125])).
% 2.02/2.21 tff(8127,plain,
% 2.02/2.21 (~b(elem!1, z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3965, 8125, 57])).
% 2.02/2.21 tff(8128,plain,
% 2.02/2.21 (r(elem!1, z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[653, 8127, 1368])).
% 2.02/2.21 tff(8129,plain,
% 2.02/2.21 (((~![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(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~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(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8130,plain,
% 2.02/2.21 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8131,plain,
% 2.02/2.21 (((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8130])).
% 2.02/2.21 tff(8132,plain,
% 2.02/2.21 (((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8131, 8129])).
% 2.02/2.21 tff(8133,plain,
% 2.02/2.21 ((~![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(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(8134,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8133, 8132])).
% 2.02/2.21 tff(8135,plain,
% 2.02/2.21 (~r(s(elem!1), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8134, 333, 509, 562, 1699])).
% 2.02/2.21 tff(8136,plain,
% 2.02/2.21 (b(s(elem!1), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[965, 8135, 960])).
% 2.02/2.21 tff(8137,plain,
% 2.02/2.21 (~r(s(z), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1979, 333, 323, 562, 1699])).
% 2.02/2.21 tff(8138,plain,
% 2.02/2.21 (b(s(z), s(s(s(z))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[170, 44, 167, 8137])).
% 2.02/2.21 tff(8139,plain,
% 2.02/2.21 (~r(s(s(s(z))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8030, 1699, 323, 562])).
% 2.02/2.21 tff(8140,plain,
% 2.02/2.21 (b(s(s(s(z))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2794, 8139])).
% 2.02/2.21 tff(8141,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1714, 144, 488, 8140, 8138, 8136])).
% 2.02/2.21 tff(8142,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(8143,plain,
% 2.02/2.21 (~r(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8142, 509, 8126, 2508, 562, 3924])).
% 2.02/2.21 tff(8144,plain,
% 2.02/2.21 (b(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[396, 8143])).
% 2.02/2.21 tff(8145,plain,
% 2.02/2.21 (b(s(s(elem!1)), z)),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[8144, 2497])).
% 2.02/2.21 tff(8146,plain,
% 2.02/2.21 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[8082, 509, 670, 114, 123, 57, 451])).
% 2.02/2.21 tff(8147,plain,
% 2.02/2.21 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[302, 8146])).
% 2.02/2.21 tff(8148,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8149,plain,
% 2.02/2.21 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(8150,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[8149])).
% 2.02/2.21 tff(8151,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[8150, 8148])).
% 2.02/2.21 tff(8152,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8153,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8152, 8151])).
% 2.02/2.22 tff(8154,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8153, 144, 8147, 259, 8145])).
% 2.02/2.22 tff(8155,plain,
% 2.02/2.22 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8154, 6702])).
% 2.02/2.22 tff(8156,plain,
% 2.02/2.22 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1137, 8155])).
% 2.02/2.22 tff(8157,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8156, 2767])).
% 2.02/2.22 tff(8158,plain,
% 2.02/2.22 (b(elem!1, s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[560, 2896, 2483])).
% 2.02/2.22 tff(8159,plain,
% 2.02/2.22 (~r(s(z), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1235, 509, 354, 8126])).
% 2.02/2.22 tff(8160,plain,
% 2.02/2.22 (b(s(z), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1244, 8159, 1237])).
% 2.02/2.22 tff(8161,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[5467, 466, 2692, 2698, 8158])).
% 2.02/2.22 tff(8162,assumption,(r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.02/2.22 tff(8163,plain,
% 2.02/2.22 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3934, 466, 123, 57, 451])).
% 2.02/2.22 tff(8164,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[130, 8163, 114])).
% 2.02/2.22 tff(8165,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[2496])).
% 2.02/2.22 tff(8166,plain,
% 2.02/2.22 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.02/2.22 inference(symmetry,[status(thm)],[5321])).
% 2.02/2.22 tff(8167,plain,
% 2.02/2.22 (b(s(s(s(z))), s(elem!1))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[1249, 8166])).
% 2.02/2.22 tff(8168,plain,
% 2.02/2.22 (~b(s(s(s(z))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4819, 8167, 451, 547])).
% 2.02/2.22 tff(8169,plain,
% 2.02/2.22 (r(s(s(s(z))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[704, 8168, 4798])).
% 2.02/2.22 tff(8170,plain,
% 2.02/2.22 (~r(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2136, 8169, 670, 408])).
% 2.02/2.22 tff(8171,plain,
% 2.02/2.22 (b(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[619, 8170])).
% 2.02/2.22 tff(8172,plain,
% 2.02/2.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[294, 8171, 285, 286])).
% 2.02/2.22 tff(8173,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[249, 8172])).
% 2.02/2.22 tff(8174,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8173, 8165])).
% 2.02/2.22 tff(8175,plain,
% 2.02/2.22 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[5352, 1249, 132, 547, 450])).
% 2.02/2.22 tff(8176,plain,
% 2.02/2.22 (r(elem!1, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2522, 8175, 2462])).
% 2.02/2.22 tff(8177,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8178,plain,
% 2.02/2.22 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8179,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[8178])).
% 2.02/2.22 tff(8180,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[8179, 8177])).
% 2.02/2.22 tff(8181,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8182,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 2.02/2.22 tff(8183,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8182, 333, 8176, 8174, 2484, 8162])).
% 2.02/2.22 tff(8184,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(8185,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8184, 8164, 8162, 57, 285, 8147, 670, 408, 451, 8158, 2692, 4769])).
% 2.02/2.22 tff(8186,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1283, 8185, 2507])).
% 2.02/2.22 tff(8187,plain,
% 2.02/2.22 (((~![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(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8188,plain,
% 2.02/2.22 ((~![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(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8189,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8188, 8187])).
% 2.02/2.22 tff(8190,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8189, 333, 2737, 509, 3654, 524])).
% 2.02/2.22 tff(8191,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(8192,plain,
% 2.02/2.22 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8191, 8186, 509, 8161])).
% 2.02/2.22 tff(8193,plain,
% 2.02/2.22 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2758, 8192, 2704])).
% 2.02/2.22 tff(8194,plain,
% 2.02/2.22 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8193, 4019])).
% 2.02/2.22 tff(8195,plain,
% 2.02/2.22 (~b(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[294, 8194, 285, 8147])).
% 2.02/2.22 tff(8196,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), 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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8197,plain,
% 2.02/2.22 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8198,plain,
% 2.02/2.22 (((~![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(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[8197])).
% 2.02/2.22 tff(8199,plain,
% 2.02/2.22 (((~![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(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[8198, 8196])).
% 2.02/2.22 tff(8200,plain,
% 2.02/2.22 ((~![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(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8201,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 2.02/2.22 tff(8202,plain,
% 2.02/2.22 (~r(z, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8201, 333, 8186, 509, 562])).
% 2.02/2.22 tff(8203,plain,
% 2.02/2.22 (~r(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2836, 8202, 57])).
% 2.02/2.22 tff(8204,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[619, 8203, 8195])).
% 2.02/2.22 tff(8205,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(8206,plain,
% 2.02/2.22 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8205, 8144, 57, 509, 562, 8157, 670, 408, 451, 114, 123])).
% 2.02/2.22 tff(8207,plain,
% 2.02/2.22 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[555, 133, 451, 547])).
% 2.02/2.22 tff(8208,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[542, 8207, 2698])).
% 2.02/2.22 tff(8209,plain,
% 2.02/2.22 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8210,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[8209])).
% 2.02/2.22 tff(8211,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[8210, 4025])).
% 2.02/2.22 tff(8212,plain,
% 2.02/2.22 ((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8213,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8212, 8211])).
% 2.02/2.22 tff(8214,plain,
% 2.02/2.22 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8213, 333, 525, 8208, 8162])).
% 2.02/2.22 tff(8215,plain,
% 2.02/2.22 (b(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1283, 8214, 2507])).
% 2.02/2.22 tff(8216,plain,
% 2.02/2.22 (b(s(s(s(z))), s(elem!1))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8215, 8166])).
% 2.02/2.22 tff(8217,plain,
% 2.02/2.22 (~b(s(s(s(z))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4819, 8216, 451, 547])).
% 2.02/2.22 tff(8218,plain,
% 2.02/2.22 (r(s(s(s(z))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[704, 8217, 4798])).
% 2.02/2.22 tff(8219,plain,
% 2.02/2.22 (~r(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2136, 8218, 670, 408])).
% 2.02/2.22 tff(8220,plain,
% 2.02/2.22 (b(z, s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[619, 8219])).
% 2.02/2.22 tff(8221,plain,
% 2.02/2.22 (b(z, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2828, 8220, 57])).
% 2.02/2.22 tff(8222,plain,
% 2.02/2.22 (~b(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1255, 144, 547, 451, 8215])).
% 2.02/2.22 tff(8223,plain,
% 2.02/2.22 (r(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1260, 44, 4575, 8222])).
% 2.02/2.22 tff(8224,plain,
% 2.02/2.22 (~r(s(s(s(elem!1))), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4662, 8223, 57, 4282, 408, 8221, 670])).
% 2.02/2.22 tff(8225,plain,
% 2.02/2.22 (b(s(s(s(elem!1))), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1101, 8224])).
% 2.02/2.22 tff(8226,plain,
% 2.02/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3588, 8225, 57])).
% 2.02/2.22 tff(8227,plain,
% 2.02/2.22 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3552, 144, 8226, 133, 132])).
% 2.02/2.22 tff(8228,plain,
% 2.02/2.22 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3556, 44, 196, 8227])).
% 2.02/2.22 tff(8229,plain,
% 2.02/2.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[294, 8220, 285, 286])).
% 2.02/2.22 tff(8230,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[249, 8229])).
% 2.02/2.22 tff(8231,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8230, 8165])).
% 2.02/2.22 tff(8232,plain,
% 2.02/2.22 (((~![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(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8233,plain,
% 2.02/2.22 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8234,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[8233])).
% 2.02/2.22 tff(8235,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[8234, 8232])).
% 2.02/2.22 tff(8236,plain,
% 2.02/2.22 ((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8237,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8236, 8235])).
% 2.02/2.22 tff(8238,plain,
% 2.02/2.22 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8237, 333, 8231, 525, 8228])).
% 2.02/2.22 tff(8239,plain,
% 2.02/2.22 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8238, 4583])).
% 2.02/2.22 tff(8240,plain,
% 2.02/2.22 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4692, 8225, 3924, 1262])).
% 2.02/2.22 tff(8241,plain,
% 2.02/2.22 (r(s(s(s(elem!1))), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4697, 8240, 3523])).
% 2.02/2.22 tff(8242,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8241, 8239])).
% 2.02/2.22 tff(8243,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(8244,plain,
% 2.02/2.22 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8243, 8206, 57, 2692, 8160, 408, 670, 8144, 8147, 451, 8158, 8157])).
% 2.02/2.22 tff(8245,plain,
% 2.02/2.22 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[130, 8244, 114])).
% 2.02/2.22 tff(8246,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8247,plain,
% 2.02/2.22 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8248,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[8247])).
% 2.02/2.22 tff(8249,plain,
% 2.02/2.22 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[8248, 8246])).
% 2.02/2.22 tff(8250,plain,
% 2.02/2.22 ((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(8251,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[8250, 8249])).
% 2.02/2.22 tff(8252,plain,
% 2.02/2.22 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[8251, 333, 8245, 8206, 8157])).
% 2.02/2.22 tff(8253,plain,
% 2.02/2.22 (b(s(s(elem!1)), s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1283, 8252, 2507])).
% 2.02/2.22 tff(8254,plain,
% 2.02/2.22 (~b(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1255, 144, 8158, 451, 8253])).
% 2.02/2.22 tff(8255,plain,
% 2.02/2.22 (r(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1260, 44, 4575, 8254])).
% 2.02/2.22 tff(8256,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(8257,plain,
% 2.02/2.22 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8258,plain,
% 2.02/2.23 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8257])).
% 2.02/2.23 tff(8259,plain,
% 2.02/2.23 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8258, 8256])).
% 2.02/2.23 tff(8260,plain,
% 2.02/2.23 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8261,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8260, 8259])).
% 2.02/2.23 tff(8262,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8261, 333, 408, 8255, 8245, 8157])).
% 2.02/2.23 tff(8263,plain,((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8264,plain,
% 2.02/2.23 (~r(s(elem!1), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8263, 8128, 451, 114, 57, 670, 562, 123, 259, 1237, 354])).
% 2.02/2.23 tff(8265,plain,
% 2.02/2.23 (b(s(elem!1), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[507, 8264])).
% 2.02/2.23 tff(8266,plain,
% 2.02/2.23 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2674, 466, 57])).
% 2.02/2.23 tff(8267,plain,
% 2.02/2.23 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1451, 8266])).
% 2.02/2.23 tff(8268,plain,
% 2.02/2.23 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1425, 8267, 123, 1417])).
% 2.02/2.23 tff(8269,plain,
% 2.02/2.23 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[319, 8268])).
% 2.02/2.23 tff(8270,plain,
% 2.02/2.23 (((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8271,plain,
% 2.02/2.23 ((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8272,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8271, 8270])).
% 2.02/2.23 tff(8273,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8272, 333, 323, 562, 322, 321])).
% 2.02/2.23 tff(8274,plain,((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8275,plain,
% 2.02/2.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8274, 8269, 323, 562])).
% 2.02/2.23 tff(8276,plain,
% 2.02/2.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[302, 8275])).
% 2.02/2.23 tff(8277,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8278,plain,
% 2.02/2.23 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8279,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8278])).
% 2.02/2.23 tff(8280,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8279, 8277])).
% 2.02/2.23 tff(8281,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8282,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8281, 8280])).
% 2.02/2.23 tff(8283,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8282, 144, 491, 8276, 4769, 259])).
% 2.02/2.23 tff(8284,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8285,plain,
% 2.02/2.23 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8284, 8265, 259, 8126, 562, 123, 4755, 57])).
% 2.02/2.23 tff(8286,plain,
% 2.02/2.23 (~r(elem!1, s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4052, 8285, 670, 562])).
% 2.02/2.23 tff(8287,plain,
% 2.02/2.23 (b(elem!1, s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[560, 8286, 2483])).
% 2.02/2.23 tff(8288,plain,
% 2.02/2.23 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8274, 321, 323, 562])).
% 2.02/2.23 tff(8289,plain,
% 2.02/2.23 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[319, 8288])).
% 2.02/2.23 tff(8290,plain,
% 2.02/2.23 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8289, 2699])).
% 2.02/2.23 tff(8291,plain,
% 2.02/2.23 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[553, 144, 547, 451, 8290])).
% 2.02/2.23 tff(8292,plain,
% 2.02/2.23 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[542, 8291, 2698])).
% 2.02/2.23 tff(8293,plain,
% 2.02/2.23 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8294,plain,
% 2.02/2.23 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8295,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8294])).
% 2.02/2.23 tff(8296,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8295, 8293])).
% 2.02/2.23 tff(8297,plain,
% 2.02/2.23 ((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8298,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 2.02/2.23 tff(8299,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8298, 333, 562, 321, 525, 8292])).
% 2.02/2.23 tff(8300,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8301,plain,
% 2.02/2.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8300, 562, 8285, 8287, 451, 57, 8126])).
% 2.02/2.23 tff(8302,plain,
% 2.02/2.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[302, 8301])).
% 2.02/2.23 tff(8303,plain,
% 2.02/2.23 (r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[704, 55, 698])).
% 2.02/2.23 tff(8304,plain,
% 2.02/2.23 (((~![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(z))), elem!1)) | (~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(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8305,plain,
% 2.02/2.23 ((~![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(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8306,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8305, 8304])).
% 2.02/2.23 tff(8307,plain,
% 2.02/2.23 (~r(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8306, 333, 670, 408, 8303])).
% 2.02/2.23 tff(8308,plain,
% 2.02/2.23 (b(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[396, 8307])).
% 2.02/2.23 tff(8309,plain,
% 2.02/2.23 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[294, 8308, 284, 286])).
% 2.02/2.23 tff(8310,plain,
% 2.02/2.23 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[249, 8309])).
% 2.02/2.23 tff(8311,plain,
% 2.02/2.23 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[982])).
% 2.02/2.23 tff(8312,plain,
% 2.02/2.23 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.02/2.23 inference(symmetry,[status(thm)],[8311])).
% 2.02/2.23 tff(8313,plain,
% 2.02/2.23 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8312])).
% 2.02/2.23 tff(8314,plain,
% 2.02/2.23 (~b(s(elem!1), elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[55, 8313])).
% 2.02/2.23 tff(8315,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[451, 8314])).
% 2.02/2.23 tff(8316,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(elem!1), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8317,plain,
% 2.02/2.23 (~(s(elem!1) = s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8316, 55, 451])).
% 2.02/2.23 tff(8318,plain,
% 2.02/2.23 (~b(s(elem!1), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1800, 144, 491, 8308, 284])).
% 2.02/2.23 tff(8319,plain,
% 2.02/2.23 (r(s(elem!1), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[965, 8318, 8317])).
% 2.02/2.23 tff(8320,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8321,plain,
% 2.02/2.23 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8322,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8321])).
% 2.02/2.23 tff(8323,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8322, 8320])).
% 2.02/2.23 tff(8324,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8325,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8324, 8323])).
% 2.02/2.23 tff(8326,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8325, 333, 8303, 8319, 8310, 525])).
% 2.02/2.23 tff(8327,plain,(b(s(s(s(z))), elem!1) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8328,plain,
% 2.02/2.23 (~b(z, s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8327, 55, 670, 408, 698, 491, 525, 286, 451])).
% 2.02/2.23 tff(8329,plain,
% 2.02/2.23 (~r(z, s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2136, 8303, 670, 408])).
% 2.02/2.23 tff(8330,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[619, 8329, 8328])).
% 2.02/2.23 tff(8331,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(8332,plain,
% 2.02/2.23 (b(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8331, 8128, 670, 4798, 8265, 8285, 8302, 451])).
% 2.02/2.23 tff(8333,plain,
% 2.02/2.23 (b(s(s(elem!1)), elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8332, 6760])).
% 2.02/2.23 tff(8334,plain,
% 2.02/2.23 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4989, 144, 8287, 451, 8333])).
% 2.02/2.23 tff(8335,plain,
% 2.02/2.23 (r(s(s(elem!1)), s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1283, 8334, 2507])).
% 2.02/2.23 tff(8336,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8337,plain,
% 2.02/2.23 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8338,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8337])).
% 2.02/2.23 tff(8339,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(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(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8338, 8336])).
% 2.02/2.23 tff(8340,plain,
% 2.02/2.23 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8341,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8340, 8339])).
% 2.02/2.23 tff(8342,plain,
% 2.02/2.23 (~r(z, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8341, 333, 8335, 562, 8285])).
% 2.02/2.23 tff(8343,plain,
% 2.02/2.23 (~r(z, s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2836, 8342, 57])).
% 2.02/2.23 tff(8344,plain,
% 2.02/2.23 (b(z, s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[619, 8343])).
% 2.02/2.23 tff(8345,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8346,plain,
% 2.02/2.23 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(8347,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[8346])).
% 2.02/2.23 tff(8348,plain,
% 2.02/2.23 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[8347, 8345])).
% 2.02/2.23 tff(8349,plain,
% 2.02/2.23 ((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(8350,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[8349, 8348])).
% 2.02/2.23 tff(8351,plain,
% 2.02/2.23 (~r(s(s(elem!1)), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[8350, 333, 8335, 562, 8285])).
% 2.02/2.23 tff(8352,plain,
% 2.02/2.23 (~r(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[6447, 8351, 57])).
% 2.02/2.23 tff(8353,plain,
% 2.02/2.23 (b(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[396, 8352])).
% 2.02/2.23 tff(8354,plain,
% 2.02/2.23 (~b(s(elem!1), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1802, 8353, 8265, 8344])).
% 2.02/2.24 tff(8355,plain,
% 2.02/2.24 (r(s(elem!1), s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[965, 8354, 2508])).
% 2.02/2.24 tff(8356,plain,
% 2.02/2.24 (r(s(elem!1), s(s(elem!1)))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8355, 2849])).
% 2.02/2.24 tff(8357,plain,
% 2.02/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[294, 8344, 8353, 8302])).
% 2.02/2.24 tff(8358,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[249, 8357])).
% 2.02/2.24 tff(8359,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8358, 8165])).
% 2.02/2.24 tff(8360,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4736, 333, 8335, 8359, 8356, 8285])).
% 2.02/2.24 tff(8361,plain,((~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8362,plain,
% 2.02/2.24 (~r(z, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8361, 57, 5779, 670, 259, 123, 114, 1237, 354, 1368])).
% 2.02/2.24 tff(8363,plain,
% 2.02/2.24 (b(z, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[583, 8362])).
% 2.02/2.24 tff(8364,plain,
% 2.02/2.24 (~r(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8082, 321, 670, 114, 123, 57, 451])).
% 2.02/2.24 tff(8365,plain,
% 2.02/2.24 (b(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[507, 8364])).
% 2.02/2.24 tff(8366,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8080, 333, 563, 670, 2484, 321])).
% 2.02/2.24 tff(8367,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8368,plain,
% 2.02/2.24 (~r(elem!1, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8367, 321, 2484, 670])).
% 2.02/2.24 tff(8369,plain,
% 2.02/2.24 (b(elem!1, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[560, 8368, 2483])).
% 2.02/2.24 tff(8370,plain,
% 2.02/2.24 (~b(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[949, 8369, 585, 8365])).
% 2.02/2.24 tff(8371,plain,
% 2.02/2.24 (r(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[653, 8370, 1368])).
% 2.02/2.24 tff(8372,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2423, 333, 670, 8371, 2484, 321])).
% 2.02/2.24 tff(8373,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = z) | (~b(z, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8374,plain,
% 2.02/2.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8373, 8164, 670, 1368, 585, 114, 123, 57, 451])).
% 2.02/2.24 tff(8375,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[302, 8374])).
% 2.02/2.24 tff(8376,plain,
% 2.02/2.24 (~b(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7741, 8375, 123, 259])).
% 2.02/2.24 tff(8377,plain,
% 2.02/2.24 (r(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[348, 8376])).
% 2.02/2.24 tff(8378,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2948, 537])).
% 2.02/2.24 tff(8379,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8380,plain,
% 2.02/2.24 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8381,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[8380])).
% 2.02/2.24 tff(8382,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[8381, 8379])).
% 2.02/2.24 tff(8383,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(8384,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 2.02/2.24 tff(8385,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8384, 144, 585, 8378, 5465, 259])).
% 2.02/2.24 tff(8386,plain,((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8387,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8386, 466, 259, 2698, 585])).
% 2.02/2.24 tff(8388,plain,
% 2.02/2.24 (~b(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8282, 144, 8375, 4769, 259])).
% 2.02/2.24 tff(8389,plain,
% 2.02/2.24 (r(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[507, 8388])).
% 2.02/2.24 tff(8390,plain,
% 2.02/2.24 (~b(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3965, 8376, 57])).
% 2.02/2.24 tff(8391,plain,
% 2.02/2.24 (r(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[653, 8390, 1368])).
% 2.02/2.24 tff(8392,plain,
% 2.02/2.24 (~r(elem!1, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[678, 8389, 670, 8391])).
% 2.02/2.24 tff(8393,plain,
% 2.02/2.24 (b(elem!1, s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[560, 8392, 2483])).
% 2.02/2.24 tff(8394,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8395,plain,
% 2.02/2.24 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8396,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[8395])).
% 2.02/2.24 tff(8397,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[8396, 8394])).
% 2.02/2.24 tff(8398,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(8399,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8398, 8397])).
% 2.02/2.24 tff(8400,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8399, 144, 585, 1249, 2811, 450, 259])).
% 2.02/2.24 tff(8401,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8402,plain,
% 2.02/2.24 (~b(z, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8401, 1249, 259, 585, 450])).
% 2.02/2.24 tff(8403,plain,
% 2.02/2.24 (~b(z, s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2828, 8402, 57])).
% 2.02/2.24 tff(8404,plain,
% 2.02/2.24 (r(z, s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[619, 8403])).
% 2.02/2.24 tff(8405,plain,
% 2.02/2.24 (~r(s(s(s(z))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2136, 8404, 670, 408])).
% 2.02/2.24 tff(8406,plain,
% 2.02/2.24 (b(s(s(s(z))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[704, 8405, 4798])).
% 2.02/2.24 tff(8407,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4819, 8406, 451, 547])).
% 2.02/2.24 tff(8408,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8407, 8167])).
% 2.02/2.24 tff(8409,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8410,plain,
% 2.02/2.24 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8409, 8393, 451, 57, 670, 8391, 259, 585, 4769])).
% 2.02/2.24 tff(8411,plain,
% 2.02/2.24 (r(s(s(elem!1)), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1283, 8410, 2507])).
% 2.02/2.24 tff(8412,plain,
% 2.02/2.24 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8191, 8411, 8389, 8387])).
% 2.02/2.24 tff(8413,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2758, 8412, 2704])).
% 2.02/2.24 tff(8414,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8413, 4019])).
% 2.02/2.24 tff(8415,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8416,plain,
% 2.02/2.24 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8417,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[8416])).
% 2.02/2.24 tff(8418,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[8417, 8415])).
% 2.02/2.24 tff(8419,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(8420,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8419, 8418])).
% 2.02/2.24 tff(8421,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8420, 144, 547, 2812, 5659, 132, 450])).
% 2.02/2.24 tff(8422,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8423,plain,
% 2.02/2.24 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8422, 8393, 8413, 2692, 4769])).
% 2.02/2.24 tff(8424,plain,
% 2.02/2.24 (r(elem!1, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2522, 8423, 2462])).
% 2.02/2.24 tff(8425,plain,
% 2.02/2.24 (~r(z, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4231, 8424, 8411, 670])).
% 2.02/2.24 tff(8426,plain,
% 2.02/2.24 (~r(z, s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2836, 8425, 57])).
% 2.02/2.24 tff(8427,plain,
% 2.02/2.24 (b(z, s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[619, 8426])).
% 2.02/2.24 tff(8428,plain,
% 2.02/2.24 (~b(s(s(s(z))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[294, 8427, 8414, 8375])).
% 2.02/2.24 tff(8429,plain,
% 2.02/2.24 (r(s(s(s(z))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[396, 8428])).
% 2.02/2.24 tff(8430,plain,
% 2.02/2.24 (~r(s(s(s(z))), s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[6555, 8429, 354, 8377])).
% 2.02/2.24 tff(8431,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1716, 8429, 3924, 2508, 8389, 354, 8377])).
% 2.02/2.24 tff(8432,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2794, 8431, 8430])).
% 2.02/2.24 tff(8433,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (elem!1 = z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8434,plain,
% 2.02/2.24 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8433, 57, 354, 670, 5779, 259, 8363, 1368, 123, 114])).
% 2.02/2.24 tff(8435,plain,
% 2.02/2.24 (b(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3965, 624, 57])).
% 2.02/2.24 tff(8436,plain,
% 2.02/2.24 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7741, 8435, 123, 259])).
% 2.02/2.24 tff(8437,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[302, 8436])).
% 2.02/2.24 tff(8438,plain,
% 2.02/2.24 (~r(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8082, 8437, 670, 114, 123, 57, 451])).
% 2.02/2.24 tff(8439,plain,
% 2.02/2.24 (b(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[507, 8438])).
% 2.02/2.24 tff(8440,plain,
% 2.02/2.24 (~r(s(s(s(elem!1))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3597, 8439, 3524, 585, 670, 8435, 2483, 1237, 624])).
% 2.02/2.24 tff(8441,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1079, 8440, 2469])).
% 2.02/2.24 tff(8442,plain,
% 2.02/2.24 (b(s(s(s(s(z)))), elem!1)),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8441, 3581])).
% 2.02/2.24 tff(8443,plain,
% 2.02/2.24 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8367, 8437, 563, 670])).
% 2.02/2.24 tff(8444,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[130, 8443, 114])).
% 2.02/2.24 tff(8445,plain,
% 2.02/2.24 (~b(s(s(s(s(z)))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3579, 8444, 451, 525, 2692, 624, 57, 8439])).
% 2.02/2.24 tff(8446,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8445, 8442])).
% 2.02/2.24 tff(8447,plain,((~b(elem!1, z)) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8448,plain,
% 2.02/2.24 (~b(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8447, 563, 451, 525, 585, 670, 1237, 114, 57, 123, 259])).
% 2.02/2.24 tff(8449,plain,
% 2.02/2.24 (r(elem!1, z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[653, 8448, 1368])).
% 2.02/2.24 tff(8450,plain,
% 2.02/2.24 (~r(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[678, 8449, 670, 563])).
% 2.02/2.24 tff(8451,plain,
% 2.02/2.24 (b(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[507, 8450])).
% 2.02/2.24 tff(8452,plain,
% 2.02/2.24 (~r(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[678, 408, 670, 563])).
% 2.02/2.24 tff(8453,plain,
% 2.02/2.24 (b(s(elem!1), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[507, 8452])).
% 2.02/2.24 tff(8454,plain,
% 2.02/2.24 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8367, 321, 563, 670])).
% 2.02/2.24 tff(8455,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[130, 8454, 114])).
% 2.02/2.24 tff(8456,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 2.02/2.24 tff(8457,plain,
% 2.02/2.24 (((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8458,plain,
% 2.02/2.24 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8459,plain,
% 2.02/2.24 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[8458])).
% 2.02/2.24 tff(8460,plain,
% 2.02/2.24 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[8459, 8457])).
% 2.02/2.24 tff(8461,plain,
% 2.02/2.24 ((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(8462,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8461, 8460])).
% 2.02/2.24 tff(8463,plain,
% 2.02/2.24 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8462, 333, 563, 2737, 525])).
% 2.02/2.24 tff(8464,plain,
% 2.02/2.24 (b(s(s(elem!1)), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1260, 44, 8463, 1257])).
% 2.02/2.24 tff(8465,plain,
% 2.02/2.24 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4064, 333, 563, 2737, 525])).
% 2.02/2.24 tff(8466,plain,
% 2.02/2.24 (b(elem!1, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2522, 8465, 1221])).
% 2.02/2.24 tff(8467,plain,
% 2.02/2.24 (~b(s(elem!1), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[6380, 144, 451, 8466, 8464])).
% 2.02/2.24 tff(8468,plain,
% 2.02/2.24 (r(s(elem!1), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2860, 44, 8467, 8456])).
% 2.02/2.24 tff(8469,plain,
% 2.02/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4728, 144, 8466, 133, 8464])).
% 2.02/2.24 tff(8470,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2758, 8469, 2725])).
% 2.02/2.24 tff(8471,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4736, 333, 2737, 8470, 8468, 525])).
% 2.02/2.24 tff(8472,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8473,plain,
% 2.02/2.24 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8472, 8455, 2857, 2704, 525, 451, 4575, 2462, 563])).
% 2.02/2.24 tff(8474,plain,
% 2.02/2.24 (b(s(s(elem!1)), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1283, 8473, 2507])).
% 2.02/2.24 tff(8475,plain,
% 2.02/2.24 (~b(s(s(elem!1)), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[5572, 8474, 585, 8453])).
% 2.02/2.24 tff(8476,plain,
% 2.02/2.24 (r(s(s(elem!1)), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[5509, 8475])).
% 2.02/2.24 tff(8477,plain,
% 2.02/2.24 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[6898, 333, 670, 321, 8476])).
% 2.02/2.24 tff(8478,plain,
% 2.02/2.24 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8477, 4024])).
% 2.02/2.24 tff(8479,plain,
% 2.02/2.24 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[5047, 8475, 408, 670])).
% 2.02/2.24 tff(8480,plain,
% 2.02/2.24 (b(s(s(elem!1)), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1260, 44, 8479, 4575])).
% 2.02/2.24 tff(8481,plain,
% 2.02/2.24 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[6709, 144, 8455, 132, 8480])).
% 2.02/2.24 tff(8482,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[8481, 6702])).
% 2.02/2.24 tff(8483,plain,
% 2.02/2.24 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1137, 8482])).
% 2.02/2.24 tff(8484,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8483, 8478])).
% 2.02/2.24 tff(8485,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(8486,plain,
% 2.02/2.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[8485, 8449, 670, 2692, 57, 585, 525, 451, 563, 114])).
% 2.02/2.24 tff(8487,plain,
% 2.02/2.24 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[302, 8486])).
% 2.02/2.24 tff(8488,plain,
% 2.02/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1668, 144, 8451, 585, 8487])).
% 2.02/2.24 tff(8489,plain,
% 2.02/2.24 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[542, 8488, 2698])).
% 2.02/2.24 tff(8490,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8491,plain,
% 2.02/2.24 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(8492,plain,
% 2.02/2.24 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[8491])).
% 2.02/2.24 tff(8493,plain,
% 2.02/2.24 (((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[8492, 8490])).
% 2.02/2.24 tff(8494,plain,
% 2.02/2.24 ((~![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(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(8495,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8494, 8493])).
% 2.02/2.25 tff(8496,plain,
% 2.02/2.25 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8495, 333, 563, 525, 8489])).
% 2.02/2.25 tff(8497,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[130, 8496, 114])).
% 2.02/2.25 tff(8498,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8472, 8497, 2857, 2704, 525, 451, 4575, 2462, 563])).
% 2.02/2.25 tff(8499,plain,
% 2.02/2.25 (b(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1283, 8498, 2507])).
% 2.02/2.25 tff(8500,plain,
% 2.02/2.25 (~b(s(s(elem!1)), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[5572, 8499, 585, 8451])).
% 2.02/2.25 tff(8501,plain,
% 2.02/2.25 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[5047, 8500, 8449, 670])).
% 2.02/2.25 tff(8502,plain,
% 2.02/2.25 (b(s(s(elem!1)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1260, 44, 8501, 4575])).
% 2.02/2.25 tff(8503,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6709, 144, 8497, 2692, 8502])).
% 2.02/2.25 tff(8504,plain,
% 2.02/2.25 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8503, 6702])).
% 2.02/2.25 tff(8505,plain,
% 2.02/2.25 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1137, 8504])).
% 2.02/2.25 tff(8506,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8505, 2767])).
% 2.02/2.25 tff(8507,plain,
% 2.02/2.25 (((~![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(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8508,plain,
% 2.02/2.25 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8509,plain,
% 2.02/2.25 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8508])).
% 2.02/2.25 tff(8510,plain,
% 2.02/2.25 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[8509, 8507])).
% 2.02/2.25 tff(8511,plain,
% 2.02/2.25 ((~![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(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(8512,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 2.02/2.25 tff(8513,plain,
% 2.02/2.25 (~r(s(elem!1), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8512, 333, 525, 8489, 8506])).
% 2.02/2.25 tff(8514,plain,
% 2.02/2.25 (r(s(s(elem!1)), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[5509, 8500])).
% 2.02/2.25 tff(8515,plain,
% 2.02/2.25 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6719, 333, 670, 8449, 8514])).
% 2.02/2.25 tff(8516,plain,
% 2.02/2.25 (b(elem!1, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2522, 8515, 2462])).
% 2.02/2.25 tff(8517,plain,
% 2.02/2.25 (~b(s(elem!1), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6380, 144, 451, 8516, 8502])).
% 2.02/2.25 tff(8518,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2860, 44, 8517, 2857, 8513])).
% 2.02/2.25 tff(8519,plain,((~r(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~b(z, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = z) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8520,plain,
% 2.02/2.25 (~r(elem!1, s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8519, 5779, 8434, 57, 670, 8363, 114, 1368, 1237, 123, 259])).
% 2.02/2.25 tff(8521,plain,
% 2.02/2.25 (b(elem!1, s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[560, 8520, 2483])).
% 2.02/2.25 tff(8522,plain,
% 2.02/2.25 (~b(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[949, 624, 585, 547])).
% 2.02/2.25 tff(8523,plain,
% 2.02/2.25 (r(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[507, 8522])).
% 2.02/2.25 tff(8524,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8082, 8437, 8523, 670, 114, 123, 57, 451])).
% 2.02/2.25 tff(8525,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8526,plain,
% 2.02/2.25 (~b(elem!1, z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8525, 57, 114, 123, 670, 5779, 259, 8363, 8521])).
% 2.02/2.25 tff(8527,plain,
% 2.02/2.25 (r(elem!1, z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[653, 8526, 1368])).
% 2.02/2.25 tff(8528,plain,
% 2.02/2.25 (r(s(z), z) <=> r(elem!1, z)),
% 2.02/2.25 inference(monotonicity,[status(thm)],[57])).
% 2.02/2.25 tff(8529,plain,
% 2.02/2.25 (r(elem!1, z) <=> r(s(z), z)),
% 2.02/2.25 inference(symmetry,[status(thm)],[8528])).
% 2.02/2.25 tff(8530,plain,
% 2.02/2.25 (r(s(z), z)),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[408, 8529])).
% 2.02/2.25 tff(8531,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8153, 144, 286, 259, 2498])).
% 2.02/2.25 tff(8532,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7819, 44, 8531, 8104])).
% 2.02/2.25 tff(8533,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8243, 285, 57, 132, 525, 4683, 670, 408, 286, 451, 547, 133])).
% 2.02/2.25 tff(8534,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7819, 44, 8531, 8533, 8104])).
% 2.02/2.25 tff(8535,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8536,plain,
% 2.02/2.25 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8535, 285, 259, 57, 132, 525, 670, 408, 451, 547, 286])).
% 2.02/2.25 tff(8537,plain,
% 2.02/2.25 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[130, 8536, 114])).
% 2.02/2.25 tff(8538,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8251, 333, 8537, 525, 8532])).
% 2.02/2.25 tff(8539,plain,
% 2.02/2.25 (b(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1283, 8538, 2507])).
% 2.02/2.25 tff(8540,plain,
% 2.02/2.25 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8541,plain,
% 2.02/2.25 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8542,plain,
% 2.02/2.25 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8541])).
% 2.02/2.25 tff(8543,plain,
% 2.02/2.25 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[8542, 8540])).
% 2.02/2.25 tff(8544,plain,
% 2.02/2.25 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(8545,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8544, 8543])).
% 2.02/2.25 tff(8546,plain,
% 2.02/2.25 (~r(s(elem!1), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8545, 333, 8537, 525, 8532])).
% 2.02/2.25 tff(8547,plain,
% 2.02/2.25 (b(s(elem!1), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2860, 44, 2857, 8546])).
% 2.02/2.25 tff(8548,plain,
% 2.02/2.25 (~b(z, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6781, 8547, 585, 8539])).
% 2.02/2.25 tff(8549,plain,
% 2.02/2.25 (~b(z, s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2828, 8548, 57])).
% 2.02/2.25 tff(8550,plain,
% 2.02/2.25 (b(s(s(s(z))), s(elem!1))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8539, 8166])).
% 2.02/2.25 tff(8551,plain,
% 2.02/2.25 (~b(s(s(s(z))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4819, 8550, 451, 547])).
% 2.02/2.25 tff(8552,plain,
% 2.02/2.25 (r(s(s(s(z))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[704, 8551, 4798])).
% 2.02/2.25 tff(8553,plain,
% 2.02/2.25 (~r(z, s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2136, 8552, 670, 408])).
% 2.02/2.25 tff(8554,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[619, 8553, 8549])).
% 2.02/2.25 tff(8555,plain,((~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~(s(z) = elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8556,plain,
% 2.02/2.25 (~b(s(s(s(z))), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8555, 286, 408, 57, 585, 451, 547, 525, 670, 259, 114, 2692])).
% 2.02/2.25 tff(8557,plain,
% 2.02/2.25 (r(s(s(s(z))), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[396, 8556])).
% 2.02/2.25 tff(8558,plain,
% 2.02/2.25 (~r(s(s(s(z))), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6555, 1699, 354, 323])).
% 2.02/2.25 tff(8559,plain,
% 2.02/2.25 (~b(s(s(s(z))), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1716, 1699, 488, 960, 509, 354, 323])).
% 2.02/2.25 tff(8560,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2794, 8559, 8558])).
% 2.02/2.25 tff(8561,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8562,plain,
% 2.02/2.25 (~r(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8561, 8557, 2508, 3924, 354, 8530])).
% 2.02/2.25 tff(8563,plain,
% 2.02/2.25 (b(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[507, 8562])).
% 2.02/2.25 tff(8564,plain,
% 2.02/2.25 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1668, 144, 8563, 585, 286])).
% 2.02/2.25 tff(8565,plain,
% 2.02/2.25 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[542, 8564, 2698])).
% 2.02/2.25 tff(8566,plain,
% 2.02/2.25 (r(s(s(elem!1)), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6447, 8557, 57])).
% 2.02/2.25 tff(8567,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8568,plain,
% 2.02/2.25 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8569,plain,
% 2.02/2.25 (((~![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(elem!1)), 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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8568])).
% 2.02/2.25 tff(8570,plain,
% 2.02/2.25 (((~![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(elem!1)), 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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 2.02/2.25 inference(transitivity,[status(thm)],[8569, 8567])).
% 2.02/2.25 tff(8571,plain,
% 2.02/2.25 ((~![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(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(8572,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8571, 8570])).
% 2.02/2.25 tff(8573,plain,
% 2.02/2.25 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8572, 333, 670, 408, 8566])).
% 2.02/2.25 tff(8574,plain,
% 2.02/2.25 (b(s(s(elem!1)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1260, 44, 8573, 4575])).
% 2.02/2.25 tff(8575,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4989, 144, 547, 451, 8574])).
% 2.02/2.25 tff(8576,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1283, 8575, 2507])).
% 2.02/2.25 tff(8577,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4030, 333, 8576, 525, 8565])).
% 2.02/2.25 tff(8578,plain,
% 2.02/2.25 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8577, 4024])).
% 2.02/2.25 tff(8579,plain,
% 2.02/2.25 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6719, 333, 670, 408, 8566])).
% 2.02/2.25 tff(8580,plain,
% 2.02/2.25 (b(elem!1, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2522, 8579, 2462])).
% 2.02/2.25 tff(8581,plain,
% 2.02/2.25 (b(s(z), s(s(s(z))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8580, 5338])).
% 2.02/2.25 tff(8582,plain,
% 2.02/2.25 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3662, 8576, 525, 8565])).
% 2.02/2.25 tff(8583,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2758, 8582, 2704])).
% 2.02/2.25 tff(8584,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8583, 4019])).
% 2.02/2.25 tff(8585,plain,
% 2.02/2.25 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2262, 8584, 123, 8581])).
% 2.02/2.25 tff(8586,plain,
% 2.02/2.25 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1137, 8585])).
% 2.02/2.25 tff(8587,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8586, 8578])).
% 2.02/2.25 tff(8588,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(z, s(elem!1))) | (~r(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8589,plain,
% 2.02/2.25 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8588, 57, 123, 8434, 8521, 5779, 670, 8527, 8363, 354, 259, 114])).
% 2.02/2.25 tff(8590,plain,
% 2.02/2.25 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[302, 8589])).
% 2.02/2.25 tff(8591,plain,
% 2.02/2.25 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8373, 8590, 670, 1368, 8363, 114, 123, 57, 5779])).
% 2.02/2.25 tff(8592,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[130, 8591, 114])).
% 2.02/2.25 tff(8593,plain,
% 2.02/2.25 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[555, 8592, 5779, 8521])).
% 2.02/2.25 tff(8594,plain,
% 2.02/2.25 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[542, 8593, 2698])).
% 2.02/2.25 tff(8595,plain,
% 2.02/2.25 (~r(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8082, 8590, 670, 114, 123, 57, 5779])).
% 2.02/2.25 tff(8596,plain,
% 2.02/2.25 (b(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[507, 8595])).
% 2.02/2.25 tff(8597,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7807, 4575, 8521, 5779, 8527, 670, 8363, 8596])).
% 2.02/2.25 tff(8598,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(elem!1))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1283, 8597, 2507])).
% 2.02/2.25 tff(8599,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4030, 333, 8598, 8434, 8594])).
% 2.02/2.25 tff(8600,plain,
% 2.02/2.25 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7819, 44, 8599, 8104])).
% 2.02/2.25 tff(8601,plain,
% 2.02/2.25 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3662, 8598, 8434, 8594])).
% 2.02/2.25 tff(8602,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2758, 8601, 2704])).
% 2.02/2.25 tff(8603,plain,
% 2.02/2.25 (r(s(s(s(z))), s(elem!1))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8598, 4010])).
% 2.02/2.25 tff(8604,plain,
% 2.02/2.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8602, 4019])).
% 2.02/2.25 tff(8605,plain,
% 2.02/2.25 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8599, 4024])).
% 2.02/2.25 tff(8606,plain,
% 2.02/2.25 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1137, 8605])).
% 2.02/2.25 tff(8607,plain,
% 2.02/2.25 (~b(s(z), s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2262, 8606, 123, 8604])).
% 2.02/2.25 tff(8608,plain,
% 2.02/2.25 (r(s(z), s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[172, 8607])).
% 2.02/2.25 tff(8609,plain,
% 2.02/2.25 (~r(z, s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3011, 8608, 354, 8603])).
% 2.02/2.25 tff(8610,plain,
% 2.02/2.25 (b(z, s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[619, 8609])).
% 2.02/2.25 tff(8611,plain,
% 2.02/2.25 (b(z, s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2828, 8610, 57])).
% 2.02/2.25 tff(8612,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8613,plain,
% 2.02/2.25 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(8614,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8613])).
% 2.02/2.25 tff(8615,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[8614, 8612])).
% 2.02/2.25 tff(8616,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(8617,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[8616, 8615])).
% 2.02/2.25 tff(8618,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8617, 144, 8611, 8602, 8600, 259])).
% 2.02/2.25 tff(8619,plain,((~(s(z) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = z) | (s(z) = s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8620,plain,
% 2.02/2.25 (~r(z, s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8619, 8096, 8064, 123, 114, 670, 1368, 1237, 259])).
% 2.02/2.25 tff(8621,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[372, 8620, 8103])).
% 2.02/2.25 tff(8622,plain,((~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (elem!1 = z) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | b(s(z), elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8623,plain,
% 2.02/2.25 (~r(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8622, 408, 114, 7265, 77, 1229, 259, 606, 350, 123, 707, 433])).
% 2.02/2.25 tff(8624,plain,
% 2.02/2.25 (b(s(elem!1), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[507, 8623])).
% 2.02/2.25 tff(8625,plain,
% 2.02/2.25 (~b(s(elem!1), s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1802, 8624, 8057, 8055])).
% 2.02/2.25 tff(8626,plain,
% 2.02/2.25 (~r(s(elem!1), s(s(s(z))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7237, 333, 435, 408, 707])).
% 2.02/2.25 tff(8627,plain,
% 2.02/2.25 (s(elem!1) = s(s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[965, 8626, 901])).
% 2.02/2.25 tff(8628,plain,
% 2.02/2.25 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[982])).
% 2.02/2.25 tff(8629,plain,
% 2.02/2.25 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 2.02/2.25 inference(symmetry,[status(thm)],[8628])).
% 2.02/2.25 tff(8630,plain,
% 2.02/2.25 ((~b(s(s(s(z))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8629])).
% 2.02/2.25 tff(8631,plain,
% 2.02/2.25 (~b(s(elem!1), s(z))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[2789, 8630])).
% 2.02/2.25 tff(8632,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[488, 8631])).
% 2.02/2.25 tff(8633,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(elem!1), s(z))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8634,plain,
% 2.02/2.25 (~b(s(elem!1), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8633, 8627, 2789])).
% 2.02/2.25 tff(8635,plain,
% 2.02/2.25 (r(s(elem!1), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[486, 8634, 1])).
% 2.02/2.25 tff(8636,plain,
% 2.02/2.25 (~r(s(z), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[443, 8635, 435, 408])).
% 2.02/2.25 tff(8637,plain,
% 2.02/2.25 (s(z) = elem!1),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[406, 8636, 350])).
% 2.02/2.25 tff(8638,plain,
% 2.02/2.25 (elem!1 = s(z)),
% 2.02/2.25 inference(symmetry,[status(thm)],[8637])).
% 2.02/2.25 tff(8639,plain,
% 2.02/2.25 (s(elem!1) = s(s(z))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8638])).
% 2.02/2.25 tff(8640,plain,
% 2.02/2.25 (s(s(z)) = s(elem!1)),
% 2.02/2.25 inference(symmetry,[status(thm)],[8639])).
% 2.02/2.25 tff(8641,plain,
% 2.02/2.25 (s(s(s(z))) = s(elem!1)),
% 2.02/2.25 inference(symmetry,[status(thm)],[8627])).
% 2.02/2.25 tff(8642,plain,
% 2.02/2.25 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[8641])).
% 2.02/2.25 tff(8643,plain,
% 2.02/2.25 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.02/2.25 inference(symmetry,[status(thm)],[8642])).
% 2.02/2.25 tff(8644,plain,
% 2.02/2.25 (elem!1 = s(s(s(z)))),
% 2.02/2.25 inference(transitivity,[status(thm)],[1193, 8643, 86, 8640, 8627])).
% 2.02/2.25 tff(8645,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1524, 8644])).
% 2.02/2.25 tff(8646,plain,((~r(s(elem!1), elem!1)) | (elem!1 = s(s(s(z)))) | b(s(z), elem!1) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8647,plain,
% 2.02/2.25 (~r(s(elem!1), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8646, 408, 350, 1524, 1, 2789, 8625, 707])).
% 2.02/2.25 tff(8648,plain,
% 2.02/2.25 (~b(z, s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8102, 57, 606])).
% 2.02/2.25 tff(8649,plain,
% 2.02/2.25 (~r(z, s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[8619, 57, 1727, 123, 114, 670, 1368, 1237, 259])).
% 2.02/2.25 tff(8650,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[372, 8649, 8648])).
% 2.02/2.25 tff(8651,plain,((~(s(z) = elem!1)) | r(s(elem!1), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (elem!1 = z) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(8652,plain,
% 2.02/2.26 (~(s(z) = elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8651, 8647, 123, 114, 7265, 77, 1229, 259, 606])).
% 2.02/2.26 tff(8653,plain,
% 2.02/2.26 (r(s(z), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[406, 8652, 350])).
% 2.02/2.26 tff(8654,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8655,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8656,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8655, 8654])).
% 2.02/2.26 tff(8657,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8656, 333, 8653, 408, 7586, 707])).
% 2.02/2.26 tff(8658,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(8659,plain,
% 2.02/2.26 (~r(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8658, 8053, 707, 123, 8049, 8045, 606, 8047, 1, 2789, 907])).
% 2.02/2.26 tff(8660,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(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(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8661,plain,
% 2.02/2.26 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8662,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8661])).
% 2.02/2.26 tff(8663,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8662, 8660])).
% 2.02/2.26 tff(8664,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8665,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8664, 8663])).
% 2.02/2.26 tff(8666,plain,
% 2.02/2.26 (~r(z, s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8665, 333, 409, 354, 3193])).
% 2.02/2.26 tff(8667,plain,
% 2.02/2.26 (b(z, s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[619, 8666])).
% 2.02/2.26 tff(8668,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8669,plain,
% 2.02/2.26 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8670,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8669])).
% 2.02/2.26 tff(8671,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8670, 8668])).
% 2.02/2.26 tff(8672,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8673,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8672, 8671])).
% 2.02/2.26 tff(8674,plain,
% 2.02/2.26 (~r(s(s(s(z))), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8673, 333, 409, 354, 3193])).
% 2.02/2.26 tff(8675,plain,
% 2.02/2.26 (b(s(s(s(z))), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[396, 8674])).
% 2.02/2.26 tff(8676,plain,
% 2.02/2.26 (r(z, elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[658, 74, 606])).
% 2.02/2.26 tff(8677,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 2.02/2.26 tff(8678,plain,
% 2.02/2.26 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8677])).
% 2.02/2.26 tff(8679,plain,
% 2.02/2.26 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.02/2.26 inference(symmetry,[status(thm)],[8678])).
% 2.02/2.26 tff(8680,plain,
% 2.02/2.26 (z = inj_0(s(z))),
% 2.02/2.26 inference(symmetry,[status(thm)],[16])).
% 2.02/2.26 tff(8681,plain,
% 2.02/2.26 (z = elem!1),
% 2.02/2.26 inference(transitivity,[status(thm)],[8680, 8679, 850])).
% 2.02/2.26 tff(8682,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[74, 8681])).
% 2.02/2.26 tff(8683,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(8684,plain,
% 2.02/2.26 (~(s(elem!1) = s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8683, 74])).
% 2.02/2.26 tff(8685,plain,
% 2.02/2.26 (r(s(elem!1), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[486, 8684, 1576])).
% 2.02/2.26 tff(8686,plain,
% 2.02/2.26 (~r(s(elem!1), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1589, 8685, 354, 409])).
% 2.02/2.26 tff(8687,plain,
% 2.02/2.26 (b(s(elem!1), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[507, 8686])).
% 2.02/2.26 tff(8688,plain,
% 2.02/2.26 (b(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1380, 730, 1378])).
% 2.02/2.26 tff(8689,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8690,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8691,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8690, 8689])).
% 2.02/2.26 tff(8692,plain,
% 2.02/2.26 (~r(z, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8691, 333, 409, 354, 8685])).
% 2.02/2.26 tff(8693,plain,
% 2.02/2.26 ((z = s(elem!1)) | b(z, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[581, 44, 8692])).
% 2.02/2.26 tff(8694,plain,
% 2.02/2.26 (b(z, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8693, 1635])).
% 2.02/2.26 tff(8695,plain,
% 2.02/2.26 (~b(elem!1, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[949, 8694, 8688, 8687])).
% 2.02/2.26 tff(8696,plain,
% 2.02/2.26 (r(elem!1, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[560, 8695, 902])).
% 2.02/2.26 tff(8697,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~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(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8698,plain,
% 2.02/2.26 (((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8699,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8698])).
% 2.02/2.26 tff(8700,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8699, 8697])).
% 2.02/2.26 tff(8701,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8702,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8701, 8700])).
% 2.02/2.26 tff(8703,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8702, 333, 8696, 8676, 409, 354])).
% 2.02/2.26 tff(8704,plain,((z = elem!1) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (elem!1 = s(elem!1)) | b(s(elem!1), s(z)) | r(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(8705,plain,
% 2.02/2.26 (b(s(elem!1), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8704, 354, 902, 74, 409, 606, 1378])).
% 2.02/2.26 tff(8706,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8707,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8708,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8707, 8706])).
% 2.02/2.26 tff(8709,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8708, 333, 563, 409, 3193, 707])).
% 2.02/2.26 tff(8710,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(8711,plain,
% 2.02/2.26 (~r(elem!1, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8710, 409, 3193, 707])).
% 2.02/2.26 tff(8712,plain,
% 2.02/2.26 (b(elem!1, s(elem!1))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[560, 8711, 902])).
% 2.02/2.26 tff(8713,plain,
% 2.02/2.26 (~b(elem!1, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[667, 144, 8712, 8705, 123, 132])).
% 2.02/2.26 tff(8714,plain,
% 2.02/2.26 (r(elem!1, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[720, 8713, 714])).
% 2.02/2.26 tff(8715,plain,
% 2.02/2.26 (r(z, elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[658, 606, 74])).
% 2.02/2.26 tff(8716,plain,
% 2.02/2.26 (~r(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[727, 8714, 8715, 354])).
% 2.02/2.26 tff(8717,plain,
% 2.02/2.26 (b(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[348, 8716])).
% 2.02/2.26 tff(8718,plain,
% 2.02/2.26 (~b(s(z), s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[2156, 8717, 8667, 8675])).
% 2.02/2.26 tff(8719,plain,
% 2.02/2.26 (r(s(z), s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[172, 8718])).
% 2.02/2.26 tff(8720,plain,
% 2.02/2.26 (~r(elem!1, s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1533, 8719, 707, 8714])).
% 2.02/2.26 tff(8721,plain,
% 2.02/2.26 (b(elem!1, s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1538, 8720, 1524])).
% 2.02/2.26 tff(8722,plain,
% 2.02/2.26 (b(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1380, 1378, 730])).
% 2.02/2.26 tff(8723,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8724,plain,
% 2.02/2.26 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8725,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8724])).
% 2.02/2.26 tff(8726,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8725, 8723])).
% 2.02/2.26 tff(8727,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8728,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8727, 8726])).
% 2.02/2.26 tff(8729,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8728, 144, 8722, 8721, 8675, 8667])).
% 2.02/2.26 tff(8730,plain,((~r(z, s(z))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(elem!1)) | (z = elem!1) | b(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(8731,plain,
% 2.02/2.26 (~r(z, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8730, 713, 707, 1524, 123, 132, 7670, 3193, 902, 74, 606, 1378])).
% 2.02/2.26 tff(8732,plain,
% 2.02/2.26 (b(z, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[372, 8731])).
% 2.02/2.26 tff(8733,plain,
% 2.02/2.26 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[757, 8732, 123, 259])).
% 2.02/2.26 tff(8734,plain,
% 2.02/2.26 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[319, 8733])).
% 2.02/2.26 tff(8735,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8736,plain,
% 2.02/2.26 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8737,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8736])).
% 2.02/2.26 tff(8738,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8737, 8735])).
% 2.02/2.26 tff(8739,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8740,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8739, 8738])).
% 2.02/2.26 tff(8741,plain,
% 2.02/2.26 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8740, 333, 7670, 3193, 8734])).
% 2.02/2.26 tff(8742,plain,
% 2.02/2.26 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1137, 8741])).
% 2.02/2.26 tff(8743,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8744,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8745,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8744, 8743])).
% 2.02/2.27 tff(8746,plain,
% 2.02/2.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8745, 333, 7670, 3193, 8734])).
% 2.02/2.27 tff(8747,plain,
% 2.02/2.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[249, 8746])).
% 2.02/2.27 tff(8748,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8749,plain,
% 2.02/2.27 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8750,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8749])).
% 2.02/2.27 tff(8751,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8750, 8748])).
% 2.02/2.27 tff(8752,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8753,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8752, 8751])).
% 2.02/2.27 tff(8754,plain,
% 2.02/2.27 (~b(elem!1, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8753, 144, 8722, 8732, 123, 132])).
% 2.02/2.27 tff(8755,plain,
% 2.02/2.27 (r(elem!1, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[720, 8754, 713])).
% 2.02/2.27 tff(8756,plain,
% 2.02/2.27 (~b(s(z), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2262, 8742, 123, 8747])).
% 2.02/2.27 tff(8757,plain,
% 2.02/2.27 (r(s(z), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[172, 8756])).
% 2.02/2.27 tff(8758,plain,
% 2.02/2.27 (~r(elem!1, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1533, 8757, 707, 8755])).
% 2.02/2.27 tff(8759,plain,
% 2.02/2.27 (b(elem!1, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1538, 8758, 1524])).
% 2.02/2.27 tff(8760,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8761,plain,
% 2.02/2.27 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8762,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8761])).
% 2.02/2.27 tff(8763,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8762, 8760])).
% 2.02/2.27 tff(8764,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8765,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8764, 8763])).
% 2.02/2.27 tff(8766,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8765, 144, 8759, 132, 8747, 8742])).
% 2.02/2.27 tff(8767,plain,((s(z) = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (z = elem!1) | b(z, elem!1) | r(elem!1, z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8768,plain,
% 2.02/2.27 (s(z) = elem!1),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8767, 8052, 8047, 707, 123, 7586, 8045, 902, 71, 606, 8659, 8053])).
% 2.02/2.27 tff(8769,plain,
% 2.02/2.27 (s(s(z)) = s(elem!1)),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8768])).
% 2.02/2.27 tff(8770,plain,
% 2.02/2.27 (s(s(s(z))) = s(s(elem!1))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8769])).
% 2.02/2.27 tff(8771,plain,
% 2.02/2.27 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8770])).
% 2.02/2.27 tff(8772,plain,
% 2.02/2.27 (r(s(s(elem!1)), elem!1)),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[707, 8771])).
% 2.02/2.27 tff(8773,plain,
% 2.02/2.27 (r(s(elem!1), elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8651, 8768, 123, 8049, 7265, 77, 1229, 8045, 606])).
% 2.02/2.27 tff(8774,plain,
% 2.02/2.27 (b(elem!1, z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1380, 8659, 77])).
% 2.02/2.27 tff(8775,plain,
% 2.02/2.27 (b(s(z), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[3965, 8768, 8774])).
% 2.02/2.27 tff(8776,plain,
% 2.02/2.27 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7741, 8775, 123, 8045])).
% 2.02/2.27 tff(8777,plain,
% 2.02/2.27 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[302, 8776])).
% 2.02/2.27 tff(8778,plain,
% 2.02/2.27 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8769])).
% 2.02/2.27 tff(8779,plain,
% 2.02/2.27 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8778, 174])).
% 2.02/2.27 tff(8780,plain,
% 2.02/2.27 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8779])).
% 2.02/2.27 tff(8781,plain,
% 2.02/2.27 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[1446, 8780])).
% 2.02/2.27 tff(8782,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[5467, 8075, 8072, 132, 537, 3626])).
% 2.02/2.27 tff(8783,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8784,plain,
% 2.02/2.27 (~r(s(elem!1), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8783, 8052, 8781, 7265, 8777, 902, 8773])).
% 2.02/2.27 tff(8785,plain,
% 2.02/2.27 (b(s(elem!1), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[507, 8784])).
% 2.02/2.27 tff(8786,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8112, 144, 547, 624, 491, 132, 259])).
% 2.02/2.27 tff(8787,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8788,plain,
% 2.02/2.27 (~b(elem!1, s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8787, 8785, 8774, 8052, 8045])).
% 2.02/2.27 tff(8789,plain,
% 2.02/2.27 (r(elem!1, s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[560, 8788, 902])).
% 2.02/2.27 tff(8790,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8791,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8792,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8791, 8790])).
% 2.02/2.27 tff(8793,plain,
% 2.02/2.27 (~r(s(s(elem!1)), s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8792, 333, 8789, 8773, 8772])).
% 2.02/2.27 tff(8794,plain,
% 2.02/2.27 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8770])).
% 2.02/2.27 tff(8795,plain,
% 2.02/2.27 (~r(s(s(s(z))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[6585, 8789, 707, 7265])).
% 2.02/2.27 tff(8796,plain,
% 2.02/2.27 (b(s(s(s(z))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[396, 8795])).
% 2.02/2.27 tff(8797,plain,
% 2.02/2.27 (b(s(s(elem!1)), z)),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8796, 8794])).
% 2.02/2.27 tff(8798,plain,
% 2.02/2.27 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8768])).
% 2.02/2.27 tff(8799,plain,
% 2.02/2.27 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.02/2.27 inference(symmetry,[status(thm)],[8798])).
% 2.02/2.27 tff(8800,plain,
% 2.02/2.27 (r(s(elem!1), s(z))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8773, 8799])).
% 2.02/2.27 tff(8801,plain,
% 2.02/2.27 (~r(z, s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2393, 8789, 7265, 8800])).
% 2.02/2.27 tff(8802,plain,
% 2.02/2.27 (b(z, s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[583, 8801])).
% 2.02/2.27 tff(8803,plain,
% 2.02/2.27 (~b(s(s(elem!1)), s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2733, 144, 8785, 8802, 8797])).
% 2.02/2.27 tff(8804,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1283, 8803, 8793, 2727])).
% 2.02/2.27 tff(8805,plain,(b(z, elem!1) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8806,plain,
% 2.02/2.27 (b(z, elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8805, 902, 707, 123, 1, 2789, 3, 54, 2303])).
% 2.02/2.27 tff(8807,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[267, 454, 452, 259, 251])).
% 2.02/2.27 tff(8808,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8809,plain,
% 2.02/2.27 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8808, 8806, 8045, 3, 54])).
% 2.02/2.27 tff(8810,plain,
% 2.02/2.27 (~r(z, elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2305, 8809, 2303])).
% 2.02/2.27 tff(8811,plain,
% 2.02/2.27 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 2.02/2.27 inference(commutativity,[status(thm)],[])).
% 2.02/2.27 tff(8812,plain,
% 2.02/2.27 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 2.02/2.27 inference(symmetry,[status(thm)],[8811])).
% 2.02/2.27 tff(8813,plain,
% 2.02/2.27 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8812])).
% 2.02/2.27 tff(8814,plain,
% 2.02/2.27 (~(s(s(s(z))) = s(s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[217, 8813])).
% 2.02/2.27 tff(8815,plain,
% 2.02/2.27 (~b(s(z), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1602, 4833, 7071, 251])).
% 2.02/2.27 tff(8816,plain,
% 2.02/2.27 (r(s(z), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[348, 8815])).
% 2.02/2.27 tff(8817,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8818,plain,
% 2.02/2.27 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8819,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8818])).
% 2.02/2.27 tff(8820,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8819, 8817])).
% 2.02/2.27 tff(8821,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8822,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8821, 8820])).
% 2.02/2.27 tff(8823,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8822, 333, 323, 722, 3193, 707])).
% 2.02/2.27 tff(8824,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8825,plain,
% 2.02/2.27 (~r(elem!1, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8824, 8816, 3193, 707])).
% 2.02/2.27 tff(8826,plain,
% 2.02/2.27 (b(elem!1, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[720, 8825, 5609])).
% 2.02/2.27 tff(8827,plain,
% 2.02/2.27 (~b(z, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7079, 8826, 251, 7071])).
% 2.02/2.27 tff(8828,plain,
% 2.02/2.27 (r(z, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[372, 8827])).
% 2.02/2.27 tff(8829,plain,
% 2.02/2.27 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8825, 5647])).
% 2.02/2.27 tff(8830,plain,
% 2.02/2.27 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[319, 8829])).
% 2.02/2.27 tff(8831,plain,
% 2.02/2.27 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7374, 8830, 251, 81, 4833, 123, 8828])).
% 2.02/2.27 tff(8832,plain,
% 2.02/2.27 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1451, 8831])).
% 2.02/2.27 tff(8833,plain,
% 2.02/2.27 (r(s(s(z)), elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7183, 8832, 81])).
% 2.02/2.27 tff(8834,plain,
% 2.02/2.27 (~r(s(s(s(z))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[6555, 8828, 3193, 8816])).
% 2.02/2.27 tff(8835,plain,
% 2.02/2.27 (b(s(s(s(z))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[396, 8834])).
% 2.02/2.27 tff(8836,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(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(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8837,plain,
% 2.02/2.27 (((~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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8838,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8837])).
% 2.02/2.27 tff(8839,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8838, 8836])).
% 2.02/2.27 tff(8840,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8841,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8840, 8839])).
% 2.02/2.27 tff(8842,plain,
% 2.02/2.27 (~r(z, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8841, 333, 8828, 8816, 3193])).
% 2.02/2.27 tff(8843,plain,
% 2.02/2.27 (b(z, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[619, 8842])).
% 2.02/2.27 tff(8844,plain,
% 2.02/2.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[294, 8843, 4887, 8835])).
% 2.02/2.27 tff(8845,plain,
% 2.02/2.27 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[249, 8844])).
% 2.02/2.27 tff(8846,plain,
% 2.02/2.27 (r(elem!1, s(s(s(z))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8845, 1685])).
% 2.02/2.27 tff(8847,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, 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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8848,plain,
% 2.02/2.27 (((~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8849,plain,
% 2.02/2.27 (((~![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(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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8848])).
% 2.02/2.27 tff(8850,plain,
% 2.02/2.27 (((~![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(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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8849, 8847])).
% 2.02/2.27 tff(8851,plain,
% 2.02/2.27 ((~![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(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8852,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8851, 8850])).
% 2.02/2.27 tff(8853,plain,
% 2.02/2.27 (~r(s(s(s(z))), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8852, 333, 8846, 707, 8833])).
% 2.02/2.27 tff(8854,plain,
% 2.02/2.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8855,plain,
% 2.02/2.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8856,plain,
% 2.02/2.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8855, 8854])).
% 2.02/2.27 tff(8857,plain,
% 2.02/2.27 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8856, 44, 8853])).
% 2.02/2.27 tff(8858,plain,
% 2.02/2.27 (b(s(s(s(z))), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8857, 8814])).
% 2.02/2.27 tff(8859,plain,
% 2.02/2.27 (~(s(elem!1) = s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7434, 5585])).
% 2.02/2.27 tff(8860,plain,
% 2.02/2.27 (~b(s(elem!1), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7468, 8846, 251, 4833, 1682, 8833, 707, 907, 8835, 8859])).
% 2.02/2.27 tff(8861,plain,
% 2.02/2.27 (r(s(elem!1), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[507, 8860])).
% 2.02/2.27 tff(8862,plain,
% 2.02/2.27 (b(s(elem!1), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1653, 8861, 1575, 5584, 8828, 1, 902])).
% 2.02/2.27 tff(8863,plain,
% 2.02/2.27 (~b(s(elem!1), elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[7338, 144, 7071, 8862, 8826])).
% 2.02/2.27 tff(8864,plain,
% 2.02/2.27 (r(s(elem!1), elem!1)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[448, 8863, 907])).
% 2.02/2.27 tff(8865,plain,
% 2.02/2.27 (~r(s(z), s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1235, 8861, 8828, 8816])).
% 2.02/2.27 tff(8866,plain,
% 2.02/2.27 (b(s(z), s(elem!1))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1244, 8865, 1229])).
% 2.02/2.27 tff(8867,plain,
% 2.02/2.28 (~b(elem!1, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4409, 8866, 8826, 8862])).
% 2.02/2.28 tff(8868,plain,
% 2.02/2.28 (r(elem!1, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[560, 8867, 902])).
% 2.02/2.28 tff(8869,plain,
% 2.02/2.28 (~r(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[957, 333, 8868, 8864, 707])).
% 2.02/2.28 tff(8870,plain,
% 2.02/2.28 (b(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[965, 8869, 1682])).
% 2.02/2.28 tff(8871,plain,
% 2.02/2.28 (~r(s(s(z)), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7445, 333, 8846, 707, 8833])).
% 2.02/2.28 tff(8872,plain,
% 2.02/2.28 (b(s(s(z)), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1473, 44, 8871, 217])).
% 2.02/2.28 tff(8873,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8874,plain,
% 2.02/2.28 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8875,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8874])).
% 2.02/2.28 tff(8876,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8875, 8873])).
% 2.02/2.28 tff(8877,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8878,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8877, 8876])).
% 2.02/2.28 tff(8879,plain,
% 2.02/2.28 (~b(s(elem!1), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8878, 144, 8872, 8870, 8858])).
% 2.02/2.28 tff(8880,plain,
% 2.02/2.28 (~r(s(elem!1), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7483, 333, 8868, 8864, 8833])).
% 2.02/2.28 tff(8881,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7466, 44, 8859, 8880, 8879])).
% 2.02/2.28 tff(8882,plain,(r(elem!1, z) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | r(z, elem!1) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8883,plain,
% 2.02/2.28 (r(elem!1, z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8882, 902, 707, 8810, 1, 8806, 8809, 123, 7586])).
% 2.02/2.28 tff(8884,plain,
% 2.02/2.28 (b(s(z), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2235, 8809, 123])).
% 2.02/2.28 tff(8885,plain,
% 2.02/2.28 (~r(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8824, 722, 3193, 707])).
% 2.02/2.28 tff(8886,plain,
% 2.02/2.28 (b(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[348, 8885])).
% 2.02/2.28 tff(8887,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8888,plain,
% 2.02/2.28 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8889,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8888])).
% 2.02/2.28 tff(8890,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8889, 8887])).
% 2.02/2.28 tff(8891,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8892,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8891, 8890])).
% 2.02/2.28 tff(8893,plain,
% 2.02/2.28 ((~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8892, 144, 251, 491, 134])).
% 2.02/2.28 tff(8894,plain,
% 2.02/2.28 (~b(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8893, 8886])).
% 2.02/2.28 tff(8895,plain,
% 2.02/2.28 (r(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1244, 8894, 1237])).
% 2.02/2.28 tff(8896,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(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(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8897,plain,
% 2.02/2.28 (((~r(s(z), s(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(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8898,plain,
% 2.02/2.28 (((~![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(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(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8897])).
% 2.02/2.28 tff(8899,plain,
% 2.02/2.28 (((~![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(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(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8898, 8896])).
% 2.02/2.28 tff(8900,plain,
% 2.02/2.28 ((~![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(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8901,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8900, 8899])).
% 2.02/2.28 tff(8902,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8901, 333, 722, 8895, 3193, 707])).
% 2.02/2.28 tff(8903,plain,((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8904,plain,
% 2.02/2.28 (~r(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8903, 491, 707, 1229, 251, 3193, 134])).
% 2.02/2.28 tff(8905,plain,
% 2.02/2.28 (b(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[720, 8904, 5609])).
% 2.02/2.28 tff(8906,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7079, 8905, 251, 134])).
% 2.02/2.28 tff(8907,plain,
% 2.02/2.28 (r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8906])).
% 2.02/2.28 tff(8908,plain,
% 2.02/2.28 (~r(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2122, 8907, 707, 408])).
% 2.02/2.28 tff(8909,plain,
% 2.02/2.28 (b(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[396, 8908])).
% 2.02/2.28 tff(8910,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8911,plain,
% 2.02/2.28 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8912,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8911])).
% 2.02/2.28 tff(8913,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8912, 8910])).
% 2.02/2.28 tff(8914,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8915,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8914, 8913])).
% 2.02/2.28 tff(8916,plain,
% 2.02/2.28 (~b(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8915, 144, 451, 251, 491, 8909])).
% 2.02/2.28 tff(8917,plain,
% 2.02/2.28 (r(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[965, 8916, 1682])).
% 2.02/2.28 tff(8918,plain,
% 2.02/2.28 (~b(s(elem!1), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4344, 144, 451, 134, 8905])).
% 2.02/2.28 tff(8919,plain,
% 2.02/2.28 (r(s(elem!1), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[486, 8918, 1])).
% 2.02/2.28 tff(8920,plain,
% 2.02/2.28 (~r(s(z), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7308, 8907, 251, 433, 408, 707, 1, 134, 8905, 81])).
% 2.02/2.28 tff(8921,plain,
% 2.02/2.28 (b(s(z), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[172, 8920])).
% 2.02/2.28 tff(8922,plain,
% 2.02/2.28 (~b(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2144, 144, 251, 134, 8909, 8921])).
% 2.02/2.28 tff(8923,plain,
% 2.02/2.28 (r(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[348, 8922])).
% 2.02/2.28 tff(8924,plain,
% 2.02/2.28 (((~![X0: $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(s(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(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8925,plain,
% 2.02/2.28 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8926,plain,
% 2.02/2.28 (((~![X0: $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(s(elem!1), s(z))) | (~r(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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8925])).
% 2.02/2.28 tff(8927,plain,
% 2.02/2.28 (((~![X0: $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(s(elem!1), s(z))) | (~r(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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8926, 8924])).
% 2.02/2.28 tff(8928,plain,
% 2.02/2.28 ((~![X0: $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(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8929,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8928, 8927])).
% 2.02/2.28 tff(8930,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8929, 333, 8923, 8919, 3193, 8917])).
% 2.02/2.28 tff(8931,plain,((~b(s(elem!1), z)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8932,plain,
% 2.02/2.28 (~b(s(elem!1), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8931, 4338, 1, 3193, 134, 251, 907, 408, 707, 81])).
% 2.02/2.28 tff(8933,plain,
% 2.02/2.28 (r(s(elem!1), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[507, 8932])).
% 2.02/2.28 tff(8934,plain,
% 2.02/2.28 (~r(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8824, 323, 3193, 707])).
% 2.02/2.28 tff(8935,plain,
% 2.02/2.28 (b(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[720, 8934, 714])).
% 2.02/2.28 tff(8936,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7079, 8935, 251, 134])).
% 2.02/2.28 tff(8937,plain,
% 2.02/2.28 (r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8936])).
% 2.02/2.28 tff(8938,plain,
% 2.02/2.28 (~r(elem!1, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1620, 8937, 408, 509])).
% 2.02/2.28 tff(8939,plain,
% 2.02/2.28 (~b(elem!1, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7524, 8937, 134, 1, 451, 323, 251, 8935])).
% 2.02/2.28 tff(8940,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[560, 8939, 8938, 902])).
% 2.02/2.28 tff(8941,plain,((~r(s(z), z)) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8942,plain,
% 2.02/2.28 (~r(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8941, 4338, 134, 1, 902, 251, 408, 8933, 5609, 3193, 707])).
% 2.02/2.28 tff(8943,plain,
% 2.02/2.28 (b(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[348, 8942])).
% 2.02/2.28 tff(8944,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7079, 305, 251, 134])).
% 2.02/2.28 tff(8945,plain,
% 2.02/2.28 (r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8944])).
% 2.02/2.28 tff(8946,plain,
% 2.02/2.28 (~r(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2122, 8945, 707, 408])).
% 2.02/2.28 tff(8947,plain,
% 2.02/2.28 (b(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[396, 8946])).
% 2.02/2.28 tff(8948,plain,
% 2.02/2.28 (~r(s(z), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7308, 8945, 251, 433, 408, 707, 1, 134, 305, 81])).
% 2.02/2.28 tff(8949,plain,
% 2.02/2.28 (b(s(z), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[172, 8948])).
% 2.02/2.28 tff(8950,plain,
% 2.02/2.28 (~r(z, s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2146, 8945, 134, 71, 707, 408, 489])).
% 2.02/2.28 tff(8951,plain,
% 2.02/2.28 (b(z, s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[619, 8950])).
% 2.02/2.28 tff(8952,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2156, 8951, 8949, 489, 8947])).
% 2.02/2.28 tff(8953,plain,((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (s(elem!1) = s(z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8954,plain,
% 2.02/2.28 (~b(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8953, 8943, 134, 707, 408, 251, 907, 1, 81])).
% 2.02/2.28 tff(8955,plain,
% 2.02/2.28 (r(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[720, 8954, 5609])).
% 2.02/2.28 tff(8956,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8901, 333, 722, 1230, 3193, 707])).
% 2.02/2.28 tff(8957,plain,((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8958,plain,
% 2.02/2.28 (~r(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8957, 8955, 3193, 707])).
% 2.02/2.28 tff(8959,plain,
% 2.02/2.28 (b(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1244, 8958, 1229])).
% 2.02/2.28 tff(8960,plain,
% 2.02/2.28 (r(elem!1, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1732, 8959, 1727, 902, 134])).
% 2.02/2.28 tff(8961,plain,
% 2.02/2.28 (~r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1620, 8960, 408, 8933])).
% 2.02/2.28 tff(8962,plain,
% 2.02/2.28 (~r(z, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[571, 563, 408, 509])).
% 2.02/2.28 tff(8963,plain,
% 2.02/2.28 (b(z, s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[583, 8962])).
% 2.02/2.28 tff(8964,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8965,plain,
% 2.02/2.28 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8966,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8965])).
% 2.02/2.28 tff(8967,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8966, 8964])).
% 2.02/2.28 tff(8968,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8969,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8968, 8967])).
% 2.02/2.28 tff(8970,plain,
% 2.02/2.28 (~b(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8969, 144, 451, 8963, 134, 489])).
% 2.02/2.28 tff(8971,plain,
% 2.02/2.28 (r(s(z), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1244, 8970, 1229])).
% 2.02/2.28 tff(8972,plain,
% 2.02/2.28 (~r(s(elem!1), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7799, 8971, 722, 563])).
% 2.02/2.28 tff(8973,plain,
% 2.02/2.28 (b(s(elem!1), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[486, 8972, 1])).
% 2.02/2.28 tff(8974,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1919, 144, 251, 8963, 134, 490, 8973])).
% 2.02/2.28 tff(8975,plain,((~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8976,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8975, 8960, 134, 251, 1, 8955, 4338, 8943, 408, 8933])).
% 2.02/2.28 tff(8977,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8976, 8961])).
% 2.02/2.28 tff(8978,plain,(r(s(elem!1), elem!1) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8979,plain,
% 2.02/2.28 (r(s(elem!1), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8978, 8884, 8806, 1, 8883, 902, 7586, 707, 8809])).
% 2.02/2.28 tff(8980,plain,
% 2.02/2.28 (~r(s(s(s(z))), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3797, 333, 8979, 8883, 707])).
% 2.02/2.28 tff(8981,plain,
% 2.02/2.28 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8809])).
% 2.02/2.28 tff(8982,plain,
% 2.02/2.28 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8981])).
% 2.02/2.28 tff(8983,plain,
% 2.02/2.28 (~(s(s(z)) = elem!1)),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[1446, 8982])).
% 2.02/2.28 tff(8984,plain,
% 2.02/2.28 (~(s(elem!1) = s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1508, 8983])).
% 2.02/2.28 tff(8985,plain,
% 2.02/2.28 (~(s(s(s(z))) = s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1934, 8984])).
% 2.02/2.28 tff(8986,plain,
% 2.02/2.28 (b(s(s(s(z))), s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1951, 44, 8985, 8980])).
% 2.02/2.28 tff(8987,plain,
% 2.02/2.28 (~r(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7237, 333, 8979, 8883, 707])).
% 2.02/2.28 tff(8988,plain,
% 2.02/2.28 (b(s(elem!1), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[965, 8987, 8984])).
% 2.02/2.28 tff(8989,plain,
% 2.02/2.28 (b(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[720, 715, 5609])).
% 2.02/2.28 tff(8990,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7079, 8989, 251, 134])).
% 2.02/2.28 tff(8991,plain,
% 2.02/2.28 (r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8990])).
% 2.02/2.28 tff(8992,plain,
% 2.02/2.29 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[715, 5647])).
% 2.02/2.29 tff(8993,plain,
% 2.02/2.29 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[319, 8992])).
% 2.02/2.29 tff(8994,plain,
% 2.02/2.29 (~r(s(elem!1), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[7282, 8993, 902, 134, 408, 8991, 81, 1])).
% 2.02/2.29 tff(8995,plain,
% 2.02/2.29 (~r(s(s(s(z))), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2122, 8991, 707, 408])).
% 2.02/2.29 tff(8996,plain,
% 2.02/2.29 (b(s(s(s(z))), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[396, 8995])).
% 2.02/2.29 tff(8997,plain,
% 2.02/2.29 (r(s(elem!1), elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8978, 134, 251, 1, 408, 902, 3193, 707, 81])).
% 2.02/2.29 tff(8998,plain,
% 2.02/2.29 (~r(s(elem!1), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[7237, 333, 8997, 408, 707])).
% 2.02/2.29 tff(8999,plain,
% 2.02/2.29 (b(s(elem!1), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[965, 8998, 1682])).
% 2.02/2.29 tff(9000,plain,
% 2.02/2.29 (~b(s(z), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8953, 8989, 134, 707, 408, 251, 907, 1, 81])).
% 2.02/2.29 tff(9001,plain,
% 2.02/2.29 (r(s(z), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[348, 9000])).
% 2.02/2.29 tff(9002,plain,
% 2.02/2.29 (~r(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8841, 333, 8991, 9001, 3193])).
% 2.02/2.29 tff(9003,plain,
% 2.02/2.29 (b(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[619, 9002])).
% 2.02/2.29 tff(9004,plain,
% 2.02/2.29 (~b(s(elem!1), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1802, 9003, 8999, 8996])).
% 2.02/2.29 tff(9005,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[507, 9004, 8994])).
% 2.02/2.29 tff(9006,plain,(r(elem!1, s(z)) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(9007,plain,
% 2.02/2.29 (r(elem!1, s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9006, 902, 8884, 8883, 8809, 1, 7586, 707, 8806])).
% 2.02/2.29 tff(9008,plain,
% 2.02/2.29 (~b(s(elem!1), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8903, 9007, 707, 1229, 8806, 7586, 8884])).
% 2.02/2.29 tff(9009,plain,
% 2.02/2.29 (r(s(elem!1), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[507, 9008])).
% 2.02/2.29 tff(9010,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9011,plain,
% 2.02/2.29 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9012,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9011])).
% 2.02/2.29 tff(9013,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[9012, 9010])).
% 2.02/2.29 tff(9014,plain,
% 2.02/2.29 ((~![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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9015,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9014, 9013])).
% 2.02/2.29 tff(9016,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9015, 333, 435, 408, 509, 562])).
% 2.02/2.29 tff(9017,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(9018,plain,
% 2.02/2.29 (~r(z, s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9017, 9009, 8883, 8979])).
% 2.02/2.29 tff(9019,plain,
% 2.02/2.29 (b(z, s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[583, 9018])).
% 2.02/2.29 tff(9020,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9021,plain,
% 2.02/2.29 (((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9022,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9021])).
% 2.02/2.29 tff(9023,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[9022, 9020])).
% 2.02/2.29 tff(9024,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9025,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9024, 9023])).
% 2.02/2.29 tff(9026,plain,
% 2.02/2.29 (~b(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9025, 144, 9019, 8988, 8986])).
% 2.02/2.29 tff(9027,plain,
% 2.02/2.29 (r(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[619, 9026])).
% 2.02/2.29 tff(9028,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9029,plain,
% 2.02/2.29 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9030,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9029])).
% 2.02/2.29 tff(9031,plain,
% 2.02/2.29 (((~![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(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[9030, 9028])).
% 2.02/2.29 tff(9032,plain,
% 2.02/2.29 ((~![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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9033,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9032, 9031])).
% 2.02/2.29 tff(9034,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9033, 333, 8979, 8883, 9009, 9027])).
% 2.02/2.29 tff(9035,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(9036,plain,
% 2.02/2.29 (elem!1 = s(elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9035, 2303, 1, 123, 8048, 3, 54, 2789])).
% 2.02/2.29 tff(9037,plain,
% 2.02/2.29 (s(elem!1) = elem!1),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1569, 9036])).
% 2.02/2.29 tff(9038,plain,
% 2.02/2.29 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1565, 9037, 8047])).
% 2.02/2.29 tff(9039,plain,
% 2.02/2.29 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[116, 9038])).
% 2.02/2.29 tff(9040,plain,
% 2.02/2.29 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[121, 9039, 3])).
% 2.02/2.29 tff(9041,plain,
% 2.02/2.29 (s(s(s(elem!1))) = elem!1),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2482, 9036])).
% 2.02/2.29 tff(9042,plain,
% 2.02/2.29 (~(s(z) = elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2468, 9041])).
% 2.02/2.29 tff(9043,plain,
% 2.02/2.29 (~(elem!1 = s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[712, 9042])).
% 2.02/2.29 tff(9044,plain,
% 2.02/2.29 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9036])).
% 2.02/2.29 tff(9045,plain,
% 2.02/2.29 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[130, 9038, 54])).
% 2.02/2.29 tff(9046,plain,
% 2.02/2.29 (~b(s(z), elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[152, 9040, 123, 9045])).
% 2.02/2.29 tff(9047,plain,
% 2.02/2.29 (r(s(z), elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[406, 9046, 9042])).
% 2.02/2.29 tff(9048,plain,
% 2.02/2.29 (r(s(z), s(elem!1))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9047, 9044])).
% 2.02/2.29 tff(9049,plain,
% 2.02/2.29 (~r(elem!1, s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8957, 9048, 7586, 8048])).
% 2.02/2.29 tff(9050,plain,
% 2.02/2.29 (b(elem!1, s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[720, 9049, 9043])).
% 2.02/2.29 tff(9051,plain,
% 2.02/2.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[313, 9050, 123, 9040])).
% 2.02/2.29 tff(9052,plain,
% 2.02/2.29 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[319, 9051])).
% 2.02/2.29 tff(9053,plain,
% 2.02/2.29 (((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9054,plain,
% 2.02/2.29 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9055,plain,
% 2.02/2.29 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9054])).
% 2.02/2.29 tff(9056,plain,
% 2.02/2.29 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[9055, 9053])).
% 2.02/2.29 tff(9057,plain,
% 2.02/2.29 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9058,plain,
% 2.02/2.29 ((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9057, 9056])).
% 2.02/2.29 tff(9059,plain,
% 2.02/2.29 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9058, 333, 9048, 7586, 9052])).
% 2.02/2.29 tff(9060,plain,
% 2.02/2.29 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1137, 9059])).
% 2.02/2.29 tff(9061,plain,
% 2.02/2.29 (((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9062,plain,
% 2.02/2.29 ((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9063,plain,
% 2.02/2.29 ((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9062, 9061])).
% 2.02/2.29 tff(9064,plain,
% 2.02/2.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9063, 333, 9048, 7586, 9052])).
% 2.02/2.29 tff(9065,plain,
% 2.02/2.29 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[249, 9064])).
% 2.02/2.29 tff(9066,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9067,plain,
% 2.02/2.29 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9068,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9067])).
% 2.02/2.29 tff(9069,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[9068, 9066])).
% 2.02/2.29 tff(9070,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(9071,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9070, 9069])).
% 2.02/2.29 tff(9072,plain,
% 2.02/2.29 (~b(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[9071, 144, 9065, 9060, 8045])).
% 2.02/2.29 tff(9073,plain,
% 2.02/2.29 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9036])).
% 2.02/2.29 tff(9074,plain,
% 2.02/2.29 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9073])).
% 2.02/2.29 tff(9075,plain,
% 2.02/2.29 (~b(s(s(s(z))), s(elem!1))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[55, 9074])).
% 2.02/2.29 tff(9076,plain,
% 2.02/2.29 (s(elem!1) = s(s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2584, 9041, 9036])).
% 2.02/2.29 tff(9077,plain,
% 2.02/2.29 (~(s(elem!1) = s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[990, 9076, 1])).
% 2.02/2.29 tff(9078,plain,
% 2.02/2.29 (~b(z, elem!1)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8808, 9038, 8045, 3, 54])).
% 2.02/2.29 tff(9079,plain,
% 2.02/2.29 (~b(z, s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2974, 9078, 9036])).
% 2.02/2.29 tff(9080,plain,
% 2.02/2.29 (r(z, s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[583, 9079])).
% 2.02/2.29 tff(9081,plain,
% 2.02/2.29 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9036])).
% 2.02/2.29 tff(9082,plain,
% 2.02/2.29 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[9040, 9081])).
% 2.02/2.29 tff(9083,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9084,plain,
% 2.02/2.29 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(9085,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[9084])).
% 2.02/2.29 tff(9086,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.30 inference(transitivity,[status(thm)],[9085, 9083])).
% 2.02/2.30 tff(9087,plain,
% 2.02/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.02/2.30 inference(quant_inst,[status(thm)],[])).
% 2.02/2.30 tff(9088,plain,
% 2.02/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.02/2.30 inference(modus_ponens,[status(thm)],[9087, 9086])).
% 2.02/2.30 tff(9089,plain,
% 2.02/2.30 (~b(s(elem!1), s(s(s(z))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[9088, 144, 9065, 9060, 9082])).
% 2.02/2.30 tff(9090,plain,
% 2.02/2.30 (~r(z, s(s(s(z))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[4807, 9089, 9080, 9077, 9075])).
% 2.02/2.30 tff(9091,plain,
% 2.02/2.30 ($false),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[619, 9090, 9072])).
% 2.02/2.30 tff(9092,plain,(r(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.30 tff(9093,plain,
% 2.02/2.30 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[9092, 55, 50, 3, 54, 1, 7582])).
% 2.02/2.30 tff(9094,plain,
% 2.02/2.30 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[2235, 350, 50])).
% 2.02/2.30 tff(9095,plain,
% 2.02/2.30 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[130, 9094, 54])).
% 2.02/2.30 tff(9096,plain,
% 2.02/2.30 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[116, 9094])).
% 2.02/2.30 tff(9097,plain,
% 2.02/2.30 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[121, 9096, 3])).
% 2.02/2.30 tff(9098,plain,
% 2.02/2.30 (~(s(z) = elem!1)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[3965, 3921, 624])).
% 2.02/2.30 tff(9099,plain,
% 2.02/2.30 (~(elem!1 = s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[712, 9098])).
% 2.02/2.30 tff(9100,plain,
% 2.02/2.30 (b(elem!1, s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[720, 9099, 715])).
% 2.02/2.30 tff(9101,plain,
% 2.02/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[313, 9100, 123, 132])).
% 2.02/2.30 tff(9102,plain,
% 2.02/2.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[319, 9101])).
% 2.02/2.30 tff(9103,plain,
% 2.02/2.30 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[632, 9100, 132, 123, 624])).
% 2.02/2.30 tff(9104,plain,
% 2.02/2.30 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[302, 9103])).
% 2.02/2.30 tff(9105,plain,
% 2.02/2.30 ($false),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[341, 9104, 9102, 51, 3922])).
% 2.02/2.30 tff(9106,plain,(b(s(z), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.30 tff(9107,plain,
% 2.02/2.30 (b(s(z), z)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[9106, 715, 132, 50, 4833, 51])).
% 2.02/2.30 tff(9108,plain,
% 2.02/2.30 (r(z, s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[372, 8648])).
% 2.02/2.30 tff(9109,plain,
% 2.02/2.30 (r(s(z), elem!1)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[7011, 9108, 1, 51, 606, 4])).
% 2.02/2.30 tff(9110,plain,
% 2.02/2.30 (b(s(elem!1), s(z))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[8704, 9108, 902, 71, 9109, 606, 1378])).
% 2.02/2.30 tff(9111,plain,
% 2.02/2.30 (b(s(elem!1), elem!1)),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[3619, 9110, 57])).
% 2.02/2.30 tff(9112,plain,
% 2.02/2.30 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[4745, 9111, 51, 7265, 132, 1229, 57, 489, 606, 77])).
% 2.02/2.30 tff(9113,plain,
% 2.02/2.30 ($false),
% 2.02/2.30 inference(unit_resolution,[status(thm)],[3934, 9112, 9111, 50, 57, 133])).
% 2.12/2.30 tff(9114,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | b(z, elem!1) | (elem!1 = s(elem!1)) | r(elem!1, z) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9115,plain,
% 2.12/2.30 (~(s(z) = elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9114, 902, 51, 132, 9107, 606, 133, 1378, 1, 4])).
% 2.12/2.30 tff(9116,plain,
% 2.12/2.30 (~(elem!1 = s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[712, 9115])).
% 2.12/2.30 tff(9117,plain,
% 2.12/2.30 (b(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[720, 9116, 715])).
% 2.12/2.30 tff(9118,plain,
% 2.12/2.30 (r(s(z), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[406, 9115, 350])).
% 2.12/2.30 tff(9119,plain,
% 2.12/2.30 (~r(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8730, 9116, 707, 1524, 50, 902, 132, 3193, 9118, 71, 606, 1378])).
% 2.12/2.30 tff(9120,plain,
% 2.12/2.30 (b(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[372, 9119])).
% 2.12/2.30 tff(9121,plain,
% 2.12/2.30 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(9122,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9121])).
% 2.12/2.30 tff(9123,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[9122, 382])).
% 2.12/2.30 tff(9124,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, z)) | (~b(elem!1, s(z))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(9125,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9124, 9123])).
% 2.12/2.30 tff(9126,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9125, 144, 4833, 9120, 9107, 9117])).
% 2.12/2.30 tff(9127,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | b(z, elem!1) | r(elem!1, z) | r(elem!1, s(z)) | b(s(z), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9128,plain,
% 2.12/2.30 (elem!1 = s(elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9127, 715, 1524, 132, 3193, 606, 1378, 707, 350, 51, 133, 1, 4])).
% 2.12/2.30 tff(9129,plain,
% 2.12/2.30 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9128])).
% 2.12/2.30 tff(9130,plain,
% 2.12/2.30 (s(s(s(elem!1))) = elem!1),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2482, 9128])).
% 2.12/2.30 tff(9131,plain,
% 2.12/2.30 (~(s(z) = elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2468, 9130])).
% 2.12/2.30 tff(9132,plain,
% 2.12/2.30 (~(elem!1 = s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[712, 9131])).
% 2.12/2.30 tff(9133,plain,
% 2.12/2.30 (b(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[720, 9132, 715])).
% 2.12/2.30 tff(9134,plain,
% 2.12/2.30 (b(s(elem!1), s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9133, 9129])).
% 2.12/2.30 tff(9135,plain,
% 2.12/2.30 (r(s(z), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[406, 9131, 350])).
% 2.12/2.30 tff(9136,plain,
% 2.12/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[313, 9133, 50, 132])).
% 2.12/2.30 tff(9137,plain,
% 2.12/2.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[319, 9136])).
% 2.12/2.30 tff(9138,plain,
% 2.12/2.30 (~r(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[429, 9137, 51, 9135])).
% 2.12/2.30 tff(9139,plain,
% 2.12/2.30 (b(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[372, 9138])).
% 2.12/2.30 tff(9140,plain,
% 2.12/2.30 (b(elem!1, z) <=> b(s(elem!1), z)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9128])).
% 2.12/2.30 tff(9141,plain,
% 2.12/2.30 (b(s(elem!1), z)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4833, 9140])).
% 2.12/2.30 tff(9142,plain,
% 2.12/2.30 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(9143,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9142])).
% 2.12/2.30 tff(9144,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[9143, 492])).
% 2.12/2.30 tff(9145,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(9146,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9145, 9144])).
% 2.12/2.30 tff(9147,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9146, 144, 9141, 9139, 9107, 9134])).
% 2.12/2.30 tff(9148,plain,(r(elem!1, s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(z, elem!1) | r(elem!1, z) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9149,plain,
% 2.12/2.30 (r(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9148, 1378, 132, 350, 1524, 3193, 606, 51, 707, 133, 1, 4])).
% 2.12/2.30 tff(9150,plain,
% 2.12/2.30 (~r(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2227, 9149, 707, 7265])).
% 2.12/2.30 tff(9151,plain,
% 2.12/2.30 (b(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[619, 9150])).
% 2.12/2.30 tff(9152,plain,
% 2.12/2.30 (~r(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1783, 333, 7265, 9149, 707])).
% 2.12/2.30 tff(9153,plain,
% 2.12/2.30 (b(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[396, 9152])).
% 2.12/2.30 tff(9154,plain,
% 2.12/2.30 (~r(s(z), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8824, 9149, 3193, 707])).
% 2.12/2.30 tff(9155,plain,
% 2.12/2.30 (b(s(z), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[348, 9154])).
% 2.12/2.30 tff(9156,plain,
% 2.12/2.30 (~b(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2156, 9153, 9155, 9151])).
% 2.12/2.30 tff(9157,plain,
% 2.12/2.30 (r(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[172, 9156])).
% 2.12/2.30 tff(9158,plain,
% 2.12/2.30 (~r(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1533, 9157, 707, 9149])).
% 2.12/2.30 tff(9159,plain,
% 2.12/2.30 (b(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1538, 9158, 1524])).
% 2.12/2.30 tff(9160,plain,
% 2.12/2.30 (((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(9161,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9160])).
% 2.12/2.30 tff(9162,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[9161, 8723])).
% 2.12/2.30 tff(9163,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(9164,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9163, 9162])).
% 2.12/2.30 tff(9165,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9164, 144, 4833, 9159, 9153, 9151])).
% 2.12/2.30 tff(9166,plain,(r(elem!1, z) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | b(z, elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9167,plain,
% 2.12/2.30 (r(elem!1, z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9166, 9097, 707, 3193, 1524, 350, 606, 51, 9095, 1, 4])).
% 2.12/2.30 tff(9168,plain,
% 2.12/2.30 (~r(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2136, 9167, 707, 7265])).
% 2.12/2.30 tff(9169,plain,
% 2.12/2.30 (b(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[619, 9168])).
% 2.12/2.30 tff(9170,plain,
% 2.12/2.30 (~r(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2079, 9167, 707, 7265])).
% 2.12/2.30 tff(9171,plain,
% 2.12/2.30 (b(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[396, 9170])).
% 2.12/2.30 tff(9172,plain,
% 2.12/2.30 (s(z) = elem!1),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[406, 2310, 350])).
% 2.12/2.30 tff(9173,plain,
% 2.12/2.30 (~r(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7011, 2310, 1, 51, 606, 4])).
% 2.12/2.30 tff(9174,plain,
% 2.12/2.30 (b(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[372, 9173])).
% 2.12/2.30 tff(9175,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8102, 9174, 9172, 606])).
% 2.12/2.30 tff(9176,plain,(r(s(z), elem!1) | b(z, elem!1) | b(s(z), elem!1) | (s(elem!1) = s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9177,plain,
% 2.12/2.30 (r(s(z), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9176, 350, 606, 1, 51, 4])).
% 2.12/2.30 tff(9178,plain,
% 2.12/2.30 (~r(s(z), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[417, 9177, 51, 9167])).
% 2.12/2.30 tff(9179,plain,
% 2.12/2.30 (b(s(z), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[348, 9178])).
% 2.12/2.30 tff(9180,plain,
% 2.12/2.30 (~b(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2156, 9179, 9171, 9169])).
% 2.12/2.30 tff(9181,plain,
% 2.12/2.30 (r(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[172, 9180])).
% 2.12/2.30 tff(9182,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2035, 333, 9177, 9167, 707, 9181])).
% 2.12/2.30 tff(9183,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9184,plain,
% 2.12/2.30 (b(s(z), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9183, 606, 9093, 8042, 1, 4, 8044, 8043, 3, 54])).
% 2.12/2.30 tff(9185,plain,
% 2.12/2.30 (~r(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8824, 3922, 3193, 707])).
% 2.12/2.30 tff(9186,plain,
% 2.12/2.30 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9106, 9185, 4833, 50, 3921, 51])).
% 2.12/2.30 tff(9187,plain,
% 2.12/2.30 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[121, 9186, 3])).
% 2.12/2.30 tff(9188,plain,
% 2.12/2.30 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[116, 9187])).
% 2.12/2.30 tff(9189,plain,
% 2.12/2.30 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[81])).
% 2.12/2.30 tff(9190,plain,
% 2.12/2.30 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[9189])).
% 2.12/2.30 tff(9191,plain,
% 2.12/2.30 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9190])).
% 2.12/2.30 tff(9192,plain,
% 2.12/2.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[55, 9191])).
% 2.12/2.30 tff(9193,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2254, 9192])).
% 2.12/2.30 tff(9194,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9195,plain,
% 2.12/2.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9194, 9188, 55])).
% 2.12/2.30 tff(9196,plain,
% 2.12/2.30 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1137, 9195])).
% 2.12/2.30 tff(9197,plain,
% 2.12/2.30 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2558, 9188, 1378])).
% 2.12/2.30 tff(9198,plain,
% 2.12/2.30 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[302, 9197])).
% 2.12/2.30 tff(9199,plain,
% 2.12/2.30 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9187])).
% 2.12/2.30 tff(9200,plain,
% 2.12/2.30 (~(s(z) = elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3965, 3921, 4833])).
% 2.12/2.30 tff(9201,plain,
% 2.12/2.30 (~(elem!1 = s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[712, 9200])).
% 2.12/2.30 tff(9202,plain,
% 2.12/2.30 (b(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[720, 9201, 9185])).
% 2.12/2.30 tff(9203,plain,
% 2.12/2.30 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9202, 9199])).
% 2.12/2.30 tff(9204,plain,
% 2.12/2.30 (~(s(elem!1) = elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1565, 9188, 1524])).
% 2.12/2.30 tff(9205,plain,
% 2.12/2.30 (~(elem!1 = s(elem!1))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1569, 9204])).
% 2.12/2.30 tff(9206,plain,
% 2.12/2.30 (~r(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7271, 9188, 1, 606, 4])).
% 2.12/2.30 tff(9207,plain,
% 2.12/2.30 (b(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[372, 9206])).
% 2.12/2.30 tff(9208,plain,
% 2.12/2.30 (~r(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7112, 9205, 7265, 3922, 9202, 1, 9207])).
% 2.12/2.30 tff(9209,plain,
% 2.12/2.30 (b(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[507, 9208])).
% 2.12/2.30 tff(9210,plain,
% 2.12/2.30 (~r(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7127, 9209, 9207, 9202, 9205, 77, 707, 7265])).
% 2.12/2.30 tff(9211,plain,
% 2.12/2.30 (b(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[396, 9210])).
% 2.12/2.30 tff(9212,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(9213,plain,
% 2.12/2.30 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(9214,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9213])).
% 2.12/2.30 tff(9215,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.30 inference(transitivity,[status(thm)],[9214, 9212])).
% 2.12/2.30 tff(9216,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(9217,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9216, 9215])).
% 2.12/2.30 tff(9218,plain,
% 2.12/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9217, 144, 9207, 9211, 9203, 9198])).
% 2.12/2.30 tff(9219,plain,
% 2.12/2.30 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[249, 9218])).
% 2.12/2.30 tff(9220,plain,
% 2.12/2.30 (~r(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1480, 333, 9219, 9196, 51])).
% 2.12/2.30 tff(9221,plain,
% 2.12/2.30 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9187])).
% 2.12/2.30 tff(9222,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.12/2.30 inference(symmetry,[status(thm)],[9221])).
% 2.12/2.30 tff(9223,plain,
% 2.12/2.30 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9222])).
% 2.12/2.30 tff(9224,plain,
% 2.12/2.30 (~(s(s(z)) = elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1446, 9223])).
% 2.12/2.30 tff(9225,plain,
% 2.12/2.30 (~(s(elem!1) = s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1508, 9224])).
% 2.12/2.30 tff(9226,plain,
% 2.12/2.30 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9187])).
% 2.12/2.30 tff(9227,plain,
% 2.12/2.30 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[9226])).
% 2.12/2.30 tff(9228,plain,
% 2.12/2.30 (r(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9219, 9227])).
% 2.12/2.30 tff(9229,plain,
% 2.12/2.30 (~b(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7260, 9228, 707, 9205, 9207, 9209, 9202, 9225, 4833, 9211])).
% 2.12/2.30 tff(9230,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[619, 9229, 9220])).
% 2.12/2.30 tff(9231,plain,(b(s(z), z) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, z) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(z)))) | b(s(s(s(z))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(9232,plain,
% 2.12/2.30 (b(s(z), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[9231, 1378, 9093, 1, 8042, 606, 4, 8043, 55, 3, 8044])).
% 2.12/2.30 tff(9233,plain,
% 2.12/2.30 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2297, 9232, 9184, 4833, 50])).
% 2.12/2.30 tff(9234,plain,
% 2.12/2.30 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[130, 9233, 54])).
% 2.12/2.30 tff(9235,plain,
% 2.12/2.30 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(elem!1, s(z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[9234])).
% 2.12/2.30 tff(9236,plain,
% 2.12/2.30 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3332, 9232, 54, 9184, 50, 1378, 77])).
% 2.12/2.30 tff(9237,plain,
% 2.12/2.30 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[302, 9236])).
% 2.12/2.30 tff(9238,plain,
% 2.12/2.30 (~r(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7271, 9234, 1, 606, 4])).
% 2.12/2.30 tff(9239,plain,
% 2.12/2.30 (b(z, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[372, 9238])).
% 2.12/2.30 tff(9240,plain,
% 2.12/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7093, 9239, 9232, 9237])).
% 2.12/2.30 tff(9241,plain,
% 2.12/2.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[319, 9240])).
% 2.12/2.30 tff(9242,plain,
% 2.12/2.30 (r(elem!1, s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[9241, 9235])).
% 2.12/2.30 tff(9243,plain,
% 2.12/2.30 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3398, 9234])).
% 2.12/2.30 tff(9244,plain,
% 2.12/2.30 (~r(s(z), s(elem!1))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8957, 9242, 8044, 8042])).
% 2.12/2.30 tff(9245,plain,
% 2.12/2.30 (b(s(z), s(elem!1))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1244, 9244, 1229])).
% 2.12/2.30 tff(9246,plain,
% 2.12/2.30 (r(s(elem!1), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2569, 9245, 50, 1378, 9243, 9232])).
% 2.12/2.30 tff(9247,plain,
% 2.12/2.30 (~r(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1788, 333, 7265, 9242, 8042])).
% 2.12/2.30 tff(9248,plain,
% 2.12/2.30 (b(z, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[619, 9247])).
% 2.12/2.30 tff(9249,plain,
% 2.12/2.30 (~r(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1783, 333, 7265, 9242, 8042])).
% 2.12/2.30 tff(9250,plain,
% 2.12/2.30 (b(s(s(s(z))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[396, 9249])).
% 2.12/2.30 tff(9251,plain,
% 2.12/2.30 (~b(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2156, 9250, 9232, 9248])).
% 2.12/2.30 tff(9252,plain,
% 2.12/2.30 (r(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[172, 9251])).
% 2.12/2.30 tff(9253,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[7731, 9252, 9246, 7265, 1, 9239, 9232, 9242])).
% 2.12/2.30 tff(9254,plain,(r(elem!1, z) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(s(s(z))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9255,plain,
% 2.12/2.31 (r(elem!1, z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9254, 606, 1, 4, 54, 55, 3])).
% 2.12/2.31 tff(9256,plain,
% 2.12/2.31 (~r(s(s(z)), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7175, 8055, 707, 7265, 408])).
% 2.12/2.31 tff(9257,plain,
% 2.12/2.31 (~r(s(z), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[417, 323, 51, 408])).
% 2.12/2.31 tff(9258,plain,
% 2.12/2.31 (~r(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7011, 9257, 1, 51, 606, 4])).
% 2.12/2.31 tff(9259,plain,
% 2.12/2.31 (b(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[372, 9258])).
% 2.12/2.31 tff(9260,plain,
% 2.12/2.31 (~(s(z) = elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8102, 9259, 606])).
% 2.12/2.31 tff(9261,plain,
% 2.12/2.31 (~(elem!1 = s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[712, 9260])).
% 2.12/2.31 tff(9262,plain,
% 2.12/2.31 (b(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[720, 9261, 8934])).
% 2.12/2.31 tff(9263,plain,
% 2.12/2.31 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4423, 9262, 54, 51, 134, 50, 7265])).
% 2.12/2.31 tff(9264,plain,
% 2.12/2.31 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[116, 9263])).
% 2.12/2.31 tff(9265,plain,
% 2.12/2.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7183, 9264, 9256])).
% 2.12/2.31 tff(9266,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1451, 9265])).
% 2.12/2.31 tff(9267,plain,
% 2.12/2.31 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9263])).
% 2.12/2.31 tff(9268,plain,
% 2.12/2.31 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9262, 9267])).
% 2.12/2.31 tff(9269,plain,
% 2.12/2.31 (~b(s(s(z)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1425, 9268, 50, 9266])).
% 2.12/2.31 tff(9270,plain,
% 2.12/2.31 (r(s(s(z)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1429, 44, 9269, 1416])).
% 2.12/2.31 tff(9271,plain,
% 2.12/2.31 (((~![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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9272,plain,
% 2.12/2.31 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9273,plain,
% 2.12/2.31 (((~![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(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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9272])).
% 2.12/2.31 tff(9274,plain,
% 2.12/2.31 (((~![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(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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[9273, 9271])).
% 2.12/2.31 tff(9275,plain,
% 2.12/2.31 ((~![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(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(9276,plain,
% 2.12/2.31 ((~![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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9275, 9274])).
% 2.12/2.31 tff(9277,plain,
% 2.12/2.31 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9276, 333, 323, 3193, 9270])).
% 2.12/2.31 tff(9278,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1473, 44, 9277, 217])).
% 2.12/2.31 tff(9279,plain,
% 2.12/2.31 (~b(s(s(z)), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1490, 144, 8055, 8057, 9278])).
% 2.12/2.31 tff(9280,plain,
% 2.12/2.31 (r(s(s(z)), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1462, 44, 164, 9279])).
% 2.12/2.31 tff(9281,plain,
% 2.12/2.31 (((~![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(z)), s(z))) | (~r(z, s(s(s(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(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9282,plain,
% 2.12/2.31 (((~r(z, s(s(s(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(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9283,plain,
% 2.12/2.31 (((~![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(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(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9282])).
% 2.12/2.31 tff(9284,plain,
% 2.12/2.31 (((~![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(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(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.31 inference(transitivity,[status(thm)],[9283, 9281])).
% 2.12/2.31 tff(9285,plain,
% 2.12/2.31 ((~![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(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(9286,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9285, 9284])).
% 2.12/2.31 tff(9287,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9286, 333, 323, 51, 9280, 9270])).
% 2.12/2.31 tff(9288,plain,((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), elem!1)) | b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9289,plain,
% 2.12/2.31 (~r(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9288, 9184, 8044, 54, 9093, 606, 1, 4, 9255, 8042])).
% 2.12/2.31 tff(9290,plain,
% 2.12/2.31 (b(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[348, 9289])).
% 2.12/2.31 tff(9291,plain,
% 2.12/2.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2113, 9290, 3, 9184, 50, 9255])).
% 2.12/2.31 tff(9292,plain,
% 2.12/2.31 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[3282, 321, 670, 408])).
% 2.12/2.31 tff(9293,plain,
% 2.12/2.31 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[121, 9292, 453])).
% 2.12/2.31 tff(9294,plain,
% 2.12/2.31 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[152, 9293, 123, 134])).
% 2.12/2.31 tff(9295,plain,
% 2.12/2.31 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[130, 9294, 114])).
% 2.12/2.31 tff(9296,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2423, 333, 670, 408, 9295, 321])).
% 2.12/2.31 tff(9297,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9298,plain,
% 2.12/2.31 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9297, 9291, 7265, 9184, 50, 9255])).
% 2.12/2.31 tff(9299,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9298])).
% 2.12/2.31 tff(9300,plain,
% 2.12/2.31 (~r(s(s(s(z))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2079, 9255, 8042, 7265])).
% 2.12/2.31 tff(9301,plain,
% 2.12/2.31 (b(s(s(s(z))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[396, 9300])).
% 2.12/2.31 tff(9302,plain,
% 2.12/2.31 (~r(s(s(z)), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7175, 9301, 8042, 7265, 9255])).
% 2.12/2.31 tff(9303,plain,
% 2.12/2.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7183, 9298, 9302])).
% 2.12/2.31 tff(9304,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1451, 9303])).
% 2.12/2.31 tff(9305,plain,
% 2.12/2.31 (b(s(s(z)), elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9304, 9299])).
% 2.12/2.31 tff(9306,plain,
% 2.12/2.31 (~(s(elem!1) = elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1565, 9298, 8043])).
% 2.12/2.31 tff(9307,plain,
% 2.12/2.31 (~r(z, s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2136, 9255, 8042, 7265])).
% 2.12/2.31 tff(9308,plain,
% 2.12/2.31 (b(z, s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[619, 9307])).
% 2.12/2.31 tff(9309,plain,
% 2.12/2.31 (~r(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7271, 9298, 1, 606, 4])).
% 2.12/2.31 tff(9310,plain,
% 2.12/2.31 (b(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[372, 9309])).
% 2.12/2.31 tff(9311,plain,
% 2.12/2.31 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9298])).
% 2.12/2.31 tff(9312,plain,
% 2.12/2.31 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9311])).
% 2.12/2.31 tff(9313,plain,
% 2.12/2.31 (~(s(s(z)) = elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[1446, 9312])).
% 2.12/2.31 tff(9314,plain,
% 2.12/2.31 (~(s(elem!1) = s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1508, 9313])).
% 2.12/2.31 tff(9315,plain,
% 2.12/2.31 (~b(s(z), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2156, 489, 285, 284])).
% 2.12/2.31 tff(9316,plain,
% 2.12/2.31 (r(s(z), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[172, 9315])).
% 2.12/2.31 tff(9317,plain,
% 2.12/2.31 (~b(s(elem!1), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[499, 491, 489, 490])).
% 2.12/2.31 tff(9318,plain,
% 2.12/2.31 (r(s(elem!1), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[486, 9317, 1])).
% 2.12/2.31 tff(9319,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7227, 9318, 1804, 707, 9316])).
% 2.12/2.31 tff(9320,plain,((~b(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9321,plain,
% 2.12/2.31 (~b(s(elem!1), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9320, 9314, 1, 8042, 9290, 9310, 9308, 9301])).
% 2.12/2.31 tff(9322,plain,
% 2.12/2.31 (r(s(elem!1), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[507, 9321])).
% 2.12/2.31 tff(9323,plain,
% 2.12/2.31 (~r(s(elem!1), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[517, 9322, 9093, 9255])).
% 2.12/2.31 tff(9324,plain,
% 2.12/2.31 (b(s(elem!1), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[448, 9323, 9306])).
% 2.12/2.31 tff(9325,plain,
% 2.12/2.31 (~(elem!1 = s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1569, 9306])).
% 2.12/2.31 tff(9326,plain,
% 2.12/2.31 (~r(elem!1, s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[678, 9322, 7265, 9255])).
% 2.12/2.31 tff(9327,plain,
% 2.12/2.31 (b(elem!1, s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[560, 9326, 9325])).
% 2.12/2.31 tff(9328,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9329,plain,
% 2.12/2.31 (((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9330,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9329])).
% 2.12/2.31 tff(9331,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[9330, 9328])).
% 2.12/2.31 tff(9332,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(9333,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9332, 9331])).
% 2.12/2.31 tff(9334,plain,
% 2.12/2.31 (~b(s(s(z)), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9333, 144, 9327, 9324, 9305])).
% 2.12/2.31 tff(9335,plain,
% 2.12/2.31 (~(s(z) = elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8102, 9310, 606])).
% 2.12/2.31 tff(9336,plain,
% 2.12/2.31 (~(s(s(z)) = s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[855, 9335])).
% 2.12/2.31 tff(9337,plain,
% 2.12/2.31 (r(s(s(z)), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1408, 44, 9336, 9334])).
% 2.12/2.31 tff(9338,plain,
% 2.12/2.31 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(elem!1, s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9298])).
% 2.12/2.31 tff(9339,plain,
% 2.12/2.31 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(symmetry,[status(thm)],[9338])).
% 2.12/2.31 tff(9340,plain,
% 2.12/2.31 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9339])).
% 2.12/2.31 tff(9341,plain,
% 2.12/2.31 (~b(s(z), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1732, 9323, 9326, 9325, 9184])).
% 2.12/2.31 tff(9342,plain,
% 2.12/2.31 (r(s(z), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1244, 9341, 1229])).
% 2.12/2.31 tff(9343,plain,
% 2.12/2.31 (~r(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8957, 9342, 8044, 8042])).
% 2.12/2.31 tff(9344,plain,
% 2.12/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9343, 9340])).
% 2.12/2.31 tff(9345,plain,
% 2.12/2.31 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[319, 9344])).
% 2.12/2.31 tff(9346,plain,
% 2.12/2.31 (~b(s(s(z)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1425, 9345, 50, 9304])).
% 2.12/2.31 tff(9347,plain,
% 2.12/2.31 (r(s(s(z)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1429, 44, 9346, 1416])).
% 2.12/2.31 tff(9348,plain,
% 2.12/2.31 (~(elem!1 = s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[712, 9335])).
% 2.12/2.31 tff(9349,plain,
% 2.12/2.31 (b(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[720, 9343, 9348])).
% 2.12/2.31 tff(9350,plain,
% 2.12/2.31 (~b(s(elem!1), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4344, 144, 9324, 9184, 9349])).
% 2.12/2.31 tff(9351,plain,
% 2.12/2.31 (r(s(elem!1), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[486, 9350, 1])).
% 2.12/2.31 tff(9352,plain,
% 2.12/2.31 (((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(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(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9353,plain,
% 2.12/2.31 ((~![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(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(9354,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[9353, 9352])).
% 2.12/2.31 tff(9355,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9354, 333, 9351, 9342, 9347, 9337])).
% 2.12/2.31 tff(9356,plain,(b(z, elem!1) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9357,plain,
% 2.12/2.31 (b(z, elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9356, 55, 4, 3, 54, 1])).
% 2.12/2.31 tff(9358,plain,
% 2.12/2.31 (r(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9106, 3921, 624, 123, 132, 51])).
% 2.12/2.31 tff(9359,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8824, 9358, 3922, 3193, 707])).
% 2.12/2.31 tff(9360,plain,(b(s(z), z) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9361,plain,
% 2.12/2.31 (b(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9360, 2241, 707, 624, 123, 3193, 51])).
% 2.12/2.31 tff(9362,assumption,(~b(z, s(z))), introduced(assumption)).
% 2.12/2.31 tff(9363,plain,
% 2.12/2.31 (r(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[372, 9362])).
% 2.12/2.31 tff(9364,plain,
% 2.12/2.31 (b(z, s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[251, 8098])).
% 2.12/2.31 tff(9365,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9362, 9364])).
% 2.12/2.31 tff(9366,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9367,plain,
% 2.12/2.31 (~(s(z) = elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9366, 9362, 251])).
% 2.12/2.31 tff(9368,plain,
% 2.12/2.31 (r(s(z), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[406, 9367, 350])).
% 2.12/2.31 tff(9369,plain,
% 2.12/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[429, 9368, 51, 9363])).
% 2.12/2.31 tff(9370,plain,
% 2.12/2.31 (~(elem!1 = s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[712, 9367])).
% 2.12/2.31 tff(9371,plain,
% 2.12/2.31 (b(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[720, 9370, 715])).
% 2.12/2.31 tff(9372,plain,
% 2.12/2.31 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[313, 9371, 123, 132])).
% 2.12/2.31 tff(9373,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[319, 9372, 9369])).
% 2.12/2.31 tff(9374,plain,(b(z, s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(z)) | b(s(z), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(9375,plain,
% 2.12/2.31 (b(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9374, 715, 2241, 51, 123, 350, 251])).
% 2.12/2.31 tff(9376,plain,
% 2.12/2.31 (~b(elem!1, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[387, 144, 624, 9375, 9361])).
% 2.12/2.31 tff(9377,plain,
% 2.12/2.31 (elem!1 = s(z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[720, 9376, 715])).
% 2.12/2.31 tff(9378,plain,
% 2.12/2.31 (s(elem!1) = s(s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9377])).
% 2.12/2.31 tff(9379,plain,
% 2.12/2.31 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9378])).
% 2.12/2.31 tff(9380,plain,
% 2.12/2.31 (s(s(elem!1)) = s(s(s(z)))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9378])).
% 2.12/2.31 tff(9381,plain,
% 2.12/2.31 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.31 inference(symmetry,[status(thm)],[9380])).
% 2.12/2.31 tff(9382,plain,
% 2.12/2.31 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[3522, 9381, 1524])).
% 2.12/2.31 tff(9383,plain,
% 2.12/2.31 (s(z) = elem!1),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[712, 709])).
% 2.12/2.31 tff(9384,plain,
% 2.12/2.31 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.31 tff(9385,plain,
% 2.12/2.31 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.12/2.31 inference(symmetry,[status(thm)],[9384])).
% 2.12/2.31 tff(9386,plain,
% 2.12/2.31 (s(elem!1) = s(s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.31 tff(9387,plain,
% 2.12/2.31 (s(s(elem!1)) = s(s(s(z)))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.31 tff(9388,plain,
% 2.12/2.31 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.31 tff(9389,plain,
% 2.12/2.31 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.12/2.31 inference(symmetry,[status(thm)],[9388])).
% 2.12/2.31 tff(9390,plain,
% 2.12/2.31 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.12/2.31 inference(transitivity,[status(thm)],[9389, 9385])).
% 2.12/2.31 tff(9391,plain,
% 2.12/2.31 (r(s(s(elem!1)), elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[3193, 9390])).
% 2.12/2.31 tff(9392,plain,
% 2.12/2.31 (b(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[9360, 454, 707, 624, 123, 3193, 51])).
% 2.12/2.31 tff(9393,plain,
% 2.12/2.31 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.31 tff(9394,plain,
% 2.12/2.31 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.12/2.31 inference(symmetry,[status(thm)],[9393])).
% 2.12/2.31 tff(9395,plain,
% 2.12/2.31 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9394])).
% 2.12/2.31 tff(9396,plain,
% 2.12/2.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[880, 452, 251, 624])).
% 2.12/2.31 tff(9397,plain,
% 2.12/2.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[302, 9396])).
% 2.12/2.31 tff(9398,plain,
% 2.12/2.31 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.31 tff(9399,plain,
% 2.12/2.31 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.31 tff(9400,plain,
% 2.12/2.31 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.31 inference(symmetry,[status(thm)],[9399])).
% 2.12/2.31 tff(9401,plain,
% 2.12/2.31 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9400])).
% 2.12/2.31 tff(9402,plain,
% 2.12/2.31 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[244, 9401])).
% 2.12/2.31 tff(9403,plain,
% 2.12/2.31 (r(z, s(s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2836, 623, 9383])).
% 2.12/2.31 tff(9404,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9405,plain,
% 2.12/2.31 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(9406,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[9405])).
% 2.12/2.31 tff(9407,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[9406, 9404])).
% 2.12/2.31 tff(9408,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(9409,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9408, 9407])).
% 2.12/2.32 tff(9410,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9409, 333, 4627, 3654, 321, 4223])).
% 2.12/2.32 tff(9411,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(9412,plain,
% 2.12/2.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9411, 9403, 9397, 4627])).
% 2.12/2.32 tff(9413,plain,
% 2.12/2.32 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2758, 9412, 9402])).
% 2.12/2.32 tff(9414,plain,
% 2.12/2.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9413, 9398])).
% 2.12/2.32 tff(9415,plain,
% 2.12/2.32 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9416,plain,
% 2.12/2.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[452, 9415])).
% 2.12/2.32 tff(9417,plain,
% 2.12/2.32 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.32 tff(9418,plain,
% 2.12/2.32 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9417])).
% 2.12/2.32 tff(9419,plain,
% 2.12/2.32 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9420,plain,
% 2.12/2.32 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9419, 9418])).
% 2.12/2.32 tff(9421,plain,
% 2.12/2.32 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2468, 9383])).
% 2.12/2.32 tff(9422,plain,
% 2.12/2.32 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9423,plain,
% 2.12/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.12/2.32 inference(symmetry,[status(thm)],[9422])).
% 2.12/2.32 tff(9424,plain,
% 2.12/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9417])).
% 2.12/2.32 tff(9425,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9424])).
% 2.12/2.32 tff(9426,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9427,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.12/2.32 inference(transitivity,[status(thm)],[9426, 9425, 9423])).
% 2.12/2.32 tff(9428,plain,
% 2.12/2.32 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9427])).
% 2.12/2.32 tff(9429,plain,
% 2.12/2.32 (r(s(s(elem!1)), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[6447, 1699, 9383])).
% 2.12/2.32 tff(9430,plain,
% 2.12/2.32 (~(elem!1 = s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2482, 9421])).
% 2.12/2.32 tff(9431,plain,
% 2.12/2.32 (((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9432,plain,
% 2.12/2.32 ((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9433,plain,
% 2.12/2.32 ((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9432, 9431])).
% 2.12/2.32 tff(9434,plain,
% 2.12/2.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9433, 333, 1699, 623, 9397])).
% 2.12/2.32 tff(9435,plain,
% 2.12/2.32 (((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9436,plain,
% 2.12/2.32 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9437,plain,
% 2.12/2.32 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9436])).
% 2.12/2.32 tff(9438,plain,
% 2.12/2.32 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9437, 9435])).
% 2.12/2.32 tff(9439,plain,
% 2.12/2.32 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9440,plain,
% 2.12/2.32 ((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9439, 9438])).
% 2.12/2.32 tff(9441,plain,
% 2.12/2.32 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9440, 333, 1699, 623, 9397])).
% 2.12/2.32 tff(9442,plain,
% 2.12/2.32 (~b(s(z), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2264, 1699, 114, 123, 251, 624, 3, 54])).
% 2.12/2.32 tff(9443,plain,
% 2.12/2.32 (r(s(z), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[172, 9442])).
% 2.12/2.32 tff(9444,plain,
% 2.12/2.32 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.32 tff(9445,plain,
% 2.12/2.32 (s(s(z)) = s(elem!1)),
% 2.12/2.32 inference(symmetry,[status(thm)],[9386])).
% 2.12/2.32 tff(9446,plain,
% 2.12/2.32 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9445])).
% 2.12/2.32 tff(9447,plain,
% 2.12/2.32 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9446])).
% 2.12/2.32 tff(9448,plain,
% 2.12/2.32 (~(s(elem!1) = s(s(s(z))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[217, 9447])).
% 2.12/2.32 tff(9449,plain,
% 2.12/2.32 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2689, 1398, 9383])).
% 2.12/2.32 tff(9450,plain,
% 2.12/2.32 (~b(s(elem!1), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[464, 9449, 54, 114, 3])).
% 2.12/2.32 tff(9451,plain,
% 2.12/2.32 (~b(s(elem!1), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[3619, 9450, 9383])).
% 2.12/2.32 tff(9452,plain,
% 2.12/2.32 (r(s(elem!1), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[486, 9451, 1])).
% 2.12/2.32 tff(9453,plain,
% 2.12/2.32 (~r(s(elem!1), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[7227, 9452, 707, 353])).
% 2.12/2.32 tff(9454,plain,
% 2.12/2.32 (b(s(elem!1), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[965, 9453, 9448])).
% 2.12/2.32 tff(9455,plain,
% 2.12/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9454, 9444])).
% 2.12/2.32 tff(9456,plain,
% 2.12/2.32 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[7952, 1398, 7927, 7926])).
% 2.12/2.32 tff(9457,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9456, 9455])).
% 2.12/2.32 tff(9458,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(9459,plain,
% 2.12/2.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9458, 9443, 707, 709, 1, 54, 114, 3, 9441, 9434])).
% 2.12/2.32 tff(9460,plain,
% 2.12/2.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1451, 9459])).
% 2.12/2.32 tff(9461,plain,
% 2.12/2.32 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2674, 9460, 9383])).
% 2.12/2.32 tff(9462,plain,
% 2.12/2.32 (~r(z, s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[940, 9461, 51, 9397])).
% 2.12/2.32 tff(9463,plain,
% 2.12/2.32 (b(z, s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[583, 9462])).
% 2.12/2.32 tff(9464,plain,
% 2.12/2.32 (~r(s(s(z)), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[7908, 333, 9460, 9397, 51])).
% 2.12/2.32 tff(9465,plain,
% 2.12/2.32 (~r(s(elem!1), z)),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9464, 9395])).
% 2.12/2.32 tff(9466,plain,
% 2.12/2.32 (b(s(elem!1), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[507, 9465])).
% 2.12/2.32 tff(9467,plain,
% 2.12/2.32 (~b(elem!1, s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[949, 9466, 624, 9463])).
% 2.12/2.32 tff(9468,plain,
% 2.12/2.32 (r(elem!1, s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[560, 9467, 9430])).
% 2.12/2.32 tff(9469,plain,
% 2.12/2.32 (~(s(elem!1) = elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[906, 9430])).
% 2.12/2.32 tff(9470,plain,
% 2.12/2.32 (~b(s(elem!1), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[916, 9466, 251, 624])).
% 2.12/2.32 tff(9471,plain,
% 2.12/2.32 (r(s(elem!1), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[448, 9470, 9469])).
% 2.12/2.32 tff(9472,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.12/2.32 tff(9473,plain,
% 2.12/2.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9472])).
% 2.12/2.32 tff(9474,plain,
% 2.12/2.32 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9473])).
% 2.12/2.32 tff(9475,plain,
% 2.12/2.32 (s(s(elem!1)) = s(s(z))),
% 2.12/2.32 inference(transitivity,[status(thm)],[1007, 9474, 86])).
% 2.12/2.32 tff(9476,plain,
% 2.12/2.32 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9475])).
% 2.12/2.32 tff(9477,plain,
% 2.12/2.32 (s(elem!1) = s(z)),
% 2.12/2.32 inference(transitivity,[status(thm)],[102, 9476, 80])).
% 2.12/2.32 tff(9478,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1, 9477])).
% 2.12/2.32 tff(9479,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(9480,plain,
% 2.12/2.32 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9479, 1])).
% 2.12/2.32 tff(9481,plain,
% 2.12/2.32 (~(s(s(elem!1)) = s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1196, 9430])).
% 2.12/2.32 tff(9482,plain,
% 2.12/2.32 (~b(s(elem!1), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[499, 9466, 489, 490])).
% 2.12/2.32 tff(9483,plain,
% 2.12/2.32 (r(s(elem!1), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[486, 9482, 1])).
% 2.12/2.32 tff(9484,plain,
% 2.12/2.32 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9485,plain,
% 2.12/2.32 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9484, 5476])).
% 2.12/2.32 tff(9486,plain,
% 2.12/2.32 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9485])).
% 2.12/2.32 tff(9487,plain,
% 2.12/2.32 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9486])).
% 2.12/2.32 tff(9488,plain,
% 2.12/2.32 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[107, 9487])).
% 2.12/2.32 tff(9489,plain,
% 2.12/2.32 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.32 tff(9490,plain,
% 2.12/2.32 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9489])).
% 2.12/2.32 tff(9491,plain,
% 2.12/2.32 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.32 tff(9492,plain,
% 2.12/2.32 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9491])).
% 2.12/2.32 tff(9493,plain,
% 2.12/2.32 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9492, 9490])).
% 2.12/2.32 tff(9494,plain,
% 2.12/2.32 ((~b(s(z), s(s(s(z))))) <=> (~b(elem!1, s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9493])).
% 2.12/2.32 tff(9495,plain,
% 2.12/2.32 (~b(elem!1, s(s(elem!1)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9442, 9494])).
% 2.12/2.32 tff(9496,plain,
% 2.12/2.32 (r(elem!1, s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2522, 9495, 9488])).
% 2.12/2.32 tff(9497,plain,
% 2.12/2.32 (~r(s(s(elem!1)), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2745, 9468, 9496, 9483])).
% 2.12/2.32 tff(9498,plain,
% 2.12/2.32 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1283, 9497, 9481])).
% 2.12/2.32 tff(9499,plain,
% 2.12/2.32 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[2496])).
% 2.12/2.32 tff(9500,plain,
% 2.12/2.32 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9499])).
% 2.12/2.32 tff(9501,plain,
% 2.12/2.32 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4296, 9500])).
% 2.12/2.32 tff(9502,plain,
% 2.12/2.32 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9501])).
% 2.12/2.32 tff(9503,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[3526])).
% 2.12/2.32 tff(9504,plain,
% 2.12/2.32 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9503])).
% 2.12/2.32 tff(9505,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[3526])).
% 2.12/2.32 tff(9506,plain,
% 2.12/2.32 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9505])).
% 2.12/2.32 tff(9507,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.12/2.32 tff(9508,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9509,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9510,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9509, 9508])).
% 2.12/2.32 tff(9511,plain,
% 2.12/2.32 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9510, 333, 563, 435, 9507])).
% 2.12/2.32 tff(9512,plain,
% 2.12/2.32 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9511, 9506])).
% 2.12/2.32 tff(9513,plain,
% 2.12/2.32 (b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4697, 9512, 3523])).
% 2.12/2.32 tff(9514,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9513, 9504])).
% 2.12/2.32 tff(9515,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9516,plain,
% 2.12/2.32 (((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9517,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9516])).
% 2.12/2.32 tff(9518,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9517, 9515])).
% 2.12/2.32 tff(9519,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9520,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9519, 9518])).
% 2.12/2.32 tff(9521,plain,
% 2.12/2.32 (~b(s(s(s(s(z)))), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9520, 144, 491, 585, 9514])).
% 2.12/2.32 tff(9522,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4243, 44, 242, 9521])).
% 2.12/2.32 tff(9523,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, 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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9524,plain,
% 2.12/2.32 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9525,plain,
% 2.12/2.32 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9524])).
% 2.12/2.32 tff(9526,plain,
% 2.12/2.32 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9525, 9523])).
% 2.12/2.32 tff(9527,plain,
% 2.12/2.32 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9528,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9527, 9526])).
% 2.12/2.32 tff(9529,plain,
% 2.12/2.32 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[9528, 333, 51, 5497, 9522])).
% 2.12/2.32 tff(9530,plain,
% 2.12/2.32 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[9529, 9502])).
% 2.12/2.32 tff(9531,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.12/2.32 tff(9532,plain,
% 2.12/2.32 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[2496])).
% 2.12/2.32 tff(9533,plain,
% 2.12/2.32 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[9532])).
% 2.12/2.32 tff(9534,plain,
% 2.12/2.32 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4298, 9533])).
% 2.12/2.32 tff(9535,plain,
% 2.12/2.32 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9534])).
% 2.12/2.32 tff(9536,plain,
% 2.12/2.32 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[3527])).
% 2.12/2.32 tff(9537,plain,
% 2.12/2.32 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[3539])).
% 2.12/2.32 tff(9538,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9539,plain,
% 2.12/2.32 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(9540,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[9539])).
% 2.12/2.32 tff(9541,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[9540, 9538])).
% 2.12/2.32 tff(9542,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(9543,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9542, 9541])).
% 2.12/2.33 tff(9544,plain,
% 2.12/2.33 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9543, 333, 563, 435, 9507])).
% 2.12/2.33 tff(9545,plain,
% 2.12/2.33 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9544, 9537])).
% 2.12/2.33 tff(9546,plain,
% 2.12/2.33 (b(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[1067, 9545, 3524])).
% 2.12/2.33 tff(9547,plain,
% 2.12/2.33 (b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9546, 9536])).
% 2.12/2.33 tff(9548,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9549,plain,
% 2.12/2.33 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9550,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9549])).
% 2.12/2.33 tff(9551,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9550, 9548])).
% 2.12/2.33 tff(9552,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9553,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9552, 9551])).
% 2.12/2.33 tff(9554,plain,
% 2.12/2.33 ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9553, 144, 1249, 9514])).
% 2.12/2.33 tff(9555,plain,
% 2.12/2.33 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9554, 9547])).
% 2.12/2.33 tff(9556,plain,
% 2.12/2.33 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9555, 9535])).
% 2.12/2.33 tff(9557,plain,
% 2.12/2.33 (((~![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)))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9558,plain,
% 2.12/2.33 ((~![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)))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9559,plain,
% 2.12/2.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9558, 9557])).
% 2.12/2.33 tff(9560,plain,
% 2.12/2.33 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9559, 44])).
% 2.12/2.33 tff(9561,plain,
% 2.12/2.33 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9560, 9556, 9531])).
% 2.12/2.33 tff(9562,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9561, 9530])).
% 2.12/2.33 tff(9563,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(z) = elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(9564,plain,
% 2.12/2.33 (~r(s(s(s(s(z)))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9563, 9498, 9480, 51, 9383, 9471, 9466, 9463, 9468, 9429])).
% 2.12/2.33 tff(9565,plain,
% 2.12/2.33 (~r(s(s(s(elem!1))), elem!1)),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9564, 9428])).
% 2.12/2.33 tff(9566,plain,
% 2.12/2.33 (b(s(s(s(elem!1))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[1079, 9565, 9421])).
% 2.12/2.33 tff(9567,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(z))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9566, 9420])).
% 2.12/2.33 tff(9568,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9569,plain,
% 2.12/2.33 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9570,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9569])).
% 2.12/2.33 tff(9571,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9570, 9568])).
% 2.12/2.33 tff(9572,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9573,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9572, 9571])).
% 2.12/2.33 tff(9574,plain,
% 2.12/2.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9573, 144, 9567, 123, 9416])).
% 2.12/2.33 tff(9575,plain,
% 2.12/2.33 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9445])).
% 2.12/2.33 tff(9576,plain,
% 2.12/2.33 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9575, 174])).
% 2.12/2.33 tff(9577,plain,
% 2.12/2.33 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9576])).
% 2.12/2.33 tff(9578,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[1446, 9577])).
% 2.12/2.33 tff(9579,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.33 tff(9580,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.33 inference(symmetry,[status(thm)],[9579])).
% 2.12/2.33 tff(9581,plain,
% 2.12/2.33 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9580])).
% 2.12/2.33 tff(9582,plain,
% 2.12/2.33 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9387, 9386])).
% 2.12/2.33 tff(9583,plain,
% 2.12/2.33 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9498, 9582])).
% 2.12/2.33 tff(9584,plain,
% 2.12/2.33 (~r(s(elem!1), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[7227, 9483, 707, 9443])).
% 2.12/2.33 tff(9585,plain,
% 2.12/2.33 (b(s(elem!1), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[965, 9584, 9448])).
% 2.12/2.33 tff(9586,plain,
% 2.12/2.33 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9585, 9444])).
% 2.12/2.33 tff(9587,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9588,plain,
% 2.12/2.33 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9589,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9588])).
% 2.12/2.33 tff(9590,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9589, 9587])).
% 2.12/2.33 tff(9591,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9592,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9591, 9590])).
% 2.12/2.33 tff(9593,plain,
% 2.12/2.33 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9592, 144, 9586, 283, 9583])).
% 2.12/2.33 tff(9594,plain,
% 2.12/2.33 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9593, 9581])).
% 2.12/2.33 tff(9595,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[542, 9594, 9578])).
% 2.12/2.33 tff(9596,plain,
% 2.12/2.33 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[6882, 9595, 51, 9383, 9466, 624, 9471])).
% 2.12/2.33 tff(9597,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[3556, 44, 196, 9596, 9574])).
% 2.12/2.33 tff(9598,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(9599,plain,
% 2.12/2.33 (~r(s(s(s(z))), z)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9598, 9414, 624, 123, 709, 51, 707, 1, 489, 490, 251, 54, 114, 3, 623])).
% 2.12/2.33 tff(9600,plain,
% 2.12/2.33 (b(s(s(s(z))), z)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[396, 9599])).
% 2.12/2.33 tff(9601,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9602,plain,
% 2.12/2.33 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9603,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9602])).
% 2.12/2.33 tff(9604,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9603, 9601])).
% 2.12/2.33 tff(9605,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9606,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9605, 9604])).
% 2.12/2.33 tff(9607,plain,
% 2.12/2.33 (~b(s(z), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9606, 144, 489, 9600, 123, 9414])).
% 2.12/2.33 tff(9608,plain,
% 2.12/2.33 (r(s(z), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[172, 9607])).
% 2.12/2.33 tff(9609,plain,
% 2.12/2.33 (~b(elem!1, s(s(elem!1)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9607, 9494])).
% 2.12/2.33 tff(9610,plain,
% 2.12/2.33 (r(elem!1, s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[2522, 9609, 9488])).
% 2.12/2.33 tff(9611,plain,
% 2.12/2.33 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(commutativity,[status(thm)],[])).
% 2.12/2.33 tff(9612,plain,
% 2.12/2.33 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.12/2.33 inference(symmetry,[status(thm)],[9611])).
% 2.12/2.33 tff(9613,plain,
% 2.12/2.33 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(z))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9612])).
% 2.12/2.33 tff(9614,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[1446, 9613])).
% 2.12/2.33 tff(9615,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 2.12/2.33 tff(9616,plain,
% 2.12/2.33 (((~![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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9617,plain,
% 2.12/2.33 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9618,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), 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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9617])).
% 2.12/2.33 tff(9619,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), 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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.33 inference(transitivity,[status(thm)],[9618, 9616])).
% 2.12/2.33 tff(9620,plain,
% 2.12/2.33 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(9621,plain,
% 2.12/2.33 ((~![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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9620, 9619])).
% 2.12/2.33 tff(9622,plain,
% 2.12/2.33 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[9621, 333, 623, 321, 9615])).
% 2.12/2.33 tff(9623,plain,
% 2.12/2.33 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[1451, 9622])).
% 2.12/2.33 tff(9624,plain,
% 2.12/2.33 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[2689, 9623, 9383])).
% 2.12/2.33 tff(9625,plain,
% 2.12/2.33 (~b(s(elem!1), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[464, 9624, 54, 114, 3])).
% 2.12/2.33 tff(9626,plain,
% 2.12/2.33 (~b(s(elem!1), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[3619, 9625, 9383])).
% 2.12/2.33 tff(9627,plain,
% 2.12/2.33 (r(s(elem!1), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[486, 9626, 1])).
% 2.12/2.33 tff(9628,plain,
% 2.12/2.33 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.33 tff(9629,plain,
% 2.12/2.33 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[9628])).
% 2.12/2.33 tff(9630,plain,
% 2.12/2.33 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9629])).
% 2.12/2.33 tff(9631,plain,
% 2.12/2.33 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[9622, 9630])).
% 2.12/2.33 tff(9632,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9445])).
% 2.12/2.33 tff(9633,plain,
% 2.12/2.33 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9632])).
% 2.12/2.33 tff(9634,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9635,plain,
% 2.12/2.33 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(9636,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[9635])).
% 2.12/2.33 tff(9637,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9636, 9634])).
% 2.12/2.34 tff(9638,plain,
% 2.12/2.34 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9639,plain,
% 2.12/2.34 ((~![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(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9638, 9637])).
% 2.12/2.34 tff(9640,plain,
% 2.12/2.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9639, 333, 623, 321, 9615])).
% 2.12/2.34 tff(9641,plain,
% 2.12/2.34 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9640, 9633])).
% 2.12/2.34 tff(9642,plain,
% 2.12/2.34 (~b(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5467, 9641, 454, 9578, 9631])).
% 2.12/2.34 tff(9643,plain,
% 2.12/2.34 (r(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[560, 9642, 9430])).
% 2.12/2.34 tff(9644,plain,
% 2.12/2.34 (~r(s(s(elem!1)), s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[2745, 9643, 2736, 9627])).
% 2.12/2.34 tff(9645,plain,
% 2.12/2.34 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1283, 9644, 9481])).
% 2.12/2.34 tff(9646,plain,
% 2.12/2.34 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9645, 9582])).
% 2.12/2.34 tff(9647,plain,
% 2.12/2.34 (~r(s(elem!1), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[7227, 9627, 707, 353])).
% 2.12/2.34 tff(9648,plain,
% 2.12/2.34 (b(s(elem!1), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[965, 9647, 9448])).
% 2.12/2.34 tff(9649,plain,
% 2.12/2.34 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9648, 9444])).
% 2.12/2.34 tff(9650,plain,
% 2.12/2.34 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9592, 144, 9649, 283, 9646])).
% 2.12/2.34 tff(9651,plain,
% 2.12/2.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9652,plain,
% 2.12/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9653,plain,
% 2.12/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9652, 9651])).
% 2.12/2.34 tff(9654,plain,
% 2.12/2.34 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9653, 44, 9640])).
% 2.12/2.34 tff(9655,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9654, 9650, 9614])).
% 2.12/2.34 tff(9656,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(9657,plain,
% 2.12/2.34 (~r(s(s(z)), z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9656, 9414, 709, 9610, 707, 9608, 1, 54, 114, 3, 623, 9397])).
% 2.12/2.34 tff(9658,plain,
% 2.12/2.34 (~r(s(elem!1), z)),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9657, 9395])).
% 2.12/2.34 tff(9659,plain,
% 2.12/2.34 (b(s(elem!1), z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[507, 9658])).
% 2.12/2.34 tff(9660,plain,
% 2.12/2.34 (~b(s(elem!1), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[499, 9659, 489, 490])).
% 2.12/2.34 tff(9661,plain,
% 2.12/2.34 (r(s(elem!1), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[486, 9660, 1])).
% 2.12/2.34 tff(9662,plain,
% 2.12/2.34 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9387])).
% 2.12/2.34 tff(9663,plain,
% 2.12/2.34 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.12/2.34 inference(symmetry,[status(thm)],[9662])).
% 2.12/2.34 tff(9664,plain,
% 2.12/2.34 (b(s(s(elem!1)), z)),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9600, 9663])).
% 2.12/2.34 tff(9665,plain,
% 2.12/2.34 (b(s(s(z)), z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1462, 44, 164, 9657])).
% 2.12/2.34 tff(9666,plain,
% 2.12/2.34 (~r(s(elem!1), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[7227, 9661, 707, 9608])).
% 2.12/2.34 tff(9667,plain,
% 2.12/2.34 (b(s(elem!1), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[965, 9666, 9448])).
% 2.12/2.34 tff(9668,plain,
% 2.12/2.34 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9667, 9444])).
% 2.12/2.34 tff(9669,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9670,plain,
% 2.12/2.34 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9671,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9670])).
% 2.12/2.34 tff(9672,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9671, 9669])).
% 2.12/2.34 tff(9673,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9674,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9673, 9672])).
% 2.12/2.34 tff(9675,plain,
% 2.12/2.34 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9674, 144, 9600, 9668, 9414, 9665])).
% 2.12/2.34 tff(9676,plain,
% 2.12/2.34 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1451, 9675])).
% 2.12/2.34 tff(9677,plain,
% 2.12/2.34 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[2674, 9676, 9383])).
% 2.12/2.34 tff(9678,plain,
% 2.12/2.34 (~r(z, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[940, 9677, 51, 9397])).
% 2.12/2.34 tff(9679,plain,
% 2.12/2.34 (b(z, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[583, 9678])).
% 2.12/2.34 tff(9680,plain,
% 2.12/2.34 (~b(s(s(elem!1)), s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5572, 9679, 9664, 9659])).
% 2.12/2.34 tff(9681,plain,
% 2.12/2.34 (r(s(s(elem!1)), s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1283, 9680, 9481])).
% 2.12/2.34 tff(9682,plain,
% 2.12/2.34 (~b(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[949, 9679, 624, 9659])).
% 2.12/2.34 tff(9683,plain,
% 2.12/2.34 (r(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[560, 9682, 9430])).
% 2.12/2.34 tff(9684,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[2745, 9683, 9681, 9610, 9661])).
% 2.12/2.34 tff(9685,plain,((~r(z, s(s(s(z))))) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(9686,plain,
% 2.12/2.34 (~r(z, s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9685, 709, 51, 624, 707, 1, 9392, 490, 54, 114, 3, 123, 251, 9391])).
% 2.12/2.34 tff(9687,plain,
% 2.12/2.34 (b(z, s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[619, 9686])).
% 2.12/2.34 tff(9688,plain,
% 2.12/2.34 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9386])).
% 2.12/2.34 tff(9689,plain,
% 2.12/2.34 (r(s(s(z)), s(z))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[434, 9688])).
% 2.12/2.34 tff(9690,plain,
% 2.12/2.34 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9387])).
% 2.12/2.34 tff(9691,plain,
% 2.12/2.34 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9690])).
% 2.12/2.34 tff(9692,plain,
% 2.12/2.34 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9691])).
% 2.12/2.34 tff(9693,plain,
% 2.12/2.34 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9417])).
% 2.12/2.34 tff(9694,plain,
% 2.12/2.34 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9387, 9693])).
% 2.12/2.34 tff(9695,plain,
% 2.12/2.34 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9694])).
% 2.12/2.34 tff(9696,plain,
% 2.12/2.34 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9387, 9693])).
% 2.12/2.34 tff(9697,plain,
% 2.12/2.34 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9690])).
% 2.12/2.34 tff(9698,plain,
% 2.12/2.34 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9697, 9696])).
% 2.12/2.34 tff(9699,plain,
% 2.12/2.34 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9698])).
% 2.12/2.34 tff(9700,plain,
% 2.12/2.34 (r(s(s(z)), z)),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[509, 9393])).
% 2.12/2.34 tff(9701,plain,
% 2.12/2.34 (((~![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(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9702,plain,
% 2.12/2.34 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9703,plain,
% 2.12/2.34 (((~![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(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9702])).
% 2.12/2.34 tff(9704,plain,
% 2.12/2.34 (((~![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(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9703, 9701])).
% 2.12/2.34 tff(9705,plain,
% 2.12/2.34 ((~![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(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9706,plain,
% 2.12/2.34 ((~![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(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 2.12/2.34 tff(9707,plain,
% 2.12/2.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9706, 333, 321, 51, 9700])).
% 2.12/2.34 tff(9708,plain,
% 2.12/2.34 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9653, 44, 9707])).
% 2.12/2.34 tff(9709,plain,
% 2.12/2.34 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9708, 9614])).
% 2.12/2.34 tff(9710,plain,
% 2.12/2.34 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9711,plain,
% 2.12/2.34 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9710])).
% 2.12/2.34 tff(9712,plain,
% 2.12/2.34 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9711, 7903])).
% 2.12/2.34 tff(9713,plain,
% 2.12/2.34 ((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9714,plain,
% 2.12/2.34 ((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9713, 9712])).
% 2.12/2.34 tff(9715,plain,
% 2.12/2.34 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9714, 333, 321, 51, 9700])).
% 2.12/2.34 tff(9716,plain,
% 2.12/2.34 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1451, 9715])).
% 2.12/2.34 tff(9717,plain,
% 2.12/2.34 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.34 tff(9718,plain,
% 2.12/2.34 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9715, 9630])).
% 2.12/2.34 tff(9719,plain,
% 2.12/2.34 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9707, 9633])).
% 2.12/2.34 tff(9720,plain,
% 2.12/2.34 (~b(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5467, 9719, 132, 9578, 9718])).
% 2.12/2.34 tff(9721,plain,
% 2.12/2.34 (r(elem!1, s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[560, 9720, 9430])).
% 2.12/2.34 tff(9722,plain,
% 2.12/2.34 (r(s(z), s(elem!1))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9721, 9717])).
% 2.12/2.34 tff(9723,plain,
% 2.12/2.34 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9418])).
% 2.12/2.34 tff(9724,plain,
% 2.12/2.34 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9723])).
% 2.12/2.34 tff(9725,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.34 tff(9726,plain,
% 2.12/2.34 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9727,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9726])).
% 2.12/2.34 tff(9728,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9727, 9568])).
% 2.12/2.34 tff(9729,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9730,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9729, 9728])).
% 2.12/2.34 tff(9731,plain,
% 2.12/2.34 (~b(s(s(s(s(z)))), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9730, 144, 123, 304, 9725])).
% 2.12/2.34 tff(9732,plain,
% 2.12/2.34 (~b(s(s(s(elem!1))), s(z))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9731, 9724])).
% 2.12/2.34 tff(9733,plain,
% 2.12/2.34 (r(s(s(s(elem!1))), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1101, 9732])).
% 2.12/2.34 tff(9734,plain,
% 2.12/2.34 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9417])).
% 2.12/2.34 tff(9735,plain,
% 2.12/2.34 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.34 inference(symmetry,[status(thm)],[9734])).
% 2.12/2.34 tff(9736,plain,
% 2.12/2.34 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9445])).
% 2.12/2.34 tff(9737,plain,
% 2.12/2.34 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9736, 9735])).
% 2.12/2.34 tff(9738,plain,
% 2.12/2.34 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9737])).
% 2.12/2.34 tff(9739,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.12/2.34 tff(9740,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9741,plain,
% 2.12/2.34 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(9742,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[9741])).
% 2.12/2.34 tff(9743,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[9742, 9740])).
% 2.12/2.34 tff(9744,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(9745,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9744, 9743])).
% 2.12/2.34 tff(9746,plain,
% 2.12/2.34 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[9745, 144, 1398, 9739, 9725])).
% 2.12/2.34 tff(9747,plain,
% 2.12/2.34 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[9746, 9738])).
% 2.12/2.34 tff(9748,plain,
% 2.12/2.34 (r(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4697, 9747, 3127])).
% 2.12/2.34 tff(9749,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.12/2.35 tff(9750,plain,
% 2.12/2.35 (((~![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), s(elem!1))) | (~r(s(s(s(elem!1))), 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(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9751,plain,
% 2.12/2.35 ((~![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), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9752,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9751, 9750])).
% 2.12/2.35 tff(9753,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9752, 333, 1024, 509, 1230, 9749])).
% 2.12/2.35 tff(9754,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(9755,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9754, 9748, 9733, 1230, 509])).
% 2.12/2.35 tff(9756,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(9757,plain,
% 2.12/2.35 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9756, 9722, 509, 3127, 709, 123, 304, 9716, 9709])).
% 2.12/2.35 tff(9758,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.35 tff(9759,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.35 tff(9760,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[3556, 44, 196, 9759, 9758])).
% 2.12/2.35 tff(9761,plain,(b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(9762,plain,
% 2.12/2.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9761, 9757])).
% 2.12/2.35 tff(9763,plain,
% 2.12/2.35 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9387, 9386])).
% 2.12/2.35 tff(9764,plain,
% 2.12/2.35 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.12/2.35 inference(symmetry,[status(thm)],[9763])).
% 2.12/2.35 tff(9765,plain,
% 2.12/2.35 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9764])).
% 2.12/2.35 tff(9766,plain,
% 2.12/2.35 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9445])).
% 2.12/2.35 tff(9767,plain,
% 2.12/2.35 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.12/2.35 inference(symmetry,[status(thm)],[9766])).
% 2.12/2.35 tff(9768,plain,
% 2.12/2.35 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9717, 9767])).
% 2.12/2.35 tff(9769,plain,
% 2.12/2.35 (r(s(z), s(s(z)))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9721, 9768])).
% 2.12/2.35 tff(9770,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 2.12/2.35 tff(9771,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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)))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9772,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9773,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9772, 9771])).
% 2.12/2.35 tff(9774,plain,
% 2.12/2.35 (~r(s(s(s(z))), s(s(z)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9773, 333, 3193, 9770, 9769])).
% 2.12/2.35 tff(9775,plain,
% 2.12/2.35 (~r(s(s(elem!1)), s(elem!1))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9774, 9765])).
% 2.12/2.35 tff(9776,plain,
% 2.12/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1283, 9775, 9481])).
% 2.12/2.35 tff(9777,plain,
% 2.12/2.35 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9776, 9582])).
% 2.12/2.35 tff(9778,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9779,plain,
% 2.12/2.35 (((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9780,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9779])).
% 2.12/2.35 tff(9781,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9780, 9778])).
% 2.12/2.35 tff(9782,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9783,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9782, 9781])).
% 2.12/2.35 tff(9784,plain,
% 2.12/2.35 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9783, 144, 9716, 9709, 9777])).
% 2.12/2.35 tff(9785,plain,
% 2.12/2.35 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1137, 9784])).
% 2.12/2.35 tff(9786,plain,
% 2.12/2.35 (((~![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(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9787,plain,
% 2.12/2.35 (((~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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9788,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9787])).
% 2.12/2.35 tff(9789,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9788, 9786])).
% 2.12/2.35 tff(9790,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9791,plain,
% 2.12/2.35 ((~![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(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9790, 9789])).
% 2.12/2.35 tff(9792,plain,
% 2.12/2.35 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9791, 333, 3193, 9770, 9769])).
% 2.12/2.35 tff(9793,plain,
% 2.12/2.35 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1473, 44, 9792, 217])).
% 2.12/2.35 tff(9794,plain,
% 2.12/2.35 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9795,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9794])).
% 2.12/2.35 tff(9796,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9795, 9587])).
% 2.12/2.35 tff(9797,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9798,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9797, 9796])).
% 2.12/2.35 tff(9799,plain,
% 2.12/2.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9798, 144, 9793, 9709, 9777])).
% 2.12/2.35 tff(9800,plain,
% 2.12/2.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[249, 9799])).
% 2.12/2.35 tff(9801,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9802,plain,
% 2.12/2.35 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9803,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9802])).
% 2.12/2.35 tff(9804,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9803, 9801])).
% 2.12/2.35 tff(9805,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9806,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9805, 9804])).
% 2.12/2.35 tff(9807,plain,
% 2.12/2.35 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9806, 333, 9800, 9785, 9762])).
% 2.12/2.35 tff(9808,plain,
% 2.12/2.35 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9807, 9699])).
% 2.12/2.35 tff(9809,plain,
% 2.12/2.35 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9560, 9808, 9531])).
% 2.12/2.35 tff(9810,plain,
% 2.12/2.35 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9809, 9695])).
% 2.12/2.35 tff(9811,plain,
% 2.12/2.35 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9810, 9692])).
% 2.12/2.35 tff(9812,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9813,plain,
% 2.12/2.35 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9814,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[9813])).
% 2.12/2.35 tff(9815,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[9814, 9812])).
% 2.12/2.35 tff(9816,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9817,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[9816, 9815])).
% 2.12/2.35 tff(9818,plain,
% 2.12/2.35 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[9817, 333, 9800, 9785, 9762])).
% 2.12/2.35 tff(9819,plain,
% 2.12/2.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(9820,plain,
% 2.12/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(9821,plain,
% 2.12/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9820, 9819])).
% 2.12/2.36 tff(9822,plain,
% 2.12/2.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9821, 44, 219, 9818])).
% 2.12/2.36 tff(9823,plain,
% 2.12/2.36 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9824,plain,
% 2.12/2.36 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9825,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9824])).
% 2.12/2.36 tff(9826,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[9825, 9823])).
% 2.12/2.36 tff(9827,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9828,plain,
% 2.12/2.36 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9827, 9826])).
% 2.12/2.36 tff(9829,plain,
% 2.12/2.36 (~r(z, s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9828, 333, 9800, 51, 9762])).
% 2.12/2.36 tff(9830,plain,
% 2.12/2.36 (b(z, s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4260, 9829])).
% 2.12/2.36 tff(9831,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9832,plain,
% 2.12/2.36 (((~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(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9833,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9832])).
% 2.12/2.36 tff(9834,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[9833, 9831])).
% 2.12/2.36 tff(9835,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9836,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9835, 9834])).
% 2.12/2.36 tff(9837,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9836, 144, 284, 9830, 9822, 9811])).
% 2.12/2.36 tff(9838,plain,((~r(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~(elem!1 = s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9839,plain,
% 2.12/2.36 (~r(s(elem!1), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9838, 9689, 709, 9480, 51, 3127, 123, 9416, 3193, 9687, 454, 9397])).
% 2.12/2.36 tff(9840,plain,
% 2.12/2.36 (b(s(elem!1), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[507, 9839])).
% 2.12/2.36 tff(9841,plain,
% 2.12/2.36 (~b(s(s(s(z))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9320, 9840, 1, 707, 9392, 490, 9448, 9687])).
% 2.12/2.36 tff(9842,plain,
% 2.12/2.36 (r(s(s(s(z))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[396, 9841])).
% 2.12/2.36 tff(9843,plain,
% 2.12/2.36 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[709])).
% 2.12/2.36 tff(9844,plain,
% 2.12/2.36 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.12/2.36 inference(symmetry,[status(thm)],[9843])).
% 2.12/2.36 tff(9845,plain,
% 2.12/2.36 (r(s(elem!1), elem!1)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[434, 9844])).
% 2.12/2.36 tff(9846,plain,
% 2.12/2.36 (~b(s(z), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2264, 9842, 114, 123, 251, 624, 3, 54])).
% 2.12/2.36 tff(9847,plain,
% 2.12/2.36 (r(s(z), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[172, 9846])).
% 2.12/2.36 tff(9848,plain,
% 2.12/2.36 (~r(s(elem!1), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7227, 9847, 707, 434])).
% 2.12/2.36 tff(9849,plain,
% 2.12/2.36 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[6618, 333, 3638, 1699, 321])).
% 2.12/2.36 tff(9850,plain,
% 2.12/2.36 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[249, 9849])).
% 2.12/2.36 tff(9851,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9852,plain,
% 2.12/2.36 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9853,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9852])).
% 2.12/2.36 tff(9854,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[9853, 9851])).
% 2.12/2.36 tff(9855,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9856,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9855, 9854])).
% 2.12/2.36 tff(9857,plain,
% 2.12/2.36 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9856, 144, 547, 1794, 133, 9850])).
% 2.12/2.36 tff(9858,plain,
% 2.12/2.36 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[540, 44, 537, 9857])).
% 2.12/2.36 tff(9859,plain,
% 2.12/2.36 (((~![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(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9860,plain,
% 2.12/2.36 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9861,plain,
% 2.12/2.36 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9860])).
% 2.12/2.36 tff(9862,plain,
% 2.12/2.36 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[9861, 9859])).
% 2.12/2.36 tff(9863,plain,
% 2.12/2.36 ((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9864,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9863, 9862])).
% 2.12/2.36 tff(9865,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9864, 333, 435, 3638, 321, 9858])).
% 2.12/2.36 tff(9866,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9867,plain,
% 2.12/2.36 (~b(elem!1, s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9866, 3294, 321, 537, 435, 133, 1699, 624, 491])).
% 2.12/2.36 tff(9868,plain,
% 2.12/2.36 (r(elem!1, s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[560, 9867, 902])).
% 2.12/2.36 tff(9869,plain,
% 2.12/2.36 (~r(s(s(s(z))), s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7346, 333, 9868, 435, 707])).
% 2.12/2.36 tff(9870,plain,
% 2.12/2.36 (b(s(s(s(z))), s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1951, 44, 3295, 9869])).
% 2.12/2.36 tff(9871,plain,
% 2.12/2.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4103, 9868, 321, 525])).
% 2.12/2.36 tff(9872,plain,
% 2.12/2.36 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[121, 9871, 3396])).
% 2.12/2.36 tff(9873,plain,
% 2.12/2.36 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[265, 144, 251, 133, 9872])).
% 2.12/2.36 tff(9874,plain,
% 2.12/2.36 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[278, 9873, 274])).
% 2.12/2.36 tff(9875,plain,
% 2.12/2.36 (~r(z, s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[938, 333, 321, 9874, 525])).
% 2.12/2.36 tff(9876,plain,
% 2.12/2.36 (b(z, s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[583, 9875])).
% 2.12/2.36 tff(9877,plain,
% 2.12/2.36 (((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9878,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9877])).
% 2.12/2.36 tff(9879,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[9878, 9020])).
% 2.12/2.36 tff(9880,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9881,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9880, 9879])).
% 2.12/2.36 tff(9882,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9881, 144, 9876, 284, 3294, 9870])).
% 2.12/2.36 tff(9883,plain,((s(elem!1) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9884,plain,
% 2.12/2.36 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9883, 9848, 707, 251, 452, 9397, 9448, 9687, 453, 9430, 9578, 9845, 624, 9840, 9842])).
% 2.12/2.36 tff(9885,plain,
% 2.12/2.36 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2674, 9884, 9383])).
% 2.12/2.36 tff(9886,plain,
% 2.12/2.36 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1451, 9885])).
% 2.12/2.36 tff(9887,plain,
% 2.12/2.36 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2251, 333, 9842, 9397, 51])).
% 2.12/2.36 tff(9888,plain,
% 2.12/2.36 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2199, 333, 9842, 9397, 51])).
% 2.12/2.36 tff(9889,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9458, 9888, 9887, 707, 709, 1, 54, 114, 3, 9847, 9886])).
% 2.12/2.36 tff(9890,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(z))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9891,plain,
% 2.12/2.36 (~r(s(elem!1), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9890, 9377, 707, 1, 54, 2236, 3, 51, 251, 624, 123, 9375, 9382, 3193])).
% 2.12/2.36 tff(9892,plain,
% 2.12/2.36 (b(s(elem!1), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[486, 9891, 1])).
% 2.12/2.36 tff(9893,plain,
% 2.12/2.36 (~b(s(elem!1), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[499, 9892, 9361, 9375])).
% 2.12/2.36 tff(9894,plain,
% 2.12/2.36 (r(s(elem!1), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[507, 9893])).
% 2.12/2.36 tff(9895,plain,
% 2.12/2.36 (r(s(s(z)), z)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9894, 9379])).
% 2.12/2.36 tff(9896,plain,
% 2.12/2.36 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[880, 2237, 251, 624])).
% 2.12/2.36 tff(9897,plain,
% 2.12/2.36 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[302, 9896])).
% 2.12/2.36 tff(9898,plain,
% 2.12/2.36 (s(z) = elem!1),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[712, 9377])).
% 2.12/2.36 tff(9899,plain,
% 2.12/2.36 (b(s(elem!1), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[3619, 9892, 9898])).
% 2.12/2.36 tff(9900,plain,
% 2.12/2.36 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[464, 9899, 54, 2236, 3])).
% 2.12/2.36 tff(9901,plain,
% 2.12/2.36 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2689, 9900, 9898])).
% 2.12/2.36 tff(9902,plain,
% 2.12/2.36 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1451, 9901])).
% 2.12/2.36 tff(9903,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9714, 333, 9902, 9897, 51, 9895])).
% 2.12/2.36 tff(9904,plain,(r(elem!1, s(z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9905,plain,
% 2.12/2.36 (r(elem!1, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9904, 350, 54, 3, 1, 707, 251, 624, 123, 3193, 1524, 51])).
% 2.12/2.36 tff(9906,plain,
% 2.12/2.36 (((~![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))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(9907,plain,
% 2.12/2.36 ((~![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))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9908,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9907, 9906])).
% 2.12/2.36 tff(9909,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9908, 333, 409, 722, 3193, 707])).
% 2.12/2.36 tff(9910,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9911,plain,
% 2.12/2.36 (~r(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9910, 9905, 3193, 707])).
% 2.12/2.36 tff(9912,plain,
% 2.12/2.36 (s(z) = elem!1),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[406, 9911, 350])).
% 2.12/2.36 tff(9913,plain,
% 2.12/2.36 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9912])).
% 2.12/2.36 tff(9914,plain,
% 2.12/2.36 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 2.12/2.36 inference(symmetry,[status(thm)],[9913])).
% 2.12/2.36 tff(9915,plain,
% 2.12/2.36 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[9914])).
% 2.12/2.36 tff(9916,plain,
% 2.12/2.36 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(9917,plain,
% 2.12/2.36 (~r(elem!1, elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9916, 3480])).
% 2.12/2.36 tff(9918,plain,
% 2.12/2.36 (~r(elem!1, s(z))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[9917, 9915])).
% 2.12/2.36 tff(9919,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9905, 9918])).
% 2.12/2.36 tff(9920,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(9921,plain,
% 2.12/2.36 (b(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[9920, 4833, 707, 54, 3, 1, 251, 3193, 123, 1524, 51])).
% 2.12/2.36 tff(9922,plain,
% 2.12/2.36 (~b(s(z), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1602, 9921, 251, 4833])).
% 2.12/2.36 tff(9923,plain,
% 2.12/2.36 (r(s(z), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[348, 9922])).
% 2.12/2.36 tff(9924,plain,
% 2.12/2.36 (~(s(z) = elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[3965, 9922, 4833])).
% 2.12/2.36 tff(9925,plain,
% 2.12/2.36 (~(elem!1 = s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[712, 9924])).
% 2.12/2.36 tff(9926,plain,
% 2.12/2.36 (~r(elem!1, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8824, 9923, 3193, 707])).
% 2.12/2.36 tff(9927,plain,
% 2.12/2.36 (b(elem!1, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[720, 9926, 9925])).
% 2.12/2.36 tff(9928,plain,
% 2.12/2.36 (~b(z, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7079, 9927, 251, 9921])).
% 2.12/2.37 tff(9929,plain,
% 2.12/2.37 (r(z, s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[372, 9928])).
% 2.12/2.37 tff(9930,plain,
% 2.12/2.37 (~r(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8841, 333, 9929, 9923, 3193])).
% 2.12/2.37 tff(9931,plain,
% 2.12/2.37 (~r(s(s(s(z))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[6555, 9929, 3193, 9923])).
% 2.12/2.37 tff(9932,plain,
% 2.12/2.37 (b(s(s(s(z))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[396, 9931])).
% 2.12/2.37 tff(9933,plain,
% 2.12/2.37 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9360, 9922, 707, 4833, 123, 3193, 51])).
% 2.12/2.37 tff(9934,plain,
% 2.12/2.37 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[121, 9933, 3])).
% 2.12/2.37 tff(9935,plain,
% 2.12/2.37 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[116, 9934])).
% 2.12/2.37 tff(9936,plain,
% 2.12/2.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2558, 9935, 1378])).
% 2.12/2.37 tff(9937,plain,
% 2.12/2.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[302, 9936])).
% 2.12/2.37 tff(9938,plain,
% 2.12/2.37 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9934])).
% 2.12/2.37 tff(9939,plain,
% 2.12/2.37 (~(s(elem!1) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1565, 9935, 1524])).
% 2.12/2.37 tff(9940,plain,
% 2.12/2.37 (~(s(s(z)) = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[855, 9924])).
% 2.12/2.37 tff(9941,plain,
% 2.12/2.37 (~(s(elem!1) = s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[7434, 9940])).
% 2.12/2.37 tff(9942,plain,
% 2.12/2.37 (~(elem!1 = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1569, 9939])).
% 2.12/2.37 tff(9943,plain,
% 2.12/2.37 (r(z, elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8882, 9942, 707, 1378, 1, 251, 9935, 123, 3193])).
% 2.12/2.37 tff(9944,plain,
% 2.12/2.37 (~r(elem!1, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[7569, 9932, 251, 1378, 1, 9929, 9925, 9935, 9927, 9923, 9943, 9941, 707, 9939, 123])).
% 2.12/2.37 tff(9945,plain,
% 2.12/2.37 (b(elem!1, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1538, 9944, 1524])).
% 2.12/2.37 tff(9946,plain,
% 2.12/2.37 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9945, 9938])).
% 2.12/2.37 tff(9947,plain,
% 2.12/2.37 (~b(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[294, 9946, 9937, 9932])).
% 2.12/2.37 tff(9948,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[619, 9947, 9930])).
% 2.12/2.37 tff(9949,plain,(r(elem!1, z) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9950,plain,
% 2.12/2.37 (r(elem!1, z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9949, 7586, 8047, 251, 1, 707, 123, 3, 51, 54])).
% 2.12/2.37 tff(9951,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8656, 333, 409, 408, 3193, 707])).
% 2.12/2.37 tff(9952,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9953,plain,
% 2.12/2.37 (~r(s(z), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9952, 9950, 7586, 707])).
% 2.12/2.37 tff(9954,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[152, 454, 452, 123, 134])).
% 2.12/2.37 tff(9955,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9956,plain,
% 2.12/2.37 (~b(s(z), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9955, 114, 123, 3, 54])).
% 2.12/2.37 tff(9957,plain,
% 2.12/2.37 (s(z) = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[406, 9956, 9953])).
% 2.12/2.37 tff(9958,plain,
% 2.12/2.37 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2468, 9957])).
% 2.12/2.37 tff(9959,plain,
% 2.12/2.37 (~(elem!1 = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2482, 9958])).
% 2.12/2.37 tff(9960,plain,
% 2.12/2.37 (~(s(elem!1) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[906, 9959])).
% 2.12/2.37 tff(9961,plain,
% 2.12/2.37 (~r(s(z), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9952, 408, 7586, 707])).
% 2.12/2.37 tff(9962,plain,
% 2.12/2.37 (s(z) = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[406, 350, 9961])).
% 2.12/2.37 tff(9963,plain,
% 2.12/2.37 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9962])).
% 2.12/2.37 tff(9964,plain,
% 2.12/2.37 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9963, 1218])).
% 2.12/2.37 tff(9965,plain,
% 2.12/2.37 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9964])).
% 2.12/2.37 tff(9966,plain,
% 2.12/2.37 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[107, 9965])).
% 2.12/2.37 tff(9967,plain,
% 2.12/2.37 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.12/2.37 inference(transitivity,[status(thm)],[9964, 4572])).
% 2.12/2.37 tff(9968,plain,
% 2.12/2.37 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9967])).
% 2.12/2.37 tff(9969,plain,
% 2.12/2.37 (~(s(s(elem!1)) = elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[107, 9968])).
% 2.12/2.37 tff(9970,plain,
% 2.12/2.37 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2468, 9962])).
% 2.12/2.37 tff(9971,plain,
% 2.12/2.37 (~(elem!1 = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2482, 9970])).
% 2.12/2.37 tff(9972,plain,
% 2.12/2.37 (~(s(elem!1) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[906, 9971])).
% 2.12/2.37 tff(9973,plain,
% 2.12/2.37 (s(s(z)) = s(elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9962])).
% 2.12/2.37 tff(9974,plain,
% 2.12/2.37 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9973])).
% 2.12/2.37 tff(9975,plain,
% 2.12/2.37 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9974])).
% 2.12/2.37 tff(9976,plain,
% 2.12/2.37 (r(s(s(elem!1)), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[707, 9975])).
% 2.12/2.37 tff(9977,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, 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(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9978,plain,
% 2.12/2.37 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9979,plain,
% 2.12/2.37 (((~![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(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9978])).
% 2.12/2.37 tff(9980,plain,
% 2.12/2.37 (((~![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(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9979, 9977])).
% 2.12/2.37 tff(9981,plain,
% 2.12/2.37 ((~![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(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9982,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9981, 9980])).
% 2.12/2.37 tff(9983,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9982, 333, 408, 4627, 51, 5497])).
% 2.12/2.37 tff(9984,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9985,plain,
% 2.12/2.37 (~r(s(s(elem!1)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9984, 9976, 408, 51])).
% 2.12/2.37 tff(9986,plain,
% 2.12/2.37 (~r(s(s(s(z))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[6447, 9985, 9962])).
% 2.12/2.37 tff(9987,plain,
% 2.12/2.37 (b(s(s(s(z))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[396, 9986])).
% 2.12/2.37 tff(9988,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9973])).
% 2.12/2.37 tff(9989,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9988, 174])).
% 2.12/2.37 tff(9990,plain,
% 2.12/2.37 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9989])).
% 2.12/2.37 tff(9991,plain,
% 2.12/2.37 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[1446, 9990])).
% 2.12/2.37 tff(9992,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9993,plain,
% 2.12/2.37 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9994,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9993])).
% 2.12/2.37 tff(9995,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9994, 9992])).
% 2.12/2.37 tff(9996,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9997,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9996, 9995])).
% 2.12/2.37 tff(9998,plain,
% 2.12/2.37 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9997, 144, 251, 491, 133])).
% 2.12/2.37 tff(9999,plain,
% 2.12/2.37 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9998, 286])).
% 2.12/2.37 tff(10000,plain,
% 2.12/2.37 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[542, 9999, 9991])).
% 2.12/2.37 tff(10001,plain,
% 2.12/2.37 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9974])).
% 2.12/2.37 tff(10002,plain,
% 2.12/2.37 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10001])).
% 2.12/2.37 tff(10003,plain,
% 2.12/2.37 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[244, 10002])).
% 2.12/2.37 tff(10004,plain,
% 2.12/2.37 (b(s(s(elem!1)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5509, 9985])).
% 2.12/2.37 tff(10005,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(10006,plain,
% 2.12/2.37 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(10007,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10006])).
% 2.12/2.37 tff(10008,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[10007, 10005])).
% 2.12/2.37 tff(10009,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(10010,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[10009, 10008])).
% 2.12/2.37 tff(10011,plain,
% 2.12/2.37 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10010, 144, 251, 133, 10004])).
% 2.12/2.37 tff(10012,plain,
% 2.12/2.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10011, 286])).
% 2.12/2.37 tff(10013,plain,
% 2.12/2.37 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2758, 10012, 10003])).
% 2.12/2.37 tff(10014,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(10015,plain,
% 2.12/2.37 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(10016,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10015])).
% 2.12/2.37 tff(10017,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, 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(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[10016, 10014])).
% 2.12/2.37 tff(10018,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(10019,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[10018, 10017])).
% 2.12/2.37 tff(10020,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10019, 333, 4627, 3654, 51, 4223])).
% 2.12/2.37 tff(10021,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(10022,plain,
% 2.12/2.37 (~r(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10021, 10013, 9976, 51])).
% 2.12/2.37 tff(10023,plain,
% 2.12/2.37 (~r(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2836, 10022, 9962])).
% 2.12/2.37 tff(10024,plain,
% 2.12/2.37 (b(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[619, 10023])).
% 2.12/2.37 tff(10025,plain,
% 2.12/2.37 (~b(s(elem!1), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1802, 10024, 9987, 491])).
% 2.12/2.37 tff(10026,plain,
% 2.12/2.37 (~r(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8646, 10025, 408, 1524, 1, 2789, 350, 707])).
% 2.12/2.37 tff(10027,plain,
% 2.12/2.37 (b(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[448, 10026, 9972])).
% 2.12/2.37 tff(10028,plain,
% 2.12/2.37 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[3934, 10027, 123, 9962, 133])).
% 2.12/2.37 tff(10029,plain,
% 2.12/2.37 (~r(z, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[3607, 10028, 51, 10000])).
% 2.12/2.37 tff(10030,plain,
% 2.12/2.37 (~(s(s(elem!1)) = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1196, 9971])).
% 2.12/2.37 tff(10031,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9973])).
% 2.12/2.37 tff(10032,plain,
% 2.12/2.37 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10031])).
% 2.12/2.37 tff(10033,plain,
% 2.12/2.37 (~(s(elem!1) = s(s(s(z))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[217, 10032])).
% 2.12/2.37 tff(10034,plain,
% 2.12/2.37 (r(s(elem!1), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[965, 10025, 10033])).
% 2.12/2.37 tff(10035,plain,
% 2.12/2.37 (~r(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5258, 10034, 10013, 10000])).
% 2.12/2.37 tff(10036,plain,
% 2.12/2.37 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1283, 10035, 10030])).
% 2.12/2.37 tff(10037,plain,
% 2.12/2.37 (~b(z, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5572, 10036, 10004, 491])).
% 2.12/2.37 tff(10038,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[583, 10037, 10029])).
% 2.12/2.37 tff(10039,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | b(s(z), elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(10040,plain,
% 2.12/2.37 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10039, 491, 51, 123, 133, 408, 1524, 1, 2789, 350, 707, 251])).
% 2.12/2.37 tff(10041,plain,
% 2.12/2.37 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[302, 10040])).
% 2.12/2.37 tff(10042,plain,
% 2.12/2.37 (~r(elem!1, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[7510, 623, 408, 707])).
% 2.12/2.37 tff(10043,plain,
% 2.12/2.37 (b(elem!1, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1538, 10042, 1524])).
% 2.12/2.37 tff(10044,plain,
% 2.12/2.37 (b(s(z), s(s(s(z))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[10043, 5335])).
% 2.12/2.37 tff(10045,plain,
% 2.12/2.37 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[2496])).
% 2.12/2.37 tff(10046,plain,
% 2.12/2.37 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10045])).
% 2.12/2.37 tff(10047,plain,
% 2.12/2.37 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[244, 10046])).
% 2.12/2.37 tff(10048,plain,
% 2.12/2.37 (r(s(s(elem!1)), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[707, 2770])).
% 2.12/2.37 tff(10049,plain,
% 2.12/2.37 (r(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2836, 623, 57])).
% 2.12/2.37 tff(10050,plain,
% 2.12/2.37 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10021, 10049, 10048, 51])).
% 2.12/2.37 tff(10051,plain,
% 2.12/2.37 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2758, 10050, 10047])).
% 2.12/2.37 tff(10052,plain,
% 2.12/2.37 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[10051, 4019])).
% 2.12/2.37 tff(10053,plain,
% 2.12/2.37 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2262, 10052, 123, 10044])).
% 2.12/2.37 tff(10054,plain,
% 2.12/2.37 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1137, 10053])).
% 2.12/2.37 tff(10055,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[10054, 2767])).
% 2.12/2.37 tff(10056,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2843, 333, 321, 51, 10049, 10055])).
% 2.12/2.37 tff(10057,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(10058,plain,
% 2.12/2.37 (~r(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10057, 10041, 51, 9962, 123, 1524, 408, 707])).
% 2.12/2.37 tff(10059,plain,
% 2.12/2.37 (b(z, s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[619, 10058])).
% 2.12/2.37 tff(10060,plain,
% 2.12/2.37 (~b(s(elem!1), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1802, 10059, 9987, 491])).
% 2.12/2.37 tff(10061,plain,
% 2.12/2.37 (~r(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8646, 10060, 408, 1524, 1, 2789, 350, 707])).
% 2.12/2.37 tff(10062,plain,
% 2.12/2.37 (b(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[448, 10061, 9972])).
% 2.12/2.37 tff(10063,plain,
% 2.12/2.37 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[3934, 10062, 123, 9962, 133])).
% 2.12/2.37 tff(10064,plain,
% 2.12/2.37 (~(s(elem!1) = s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2856, 10030])).
% 2.12/2.37 tff(10065,plain,
% 2.12/2.37 (~r(z, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[940, 10063, 51, 10041])).
% 2.12/2.37 tff(10066,plain,
% 2.12/2.37 (b(z, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[583, 10065])).
% 2.12/2.37 tff(10067,plain,
% 2.12/2.37 (~b(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5572, 10066, 10004, 491])).
% 2.12/2.37 tff(10068,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1283, 10067, 10030])).
% 2.12/2.37 tff(10069,plain,
% 2.12/2.37 (~b(elem!1, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1642, 10066, 251, 10062])).
% 2.12/2.37 tff(10070,plain,
% 2.12/2.37 (r(elem!1, s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[560, 10069, 9971])).
% 2.12/2.37 tff(10071,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8472, 10070, 10068, 10064, 10003, 10063, 10062, 9969, 9966, 133])).
% 2.12/2.37 tff(10072,plain,((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | b(s(z), elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(10073,plain,
% 2.12/2.37 (~b(s(elem!1), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10072, 452, 251, 51, 123, 9950, 8047, 1, 2789, 9956, 707])).
% 2.12/2.37 tff(10074,plain,
% 2.12/2.37 (r(s(elem!1), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[507, 10073])).
% 2.12/2.37 tff(10075,plain,
% 2.12/2.37 (~r(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[517, 10074, 51, 9950])).
% 2.12/2.37 tff(10076,plain,
% 2.12/2.37 (b(s(elem!1), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[448, 10075, 9960])).
% 2.12/2.37 tff(10077,plain,
% 2.12/2.37 (s(s(z)) = s(elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9957])).
% 2.12/2.37 tff(10078,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10077])).
% 2.12/2.37 tff(10079,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.37 inference(transitivity,[status(thm)],[10078, 174])).
% 2.12/2.37 tff(10080,plain,
% 2.12/2.37 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[10079])).
% 2.12/2.37 tff(10081,plain,
% 2.12/2.37 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[1446, 10080])).
% 2.12/2.37 tff(10082,plain,
% 2.12/2.37 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[7622, 10076, 51, 9950, 452, 10074, 9959, 10081])).
% 2.12/2.37 tff(10083,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[3934, 10082, 10076, 123, 9957, 452])).
% 2.12/2.37 tff(10084,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | (~r(s(s(s(z))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(10085,plain,
% 2.12/2.37 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[10084, 9093, 50, 9357, 1, 7582, 8042, 3, 54])).
% 2.12/2.37 tff(10086,plain,
% 2.12/2.37 (b(s(z), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2235, 10085, 50])).
% 2.12/2.37 tff(10087,plain,
% 2.12/2.37 (r(elem!1, z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9949, 8044, 8043, 9357, 1, 8042, 50, 3, 9093, 54])).
% 2.12/2.37 tff(10088,plain,
% 2.12/2.37 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9955, 134, 123, 3, 54])).
% 2.12/2.37 tff(10089,plain,
% 2.12/2.37 (~(s(elem!1) = elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1565, 10088, 1524])).
% 2.12/2.38 tff(10090,plain,
% 2.12/2.38 (elem!1 = s(elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9006, 10088, 251, 408, 715, 1, 3193, 707, 134])).
% 2.12/2.38 tff(10091,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1569, 10090, 10089])).
% 2.12/2.38 tff(10092,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z)) | r(elem!1, s(z)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10093,plain,
% 2.12/2.38 (r(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10092, 10086, 10087, 9357, 1, 8044, 8042, 8043, 50, 3, 54])).
% 2.12/2.38 tff(10094,plain,
% 2.12/2.38 (~b(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8903, 10093, 8042, 1229, 9357, 8044, 10086])).
% 2.12/2.38 tff(10095,plain,
% 2.12/2.38 (~(s(elem!1) = elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1565, 10085, 8043])).
% 2.12/2.38 tff(10096,plain,
% 2.12/2.38 (~(elem!1 = s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1569, 10095])).
% 2.12/2.38 tff(10097,plain,
% 2.12/2.38 (r(s(elem!1), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8978, 10086, 9357, 1, 10087, 10096, 8044, 8042, 10085])).
% 2.12/2.38 tff(10098,plain,
% 2.12/2.38 (~r(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[517, 10097, 9093, 10087])).
% 2.12/2.38 tff(10099,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[507, 10098, 10094])).
% 2.12/2.38 tff(10100,plain,(b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10101,plain,
% 2.12/2.38 (b(s(s(s(z))), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10100, 54, 3, 1, 4])).
% 2.12/2.38 tff(10102,plain,
% 2.12/2.38 (~b(s(z), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9955, 8049, 123, 3, 54])).
% 2.12/2.38 tff(10103,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10104,plain,
% 2.12/2.38 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10105,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10104])).
% 2.12/2.38 tff(10106,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[10105, 10103])).
% 2.12/2.38 tff(10107,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(10108,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[10107, 10106])).
% 2.12/2.38 tff(10109,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10108, 144, 452, 454, 2254, 4367])).
% 2.12/2.38 tff(10110,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10111,plain,
% 2.12/2.38 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10110, 8049, 4367, 3, 54])).
% 2.12/2.38 tff(10112,plain,
% 2.12/2.38 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1137, 10111])).
% 2.12/2.38 tff(10113,plain,
% 2.12/2.38 (r(s(z), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[406, 706, 9956])).
% 2.12/2.38 tff(10114,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8753, 144, 624, 490, 305, 123, 132])).
% 2.12/2.38 tff(10115,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10116,plain,
% 2.12/2.38 (~b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10115, 305, 8722, 123, 454])).
% 2.12/2.38 tff(10117,plain,
% 2.12/2.38 (r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10116])).
% 2.12/2.38 tff(10118,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8702, 333, 563, 670, 409, 354])).
% 2.12/2.38 tff(10119,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10120,plain,
% 2.12/2.38 (~r(elem!1, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10119, 354, 409, 8715])).
% 2.12/2.38 tff(10121,plain,
% 2.12/2.38 (b(elem!1, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[560, 10120, 902])).
% 2.12/2.38 tff(10122,plain,
% 2.12/2.38 (b(s(elem!1), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8704, 354, 409, 74, 902, 606, 1378])).
% 2.12/2.38 tff(10123,plain,
% 2.12/2.38 (~b(s(z), s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4409, 10122, 305, 10121])).
% 2.12/2.38 tff(10124,plain,
% 2.12/2.38 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2946, 10123, 123])).
% 2.12/2.38 tff(10125,plain,
% 2.12/2.38 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[930, 10124])).
% 2.12/2.38 tff(10126,plain,
% 2.12/2.38 (~b(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8787, 10121, 454, 259, 8722])).
% 2.12/2.38 tff(10127,plain,
% 2.12/2.38 (r(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[507, 10126])).
% 2.12/2.38 tff(10128,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[632, 305, 8722, 123, 454])).
% 2.12/2.38 tff(10129,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[302, 10128])).
% 2.12/2.38 tff(10130,plain,
% 2.12/2.38 (~r(s(elem!1), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8783, 10124, 8715, 454, 902, 10129, 10127])).
% 2.12/2.38 tff(10131,plain,
% 2.12/2.38 (b(s(elem!1), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[448, 10130, 907])).
% 2.12/2.38 tff(10132,plain,
% 2.12/2.38 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[464, 10131, 54, 114, 3])).
% 2.12/2.38 tff(10133,plain,
% 2.12/2.38 (r(s(z), s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1244, 10123, 1237])).
% 2.12/2.38 tff(10134,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1235, 10133, 354, 10127])).
% 2.12/2.38 tff(10135,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[348, 10134])).
% 2.12/2.38 tff(10136,plain,
% 2.12/2.38 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7745, 10131, 452, 123, 8715, 8722, 10124, 10127, 10135])).
% 2.12/2.38 tff(10137,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[472, 10136, 10132, 10125])).
% 2.12/2.38 tff(10138,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (z = elem!1) | b(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10139,plain,
% 2.12/2.38 (elem!1 = s(elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10138, 10117, 54, 114, 3, 123, 1237, 259, 305, 409, 74, 606, 1378])).
% 2.12/2.38 tff(10140,plain,
% 2.12/2.38 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10139])).
% 2.12/2.38 tff(10141,plain,
% 2.12/2.38 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[454, 10140])).
% 2.12/2.38 tff(10142,plain,
% 2.12/2.38 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10139])).
% 2.12/2.38 tff(10143,plain,
% 2.12/2.38 (b(s(elem!1), s(z))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[305, 10142])).
% 2.12/2.38 tff(10144,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[313, 305, 123, 454])).
% 2.12/2.38 tff(10145,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[319, 10144])).
% 2.12/2.38 tff(10146,plain,
% 2.12/2.38 (~b(z, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2974, 10139, 606])).
% 2.12/2.38 tff(10147,plain,
% 2.12/2.38 (r(z, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[583, 10146])).
% 2.12/2.38 tff(10148,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8274, 10147, 10145, 10129])).
% 2.12/2.38 tff(10149,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[348, 10148])).
% 2.12/2.38 tff(10150,plain,
% 2.12/2.38 (b(elem!1, z) <=> b(s(elem!1), z)),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10139])).
% 2.12/2.38 tff(10151,plain,
% 2.12/2.38 (b(s(elem!1), z)),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[8722, 10150])).
% 2.12/2.38 tff(10152,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10153,plain,
% 2.12/2.38 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10154,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10153])).
% 2.12/2.38 tff(10155,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[10154, 10152])).
% 2.12/2.38 tff(10156,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(10157,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[10156, 10155])).
% 2.12/2.38 tff(10158,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10157, 144, 10151, 10149, 10143, 10141, 259])).
% 2.12/2.38 tff(10159,plain,((~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (~r(s(z), elem!1)) | (z = elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10160,plain,
% 2.12/2.38 (~b(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10159, 10113, 606, 54, 114, 3, 123, 1237, 259, 74, 1378])).
% 2.12/2.38 tff(10161,plain,
% 2.12/2.38 (r(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[720, 10160, 713])).
% 2.12/2.38 tff(10162,plain,
% 2.12/2.38 (~r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7717, 333, 8715, 10113, 10161])).
% 2.12/2.38 tff(10163,plain,
% 2.12/2.38 (b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10162])).
% 2.12/2.38 tff(10164,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[757, 10163, 123, 259])).
% 2.12/2.38 tff(10165,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[319, 10164])).
% 2.12/2.38 tff(10166,plain,
% 2.12/2.38 (~b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7741, 286, 123, 259])).
% 2.12/2.38 tff(10167,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1769, 286, 624, 114, 74, 123, 706, 722, 3, 54])).
% 2.12/2.38 tff(10168,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[348, 10167, 10166])).
% 2.12/2.38 tff(10169,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (z = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(elem!1, s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10170,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10169, 722, 114, 74, 123, 706, 624, 3, 54, 259])).
% 2.12/2.38 tff(10171,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[302, 10170])).
% 2.12/2.38 tff(10172,plain,
% 2.12/2.38 (~r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[727, 323, 670, 722])).
% 2.12/2.38 tff(10173,plain,
% 2.12/2.38 (b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10172])).
% 2.12/2.38 tff(10174,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[757, 10173, 123, 259])).
% 2.12/2.38 tff(10175,plain,
% 2.12/2.38 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[779, 10173, 56, 123, 321, 323])).
% 2.12/2.38 tff(10176,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[319, 10175, 10174])).
% 2.12/2.38 tff(10177,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10178,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10177, 10171, 123, 56, 259, 670, 722])).
% 2.12/2.38 tff(10179,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[348, 10178])).
% 2.12/2.38 tff(10180,plain,
% 2.12/2.38 (~r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7717, 333, 670, 10113, 722])).
% 2.12/2.38 tff(10181,plain,
% 2.12/2.38 (b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10180])).
% 2.12/2.38 tff(10182,plain,
% 2.12/2.38 (~b(s(s(s(z))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2273, 10181, 56, 10179])).
% 2.12/2.38 tff(10183,plain,
% 2.12/2.38 (r(s(s(s(z))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[396, 10182])).
% 2.12/2.38 tff(10184,plain,
% 2.12/2.38 (((~![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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10185,plain,
% 2.12/2.38 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10186,plain,
% 2.12/2.38 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10185])).
% 2.12/2.38 tff(10187,plain,
% 2.12/2.38 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(transitivity,[status(thm)],[10186, 10184])).
% 2.12/2.38 tff(10188,plain,
% 2.12/2.38 ((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(10189,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[10188, 10187])).
% 2.12/2.38 tff(10190,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10189, 333, 670, 10183, 6107, 10171])).
% 2.12/2.38 tff(10191,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (z = elem!1) | (s(z) = elem!1) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10192,plain,
% 2.12/2.38 (~r(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10191, 56, 6107, 8715, 123, 259, 114, 74, 706, 8722, 3, 54])).
% 2.12/2.38 tff(10193,plain,
% 2.12/2.38 (b(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[720, 10192, 713])).
% 2.12/2.38 tff(10194,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[632, 10193, 8722, 123, 454])).
% 2.12/2.38 tff(10195,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[302, 10194])).
% 2.12/2.38 tff(10196,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[313, 10193, 123, 454])).
% 2.12/2.38 tff(10197,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[319, 10196])).
% 2.12/2.38 tff(10198,plain,
% 2.12/2.38 (~b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7064, 10145, 56, 305, 123, 10129, 8722])).
% 2.12/2.38 tff(10199,plain,
% 2.12/2.38 (r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10198])).
% 2.12/2.38 tff(10200,plain,
% 2.12/2.38 (~r(elem!1, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10119, 10199, 409, 8715])).
% 2.12/2.38 tff(10201,plain,
% 2.12/2.38 (b(elem!1, s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[560, 10200, 902])).
% 2.12/2.38 tff(10202,plain,
% 2.12/2.38 (b(s(elem!1), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8704, 10199, 409, 74, 902, 606, 1378])).
% 2.12/2.38 tff(10203,plain,
% 2.12/2.38 (~b(s(z), s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4409, 10202, 305, 10201])).
% 2.12/2.38 tff(10204,plain,
% 2.12/2.38 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2946, 10203, 123])).
% 2.12/2.38 tff(10205,plain,
% 2.12/2.38 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[930, 10204])).
% 2.12/2.38 tff(10206,plain,
% 2.12/2.38 (~b(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8787, 10201, 454, 259, 8722])).
% 2.12/2.38 tff(10207,plain,
% 2.12/2.38 (r(s(elem!1), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[507, 10206])).
% 2.12/2.38 tff(10208,plain,
% 2.12/2.38 (~r(s(elem!1), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8783, 10207, 8715, 454, 902, 10129, 10204])).
% 2.12/2.38 tff(10209,plain,
% 2.12/2.38 (b(s(elem!1), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[448, 10208, 907])).
% 2.12/2.38 tff(10210,plain,
% 2.12/2.38 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[464, 10209, 54, 114, 3])).
% 2.12/2.38 tff(10211,plain,
% 2.12/2.38 (r(s(z), s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1244, 10203, 1237])).
% 2.12/2.38 tff(10212,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1235, 10211, 10199, 10207])).
% 2.12/2.38 tff(10213,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[348, 10212])).
% 2.12/2.38 tff(10214,plain,
% 2.12/2.38 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7745, 10209, 452, 123, 8715, 8722, 10204, 10207, 10213])).
% 2.12/2.38 tff(10215,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[472, 10214, 10210, 10205])).
% 2.12/2.38 tff(10216,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (z = elem!1) | b(z, elem!1) | r(elem!1, z) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10217,plain,
% 2.12/2.38 (elem!1 = s(elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10216, 10193, 54, 114, 3, 123, 1237, 259, 10113, 74, 606, 1378, 56])).
% 2.12/2.38 tff(10218,plain,
% 2.12/2.38 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10217])).
% 2.12/2.38 tff(10219,plain,
% 2.12/2.38 (r(s(z), s(elem!1))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[10113, 10218])).
% 2.12/2.38 tff(10220,plain,
% 2.12/2.38 (~b(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7064, 10197, 56, 10193, 123, 10195, 8722])).
% 2.12/2.38 tff(10221,plain,
% 2.12/2.38 (r(z, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[372, 10220])).
% 2.12/2.38 tff(10222,plain,
% 2.12/2.38 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10223,plain,
% 2.12/2.38 (((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(10224,plain,
% 2.12/2.38 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10223])).
% 2.12/2.38 tff(10225,plain,
% 2.12/2.38 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(transitivity,[status(thm)],[10224, 10222])).
% 2.12/2.38 tff(10226,plain,
% 2.12/2.38 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(10227,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[10226, 10225])).
% 2.12/2.38 tff(10228,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10227, 333, 10221, 10219, 10197, 10195])).
% 2.12/2.38 tff(10229,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | b(z, elem!1) | r(elem!1, z) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10230,plain,
% 2.12/2.38 (~b(s(s(s(z))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10229, 706, 54, 114, 3, 1237, 259, 74, 606, 1378, 6107, 123])).
% 2.12/2.38 tff(10231,plain,
% 2.12/2.38 (r(s(s(s(z))), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2794, 10230])).
% 2.12/2.38 tff(10232,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8740, 333, 10113, 10231, 6107, 10165])).
% 2.12/2.38 tff(10233,plain,((s(z) = elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(z) = s(elem!1)) | (z = elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10234,plain,
% 2.12/2.38 (s(z) = elem!1),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10233, 1378, 123, 259, 606, 54, 114, 3, 1237, 74, 6107])).
% 2.12/2.38 tff(10235,plain,
% 2.12/2.38 (s(s(z)) = s(elem!1)),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10234])).
% 2.12/2.38 tff(10236,plain,
% 2.12/2.38 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10235])).
% 2.12/2.38 tff(10237,plain,
% 2.12/2.38 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[10236])).
% 2.12/2.38 tff(10238,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[6107, 10237])).
% 2.12/2.38 tff(10239,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[3965, 10234, 8722])).
% 2.12/2.38 tff(10240,plain,
% 2.12/2.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7741, 10239, 123, 259])).
% 2.12/2.38 tff(10241,plain,
% 2.12/2.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[302, 10240])).
% 2.12/2.38 tff(10242,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[6898, 333, 670, 321, 5497, 8162])).
% 2.12/2.38 tff(10243,plain,((~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(10244,plain,
% 2.12/2.38 (~r(s(s(elem!1)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[10243, 10241, 8715, 10238])).
% 2.12/2.38 tff(10245,plain,
% 2.12/2.38 (b(s(s(elem!1)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5509, 10244])).
% 2.12/2.39 tff(10246,plain,
% 2.12/2.39 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10234])).
% 2.12/2.39 tff(10247,plain,
% 2.12/2.39 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10246, 1218])).
% 2.12/2.39 tff(10248,plain,
% 2.12/2.39 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10247])).
% 2.12/2.39 tff(10249,plain,
% 2.12/2.39 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[107, 10248])).
% 2.12/2.39 tff(10250,plain,
% 2.12/2.39 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10234])).
% 2.12/2.39 tff(10251,plain,
% 2.12/2.39 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10250])).
% 2.12/2.39 tff(10252,plain,
% 2.12/2.39 (r(s(elem!1), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8651, 10234, 123, 259, 8715, 730, 1237, 114, 606])).
% 2.12/2.39 tff(10253,plain,
% 2.12/2.39 (r(s(elem!1), s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10252, 10251])).
% 2.12/2.39 tff(10254,plain,
% 2.12/2.39 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2468, 10234])).
% 2.12/2.39 tff(10255,plain,
% 2.12/2.39 (~(elem!1 = s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2482, 10254])).
% 2.12/2.39 tff(10256,plain,
% 2.12/2.39 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10235])).
% 2.12/2.39 tff(10257,plain,
% 2.12/2.39 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10256, 174])).
% 2.12/2.39 tff(10258,plain,
% 2.12/2.39 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10257])).
% 2.12/2.39 tff(10259,plain,
% 2.12/2.39 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[1446, 10258])).
% 2.12/2.39 tff(10260,plain,
% 2.12/2.39 (~r(s(elem!1), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8783, 10259, 8715, 454, 10255, 10252, 10241])).
% 2.12/2.39 tff(10261,plain,
% 2.12/2.39 (b(s(elem!1), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[507, 10260])).
% 2.12/2.39 tff(10262,plain,
% 2.12/2.39 (~b(elem!1, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8787, 10261, 454, 259, 8722])).
% 2.12/2.39 tff(10263,plain,
% 2.12/2.39 (r(elem!1, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[560, 10262, 10255])).
% 2.12/2.39 tff(10264,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1196, 10255])).
% 2.12/2.39 tff(10265,plain,
% 2.12/2.39 (~r(z, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2393, 10263, 8715, 10253])).
% 2.12/2.39 tff(10266,plain,
% 2.12/2.39 (b(z, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[583, 10265])).
% 2.12/2.39 tff(10267,plain,
% 2.12/2.39 (~b(s(s(elem!1)), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5572, 10245, 10266, 10261])).
% 2.12/2.39 tff(10268,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1283, 10267, 10264])).
% 2.12/2.39 tff(10269,plain,
% 2.12/2.39 (~r(elem!1, s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2745, 10268, 10263, 10253])).
% 2.12/2.39 tff(10270,plain,
% 2.12/2.39 (b(elem!1, s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2522, 10269, 10249])).
% 2.12/2.39 tff(10271,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10272,plain,
% 2.12/2.39 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10273,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10272])).
% 2.12/2.39 tff(10274,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10273, 10271])).
% 2.12/2.39 tff(10275,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(10276,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10275, 10274])).
% 2.12/2.39 tff(10277,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10276, 144, 8722, 10270, 454, 259, 10245])).
% 2.12/2.39 tff(10278,plain,(r(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(z, elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(10279,plain,
% 2.12/2.39 (r(elem!1, z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10278, 10112, 8045, 123, 1229, 8049, 606, 54, 3, 71])).
% 2.12/2.39 tff(10280,plain,
% 2.12/2.39 (r(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[348, 10166])).
% 2.12/2.39 tff(10281,plain,
% 2.12/2.39 (~r(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8094, 333, 670, 10280, 408])).
% 2.12/2.39 tff(10282,plain,
% 2.12/2.39 (s(z) = elem!1),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[406, 10281, 350])).
% 2.12/2.39 tff(10283,plain,
% 2.12/2.39 (s(s(z)) = s(elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10282])).
% 2.12/2.39 tff(10284,plain,
% 2.12/2.39 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10283])).
% 2.12/2.39 tff(10285,plain,
% 2.12/2.39 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10284])).
% 2.12/2.39 tff(10286,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10285])).
% 2.12/2.39 tff(10287,plain,
% 2.12/2.39 (s(s(elem!1)) = s(s(s(z)))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10284])).
% 2.12/2.39 tff(10288,plain,
% 2.12/2.39 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10287])).
% 2.12/2.39 tff(10289,plain,
% 2.12/2.39 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10288])).
% 2.12/2.39 tff(10290,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10289])).
% 2.12/2.39 tff(10291,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10290, 10286])).
% 2.12/2.39 tff(10292,plain,
% 2.12/2.39 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10291])).
% 2.12/2.39 tff(10293,plain,
% 2.12/2.39 (r(s(elem!1), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8651, 10282, 123, 259, 670, 1368, 1237, 114, 606])).
% 2.12/2.39 tff(10294,plain,
% 2.12/2.39 (((~![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(elem!1), elem!1)) | (~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(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10295,plain,
% 2.12/2.39 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(10296,plain,
% 2.12/2.39 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10295, 10294])).
% 2.12/2.39 tff(10297,plain,
% 2.12/2.39 (~r(s(elem!1), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10296, 333, 10293, 670, 408])).
% 2.12/2.39 tff(10298,plain,
% 2.12/2.39 (b(s(elem!1), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[507, 10297])).
% 2.12/2.39 tff(10299,plain,
% 2.12/2.39 (~r(z, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2453, 333, 10293, 670, 408])).
% 2.12/2.39 tff(10300,plain,
% 2.12/2.39 (b(z, s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[583, 10299])).
% 2.12/2.39 tff(10301,plain,
% 2.12/2.39 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10282])).
% 2.12/2.39 tff(10302,plain,
% 2.12/2.39 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10301])).
% 2.12/2.39 tff(10303,plain,
% 2.12/2.39 (r(s(elem!1), s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10293, 10302])).
% 2.12/2.39 tff(10304,plain,
% 2.12/2.39 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10282])).
% 2.12/2.39 tff(10305,plain,
% 2.12/2.39 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10304, 2])).
% 2.12/2.39 tff(10306,plain,
% 2.12/2.39 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10305])).
% 2.12/2.39 tff(10307,plain,
% 2.12/2.39 (~(elem!1 = s(s(s(z))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[166, 10306])).
% 2.12/2.39 tff(10308,plain,
% 2.12/2.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3522, 10284, 10307])).
% 2.12/2.39 tff(10309,plain,
% 2.12/2.39 (~r(s(s(s(elem!1))), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4215, 10308, 10280, 10303, 670, 10300, 10298])).
% 2.12/2.39 tff(10310,plain,
% 2.12/2.39 (b(s(s(s(elem!1))), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1101, 10309])).
% 2.12/2.39 tff(10311,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3588, 10310, 10282])).
% 2.12/2.39 tff(10312,plain,
% 2.12/2.39 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3552, 144, 10311, 133, 132])).
% 2.12/2.39 tff(10313,plain,
% 2.12/2.39 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9761, 10312])).
% 2.12/2.39 tff(10314,plain,
% 2.12/2.39 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10284])).
% 2.12/2.39 tff(10315,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[6107, 10314])).
% 2.12/2.39 tff(10316,plain,
% 2.12/2.39 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10283])).
% 2.12/2.39 tff(10317,plain,
% 2.12/2.39 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10316, 174])).
% 2.12/2.39 tff(10318,plain,
% 2.12/2.39 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10317])).
% 2.12/2.39 tff(10319,plain,
% 2.12/2.39 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[1446, 10318])).
% 2.12/2.39 tff(10320,plain,
% 2.12/2.39 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1668, 144, 10298, 10300, 286])).
% 2.12/2.39 tff(10321,plain,
% 2.12/2.39 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[542, 10320, 10319])).
% 2.12/2.39 tff(10322,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10323,plain,
% 2.12/2.39 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10324,plain,
% 2.12/2.39 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10323])).
% 2.12/2.39 tff(10325,plain,
% 2.12/2.39 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10324, 10322])).
% 2.12/2.39 tff(10326,plain,
% 2.12/2.39 ((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(10327,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10326, 10325])).
% 2.12/2.39 tff(10328,plain,
% 2.12/2.39 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10327, 333, 10321, 10315, 10313])).
% 2.12/2.39 tff(10329,plain,
% 2.12/2.39 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10328, 10292])).
% 2.12/2.39 tff(10330,plain,
% 2.12/2.39 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10284])).
% 2.12/2.39 tff(10331,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[10330])).
% 2.12/2.39 tff(10332,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10289])).
% 2.12/2.39 tff(10333,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10332, 10331])).
% 2.12/2.39 tff(10334,plain,
% 2.12/2.39 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10333])).
% 2.12/2.39 tff(10335,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10284])).
% 2.12/2.39 tff(10336,plain,
% 2.12/2.39 (b(s(s(elem!1)), elem!1)),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[4367, 10335])).
% 2.12/2.39 tff(10337,plain,
% 2.12/2.39 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3254, 10308])).
% 2.12/2.39 tff(10338,plain,
% 2.12/2.39 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10317, 175])).
% 2.12/2.39 tff(10339,plain,
% 2.12/2.39 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10338])).
% 2.12/2.39 tff(10340,plain,
% 2.12/2.39 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[1446, 10339])).
% 2.12/2.39 tff(10341,plain,
% 2.12/2.39 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10342,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10341])).
% 2.12/2.39 tff(10343,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10342, 8277])).
% 2.12/2.39 tff(10344,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(10345,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10344, 10343])).
% 2.12/2.39 tff(10346,plain,
% 2.12/2.39 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10345, 144, 10298, 286, 259])).
% 2.12/2.39 tff(10347,plain,
% 2.12/2.39 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[472, 10346, 10340])).
% 2.12/2.39 tff(10348,plain,
% 2.12/2.39 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3567, 10347, 10313, 10321])).
% 2.12/2.39 tff(10349,plain,
% 2.12/2.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3545, 10348, 10282])).
% 2.12/2.39 tff(10350,plain,
% 2.12/2.39 (b(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1067, 10349, 10337])).
% 2.12/2.39 tff(10351,plain,
% 2.12/2.39 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2468, 10282])).
% 2.12/2.39 tff(10352,plain,
% 2.12/2.39 (~(elem!1 = s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2482, 10351])).
% 2.12/2.39 tff(10353,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1196, 10352])).
% 2.12/2.39 tff(10354,plain,
% 2.12/2.39 (~r(s(s(elem!1)), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8213, 333, 10347, 10321, 10315])).
% 2.12/2.39 tff(10355,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1283, 10354, 10353])).
% 2.12/2.39 tff(10356,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.12/2.39 tff(10357,plain,
% 2.12/2.39 (b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10356, 9536])).
% 2.12/2.39 tff(10358,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 2.12/2.39 tff(10359,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10360,plain,
% 2.12/2.39 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(10361,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[10360])).
% 2.12/2.39 tff(10362,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[10361, 10359])).
% 2.12/2.39 tff(10363,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(10364,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10363, 10362])).
% 2.12/2.39 tff(10365,plain,
% 2.12/2.39 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10364, 144, 1249, 3529, 4972, 10358])).
% 2.12/2.39 tff(10366,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10365, 10357])).
% 2.12/2.39 tff(10367,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(10368,plain,
% 2.12/2.39 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[10367, 10355, 10282, 10350, 10336, 10311])).
% 2.12/2.39 tff(10369,plain,
% 2.12/2.39 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[10368, 10334])).
% 2.12/2.39 tff(10370,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9560, 10369, 10329, 9531])).
% 2.12/2.40 tff(10371,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (s(z) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(z, elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.40 tff(10372,plain,
% 2.12/2.40 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[10371, 8050, 9480, 8052, 8045, 7265, 10279, 4367, 10112, 123, 77, 1229, 8049, 606, 10102])).
% 2.12/2.40 tff(10373,plain,
% 2.12/2.40 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[302, 10372])).
% 2.12/2.40 tff(10374,plain,
% 2.12/2.40 (r(elem!1, z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[10278, 6107, 259, 123, 1229, 114, 606, 54, 3, 71])).
% 2.12/2.40 tff(10375,plain,
% 2.12/2.40 (~r(z, s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[690, 333, 7265, 409, 10374])).
% 2.12/2.40 tff(10376,plain,
% 2.12/2.40 (b(z, s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[372, 10375])).
% 2.12/2.40 tff(10377,plain,
% 2.12/2.40 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[757, 10376, 123, 259])).
% 2.12/2.40 tff(10378,plain,
% 2.12/2.40 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[319, 10377])).
% 2.12/2.40 tff(10379,plain,
% 2.12/2.40 (~r(s(z), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[682, 333, 7265, 409, 10374])).
% 2.12/2.40 tff(10380,plain,
% 2.12/2.40 (b(s(z), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[348, 10379])).
% 2.12/2.40 tff(10381,plain,
% 2.12/2.40 (~r(z, s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[690, 333, 670, 409, 408])).
% 2.12/2.40 tff(10382,plain,
% 2.12/2.40 (b(z, s(z))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[372, 10381])).
% 2.12/2.40 tff(10383,plain,
% 2.12/2.40 (~r(s(z), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[682, 333, 670, 409, 408])).
% 2.12/2.40 tff(10384,plain,
% 2.12/2.40 (b(s(z), z)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[348, 10383])).
% 2.12/2.40 tff(10385,plain,
% 2.12/2.40 (b(s(elem!1), elem!1)),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[448, 8064, 907])).
% 2.12/2.40 tff(10386,plain,
% 2.12/2.40 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[464, 10385, 54, 114, 3])).
% 2.12/2.40 tff(10387,plain,
% 2.12/2.40 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[472, 10386, 8072])).
% 2.12/2.40 tff(10388,plain,
% 2.12/2.40 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.40 inference(monotonicity,[status(thm)],[10387])).
% 2.12/2.40 tff(10389,plain,
% 2.12/2.40 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.12/2.40 inference(monotonicity,[status(thm)],[10387])).
% 2.12/2.40 tff(10390,plain,
% 2.12/2.40 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.12/2.40 inference(symmetry,[status(thm)],[10389])).
% 2.12/2.40 tff(10391,plain,
% 2.12/2.40 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.12/2.40 inference(monotonicity,[status(thm)],[10390])).
% 2.12/2.40 tff(10392,plain,
% 2.12/2.40 (~(s(elem!1) = s(s(s(z))))),
% 2.12/2.40 inference(modus_ponens,[status(thm)],[244, 10391])).
% 2.12/2.40 tff(10393,plain,
% 2.12/2.40 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, elem!1)),
% 2.12/2.40 inference(monotonicity,[status(thm)],[6165])).
% 2.12/2.40 tff(10394,plain,
% 2.12/2.40 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(z)))))))),
% 2.12/2.40 inference(symmetry,[status(thm)],[10393])).
% 2.12/2.40 tff(10395,plain,
% 2.12/2.40 (r(z, s(s(s(s(s(s(z)))))))),
% 2.12/2.40 inference(modus_ponens,[status(thm)],[670, 10394])).
% 2.12/2.40 tff(10396,assumption,(~r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.12/2.40 tff(10397,plain,
% 2.12/2.40 ($false),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[10396, 10395])).
% 2.12/2.40 tff(10398,plain,(r(z, s(s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.40 tff(10399,plain,
% 2.12/2.40 (r(z, s(s(s(s(s(s(z)))))))),
% 2.12/2.40 inference(unit_resolution,[status(thm)],[10398, 10387, 670])).
% 2.12/2.40 tff(10400,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.12/2.40 tff(10401,plain,
% 2.12/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10402,plain,
% 2.22/2.40 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10403,plain,
% 2.22/2.40 (((~![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(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10402])).
% 2.22/2.40 tff(10404,plain,
% 2.22/2.40 (((~![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(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(transitivity,[status(thm)],[10403, 10401])).
% 2.22/2.40 tff(10405,plain,
% 2.22/2.40 ((~![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(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(10406,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10405, 10404])).
% 2.22/2.40 tff(10407,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10406, 333, 1699, 6107, 321, 10400])).
% 2.22/2.40 tff(10408,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10409,plain,
% 2.22/2.40 (~r(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10408, 10399, 321, 6107])).
% 2.22/2.40 tff(10410,plain,
% 2.22/2.40 (b(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[396, 10409])).
% 2.22/2.40 tff(10411,plain,
% 2.22/2.40 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5467, 8072, 454, 3716, 8075])).
% 2.22/2.40 tff(10412,plain,
% 2.22/2.40 (b(s(z), s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2946, 10411, 123])).
% 2.22/2.40 tff(10413,plain,
% 2.22/2.40 (~b(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2273, 10410, 490, 489])).
% 2.22/2.40 tff(10414,plain,
% 2.22/2.40 (r(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2794, 10413])).
% 2.22/2.40 tff(10415,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10416,plain,
% 2.22/2.40 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10417,plain,
% 2.22/2.40 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10416])).
% 2.22/2.40 tff(10418,plain,
% 2.22/2.40 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[10417, 10415])).
% 2.22/2.40 tff(10419,plain,
% 2.22/2.40 ((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(10420,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10419, 10418])).
% 2.22/2.40 tff(10421,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10420, 333, 3193, 353, 6107, 322])).
% 2.22/2.40 tff(10422,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10423,plain,
% 2.22/2.40 (~r(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10422, 10414, 6107, 322])).
% 2.22/2.40 tff(10424,plain,
% 2.22/2.40 (b(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[172, 10423])).
% 2.22/2.40 tff(10425,plain,
% 2.22/2.40 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2631, 10424, 10412, 10410, 489])).
% 2.22/2.40 tff(10426,plain,
% 2.22/2.40 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[965, 10425, 10392])).
% 2.22/2.40 tff(10427,plain,
% 2.22/2.40 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10426, 10388])).
% 2.22/2.40 tff(10428,plain,
% 2.22/2.40 (~b(z, s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2156, 10424, 10410, 489])).
% 2.22/2.40 tff(10429,plain,
% 2.22/2.40 (r(z, s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[619, 10428])).
% 2.22/2.40 tff(10430,plain,
% 2.22/2.40 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10431,plain,
% 2.22/2.40 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10432,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10431])).
% 2.22/2.40 tff(10433,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(transitivity,[status(thm)],[10432, 10430])).
% 2.22/2.40 tff(10434,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(10435,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10434, 10433])).
% 2.22/2.40 tff(10436,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10435, 333, 10429, 10427, 6107, 321])).
% 2.22/2.40 tff(10437,plain,((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10438,plain,
% 2.22/2.40 (~r(s(elem!1), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10437, 902, 321, 10384, 322, 10382, 670, 123, 54, 114, 3, 408, 6107])).
% 2.22/2.40 tff(10439,plain,
% 2.22/2.40 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[925, 10438, 321])).
% 2.22/2.40 tff(10440,plain,
% 2.22/2.40 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[930, 10439])).
% 2.22/2.40 tff(10441,plain,
% 2.22/2.40 (b(s(elem!1), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[507, 10438])).
% 2.22/2.40 tff(10442,plain,
% 2.22/2.40 (~b(s(elem!1), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[499, 10441, 10384, 10382])).
% 2.22/2.40 tff(10443,plain,
% 2.22/2.40 (r(s(elem!1), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[486, 10442, 1])).
% 2.22/2.40 tff(10444,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[481, 10443, 10440, 408, 409, 54, 114, 3, 322, 907])).
% 2.22/2.40 tff(10445,plain,((elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10446,plain,
% 2.22/2.40 (elem!1 = s(elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10445, 409, 10374, 54, 114, 3, 10378, 1, 321, 7265, 123, 6107])).
% 2.22/2.40 tff(10447,plain,
% 2.22/2.40 (~b(z, s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2974, 10446, 606])).
% 2.22/2.40 tff(10448,plain,
% 2.22/2.40 (r(z, s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[583, 10447])).
% 2.22/2.40 tff(10449,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[6626, 333, 562, 1699, 6107, 321])).
% 2.22/2.40 tff(10450,plain,((~r(s(s(s(z))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10451,plain,
% 2.22/2.40 (~r(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10450, 10448, 6107, 321])).
% 2.22/2.40 tff(10452,plain,
% 2.22/2.40 (b(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[396, 10451])).
% 2.22/2.40 tff(10453,plain,
% 2.22/2.40 (~b(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2273, 10452, 10376, 10380])).
% 2.22/2.40 tff(10454,plain,
% 2.22/2.40 (r(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2794, 10453])).
% 2.22/2.40 tff(10455,plain,
% 2.22/2.40 (~r(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10422, 10454, 6107, 10378])).
% 2.22/2.40 tff(10456,plain,
% 2.22/2.40 (b(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[172, 10455])).
% 2.22/2.40 tff(10457,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10458,plain,
% 2.22/2.40 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(10459,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10458])).
% 2.22/2.40 tff(10460,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[10459, 10457])).
% 2.22/2.40 tff(10461,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(10462,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10461, 10460])).
% 2.22/2.40 tff(10463,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10462, 144, 10380, 10452, 10456, 123, 259])).
% 2.22/2.40 tff(10464,plain,((~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | b(z, elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(10465,plain,
% 2.22/2.40 (~r(s(z), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10464, 10112, 8045, 123, 10373, 606, 54, 8049, 3, 1])).
% 2.22/2.40 tff(10466,plain,
% 2.22/2.40 (s(z) = elem!1),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[406, 10465, 10102])).
% 2.22/2.40 tff(10467,plain,
% 2.22/2.40 (s(s(z)) = s(elem!1)),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10466])).
% 2.22/2.40 tff(10468,plain,
% 2.22/2.40 (s(s(s(z))) = s(s(elem!1))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10467])).
% 2.22/2.40 tff(10469,plain,
% 2.22/2.40 (s(s(elem!1)) = s(s(s(z)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[10468])).
% 2.22/2.40 tff(10470,plain,
% 2.22/2.40 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10469])).
% 2.22/2.40 tff(10471,plain,
% 2.22/2.40 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[10470])).
% 2.22/2.40 tff(10472,plain,
% 2.22/2.40 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10467])).
% 2.22/2.40 tff(10473,plain,
% 2.22/2.40 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10472])).
% 2.22/2.40 tff(10474,plain,
% 2.22/2.40 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[217, 10473])).
% 2.22/2.40 tff(10475,plain,
% 2.22/2.40 (r(s(elem!1), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[8651, 10466, 123, 8045, 7265, 77, 1229, 8049, 606])).
% 2.22/2.40 tff(10476,plain,
% 2.22/2.40 (~r(s(elem!1), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10296, 333, 10475, 7265, 10279])).
% 2.22/2.40 tff(10477,plain,
% 2.22/2.40 (b(s(elem!1), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[507, 10476])).
% 2.22/2.40 tff(10478,plain,
% 2.22/2.40 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10468])).
% 2.22/2.40 tff(10479,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10112, 10478])).
% 2.22/2.40 tff(10480,plain,
% 2.22/2.40 (~r(s(s(elem!1)), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[10243, 10479, 7265, 10373])).
% 2.22/2.40 tff(10481,plain,
% 2.22/2.40 (~r(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[6447, 10480, 10466])).
% 2.22/2.40 tff(10482,plain,
% 2.22/2.40 (b(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[396, 10481])).
% 2.22/2.40 tff(10483,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10469])).
% 2.22/2.40 tff(10484,plain,
% 2.22/2.40 (~(s(s(s(elem!1))) = elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2468, 10466])).
% 2.22/2.40 tff(10485,plain,
% 2.22/2.40 (~(elem!1 = s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2482, 10484])).
% 2.22/2.40 tff(10486,plain,
% 2.22/2.40 (~(s(s(elem!1)) = s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1196, 10485])).
% 2.22/2.40 tff(10487,plain,
% 2.22/2.40 (~r(z, s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2453, 333, 10475, 7265, 10279])).
% 2.22/2.40 tff(10488,plain,
% 2.22/2.40 (b(z, s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[583, 10487])).
% 2.22/2.40 tff(10489,plain,
% 2.22/2.40 (b(s(s(elem!1)), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5509, 10480])).
% 2.22/2.40 tff(10490,plain,
% 2.22/2.40 (~b(s(s(elem!1)), s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5572, 10489, 10488, 10477])).
% 2.22/2.40 tff(10491,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1283, 10490, 10486])).
% 2.22/2.40 tff(10492,plain,
% 2.22/2.40 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[10491, 10483])).
% 2.22/2.40 tff(10493,plain,
% 2.22/2.40 (~b(z, s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[8102, 10466, 606])).
% 2.22/2.40 tff(10494,plain,
% 2.22/2.40 (r(z, s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[372, 10493])).
% 2.22/2.40 tff(10495,plain,
% 2.22/2.40 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10469])).
% 2.22/2.40 tff(10496,plain,
% 2.22/2.40 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[10495])).
% 2.22/2.40 tff(10497,plain,
% 2.22/2.40 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10496, 10469])).
% 2.22/2.40 tff(10498,plain,
% 2.22/2.40 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[10497])).
% 2.22/2.40 tff(10499,plain,
% 2.22/2.40 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[972])).
% 2.22/2.40 tff(10500,plain,
% 2.22/2.40 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9480, 10499])).
% 2.22/2.40 tff(10501,plain,
% 2.22/2.40 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[10495, 10468])).
% 2.22/2.41 tff(10502,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.41 inference(symmetry,[status(thm)],[10501])).
% 2.22/2.41 tff(10503,plain,
% 2.22/2.41 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10502])).
% 2.22/2.41 tff(10504,plain,
% 2.22/2.41 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10466])).
% 2.22/2.41 tff(10505,plain,
% 2.22/2.41 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.22/2.41 inference(symmetry,[status(thm)],[10504])).
% 2.22/2.41 tff(10506,plain,
% 2.22/2.41 (r(s(elem!1), s(z))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10475, 10505])).
% 2.22/2.41 tff(10507,plain,
% 2.22/2.41 (r(s(z), z) <=> r(elem!1, z)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10466])).
% 2.22/2.41 tff(10508,plain,
% 2.22/2.41 (r(elem!1, z) <=> r(s(z), z)),
% 2.22/2.41 inference(symmetry,[status(thm)],[10507])).
% 2.22/2.41 tff(10509,plain,
% 2.22/2.41 (r(s(z), z)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10279, 10508])).
% 2.22/2.41 tff(10510,plain,
% 2.22/2.41 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10466])).
% 2.22/2.41 tff(10511,plain,
% 2.22/2.41 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10510, 2])).
% 2.22/2.41 tff(10512,plain,
% 2.22/2.41 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10511])).
% 2.22/2.41 tff(10513,plain,
% 2.22/2.41 (~(elem!1 = s(s(s(z))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[166, 10512])).
% 2.22/2.41 tff(10514,plain,
% 2.22/2.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3522, 10468, 10513])).
% 2.22/2.41 tff(10515,plain,
% 2.22/2.41 (~r(s(s(s(elem!1))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4215, 10514, 10509, 10506, 7265, 10488, 10477])).
% 2.22/2.41 tff(10516,plain,
% 2.22/2.41 (b(s(s(s(elem!1))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1101, 10515])).
% 2.22/2.41 tff(10517,plain,
% 2.22/2.41 (b(s(s(s(s(z)))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3588, 10516, 10466])).
% 2.22/2.41 tff(10518,plain,
% 2.22/2.41 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3552, 144, 10517, 8050, 8052])).
% 2.22/2.41 tff(10519,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9761, 10518])).
% 2.22/2.41 tff(10520,plain,
% 2.22/2.41 (((~![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(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10521,plain,
% 2.22/2.41 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10522,plain,
% 2.22/2.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10521])).
% 2.22/2.41 tff(10523,plain,
% 2.22/2.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10522, 10520])).
% 2.22/2.41 tff(10524,plain,
% 2.22/2.41 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(10525,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10524, 10523])).
% 2.22/2.41 tff(10526,plain,
% 2.22/2.41 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10525, 333, 10373, 10479, 10519])).
% 2.22/2.41 tff(10527,plain,
% 2.22/2.41 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10526, 10503])).
% 2.22/2.41 tff(10528,plain,
% 2.22/2.41 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1116, 10527, 10500])).
% 2.22/2.41 tff(10529,plain,
% 2.22/2.41 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10528, 10498])).
% 2.22/2.41 tff(10530,plain,
% 2.22/2.41 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10468])).
% 2.22/2.41 tff(10531,plain,
% 2.22/2.41 (b(s(s(elem!1)), elem!1)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[4367, 10530])).
% 2.22/2.41 tff(10532,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 2.22/2.41 tff(10533,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[6730, 144, 2812, 3529, 4972, 10532])).
% 2.22/2.41 tff(10534,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10535,plain,
% 2.22/2.41 (~b(elem!1, s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10534, 10517, 10531, 10529])).
% 2.22/2.41 tff(10536,plain,
% 2.22/2.41 (~b(s(z), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5343, 10535, 10466])).
% 2.22/2.41 tff(10537,plain,
% 2.22/2.41 (r(s(z), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[172, 10536])).
% 2.22/2.41 tff(10538,plain,
% 2.22/2.41 (~r(z, s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3011, 10537, 10494, 10492])).
% 2.22/2.41 tff(10539,plain,
% 2.22/2.41 (b(z, s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[619, 10538])).
% 2.22/2.41 tff(10540,plain,
% 2.22/2.41 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1802, 10539, 10482, 10477])).
% 2.22/2.41 tff(10541,plain,
% 2.22/2.41 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[965, 10540, 10474])).
% 2.22/2.41 tff(10542,plain,
% 2.22/2.41 (r(s(elem!1), s(s(elem!1)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10541, 10471])).
% 2.22/2.41 tff(10543,plain,
% 2.22/2.41 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10466])).
% 2.22/2.41 tff(10544,plain,
% 2.22/2.41 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10543, 1218])).
% 2.22/2.41 tff(10545,plain,
% 2.22/2.41 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10544])).
% 2.22/2.41 tff(10546,plain,
% 2.22/2.41 (~(elem!1 = s(s(elem!1)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[107, 10545])).
% 2.22/2.41 tff(10547,plain,
% 2.22/2.41 (r(elem!1, s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2522, 10535, 10546])).
% 2.22/2.41 tff(10548,plain,
% 2.22/2.41 (~r(s(elem!1), s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5242, 10547, 10491, 10475])).
% 2.22/2.41 tff(10549,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10548, 10542])).
% 2.22/2.41 tff(10550,plain,(b(z, elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10551,plain,
% 2.22/2.41 (b(z, elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10550, 2303, 123, 54, 3, 1, 4367])).
% 2.22/2.41 tff(10552,plain,
% 2.22/2.41 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[8808, 10551, 8045, 3, 54])).
% 2.22/2.41 tff(10553,plain,
% 2.22/2.41 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10552])).
% 2.22/2.41 tff(10554,plain,
% 2.22/2.41 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10553])).
% 2.22/2.41 tff(10555,plain,
% 2.22/2.41 (~(elem!1 = s(s(s(z))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[244, 10554])).
% 2.22/2.41 tff(10556,plain,
% 2.22/2.41 (~r(z, elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2305, 10552, 2303])).
% 2.22/2.41 tff(10557,plain,
% 2.22/2.41 (b(elem!1, z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[787, 286, 81])).
% 2.22/2.41 tff(10558,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10559,plain,
% 2.22/2.41 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10560,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10559])).
% 2.22/2.41 tff(10561,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10560, 10558])).
% 2.22/2.41 tff(10562,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(10563,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10562, 10561])).
% 2.22/2.41 tff(10564,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10563, 144, 251, 624, 285, 4367])).
% 2.22/2.41 tff(10565,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10566,plain,
% 2.22/2.41 (~b(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10565, 10557, 4367, 251])).
% 2.22/2.41 tff(10567,plain,
% 2.22/2.41 (r(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[396, 10566])).
% 2.22/2.41 tff(10568,plain,
% 2.22/2.41 (~(s(elem!1) = elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5813, 5604])).
% 2.22/2.41 tff(10569,plain,
% 2.22/2.41 (~b(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10565, 624, 4367, 251])).
% 2.22/2.41 tff(10570,plain,
% 2.22/2.41 (r(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[396, 10569])).
% 2.22/2.41 tff(10571,plain,
% 2.22/2.41 (~r(s(z), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[7314, 354, 323, 10570])).
% 2.22/2.41 tff(10572,plain,
% 2.22/2.41 (b(s(z), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[172, 10571])).
% 2.22/2.41 tff(10573,plain,
% 2.22/2.41 (~r(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[6555, 354, 323, 10570])).
% 2.22/2.41 tff(10574,plain,
% 2.22/2.41 (b(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2794, 10573])).
% 2.22/2.41 tff(10575,plain,
% 2.22/2.41 (~(elem!1 = s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1569, 10568])).
% 2.22/2.41 tff(10576,plain,
% 2.22/2.41 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[7186])).
% 2.22/2.41 tff(10577,plain,
% 2.22/2.41 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10575, 10576])).
% 2.22/2.41 tff(10578,plain,
% 2.22/2.41 (~b(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4375, 10574, 4367, 7071])).
% 2.22/2.41 tff(10579,plain,
% 2.22/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[735, 10578, 81])).
% 2.22/2.41 tff(10580,plain,
% 2.22/2.41 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[319, 10579])).
% 2.22/2.41 tff(10581,plain,
% 2.22/2.41 (b(s(elem!1), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1673, 10580, 323, 354, 10577, 1575, 5584, 10575, 1])).
% 2.22/2.41 tff(10582,plain,
% 2.22/2.41 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[899, 144, 10581, 10574, 10572])).
% 2.22/2.41 tff(10583,plain,
% 2.22/2.41 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[965, 10582, 1682])).
% 2.22/2.41 tff(10584,plain,
% 2.22/2.41 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[4367, 9190])).
% 2.22/2.41 tff(10585,plain,
% 2.22/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2262, 10572, 123, 10584])).
% 2.22/2.41 tff(10586,plain,
% 2.22/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[249, 10585])).
% 2.22/2.41 tff(10587,plain,
% 2.22/2.41 (r(elem!1, s(s(s(z))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10586, 1685])).
% 2.22/2.41 tff(10588,plain,
% 2.22/2.41 (~r(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[7383, 10574, 1575, 5584, 1, 10575, 1682, 10570, 354, 323])).
% 2.22/2.41 tff(10589,plain,
% 2.22/2.41 (b(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[507, 10588])).
% 2.22/2.41 tff(10590,plain,
% 2.22/2.41 (~b(s(elem!1), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[916, 10589, 251, 624])).
% 2.22/2.41 tff(10591,plain,
% 2.22/2.41 (r(s(elem!1), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[448, 10590, 10568])).
% 2.22/2.41 tff(10592,plain,
% 2.22/2.41 (((~![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(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), 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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10593,plain,
% 2.22/2.41 (((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10594,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10593])).
% 2.22/2.41 tff(10595,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10594, 10592])).
% 2.22/2.41 tff(10596,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(10597,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10596, 10595])).
% 2.22/2.41 tff(10598,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10597, 333, 10591, 10587, 10570, 10583])).
% 2.22/2.41 tff(10599,plain,((~r(z, s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(z), z)) | r(z, elem!1) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10600,plain,
% 2.22/2.41 (~r(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10599, 10280, 81, 1575, 1, 251, 10557, 123, 4367])).
% 2.22/2.41 tff(10601,plain,
% 2.22/2.41 (b(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[372, 10600])).
% 2.22/2.41 tff(10602,plain,
% 2.22/2.41 (~b(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[813, 10601, 123, 259, 251])).
% 2.22/2.41 tff(10603,plain,
% 2.22/2.41 (r(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[720, 10602, 5609])).
% 2.22/2.41 tff(10604,plain,
% 2.22/2.41 (~r(s(elem!1), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1911, 10603, 251, 10280, 10568, 10557])).
% 2.22/2.41 tff(10605,plain,
% 2.22/2.41 (b(s(elem!1), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[486, 10604, 1])).
% 2.22/2.41 tff(10606,plain,
% 2.22/2.41 (~b(z, s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1919, 144, 251, 7071, 10601, 10605])).
% 2.22/2.41 tff(10607,plain,
% 2.22/2.41 (r(z, s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[583, 10606])).
% 2.22/2.41 tff(10608,plain,
% 2.22/2.41 (~r(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[8030, 10607, 10280, 10567])).
% 2.22/2.41 tff(10609,plain,
% 2.22/2.41 (b(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2794, 10608])).
% 2.22/2.41 tff(10610,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10611,plain,
% 2.22/2.41 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10612,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10611])).
% 2.22/2.41 tff(10613,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10612, 10610])).
% 2.22/2.41 tff(10614,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(10615,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10614, 10613])).
% 2.22/2.41 tff(10616,plain,
% 2.22/2.41 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10615, 144, 7071, 10605, 4367])).
% 2.22/2.41 tff(10617,plain,
% 2.22/2.41 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10616, 10609])).
% 2.22/2.41 tff(10618,plain,
% 2.22/2.41 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 10617])).
% 2.22/2.41 tff(10619,plain,
% 2.22/2.41 (~r(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[8142, 10607, 10280, 1682, 10567, 10605])).
% 2.22/2.41 tff(10620,plain,
% 2.22/2.41 (b(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[507, 10619])).
% 2.22/2.41 tff(10621,plain,
% 2.22/2.41 (~b(s(elem!1), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[916, 10620, 251, 10557])).
% 2.22/2.41 tff(10622,plain,
% 2.22/2.41 (r(s(elem!1), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[448, 10621, 10568])).
% 2.22/2.41 tff(10623,plain,
% 2.22/2.41 (((~![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(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~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(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10624,plain,
% 2.22/2.41 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(10625,plain,
% 2.22/2.41 (((~![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(s(s(z))), s(elem!1))) | (~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(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10624])).
% 2.22/2.41 tff(10626,plain,
% 2.22/2.41 (((~![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(s(s(z))), s(elem!1))) | (~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(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[10625, 10623])).
% 2.22/2.41 tff(10627,plain,
% 2.22/2.41 ((~![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(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(10628,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10627, 10626])).
% 2.22/2.41 tff(10629,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10628, 333, 10622, 10607, 10567, 10618])).
% 2.22/2.41 tff(10630,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10631,plain,
% 2.22/2.41 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10630, 10551, 4367, 1, 123, 8045, 10552, 10556])).
% 2.22/2.41 tff(10632,plain,
% 2.22/2.41 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[302, 10631])).
% 2.22/2.41 tff(10633,plain,
% 2.22/2.41 (b(s(z), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2235, 10552, 123])).
% 2.22/2.41 tff(10634,plain,
% 2.22/2.41 (r(elem!1, z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2558, 321, 81])).
% 2.22/2.41 tff(10635,plain,
% 2.22/2.41 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[81])).
% 2.22/2.41 tff(10636,plain,
% 2.22/2.41 (r(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(z), s(elem!1))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[10635])).
% 2.22/2.41 tff(10637,plain,
% 2.22/2.41 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.41 inference(symmetry,[status(thm)],[10636])).
% 2.22/2.41 tff(10638,plain,
% 2.22/2.41 (~r(elem!1, s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1620, 509, 10634, 354])).
% 2.22/2.41 tff(10639,plain,
% 2.22/2.41 (b(s(elem!1), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1653, 509, 1575, 5584, 354, 1, 10575])).
% 2.22/2.41 tff(10640,plain,
% 2.22/2.41 (~r(z, s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9017, 408, 435, 509])).
% 2.22/2.41 tff(10641,plain,
% 2.22/2.41 (b(z, s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[583, 10640])).
% 2.22/2.41 tff(10642,plain,
% 2.22/2.41 ((~b(z, s(elem!1))) | (~b(z, s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1919, 144, 251, 134, 488])).
% 2.22/2.41 tff(10643,plain,
% 2.22/2.41 (~b(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10642, 10641])).
% 2.22/2.41 tff(10644,plain,
% 2.22/2.41 (r(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[372, 10643])).
% 2.22/2.41 tff(10645,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1610, 333, 435, 10644, 408, 509])).
% 2.22/2.41 tff(10646,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10647,plain,
% 2.22/2.41 (~r(s(elem!1), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10646, 10639, 134, 10634, 509, 251])).
% 2.22/2.41 tff(10648,plain,
% 2.22/2.41 (~b(s(z), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1732, 10647, 134, 10575, 10638])).
% 2.22/2.41 tff(10649,plain,
% 2.22/2.41 (r(s(z), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1244, 10648, 1229])).
% 2.22/2.41 tff(10650,plain,
% 2.22/2.41 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[10649, 10637])).
% 2.22/2.41 tff(10651,plain,
% 2.22/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[7282, 509, 134, 10575, 10634, 354, 81, 1])).
% 2.22/2.41 tff(10652,plain,
% 2.22/2.41 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[319, 10651])).
% 2.22/2.41 tff(10653,plain,
% 2.22/2.41 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2348, 10652, 321, 354])).
% 2.22/2.41 tff(10654,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10653, 10650])).
% 2.22/2.41 tff(10655,plain,((~r(s(elem!1), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(10656,plain,
% 2.22/2.41 (~r(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[10655, 354, 321, 81, 134, 251, 1, 1575])).
% 2.22/2.41 tff(10657,plain,
% 2.22/2.41 (b(s(elem!1), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[507, 10656])).
% 2.22/2.41 tff(10658,plain,
% 2.22/2.41 (~r(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[747, 323, 408, 354])).
% 2.22/2.41 tff(10659,plain,
% 2.22/2.41 (b(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[720, 10658, 714])).
% 2.22/2.41 tff(10660,plain,
% 2.22/2.41 (~b(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4375, 10659, 4367, 134])).
% 2.22/2.41 tff(10661,plain,
% 2.22/2.41 (r(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2794, 10660])).
% 2.22/2.41 tff(10662,plain,
% 2.22/2.41 (~r(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[6555, 10661, 354, 323])).
% 2.22/2.41 tff(10663,plain,
% 2.22/2.41 (b(s(s(s(z))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[396, 10662])).
% 2.22/2.41 tff(10664,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10665,plain,
% 2.22/2.42 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10666,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10665])).
% 2.22/2.42 tff(10667,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10666, 10664])).
% 2.22/2.42 tff(10668,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10669,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10668, 10667])).
% 2.22/2.42 tff(10670,plain,
% 2.22/2.42 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10669, 144, 251, 491, 4367])).
% 2.22/2.42 tff(10671,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10670, 10663])).
% 2.22/2.42 tff(10672,plain,
% 2.22/2.42 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1951, 44, 3295, 10671])).
% 2.22/2.42 tff(10673,plain,
% 2.22/2.42 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[8915, 144, 451, 251, 491, 10663])).
% 2.22/2.42 tff(10674,plain,
% 2.22/2.42 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[965, 10673, 960])).
% 2.22/2.42 tff(10675,plain,
% 2.22/2.42 (~b(elem!1, s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[7524, 10659, 134, 1, 323, 354, 251, 451])).
% 2.22/2.42 tff(10676,plain,
% 2.22/2.42 (r(elem!1, s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[560, 10675, 902])).
% 2.22/2.42 tff(10677,plain,
% 2.22/2.42 (~r(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5084, 333, 10676, 10674, 10672])).
% 2.22/2.42 tff(10678,plain,
% 2.22/2.42 (b(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1538, 10677, 1524])).
% 2.22/2.42 tff(10679,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10680,plain,
% 2.22/2.42 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10681,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10680])).
% 2.22/2.42 tff(10682,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10681, 10679])).
% 2.22/2.42 tff(10683,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, s(s(s(z))))) | (~b(z, elem!1)))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10684,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10683, 10682])).
% 2.22/2.42 tff(10685,plain,
% 2.22/2.42 (~b(z, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10684, 144, 251, 10678, 4367])).
% 2.22/2.42 tff(10686,plain,
% 2.22/2.42 (r(z, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[619, 10685])).
% 2.22/2.42 tff(10687,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10688,plain,
% 2.22/2.42 (((~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))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10689,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10688])).
% 2.22/2.42 tff(10690,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10689, 10687])).
% 2.22/2.42 tff(10691,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))) | (~b(s(z), elem!1)))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10692,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10691, 10690])).
% 2.22/2.42 tff(10693,plain,
% 2.22/2.42 (~b(s(z), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10692, 144, 134, 10678, 4367])).
% 2.22/2.42 tff(10694,plain,
% 2.22/2.42 (r(s(z), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[172, 10693])).
% 2.22/2.42 tff(10695,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3011, 10694, 10686, 354, 10672])).
% 2.22/2.42 tff(10696,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(10697,plain,
% 2.22/2.42 (~r(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10696, 451, 134, 4367, 251, 3843, 1682, 354, 491, 10575, 1, 5609, 10634])).
% 2.22/2.42 tff(10698,plain,
% 2.22/2.42 (b(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[348, 10697])).
% 2.22/2.42 tff(10699,plain,
% 2.22/2.42 (~b(s(z), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[8893, 10698])).
% 2.22/2.42 tff(10700,plain,
% 2.22/2.42 (r(s(z), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1244, 10699, 1229])).
% 2.22/2.42 tff(10701,plain,
% 2.22/2.42 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10700, 10637])).
% 2.22/2.42 tff(10702,plain,
% 2.22/2.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2348, 10701, 321, 354])).
% 2.22/2.42 tff(10703,plain,
% 2.22/2.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[319, 10702])).
% 2.22/2.42 tff(10704,plain,
% 2.22/2.42 (b(elem!1, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[735, 10703, 81])).
% 2.22/2.42 tff(10705,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[4375, 10704, 4367, 134])).
% 2.22/2.42 tff(10706,plain,
% 2.22/2.42 (r(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2794, 10705])).
% 2.22/2.42 tff(10707,plain,
% 2.22/2.42 (~r(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[6565, 10706, 10700, 354])).
% 2.22/2.42 tff(10708,plain,
% 2.22/2.42 (b(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[396, 10707])).
% 2.22/2.42 tff(10709,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10670, 10708])).
% 2.22/2.42 tff(10710,plain,
% 2.22/2.42 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 10709])).
% 2.22/2.42 tff(10711,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10712,plain,
% 2.22/2.42 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10713,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10712])).
% 2.22/2.42 tff(10714,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10713, 10711])).
% 2.22/2.42 tff(10715,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10716,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10715, 10714])).
% 2.22/2.42 tff(10717,plain,
% 2.22/2.42 (~b(s(elem!1), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10716, 144, 451, 251, 491, 10698])).
% 2.22/2.42 tff(10718,plain,
% 2.22/2.42 (r(s(elem!1), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[486, 10717, 1])).
% 2.22/2.42 tff(10719,plain,
% 2.22/2.42 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(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(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10720,plain,
% 2.22/2.42 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10721,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10720])).
% 2.22/2.42 tff(10722,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10721, 10719])).
% 2.22/2.42 tff(10723,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10724,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10723, 10722])).
% 2.22/2.42 tff(10725,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10724, 333, 10718, 10700, 10706, 10710])).
% 2.22/2.42 tff(10726,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(10727,plain,
% 2.22/2.42 (~b(s(elem!1), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10726, 10657, 251, 4367, 354, 134, 81, 321, 1])).
% 2.22/2.42 tff(10728,plain,
% 2.22/2.42 (r(s(elem!1), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[448, 10727, 10568])).
% 2.22/2.42 tff(10729,plain,
% 2.22/2.42 (~b(s(z), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[8893, 489])).
% 2.22/2.42 tff(10730,plain,
% 2.22/2.42 (r(s(z), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1244, 10729, 1237])).
% 2.22/2.42 tff(10731,plain,
% 2.22/2.42 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10730, 10637])).
% 2.22/2.42 tff(10732,plain,
% 2.22/2.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2348, 10731, 321, 354])).
% 2.22/2.42 tff(10733,plain,
% 2.22/2.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[319, 10732])).
% 2.22/2.42 tff(10734,plain,
% 2.22/2.42 (b(elem!1, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[735, 10733, 81])).
% 2.22/2.42 tff(10735,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[4375, 10734, 4367, 134])).
% 2.22/2.42 tff(10736,plain,
% 2.22/2.42 (r(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2794, 10735])).
% 2.22/2.42 tff(10737,plain,
% 2.22/2.42 (~r(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[6565, 10736, 10730, 354])).
% 2.22/2.42 tff(10738,plain,
% 2.22/2.42 (b(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[396, 10737])).
% 2.22/2.42 tff(10739,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10670, 10738])).
% 2.22/2.42 tff(10740,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3799, 10739, 10738, 81, 4363, 435, 489, 10733, 10634, 10730])).
% 2.22/2.42 tff(10741,plain,((~b(s(z), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(10742,plain,
% 2.22/2.42 (~b(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10741, 10728, 81, 251, 10657, 4367, 354, 134, 321, 1229])).
% 2.22/2.42 tff(10743,plain,
% 2.22/2.42 (r(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[348, 10742])).
% 2.22/2.42 tff(10744,plain,
% 2.22/2.42 (~r(elem!1, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[747, 10743, 10634, 354])).
% 2.22/2.42 tff(10745,plain,
% 2.22/2.42 (b(elem!1, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[720, 10744, 5609])).
% 2.22/2.42 tff(10746,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[4375, 10745, 4367, 134])).
% 2.22/2.42 tff(10747,plain,
% 2.22/2.42 (r(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2794, 10746])).
% 2.22/2.42 tff(10748,plain,
% 2.22/2.42 (~r(z, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[8841, 333, 354, 10743, 10747])).
% 2.22/2.42 tff(10749,plain,
% 2.22/2.42 (b(z, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[619, 10748])).
% 2.22/2.42 tff(10750,plain,
% 2.22/2.42 (~r(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[6555, 10747, 354, 10743])).
% 2.22/2.42 tff(10751,plain,
% 2.22/2.42 (b(s(s(s(z))), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[396, 10750])).
% 2.22/2.42 tff(10752,plain,
% 2.22/2.42 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1802, 10749, 10751, 10657])).
% 2.22/2.42 tff(10753,plain,
% 2.22/2.42 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[965, 10752, 1682])).
% 2.22/2.42 tff(10754,plain,
% 2.22/2.42 (((~![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(s(elem!1), s(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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10755,plain,
% 2.22/2.42 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(10756,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10755])).
% 2.22/2.42 tff(10757,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10756, 10754])).
% 2.22/2.42 tff(10758,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(10759,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[10758, 10757])).
% 2.22/2.42 tff(10760,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10759, 333, 435, 1525, 3193, 1686])).
% 2.22/2.42 tff(10761,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(10762,plain,
% 2.22/2.42 (~r(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10761, 10728, 10747, 10753])).
% 2.22/2.42 tff(10763,plain,
% 2.22/2.42 (b(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1538, 10762, 3843])).
% 2.22/2.42 tff(10764,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10684, 144, 251, 10763, 10749, 4367])).
% 2.22/2.42 tff(10765,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(10766,plain,
% 2.22/2.42 (~r(z, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[10765, 10551, 4367, 10633, 10552, 10632, 1, 10556])).
% 2.22/2.42 tff(10767,plain,
% 2.22/2.42 (b(z, s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[372, 10766])).
% 2.22/2.42 tff(10768,plain,
% 2.22/2.42 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[757, 10767, 123, 8045])).
% 2.22/2.42 tff(10769,plain,
% 2.22/2.42 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[319, 10768])).
% 2.22/2.42 tff(10770,plain,
% 2.22/2.42 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10552])).
% 2.22/2.42 tff(10771,plain,
% 2.22/2.42 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10770])).
% 2.22/2.42 tff(10772,plain,
% 2.22/2.42 (~(s(s(z)) = elem!1)),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[1446, 10771])).
% 2.22/2.42 tff(10773,plain,
% 2.22/2.42 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1508, 10772])).
% 2.22/2.42 tff(10774,plain,
% 2.22/2.42 (~(s(s(elem!1)) = elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5010, 10552])).
% 2.22/2.42 tff(10775,plain,
% 2.22/2.42 (~(elem!1 = s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5603, 10774])).
% 2.22/2.42 tff(10776,plain,
% 2.22/2.42 (~(s(elem!1) = elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5813, 10775])).
% 2.22/2.42 tff(10777,plain,
% 2.22/2.42 (r(elem!1, z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2558, 10632, 10552])).
% 2.22/2.42 tff(10778,plain,
% 2.22/2.42 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = elem!1)),
% 2.22/2.42 inference(monotonicity,[status(thm)],[10552])).
% 2.22/2.42 tff(10779,plain,
% 2.22/2.42 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(z))),
% 2.22/2.42 inference(transitivity,[status(thm)],[10778, 53])).
% 2.22/2.42 tff(10780,plain,
% 2.22/2.43 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(z)))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10779])).
% 2.22/2.43 tff(10781,plain,
% 2.22/2.43 (~(elem!1 = s(z))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[34, 10780])).
% 2.22/2.43 tff(10782,plain,
% 2.22/2.43 (~b(elem!1, s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[813, 10767, 123, 8045, 10551])).
% 2.22/2.43 tff(10783,plain,
% 2.22/2.43 (r(elem!1, s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[720, 10782, 10781])).
% 2.22/2.43 tff(10784,plain,
% 2.22/2.43 (~r(s(z), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[779, 56, 321, 123, 490, 322])).
% 2.22/2.43 tff(10785,plain,
% 2.22/2.43 (b(s(z), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[348, 10784])).
% 2.22/2.43 tff(10786,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10787,plain,
% 2.22/2.43 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10788,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10787])).
% 2.22/2.43 tff(10789,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10788, 10786])).
% 2.22/2.43 tff(10790,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10791,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10790, 10789])).
% 2.22/2.43 tff(10792,plain,
% 2.22/2.43 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10791, 144, 134, 490, 4367])).
% 2.22/2.43 tff(10793,plain,
% 2.22/2.43 (~b(s(s(s(z))), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10792, 56])).
% 2.22/2.43 tff(10794,plain,
% 2.22/2.43 (r(s(s(s(z))), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[396, 10793])).
% 2.22/2.43 tff(10795,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10796,plain,
% 2.22/2.43 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10797,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10796])).
% 2.22/2.43 tff(10798,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10797, 10795])).
% 2.22/2.43 tff(10799,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10800,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10799, 10798])).
% 2.22/2.43 tff(10801,plain,
% 2.22/2.43 (~b(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10800, 144, 134, 489, 284, 4367])).
% 2.22/2.43 tff(10802,plain,
% 2.22/2.43 (r(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[172, 10801])).
% 2.22/2.43 tff(10803,plain,
% 2.22/2.43 (~b(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[2090, 284, 251, 134, 490])).
% 2.22/2.43 tff(10804,plain,
% 2.22/2.43 (r(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1538, 10803, 1524])).
% 2.22/2.43 tff(10805,plain,
% 2.22/2.43 (((~![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))), z)) | (~r(elem!1, 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(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10806,plain,
% 2.22/2.43 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10807,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10806])).
% 2.22/2.43 tff(10808,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10807, 10805])).
% 2.22/2.43 tff(10809,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10810,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10809, 10808])).
% 2.22/2.43 tff(10811,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10810, 333, 10804, 722, 1699, 10802])).
% 2.22/2.43 tff(10812,plain,((~b(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(10813,plain,
% 2.22/2.43 (~b(z, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10812, 10794, 722, 134, 10785, 4367, 1524, 251, 490])).
% 2.22/2.43 tff(10814,plain,
% 2.22/2.43 (r(z, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[619, 10813])).
% 2.22/2.43 tff(10815,plain,
% 2.22/2.43 (((~![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(s(s(z))))) | (~r(s(s(s(z))), 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, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10816,plain,
% 2.22/2.43 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10817,plain,
% 2.22/2.43 (((~![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(elem!1, 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, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10816])).
% 2.22/2.43 tff(10818,plain,
% 2.22/2.43 (((~![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(elem!1, 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, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10817, 10815])).
% 2.22/2.43 tff(10819,plain,
% 2.22/2.43 ((~![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(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10820,plain,
% 2.22/2.43 ((~![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(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10819, 10818])).
% 2.22/2.43 tff(10821,plain,
% 2.22/2.43 (~r(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10820, 333, 408, 10794, 10814])).
% 2.22/2.43 tff(10822,plain,
% 2.22/2.43 (b(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1538, 10821, 1524])).
% 2.22/2.43 tff(10823,plain,
% 2.22/2.43 (~b(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10692, 144, 134, 10822, 4367])).
% 2.22/2.43 tff(10824,plain,
% 2.22/2.43 (r(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[172, 10823])).
% 2.22/2.43 tff(10825,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10826,plain,
% 2.22/2.43 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10827,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10826])).
% 2.22/2.43 tff(10828,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10827, 10825])).
% 2.22/2.43 tff(10829,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10830,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10829, 10828])).
% 2.22/2.43 tff(10831,plain,
% 2.22/2.43 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10830, 144, 451, 2082, 4367])).
% 2.22/2.43 tff(10832,plain,
% 2.22/2.43 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[965, 10831, 960])).
% 2.22/2.43 tff(10833,plain,
% 2.22/2.43 (~r(z, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1972, 10832, 1699, 623])).
% 2.22/2.43 tff(10834,plain,
% 2.22/2.43 (~b(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10692, 144, 134, 2082, 4367])).
% 2.22/2.43 tff(10835,plain,
% 2.22/2.43 (r(s(z), s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[172, 10834])).
% 2.22/2.43 tff(10836,plain,
% 2.22/2.43 (~r(elem!1, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[8975, 451, 134, 251, 1, 490, 722, 489, 408, 509])).
% 2.22/2.43 tff(10837,plain,
% 2.22/2.43 (b(elem!1, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[560, 10836, 902])).
% 2.22/2.43 tff(10838,plain,
% 2.22/2.43 (~b(z, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1642, 10837, 251, 451])).
% 2.22/2.43 tff(10839,plain,
% 2.22/2.43 (r(z, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[583, 10838])).
% 2.22/2.43 tff(10840,plain,
% 2.22/2.43 (((~![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), z)) | (~r(s(s(s(z))), z)) | (~r(s(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(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10841,plain,
% 2.22/2.43 ((~![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), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10842,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10841, 10840])).
% 2.22/2.43 tff(10843,plain,
% 2.22/2.43 (~r(s(s(s(z))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10842, 333, 509, 10839, 1699])).
% 2.22/2.43 tff(10844,plain,
% 2.22/2.43 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[4819, 10837, 4367, 451])).
% 2.22/2.43 tff(10845,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 10844, 10843])).
% 2.22/2.43 tff(10846,plain,((~b(s(elem!1), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(10847,plain,
% 2.22/2.43 (~r(s(elem!1), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10846, 451, 3295, 1699, 251, 4367, 902, 134, 1, 490, 722, 489, 408])).
% 2.22/2.43 tff(10848,plain,
% 2.22/2.43 (b(s(elem!1), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[507, 10847])).
% 2.22/2.43 tff(10849,plain,
% 2.22/2.43 (~b(s(elem!1), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1820, 10848, 134, 490, 451])).
% 2.22/2.43 tff(10850,plain,
% 2.22/2.43 (r(s(elem!1), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[486, 10849, 1])).
% 2.22/2.43 tff(10851,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10852,plain,
% 2.22/2.43 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10853,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10852])).
% 2.22/2.43 tff(10854,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[10853, 10851])).
% 2.22/2.43 tff(10855,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(10856,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[10855, 10854])).
% 2.22/2.43 tff(10857,plain,
% 2.22/2.43 (~r(elem!1, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10856, 333, 10850, 722, 10835])).
% 2.22/2.43 tff(10858,plain,
% 2.22/2.43 (b(elem!1, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[560, 10857, 902])).
% 2.22/2.43 tff(10859,plain,
% 2.22/2.43 (~b(z, s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1642, 10858, 251, 451])).
% 2.22/2.43 tff(10860,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[583, 10859, 10833])).
% 2.22/2.43 tff(10861,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(10862,plain,
% 2.22/2.43 (~b(s(elem!1), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10861, 10794, 251, 10814, 1722, 960, 722, 10822, 4367, 1, 134, 490, 10785, 408])).
% 2.22/2.43 tff(10863,plain,
% 2.22/2.43 (r(s(elem!1), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[448, 10862, 433])).
% 2.22/2.43 tff(10864,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9033, 333, 435, 408, 509, 623])).
% 2.22/2.43 tff(10865,plain,((~r(z, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(10866,plain,
% 2.22/2.43 (~r(s(elem!1), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10865, 10863, 408, 10814])).
% 2.22/2.43 tff(10867,plain,
% 2.22/2.43 (b(s(elem!1), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[507, 10866])).
% 2.22/2.43 tff(10868,plain,
% 2.22/2.43 (~b(s(elem!1), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[499, 10867, 490, 10785])).
% 2.22/2.43 tff(10869,plain,
% 2.22/2.43 (r(s(elem!1), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[486, 10868, 1])).
% 2.22/2.43 tff(10870,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[7729, 333, 10863, 10869, 722, 10824])).
% 2.22/2.43 tff(10871,plain,((~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(10872,plain,
% 2.22/2.43 (~b(s(s(s(z))), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[10871, 10783, 1, 10767, 10777, 10776, 10551, 10773, 4367, 10633, 10555, 10632, 123, 10769])).
% 2.22/2.43 tff(10873,plain,
% 2.22/2.43 (r(s(s(s(z))), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[2794, 10872])).
% 2.22/2.43 tff(10874,plain,
% 2.22/2.43 (~r(z, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[642, 323, 321, 322])).
% 2.22/2.43 tff(10875,plain,
% 2.22/2.43 (b(z, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[619, 10874])).
% 2.22/2.43 tff(10876,plain,
% 2.22/2.43 (~b(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[2090, 10875, 251, 134, 490])).
% 2.22/2.43 tff(10877,plain,
% 2.22/2.43 (r(elem!1, s(s(s(z))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1538, 10876, 1524])).
% 2.22/2.43 tff(10878,plain,
% 2.22/2.43 (((~![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(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10879,plain,
% 2.22/2.43 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(10880,plain,
% 2.22/2.43 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[10879])).
% 2.22/2.43 tff(10881,plain,
% 2.22/2.43 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[10880, 10878])).
% 2.22/2.44 tff(10882,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(10883,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[10882, 10881])).
% 2.22/2.44 tff(10884,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10883, 333, 323, 10877, 722, 3193])).
% 2.22/2.44 tff(10885,plain,((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10886,plain,
% 2.22/2.44 (~r(s(z), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10885, 10783, 10873, 10555, 10551, 10633, 10767, 10632, 10769])).
% 2.22/2.44 tff(10887,plain,
% 2.22/2.44 (b(s(z), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[348, 10886])).
% 2.22/2.44 tff(10888,plain,
% 2.22/2.44 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(elem!1, z)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10552])).
% 2.22/2.44 tff(10889,plain,
% 2.22/2.44 ((~b(s(s(s(s(s(s(s(z))))))), z)) <=> (~b(elem!1, z))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10888])).
% 2.22/2.44 tff(10890,plain,
% 2.22/2.44 (~b(elem!1, z)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[10631, 10889])).
% 2.22/2.44 tff(10891,plain,
% 2.22/2.44 (~b(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2144, 144, 251, 134, 489, 285])).
% 2.22/2.44 tff(10892,plain,
% 2.22/2.44 (r(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[172, 10891])).
% 2.22/2.44 tff(10893,plain,
% 2.22/2.44 (((~![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(s(z))))) | (~r(s(s(s(z))), 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(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(10894,plain,
% 2.22/2.44 (((~r(s(z), s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(10895,plain,
% 2.22/2.44 (((~![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(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10894])).
% 2.22/2.44 tff(10896,plain,
% 2.22/2.44 (((~![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(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[10895, 10893])).
% 2.22/2.44 tff(10897,plain,
% 2.22/2.44 ((~![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(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(10898,plain,
% 2.22/2.44 ((~![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(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[10897, 10896])).
% 2.22/2.44 tff(10899,plain,
% 2.22/2.44 (~r(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10898, 333, 722, 3193, 10892])).
% 2.22/2.44 tff(10900,plain,
% 2.22/2.44 (b(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1538, 10899, 1524])).
% 2.22/2.44 tff(10901,plain,
% 2.22/2.44 (~b(s(elem!1), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[499, 491, 490, 489])).
% 2.22/2.44 tff(10902,plain,
% 2.22/2.44 (r(s(elem!1), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[486, 10901, 1])).
% 2.22/2.44 tff(10903,plain,
% 2.22/2.44 (~r(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[7729, 333, 10902, 722, 353])).
% 2.22/2.44 tff(10904,plain,
% 2.22/2.44 (b(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[448, 10903, 433])).
% 2.22/2.44 tff(10905,plain,
% 2.22/2.44 (((~![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(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), 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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(10906,plain,
% 2.22/2.44 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(10907,plain,
% 2.22/2.44 (((~![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(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10906])).
% 2.22/2.44 tff(10908,plain,
% 2.22/2.44 (((~![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(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[10907, 10905])).
% 2.22/2.44 tff(10909,plain,
% 2.22/2.44 ((~![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(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(10910,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[10909, 10908])).
% 2.22/2.44 tff(10911,plain,
% 2.22/2.44 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10910, 333, 10902, 3193, 353])).
% 2.22/2.44 tff(10912,plain,
% 2.22/2.44 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[965, 10911, 960])).
% 2.22/2.44 tff(10913,plain,
% 2.22/2.44 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3211, 144, 491, 2082, 285])).
% 2.22/2.44 tff(10914,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10913, 10912, 10904])).
% 2.22/2.44 tff(10915,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10916,plain,
% 2.22/2.44 (~b(s(elem!1), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10915, 10900, 285, 960, 433, 3193, 10892, 722, 1, 490, 489])).
% 2.22/2.44 tff(10917,plain,
% 2.22/2.44 (r(s(elem!1), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[507, 10916])).
% 2.22/2.44 tff(10918,plain,
% 2.22/2.44 (~b(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2090, 10900, 251, 134, 490])).
% 2.22/2.44 tff(10919,plain,
% 2.22/2.44 (r(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[619, 10918])).
% 2.22/2.44 tff(10920,plain,
% 2.22/2.44 (~r(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10865, 10917, 408, 10919])).
% 2.22/2.44 tff(10921,plain,
% 2.22/2.44 (b(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[448, 10920, 433])).
% 2.22/2.44 tff(10922,plain,
% 2.22/2.44 (~r(elem!1, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[8975, 10921, 134, 251, 1, 490, 722, 489, 408, 10917])).
% 2.22/2.44 tff(10923,plain,
% 2.22/2.44 (b(elem!1, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[560, 10922, 1722])).
% 2.22/2.44 tff(10924,plain,
% 2.22/2.44 (~b(z, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1642, 10923, 251, 10921])).
% 2.22/2.44 tff(10925,plain,
% 2.22/2.44 (r(z, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[583, 10924])).
% 2.22/2.44 tff(10926,plain,
% 2.22/2.44 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[965, 901, 960])).
% 2.22/2.44 tff(10927,plain,
% 2.22/2.44 (~r(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1929, 562, 10926, 623])).
% 2.22/2.44 tff(10928,plain,
% 2.22/2.44 (b(s(s(s(z))), s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[4807, 562, 960, 901, 623])).
% 2.22/2.44 tff(10929,plain,
% 2.22/2.44 (~b(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[4819, 10928, 451, 547])).
% 2.22/2.44 tff(10930,plain,
% 2.22/2.44 (~r(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1972, 562, 10926, 623])).
% 2.22/2.44 tff(10931,plain,
% 2.22/2.44 (b(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[396, 10930])).
% 2.22/2.44 tff(10932,plain,
% 2.22/2.44 (~(s(s(s(z))) = elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[380, 10931, 377])).
% 2.22/2.44 tff(10933,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[704, 10932, 10929, 10927])).
% 2.22/2.44 tff(10934,plain,((~r(z, s(elem!1))) | b(elem!1, z) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10935,plain,
% 2.22/2.44 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10934, 10925, 10919, 377, 960, 10921, 10923])).
% 2.22/2.44 tff(10936,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10830, 144, 10921, 10900, 10935, 4367])).
% 2.22/2.44 tff(10937,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | b(elem!1, z) | (s(elem!1) = s(s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10938,plain,
% 2.22/2.44 (~b(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10937, 10890, 4367, 10773, 10551, 10633, 1, 10767, 10783, 10887, 10777, 10776, 10873, 10555])).
% 2.22/2.44 tff(10939,plain,
% 2.22/2.44 (r(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[396, 10938])).
% 2.22/2.44 tff(10940,plain,
% 2.22/2.44 (~b(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10812, 10939, 10783, 10633, 10887, 4367, 10555, 10551, 10767])).
% 2.22/2.44 tff(10941,plain,
% 2.22/2.44 (r(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[619, 10940])).
% 2.22/2.44 tff(10942,plain,
% 2.22/2.44 (~r(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10820, 333, 10777, 10939, 10941])).
% 2.22/2.44 tff(10943,plain,
% 2.22/2.44 (b(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1538, 10942, 10555])).
% 2.22/2.44 tff(10944,plain,
% 2.22/2.44 (~b(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10692, 144, 10633, 10943, 4367])).
% 2.22/2.44 tff(10945,plain,
% 2.22/2.44 (r(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[172, 10944])).
% 2.22/2.44 tff(10946,plain,
% 2.22/2.44 (~(elem!1 = s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1569, 10776])).
% 2.22/2.44 tff(10947,plain,
% 2.22/2.44 (~b(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10861, 10943, 10551, 10939, 10946, 10773, 10783, 10941, 4367, 1, 10633, 10767, 10887, 10777])).
% 2.22/2.44 tff(10948,plain,
% 2.22/2.44 (r(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[448, 10947, 10776])).
% 2.22/2.44 tff(10949,plain,
% 2.22/2.44 (~r(s(elem!1), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10865, 10948, 10777, 10941])).
% 2.22/2.44 tff(10950,plain,
% 2.22/2.44 (b(s(elem!1), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[507, 10949])).
% 2.22/2.44 tff(10951,plain,
% 2.22/2.44 (~b(s(elem!1), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[499, 10950, 10767, 10887])).
% 2.22/2.44 tff(10952,plain,
% 2.22/2.44 (r(s(elem!1), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[486, 10951, 1])).
% 2.22/2.44 tff(10953,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[7729, 333, 10948, 10952, 10783, 10945])).
% 2.22/2.44 tff(10954,plain,(r(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10955,plain,
% 2.22/2.44 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10954, 10101, 1, 50, 3, 54])).
% 2.22/2.44 tff(10956,plain,
% 2.22/2.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10110, 114, 10101, 3, 54])).
% 2.22/2.44 tff(10957,plain,
% 2.22/2.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1137, 10956])).
% 2.22/2.44 tff(10958,plain,
% 2.22/2.44 (r(s(z), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[7011, 354, 1, 51, 606, 4])).
% 2.22/2.44 tff(10959,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2181, 333, 670, 409, 354, 722])).
% 2.22/2.44 tff(10960,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10961,plain,
% 2.22/2.44 (~r(elem!1, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10960, 10958, 7265, 354])).
% 2.22/2.44 tff(10962,plain,
% 2.22/2.44 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[7271, 354, 1, 606, 4])).
% 2.22/2.44 tff(10963,plain,
% 2.22/2.44 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[116, 10962])).
% 2.22/2.44 tff(10964,plain,
% 2.22/2.44 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[121, 10963, 3])).
% 2.22/2.44 tff(10965,plain,
% 2.22/2.44 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[429, 10958, 51, 354])).
% 2.22/2.44 tff(10966,plain,
% 2.22/2.44 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[319, 10965])).
% 2.22/2.44 tff(10967,plain,
% 2.22/2.44 (~b(elem!1, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[313, 10966, 50, 10964])).
% 2.22/2.44 tff(10968,plain,
% 2.22/2.44 (elem!1 = s(z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[720, 10967, 10961])).
% 2.22/2.44 tff(10969,plain,
% 2.22/2.44 (s(z) = elem!1),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[712, 10968])).
% 2.22/2.44 tff(10970,plain,
% 2.22/2.44 (r(s(z), elem!1) <=> r(elem!1, elem!1)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10969])).
% 2.22/2.44 tff(10971,plain,
% 2.22/2.44 (r(elem!1, elem!1) <=> r(s(z), elem!1)),
% 2.22/2.44 inference(symmetry,[status(thm)],[10970])).
% 2.22/2.44 tff(10972,plain,
% 2.22/2.44 ((~r(elem!1, elem!1)) <=> (~r(s(z), elem!1))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[10971])).
% 2.22/2.44 tff(10973,plain,
% 2.22/2.44 (~r(s(z), elem!1)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9917, 10972])).
% 2.22/2.44 tff(10974,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10958, 10973])).
% 2.22/2.44 tff(10975,plain,((~r(z, s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10976,plain,
% 2.22/2.44 (~r(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10975, 606, 10955, 1, 3, 4])).
% 2.22/2.44 tff(10977,plain,
% 2.22/2.44 (b(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[372, 10976])).
% 2.22/2.44 tff(10978,plain,
% 2.22/2.44 (r(s(z), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9176, 350, 10955, 1, 606, 4])).
% 2.22/2.44 tff(10979,plain,
% 2.22/2.44 (r(elem!1, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9106, 3921, 51, 123, 624, 132])).
% 2.22/2.44 tff(10980,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1767, 333, 670, 409, 3922, 10979])).
% 2.22/2.44 tff(10981,plain,(b(s(z), z) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10982,plain,
% 2.22/2.44 (b(s(z), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10981, 10978, 7265, 10955, 50, 4833, 9097])).
% 2.22/2.44 tff(10983,plain,
% 2.22/2.44 (elem!1 = s(elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9114, 57, 51, 606, 132, 489, 133, 1378, 1, 4])).
% 2.22/2.44 tff(10984,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2482, 10983, 2469])).
% 2.22/2.44 tff(10985,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(elem!1, z) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10986,plain,
% 2.22/2.44 (~(s(z) = elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10985, 9097, 606, 10955, 10982, 9095, 1378, 1, 4])).
% 2.22/2.44 tff(10987,plain,
% 2.22/2.44 (~(elem!1 = s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[712, 10986])).
% 2.22/2.44 tff(10988,plain,
% 2.22/2.44 (~b(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10115, 305, 624, 123, 132])).
% 2.22/2.44 tff(10989,plain,
% 2.22/2.44 (r(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[372, 10988])).
% 2.22/2.44 tff(10990,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[429, 622, 10989, 51, 409])).
% 2.22/2.44 tff(10991,plain,((~b(elem!1, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10992,plain,
% 2.22/2.44 (~b(elem!1, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10991, 10978, 10955, 50, 9097, 4833])).
% 2.22/2.44 tff(10993,plain,
% 2.22/2.44 (r(elem!1, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[720, 10992, 10987])).
% 2.22/2.44 tff(10994,plain,
% 2.22/2.44 (~(s(s(s(z))) = elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[8013, 10993, 50, 4833, 54, 3, 1, 10992])).
% 2.22/2.44 tff(10995,plain,
% 2.22/2.44 (s(s(s(z))) = elem!1),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[3238, 4795])).
% 2.22/2.44 tff(10996,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[698, 10995])).
% 2.22/2.44 tff(10997,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(10998,plain,
% 2.22/2.44 (~(elem!1 = s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10997, 10994])).
% 2.22/2.44 tff(10999,plain,
% 2.22/2.44 (~r(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10960, 10978, 7265, 10993])).
% 2.22/2.44 tff(11000,plain,
% 2.22/2.44 (b(z, s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[372, 10999])).
% 2.22/2.44 tff(11001,plain,
% 2.22/2.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[10110, 9094, 10101, 3, 54])).
% 2.22/2.44 tff(11002,plain,
% 2.22/2.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1137, 11001])).
% 2.22/2.44 tff(11003,plain,
% 2.22/2.44 (elem!1 = s(elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[906, 903])).
% 2.22/2.44 tff(11004,plain,
% 2.22/2.44 (~b(z, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2974, 11003, 606])).
% 2.22/2.44 tff(11005,plain,
% 2.22/2.44 (r(z, s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[583, 11004])).
% 2.22/2.44 tff(11006,plain,
% 2.22/2.44 (elem!1 = s(s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5813, 903])).
% 2.22/2.44 tff(11007,plain,
% 2.22/2.44 (s(s(elem!1)) = elem!1),
% 2.22/2.44 inference(symmetry,[status(thm)],[11006])).
% 2.22/2.44 tff(11008,plain,
% 2.22/2.44 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[11007])).
% 2.22/2.44 tff(11009,plain,
% 2.22/2.44 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.22/2.44 inference(symmetry,[status(thm)],[11008])).
% 2.22/2.44 tff(11010,plain,
% 2.22/2.44 (b(s(s(elem!1)), z)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[624, 11009])).
% 2.22/2.44 tff(11011,plain,
% 2.22/2.44 (~b(s(s(s(z))), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2273, 285, 489, 490])).
% 2.22/2.44 tff(11012,plain,
% 2.22/2.44 (r(s(s(s(z))), s(z))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2794, 11011])).
% 2.22/2.44 tff(11013,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11014,plain,
% 2.22/2.44 (((~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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11015,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[11014])).
% 2.22/2.44 tff(11016,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[11015, 11013])).
% 2.22/2.44 tff(11017,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(11018,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[11017, 11016])).
% 2.22/2.44 tff(11019,plain,
% 2.22/2.44 (~r(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[11018, 333, 409, 722, 11012])).
% 2.22/2.44 tff(11020,plain,
% 2.22/2.44 (b(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1538, 11019, 1524])).
% 2.22/2.44 tff(11021,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11022,plain,
% 2.22/2.44 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11023,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[11022])).
% 2.22/2.44 tff(11024,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.44 inference(transitivity,[status(thm)],[11023, 11021])).
% 2.22/2.44 tff(11025,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(11026,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[11025, 11024])).
% 2.22/2.44 tff(11027,plain,
% 2.22/2.44 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[11026, 144, 11020, 133, 4367])).
% 2.22/2.44 tff(11028,plain,
% 2.22/2.44 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[249, 11027])).
% 2.22/2.44 tff(11029,plain,
% 2.22/2.44 (s(s(elem!1)) = elem!1),
% 2.22/2.44 inference(symmetry,[status(thm)],[1202])).
% 2.22/2.44 tff(11030,plain,
% 2.22/2.44 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[11029])).
% 2.22/2.44 tff(11031,plain,
% 2.22/2.44 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.44 inference(symmetry,[status(thm)],[11030])).
% 2.22/2.44 tff(11032,plain,
% 2.22/2.44 (b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[11020, 11031])).
% 2.22/2.44 tff(11033,plain,
% 2.22/2.44 (~b(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5708, 11032, 2726, 285])).
% 2.22/2.44 tff(11034,plain,
% 2.22/2.44 (r(z, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[619, 11033])).
% 2.22/2.44 tff(11035,plain,
% 2.22/2.44 (((~![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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11036,plain,
% 2.22/2.44 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(11037,plain,
% 2.22/2.44 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[11036])).
% 2.22/2.44 tff(11038,plain,
% 2.22/2.44 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[11037, 11035])).
% 2.22/2.44 tff(11039,plain,
% 2.22/2.44 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(11040,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[11039, 11038])).
% 2.22/2.45 tff(11041,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11040, 333, 11034, 11012, 11028, 51])).
% 2.22/2.45 tff(11042,plain,((~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (elem!1 = s(s(s(z)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11043,plain,
% 2.22/2.45 (~b(s(s(s(z))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11042, 11010, 51, 133, 4367, 11006, 1524, 409, 722, 489, 490])).
% 2.22/2.45 tff(11044,plain,
% 2.22/2.45 (r(s(s(s(z))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[396, 11043])).
% 2.22/2.45 tff(11045,plain,
% 2.22/2.45 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[10450, 11044, 6107, 11005])).
% 2.22/2.45 tff(11046,plain,
% 2.22/2.45 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[302, 11045])).
% 2.22/2.45 tff(11047,plain,
% 2.22/2.45 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[7093, 11046, 489, 490])).
% 2.22/2.45 tff(11048,plain,
% 2.22/2.45 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[319, 11047])).
% 2.22/2.45 tff(11049,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(11050,plain,
% 2.22/2.45 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(11051,plain,
% 2.22/2.45 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11050])).
% 2.22/2.45 tff(11052,plain,
% 2.22/2.45 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[11051, 11049])).
% 2.22/2.45 tff(11053,plain,
% 2.22/2.45 ((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(11054,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[11053, 11052])).
% 2.22/2.45 tff(11055,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11054, 333, 11044, 6107, 11048, 51])).
% 2.22/2.45 tff(11056,plain,((~(s(elem!1) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11057,plain,
% 2.22/2.45 (~(s(elem!1) = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11056, 11002, 10955, 10982, 11000, 9095, 10101, 10998, 10978, 10993, 4833, 606])).
% 2.22/2.45 tff(11058,plain,
% 2.22/2.45 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[10954, 4367, 1, 123, 3, 54])).
% 2.22/2.45 tff(11059,plain,
% 2.22/2.45 (b(s(z), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[10981, 409, 670, 11058, 123, 624, 454])).
% 2.22/2.45 tff(11060,plain,
% 2.22/2.45 (~r(z, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[10960, 409, 670, 722])).
% 2.22/2.45 tff(11061,plain,
% 2.22/2.45 (b(z, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[372, 11060])).
% 2.22/2.45 tff(11062,plain,
% 2.22/2.45 (~b(s(elem!1), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[499, 908, 11061, 11059])).
% 2.22/2.45 tff(11063,plain,
% 2.22/2.45 (r(s(elem!1), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[486, 11062, 1])).
% 2.22/2.45 tff(11064,plain,
% 2.22/2.45 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(11065,plain,
% 2.22/2.45 (((~![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(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(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11064])).
% 2.22/2.45 tff(11066,plain,
% 2.22/2.45 (((~![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(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(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[11065, 7859])).
% 2.22/2.45 tff(11067,plain,
% 2.22/2.45 ((~![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(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(11068,plain,
% 2.22/2.45 ((~![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(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[11067, 11066])).
% 2.22/2.45 tff(11069,plain,
% 2.22/2.45 (~r(s(elem!1), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11068, 333, 409, 11063, 722])).
% 2.22/2.45 tff(11070,plain,
% 2.22/2.45 (b(s(elem!1), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[448, 11069, 433])).
% 2.22/2.45 tff(11071,plain,
% 2.22/2.45 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[464, 11070, 54, 114, 3])).
% 2.22/2.45 tff(11072,plain,
% 2.22/2.45 (~r(elem!1, s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[7755, 333, 409, 11063, 722])).
% 2.22/2.45 tff(11073,plain,
% 2.22/2.45 (b(elem!1, s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[560, 11072, 1722])).
% 2.22/2.45 tff(11074,plain,
% 2.22/2.45 (~b(z, s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[949, 11073, 624, 908])).
% 2.22/2.45 tff(11075,plain,
% 2.22/2.45 (r(z, s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[583, 11074])).
% 2.22/2.45 tff(11076,plain,
% 2.22/2.45 (s(elem!1) = s(s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1934, 1002])).
% 2.22/2.45 tff(11077,plain,
% 2.22/2.45 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[87, 984, 7601, 92])).
% 2.22/2.45 tff(11078,plain,
% 2.22/2.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11077])).
% 2.22/2.45 tff(11079,plain,
% 2.22/2.45 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[11078])).
% 2.22/2.45 tff(11080,plain,
% 2.22/2.45 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[983])).
% 2.22/2.45 tff(11081,plain,
% 2.22/2.45 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.22/2.45 inference(symmetry,[status(thm)],[11080])).
% 2.22/2.45 tff(11082,plain,
% 2.22/2.45 (s(s(elem!1)) = s(z)),
% 2.22/2.45 inference(transitivity,[status(thm)],[11081, 239, 11079, 80])).
% 2.22/2.45 tff(11083,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[107, 11082])).
% 2.22/2.45 tff(11084,plain,((~(s(elem!1) = s(s(s(z))))) | (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11085,plain,
% 2.22/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11084, 11076])).
% 2.22/2.45 tff(11086,plain,
% 2.22/2.45 (~b(s(elem!1), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[499, 491, 11061, 489])).
% 2.22/2.45 tff(11087,plain,
% 2.22/2.45 (r(s(elem!1), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[486, 11086, 1])).
% 2.22/2.45 tff(11088,plain,
% 2.22/2.45 (~r(s(elem!1), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11068, 333, 409, 11087, 722])).
% 2.22/2.45 tff(11089,plain,
% 2.22/2.45 (b(s(elem!1), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[448, 11088, 433])).
% 2.22/2.45 tff(11090,plain,
% 2.22/2.45 (s(s(z)) = s(s(elem!1))),
% 2.22/2.45 inference(transitivity,[status(thm)],[87, 1003, 850, 4998])).
% 2.22/2.45 tff(11091,plain,
% 2.22/2.45 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11090])).
% 2.22/2.45 tff(11092,plain,
% 2.22/2.45 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[11091])).
% 2.22/2.45 tff(11093,plain,
% 2.22/2.45 (s(elem!1) = s(z)),
% 2.22/2.45 inference(transitivity,[status(thm)],[102, 11092, 80])).
% 2.22/2.45 tff(11094,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1, 11093])).
% 2.22/2.45 tff(11095,plain,((~(s(s(elem!1)) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(z))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11096,plain,
% 2.22/2.45 (~(s(s(elem!1)) = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11095, 1002, 1])).
% 2.22/2.45 tff(11097,plain,
% 2.22/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[1002])).
% 2.22/2.45 tff(11098,plain,
% 2.22/2.45 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11097])).
% 2.22/2.45 tff(11099,plain,
% 2.22/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[244, 11098])).
% 2.22/2.45 tff(11100,plain,
% 2.22/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[11097, 175])).
% 2.22/2.45 tff(11101,plain,
% 2.22/2.45 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11100])).
% 2.22/2.45 tff(11102,plain,
% 2.22/2.45 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[244, 11101])).
% 2.22/2.45 tff(11103,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[7838, 11102, 11099, 670, 722, 123, 489, 491, 1722, 11096, 11089, 433, 409, 54, 114, 3, 11085, 1])).
% 2.22/2.45 tff(11104,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(elem!1) = elem!1) | (~r(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11105,plain,
% 2.22/2.45 (~(s(s(s(z))) = s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11104, 908, 722, 123, 11059, 670, 433, 409, 54, 114, 3, 1])).
% 2.22/2.45 tff(11106,plain,
% 2.22/2.45 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4819, 11073, 4367, 11070])).
% 2.22/2.45 tff(11107,plain,
% 2.22/2.45 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1951, 44, 11106])).
% 2.22/2.45 tff(11108,plain,
% 2.22/2.45 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11107, 11105])).
% 2.22/2.45 tff(11109,plain,
% 2.22/2.45 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(11110,plain,
% 2.22/2.45 (((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(11111,plain,
% 2.22/2.45 (((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[11110])).
% 2.22/2.45 tff(11112,plain,
% 2.22/2.45 (((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.22/2.45 inference(transitivity,[status(thm)],[11111, 11109])).
% 2.22/2.45 tff(11113,plain,
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% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
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% 2.22/2.45 inference(modus_ponens,[status(thm)],[11113, 11112])).
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% 2.22/2.45 tff(11118,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[2794, 11117])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[1137, 11119])).
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% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
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% 2.22/2.45 inference(modus_ponens,[status(thm)],[11122, 11121])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[11123, 333, 11063, 11075, 11108])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[619, 11124])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[172, 11126])).
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% 2.22/2.45 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[10422, 11127, 11120, 11118])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[319, 11128])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[7093, 11129, 11059, 11061])).
% 2.22/2.45 tff(11131,plain,
% 2.22/2.45 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[302, 11130])).
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% 2.22/2.45 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[940, 11131, 11058, 11075])).
% 2.22/2.45 tff(11133,plain,
% 2.22/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[925, 11131, 501])).
% 2.22/2.45 tff(11134,plain,
% 2.22/2.45 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[930, 11133])).
% 2.22/2.45 tff(11135,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[472, 11134, 11132, 11071])).
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% 2.22/2.45 tff(11137,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[11136, 10993, 50, 7265, 11057, 10978, 54, 9094, 3, 1, 10101, 4833])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[5438, 333, 435, 670, 509, 722])).
% 2.22/2.45 tff(11139,plain,((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11140,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[11139, 11137, 7265, 10993])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[448, 11140, 11057])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[464, 11141, 54, 9094, 3])).
% 2.22/2.45 tff(11143,plain,
% 2.22/2.45 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 2.22/2.45 tff(11144,plain,
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% 2.22/2.45 tff(11146,plain,
% 2.22/2.45 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[11145, 11141, 10955, 7265, 4833, 9095, 11137, 11142])).
% 2.22/2.45 tff(11147,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[2899, 11146, 11137])).
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[3508, 333, 7265, 11137, 11147])).
% 2.22/2.45 tff(11149,plain,
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% 2.22/2.45 inference(unit_resolution,[status(thm)],[472, 11148, 11142])).
% 2.22/2.45 tff(11150,plain,
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% 2.22/2.45 tff(11151,plain,
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% 2.22/2.45 inference(symmetry,[status(thm)],[11150])).
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% 2.22/2.45 inference(monotonicity,[status(thm)],[11152])).
% 2.22/2.45 tff(11154,plain,
% 2.22/2.45 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.22/2.45 inference(symmetry,[status(thm)],[11153])).
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% 2.22/2.45 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
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% 2.22/2.45 inference(monotonicity,[status(thm)],[11156])).
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% 2.22/2.45 inference(modus_ponens,[status(thm)],[11159, 11158])).
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% 2.22/2.45 tff(11163,plain,
% 2.22/2.45 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
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% 2.22/2.45 tff(11164,plain,
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% 2.22/2.45 tff(11166,plain,
% 2.22/2.45 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
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% 2.22/2.45 tff(11167,plain,
% 2.22/2.45 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 2.22/2.45 tff(11168,plain,
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% 2.22/2.45 tff(11169,plain,((~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(11170,plain,
% 2.22/2.45 (~r(s(s(s(z))), z)),
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% 2.22/2.45 tff(11171,plain,
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% 2.22/2.46 tff(11172,plain,
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% 2.22/2.46 tff(11173,plain,
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% 2.22/2.46 tff(11175,plain,
% 2.22/2.46 (r(s(z), s(s(s(s(s(s(z))))))) <=> r(s(z), elem!1)),
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% 2.22/2.46 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(s(z)))))))),
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% 2.22/2.46 tff(11180,plain,
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% 2.22/2.46 inference(unit_resolution,[status(thm)],[2273, 11171, 10982, 11000])).
% 2.22/2.46 tff(11181,plain,
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% 2.22/2.46 inference(unit_resolution,[status(thm)],[2794, 11180])).
% 2.22/2.46 tff(11182,plain,
% 2.22/2.46 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(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(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11183,plain,
% 2.22/2.46 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11184,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11183])).
% 2.22/2.46 tff(11185,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11184, 11182])).
% 2.22/2.46 tff(11186,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11187,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11186, 11185])).
% 2.22/2.46 tff(11188,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11187, 333, 11181, 11179, 11177, 11174])).
% 2.22/2.46 tff(11189,plain,(b(s(z), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(elem!1, z) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11190,plain,
% 2.22/2.46 (b(s(z), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11189, 1378, 3, 1, 606, 54, 4])).
% 2.22/2.46 tff(11191,plain,
% 2.22/2.46 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9955, 11190, 50, 3, 54])).
% 2.22/2.46 tff(11192,plain,
% 2.22/2.46 (~r(z, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[7271, 11191, 1, 606, 4])).
% 2.22/2.46 tff(11193,plain,
% 2.22/2.46 (b(z, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[372, 11192])).
% 2.22/2.46 tff(11194,plain,
% 2.22/2.46 (~(s(z) = elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[8102, 11193, 606])).
% 2.22/2.46 tff(11195,plain,
% 2.22/2.46 (~(elem!1 = s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[712, 11194])).
% 2.22/2.46 tff(11196,plain,
% 2.22/2.46 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2558, 11191, 1378])).
% 2.22/2.46 tff(11197,plain,
% 2.22/2.46 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[302, 11196])).
% 2.22/2.46 tff(11198,plain,
% 2.22/2.46 (~b(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[7093, 8993, 286, 490])).
% 2.22/2.46 tff(11199,plain,
% 2.22/2.46 (r(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[348, 11198])).
% 2.22/2.46 tff(11200,plain,
% 2.22/2.46 (b(elem!1, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[720, 715, 714])).
% 2.22/2.46 tff(11201,plain,
% 2.22/2.46 (~b(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4375, 11200, 4367, 134])).
% 2.22/2.46 tff(11202,plain,
% 2.22/2.46 (r(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2794, 11201])).
% 2.22/2.46 tff(11203,plain,
% 2.22/2.46 (~(elem!1 = s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10997, 4363])).
% 2.22/2.46 tff(11204,plain,
% 2.22/2.46 (~(s(elem!1) = elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1565, 11203, 81])).
% 2.22/2.46 tff(11205,plain,
% 2.22/2.46 (~(elem!1 = s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1569, 11204])).
% 2.22/2.46 tff(11206,plain,
% 2.22/2.46 (~r(s(elem!1), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[7112, 11199, 11200, 11205, 490, 1, 670])).
% 2.22/2.46 tff(11207,plain,
% 2.22/2.46 (b(s(elem!1), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[507, 11206])).
% 2.22/2.46 tff(11208,plain,
% 2.22/2.46 (((~![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(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, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11209,plain,
% 2.22/2.46 ((~![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(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11210,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11209, 11208])).
% 2.22/2.46 tff(11211,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11210, 333, 670, 323, 1699, 3193])).
% 2.22/2.46 tff(11212,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11213,plain,
% 2.22/2.46 (~r(s(s(s(z))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11212, 11199, 670, 11202])).
% 2.22/2.46 tff(11214,plain,
% 2.22/2.46 (b(s(s(s(z))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[396, 11213])).
% 2.22/2.46 tff(11215,plain,
% 2.22/2.46 (~b(elem!1, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[7247, 144, 624, 490, 305, 285])).
% 2.22/2.46 tff(11216,plain,
% 2.22/2.46 (r(elem!1, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1538, 11215, 1524])).
% 2.22/2.46 tff(11217,plain,
% 2.22/2.46 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10761, 11216, 435, 3193])).
% 2.22/2.46 tff(11218,plain,
% 2.22/2.46 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[965, 11217, 960])).
% 2.22/2.46 tff(11219,plain,
% 2.22/2.46 (~r(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3201, 11216, 670, 3193])).
% 2.22/2.46 tff(11220,plain,
% 2.22/2.46 (b(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[619, 11219])).
% 2.22/2.46 tff(11221,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1802, 11220, 11218, 491, 285])).
% 2.22/2.46 tff(11222,plain,((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11223,plain,
% 2.22/2.46 (~r(s(elem!1), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11222, 11214, 1682, 670, 11202, 11207, 11203, 624, 490, 11200])).
% 2.22/2.46 tff(11224,plain,
% 2.22/2.46 (b(s(elem!1), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[448, 11223, 11204])).
% 2.22/2.46 tff(11225,plain,
% 2.22/2.46 (~b(s(elem!1), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1820, 11224, 134, 490, 11207])).
% 2.22/2.46 tff(11226,plain,
% 2.22/2.46 (r(s(elem!1), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[486, 11225, 1])).
% 2.22/2.46 tff(11227,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11228,plain,
% 2.22/2.46 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11229,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11228])).
% 2.22/2.46 tff(11230,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11229, 11227])).
% 2.22/2.46 tff(11231,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11232,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11231, 11230])).
% 2.22/2.46 tff(11233,plain,
% 2.22/2.46 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11232, 144, 624, 11207, 4367])).
% 2.22/2.46 tff(11234,plain,
% 2.22/2.46 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11233, 11224])).
% 2.22/2.46 tff(11235,plain,
% 2.22/2.46 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[965, 11234, 1682])).
% 2.22/2.46 tff(11236,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[8929, 333, 323, 434, 3193, 1686])).
% 2.22/2.46 tff(11237,plain,((~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11238,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11237, 11235, 11226, 11202, 11199])).
% 2.22/2.46 tff(11239,plain,(r(elem!1, s(z)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11240,plain,
% 2.22/2.46 (r(elem!1, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11239, 4833, 1, 10101, 11190, 11193, 7265, 11197, 11191, 11195])).
% 2.22/2.46 tff(11241,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(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(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11242,plain,
% 2.22/2.46 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11243,plain,
% 2.22/2.46 (((~![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(z))), z)) | (~r(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(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11242])).
% 2.22/2.46 tff(11244,plain,
% 2.22/2.46 (((~![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(z))), z)) | (~r(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(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11243, 11241])).
% 2.22/2.46 tff(11245,plain,
% 2.22/2.46 ((~![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(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11246,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 2.22/2.46 tff(11247,plain,
% 2.22/2.46 (~r(s(z), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11246, 333, 670, 323, 10794])).
% 2.22/2.46 tff(11248,plain,
% 2.22/2.46 (b(s(z), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[172, 11247])).
% 2.22/2.46 tff(11249,plain,
% 2.22/2.46 (~b(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2025, 144, 490, 56, 11248])).
% 2.22/2.46 tff(11250,plain,
% 2.22/2.46 (r(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[619, 11249])).
% 2.22/2.46 tff(11251,plain,
% 2.22/2.46 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2262, 11248, 123, 10584])).
% 2.22/2.46 tff(11252,plain,
% 2.22/2.46 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[249, 11251])).
% 2.22/2.46 tff(11253,plain,
% 2.22/2.46 (r(elem!1, s(s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11252, 1685])).
% 2.22/2.46 tff(11254,plain,
% 2.22/2.46 (((~![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(z, s(s(s(z))))) | (~r(s(s(s(z))), 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(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11255,plain,
% 2.22/2.46 (((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11256,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11255])).
% 2.22/2.46 tff(11257,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11256, 11254])).
% 2.22/2.46 tff(11258,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11259,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11258, 11257])).
% 2.22/2.46 tff(11260,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11259, 333, 670, 11253, 10794, 11250])).
% 2.22/2.46 tff(11261,plain,((~b(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11262,plain,
% 2.22/2.46 (~b(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11261, 323, 490, 81, 123, 670, 134, 4367])).
% 2.22/2.46 tff(11263,plain,
% 2.22/2.46 (r(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2794, 11262])).
% 2.22/2.46 tff(11264,plain,
% 2.22/2.46 (~r(elem!1, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10883, 333, 323, 722, 11263])).
% 2.22/2.46 tff(11265,plain,
% 2.22/2.46 (b(elem!1, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1538, 11264, 11203])).
% 2.22/2.46 tff(11266,plain,
% 2.22/2.46 (~b(s(z), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10692, 144, 134, 11265, 4367])).
% 2.22/2.46 tff(11267,plain,
% 2.22/2.46 (r(s(z), s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[172, 11266])).
% 2.22/2.46 tff(11268,plain,
% 2.22/2.46 (~r(s(s(s(z))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11212, 11263, 670, 323])).
% 2.22/2.46 tff(11269,plain,
% 2.22/2.46 (b(s(s(s(z))), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[396, 11268])).
% 2.22/2.46 tff(11270,plain,
% 2.22/2.46 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11265, 1523])).
% 2.22/2.46 tff(11271,plain,
% 2.22/2.46 (~b(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[294, 11270, 286, 11269])).
% 2.22/2.46 tff(11272,plain,
% 2.22/2.46 (r(z, s(s(s(z))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[619, 11271])).
% 2.22/2.46 tff(11273,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), 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), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11274,plain,
% 2.22/2.46 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11275,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11274])).
% 2.22/2.46 tff(11276,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11275, 11273])).
% 2.22/2.46 tff(11277,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11278,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[11277, 11276])).
% 2.22/2.46 tff(11279,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11278, 333, 323, 11272, 11263, 11267])).
% 2.22/2.46 tff(11280,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(11281,plain,
% 2.22/2.46 (~r(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[11280, 11197, 11190, 10101, 11191, 11240, 7265, 11193, 50])).
% 2.22/2.46 tff(11282,plain,
% 2.22/2.46 (b(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[348, 11281])).
% 2.22/2.46 tff(11283,plain,
% 2.22/2.46 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3398, 11191])).
% 2.22/2.46 tff(11284,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11285,plain,
% 2.22/2.46 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(11286,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[11285])).
% 2.22/2.46 tff(11287,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.46 inference(transitivity,[status(thm)],[11286, 11284])).
% 2.22/2.46 tff(11288,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(11289,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11288, 11287])).
% 2.22/2.47 tff(11290,plain,
% 2.22/2.47 (~b(s(z), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11289, 144, 4833, 11190, 11282, 10101])).
% 2.22/2.47 tff(11291,plain,
% 2.22/2.47 (r(s(z), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[172, 11290])).
% 2.22/2.47 tff(11292,plain,
% 2.22/2.47 (~r(s(elem!1), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[7731, 11291, 7265, 1, 11240, 11282, 11193])).
% 2.22/2.47 tff(11293,plain,
% 2.22/2.47 (~b(s(z), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2569, 11292, 50, 1378, 11283, 11282])).
% 2.22/2.47 tff(11294,plain,
% 2.22/2.47 (r(s(z), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1244, 11293, 1229])).
% 2.22/2.47 tff(11295,plain,
% 2.22/2.47 (~(s(s(s(z))) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[109, 11191])).
% 2.22/2.47 tff(11296,plain,
% 2.22/2.47 (~(elem!1 = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10997, 11295])).
% 2.22/2.47 tff(11297,plain,
% 2.22/2.47 (~(s(elem!1) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1565, 11296, 11191])).
% 2.22/2.47 tff(11298,plain,
% 2.22/2.47 (b(s(elem!1), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[448, 11292, 11297])).
% 2.22/2.47 tff(11299,plain,
% 2.22/2.47 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11191])).
% 2.22/2.47 tff(11300,plain,
% 2.22/2.47 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11299])).
% 2.22/2.47 tff(11301,plain,
% 2.22/2.47 (~(s(s(z)) = elem!1)),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[1446, 11300])).
% 2.22/2.47 tff(11302,plain,
% 2.22/2.47 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1508, 11301])).
% 2.22/2.47 tff(11303,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11304,plain,
% 2.22/2.47 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11305,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11304])).
% 2.22/2.47 tff(11306,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.47 inference(transitivity,[status(thm)],[11305, 11303])).
% 2.22/2.47 tff(11307,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(11308,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11307, 11306])).
% 2.22/2.47 tff(11309,plain,
% 2.22/2.47 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11308, 144, 451, 624, 285, 4367])).
% 2.22/2.47 tff(11310,plain,
% 2.22/2.47 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1951, 44, 3295, 11309])).
% 2.22/2.47 tff(11311,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(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), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11312,plain,
% 2.22/2.47 (((~r(s(z), s(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), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11313,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11312])).
% 2.22/2.47 tff(11314,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[11313, 11311])).
% 2.22/2.47 tff(11315,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(11316,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11315, 11314])).
% 2.22/2.47 tff(11317,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11316, 333, 722, 1230, 11012])).
% 2.22/2.47 tff(11318,plain,
% 2.22/2.47 (b(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1538, 11317, 1524])).
% 2.22/2.47 tff(11319,plain,
% 2.22/2.47 (~b(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10915, 11318, 433, 489, 960, 11012, 285, 722, 1, 490, 353])).
% 2.22/2.47 tff(11320,plain,
% 2.22/2.47 (r(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[507, 11319])).
% 2.22/2.47 tff(11321,plain,
% 2.22/2.47 (((~![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), s(elem!1))) | (~r(s(s(s(z))), s(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(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11322,plain,
% 2.22/2.47 ((~![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), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(11323,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11322, 11321])).
% 2.22/2.47 tff(11324,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11323, 333, 11320, 1230, 11012, 11310])).
% 2.22/2.47 tff(11325,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(elem!1))) | (s(elem!1) = elem!1) | (~b(s(z), z)) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11326,plain,
% 2.22/2.47 (~b(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11325, 11294, 11297, 11282, 11302, 11240, 1, 11193, 11291, 11296, 11298, 4833, 10101])).
% 2.22/2.47 tff(11327,plain,
% 2.22/2.47 (r(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[396, 11326])).
% 2.22/2.47 tff(11328,plain,
% 2.22/2.47 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11232, 144, 451, 624, 491, 4367])).
% 2.22/2.47 tff(11329,plain,
% 2.22/2.47 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[965, 11328, 960])).
% 2.22/2.47 tff(11330,plain,
% 2.22/2.47 (((~![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(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(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(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11331,plain,
% 2.22/2.47 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11332,plain,
% 2.22/2.47 (((~![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))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(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), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11331])).
% 2.22/2.47 tff(11333,plain,
% 2.22/2.47 (((~![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))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(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), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[11332, 11330])).
% 2.22/2.47 tff(11334,plain,
% 2.22/2.47 ((~![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))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(11335,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11334, 11333])).
% 2.22/2.47 tff(11336,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11335, 333, 10902, 1699, 11329, 353])).
% 2.22/2.47 tff(11337,plain,((~b(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11338,plain,
% 2.22/2.47 (~b(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11337, 11327, 11291, 11302, 11298, 4833, 10101, 1, 11193, 11282])).
% 2.22/2.47 tff(11339,plain,
% 2.22/2.47 (r(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[507, 11338])).
% 2.22/2.47 tff(11340,plain,
% 2.22/2.47 (~(elem!1 = s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1569, 11297])).
% 2.22/2.47 tff(11341,plain,
% 2.22/2.47 (~r(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5824, 333, 7265, 11339, 11327])).
% 2.22/2.47 tff(11342,plain,
% 2.22/2.47 (~(s(s(s(z))) = s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1934, 11302])).
% 2.22/2.47 tff(11343,plain,
% 2.22/2.47 (b(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1951, 44, 11342, 11341])).
% 2.22/2.47 tff(11344,plain,
% 2.22/2.47 (~b(elem!1, s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4819, 11343, 10101, 11298])).
% 2.22/2.47 tff(11345,plain,
% 2.22/2.47 (r(elem!1, s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[560, 11344, 11340])).
% 2.22/2.47 tff(11346,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), 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(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11347,plain,
% 2.22/2.47 (((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(11348,plain,
% 2.22/2.47 (((~![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), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11347])).
% 2.22/2.47 tff(11349,plain,
% 2.22/2.47 (((~![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), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[11348, 11346])).
% 2.22/2.47 tff(11350,plain,
% 2.22/2.47 ((~![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), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(11351,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11350, 11349])).
% 2.22/2.47 tff(11352,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11351, 333, 11345, 11339, 11240, 11294])).
% 2.22/2.47 tff(11353,plain,(r(elem!1, z) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11354,plain,
% 2.22/2.47 (r(elem!1, z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11353, 606, 1, 4, 3, 54])).
% 2.22/2.47 tff(11355,plain,
% 2.22/2.47 (~b(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9955, 114, 50, 3, 54])).
% 2.22/2.47 tff(11356,plain,
% 2.22/2.47 (r(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9176, 11355, 10955, 1, 606, 4])).
% 2.22/2.47 tff(11357,plain,
% 2.22/2.47 (~r(s(z), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[417, 11356, 10955, 11354])).
% 2.22/2.47 tff(11358,plain,
% 2.22/2.47 (b(s(z), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[348, 11357])).
% 2.22/2.47 tff(11359,plain,
% 2.22/2.47 (~(elem!1 = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10997, 1510])).
% 2.22/2.47 tff(11360,plain,
% 2.22/2.47 (~b(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2273, 56, 489, 490])).
% 2.22/2.47 tff(11361,plain,
% 2.22/2.47 (r(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[396, 11360])).
% 2.22/2.47 tff(11362,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 11361])).
% 2.22/2.47 tff(11363,plain,
% 2.22/2.47 (b(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1538, 11362, 11359])).
% 2.22/2.47 tff(11364,plain,
% 2.22/2.47 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11026, 144, 11363, 133, 4367])).
% 2.22/2.47 tff(11365,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[249, 11364])).
% 2.22/2.47 tff(11366,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1340, 333, 11361, 11365, 6107, 11058])).
% 2.22/2.47 tff(11367,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11368,plain,
% 2.22/2.47 (~b(s(s(s(z))), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11367, 10957, 452, 10101, 7265, 11354, 11358, 10977, 1, 54, 3, 50])).
% 2.22/2.47 tff(11369,plain,
% 2.22/2.47 (~(s(s(s(z))) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[8040, 11368, 1, 54, 3, 50])).
% 2.22/2.47 tff(11370,plain,
% 2.22/2.47 (~(elem!1 = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10997, 11369])).
% 2.22/2.47 tff(11371,plain,
% 2.22/2.47 (r(s(s(s(z))), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2794, 11368])).
% 2.22/2.47 tff(11372,plain,
% 2.22/2.47 (~(s(z) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[8102, 10977, 606])).
% 2.22/2.47 tff(11373,plain,
% 2.22/2.47 (~(elem!1 = s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[712, 11372])).
% 2.22/2.47 tff(11374,plain,
% 2.22/2.47 (~(s(s(z)) = s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[855, 11372])).
% 2.22/2.47 tff(11375,plain,
% 2.22/2.47 (~r(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[417, 323, 10955, 11354])).
% 2.22/2.47 tff(11376,plain,
% 2.22/2.47 (b(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9176, 11375, 10955, 1, 606, 4])).
% 2.22/2.47 tff(11377,plain,
% 2.22/2.47 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9955, 11376, 50, 3, 54])).
% 2.22/2.47 tff(11378,plain,
% 2.22/2.47 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11377])).
% 2.22/2.47 tff(11379,plain,
% 2.22/2.47 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11378])).
% 2.22/2.47 tff(11380,plain,
% 2.22/2.47 (~(s(s(z)) = elem!1)),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[1446, 11379])).
% 2.22/2.47 tff(11381,plain,
% 2.22/2.47 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1508, 11380])).
% 2.22/2.47 tff(11382,plain,
% 2.22/2.47 (~b(s(s(s(z))), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4375, 11376, 10101, 305])).
% 2.22/2.47 tff(11383,plain,
% 2.22/2.47 (r(s(s(s(z))), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2794, 11382])).
% 2.22/2.47 tff(11384,plain,
% 2.22/2.47 (~(s(s(s(z))) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[109, 11377])).
% 2.22/2.47 tff(11385,plain,
% 2.22/2.47 (~(elem!1 = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10997, 11384])).
% 2.22/2.47 tff(11386,plain,
% 2.22/2.47 (~(s(elem!1) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1565, 11385, 11377])).
% 2.22/2.47 tff(11387,plain,
% 2.22/2.47 (~(elem!1 = s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1569, 11386])).
% 2.22/2.47 tff(11388,plain,
% 2.22/2.47 (~r(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[7112, 11387, 305, 323, 10977, 1, 7265])).
% 2.22/2.47 tff(11389,plain,
% 2.22/2.47 (b(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[507, 11388])).
% 2.22/2.47 tff(11390,plain,
% 2.22/2.47 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4423, 11376, 54, 10955, 7265, 50, 305])).
% 2.22/2.47 tff(11391,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11377])).
% 2.22/2.47 tff(11392,plain,
% 2.22/2.47 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(symmetry,[status(thm)],[11391])).
% 2.22/2.47 tff(11393,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11354, 11392])).
% 2.22/2.47 tff(11394,plain,
% 2.22/2.47 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11377])).
% 2.22/2.47 tff(11395,plain,
% 2.22/2.47 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.47 inference(symmetry,[status(thm)],[11394])).
% 2.22/2.47 tff(11396,plain,
% 2.22/2.47 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[305, 11395])).
% 2.22/2.47 tff(11397,plain,
% 2.22/2.47 (~(s(s(elem!1)) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5010, 11377])).
% 2.22/2.47 tff(11398,plain,
% 2.22/2.47 (b(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5056, 11397, 7265, 11354, 323, 11376, 305])).
% 2.22/2.47 tff(11399,plain,
% 2.22/2.47 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11377])).
% 2.22/2.47 tff(11400,plain,
% 2.22/2.47 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(symmetry,[status(thm)],[11399])).
% 2.22/2.47 tff(11401,plain,
% 2.22/2.47 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11400])).
% 2.22/2.47 tff(11402,plain,
% 2.22/2.47 (~r(s(s(s(z))), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9288, 11383, 10955, 54, 606, 11354, 1, 4, 323, 11376])).
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% 2.22/2.47 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11402, 11401])).
% 2.22/2.47 tff(11404,plain,
% 2.22/2.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2623, 435, 112])).
% 2.22/2.47 tff(11405,plain,
% 2.22/2.47 (~r(z, s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[940, 11404, 51, 321])).
% 2.22/2.47 tff(11406,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[583, 11405])).
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% 2.22/2.47 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[7918, 11406, 51, 860, 491, 321, 11404])).
% 2.22/2.47 tff(11408,plain,
% 2.22/2.47 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1451, 11407])).
% 2.22/2.47 tff(11409,plain,
% 2.22/2.47 (~b(s(s(z)), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1425, 11408, 123, 304])).
% 2.22/2.47 tff(11410,plain,
% 2.22/2.47 (r(s(s(z)), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1429, 44, 11409, 1416])).
% 2.22/2.47 tff(11411,plain,
% 2.22/2.47 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9276, 333, 323, 3193, 11410])).
% 2.22/2.47 tff(11412,plain,
% 2.22/2.47 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1473, 44, 11411, 217])).
% 2.22/2.47 tff(11413,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[7952, 11412, 7927, 11408])).
% 2.22/2.47 tff(11414,plain,
% 2.22/2.47 (r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[11413, 1685])).
% 2.22/2.47 tff(11415,plain,
% 2.22/2.47 (~r(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11212, 3193, 670, 323])).
% 2.22/2.47 tff(11416,plain,
% 2.22/2.47 (b(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[396, 11415])).
% 2.22/2.47 tff(11417,plain,
% 2.22/2.47 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[3170, 144, 491, 11406, 11416])).
% 2.22/2.47 tff(11418,plain,
% 2.22/2.47 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1951, 44, 3785, 11417])).
% 2.22/2.47 tff(11419,plain,
% 2.22/2.47 (~(s(s(elem!1)) = s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1196, 11205])).
% 2.22/2.47 tff(11420,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5572, 11406, 2726, 491])).
% 2.22/2.47 tff(11421,plain,
% 2.22/2.47 (r(s(s(elem!1)), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1283, 11420, 11419])).
% 2.22/2.47 tff(11422,plain,
% 2.22/2.47 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5580, 333, 435, 11421, 11418])).
% 2.22/2.47 tff(11423,plain,
% 2.22/2.47 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[862, 860])).
% 2.22/2.47 tff(11424,plain,
% 2.22/2.47 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4917, 11423])).
% 2.22/2.47 tff(11425,plain,
% 2.22/2.47 (b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5022, 44, 11424, 11422])).
% 2.22/2.47 tff(11426,plain,
% 2.22/2.47 (~b(z, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5708, 11425, 2726, 11416])).
% 2.22/2.47 tff(11427,plain,
% 2.22/2.47 (r(z, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[619, 11426])).
% 2.22/2.47 tff(11428,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[3201, 11427, 670, 3193])).
% 2.22/2.47 tff(11429,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11428, 11414])).
% 2.22/2.47 tff(11430,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11431,plain,
% 2.22/2.47 (~r(s(elem!1), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11430, 11377, 7265, 11383, 11403, 11398, 323, 11389, 50, 11396, 10955, 11374, 11393, 11390])).
% 2.22/2.47 tff(11432,plain,
% 2.22/2.47 (b(s(elem!1), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[448, 11431, 11386])).
% 2.22/2.47 tff(11433,plain,
% 2.22/2.47 (~b(s(elem!1), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1820, 11432, 11376, 10977, 11389])).
% 2.22/2.47 tff(11434,plain,
% 2.22/2.47 (r(s(elem!1), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[486, 11433, 1])).
% 2.22/2.47 tff(11435,plain,
% 2.22/2.47 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11237, 11434, 11383, 323])).
% 2.22/2.47 tff(11436,plain,
% 2.22/2.47 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[965, 11435, 11381])).
% 2.22/2.47 tff(11437,plain,
% 2.22/2.47 (~r(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11212, 11383, 7265, 323])).
% 2.22/2.47 tff(11438,plain,
% 2.22/2.47 (b(s(s(s(z))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[396, 11437])).
% 2.22/2.47 tff(11439,plain,
% 2.22/2.47 (~b(z, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1802, 11436, 11389, 11438])).
% 2.22/2.47 tff(11440,plain,
% 2.22/2.47 (r(z, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[619, 11439])).
% 2.22/2.47 tff(11441,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[3201, 11440, 7265, 11383])).
% 2.22/2.47 tff(11442,plain,
% 2.22/2.47 (b(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1538, 11441, 11385])).
% 2.22/2.47 tff(11443,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10830, 144, 11432, 11442, 11436, 10101])).
% 2.22/2.47 tff(11444,plain,((~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11445,plain,
% 2.22/2.47 (~r(s(z), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11444, 305, 1, 54, 606, 4, 3])).
% 2.22/2.47 tff(11446,plain,
% 2.22/2.47 (b(s(z), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[348, 11445])).
% 2.22/2.47 tff(11447,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11054, 333, 1699, 11120, 7018, 51])).
% 2.22/2.47 tff(11448,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(11449,plain,
% 2.22/2.47 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[11448, 1699, 11058, 123, 305, 3, 4367, 54])).
% 2.22/2.47 tff(11450,plain,
% 2.22/2.47 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11449])).
% 2.22/2.47 tff(11451,plain,
% 2.22/2.47 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.47 inference(symmetry,[status(thm)],[11450])).
% 2.22/2.47 tff(11452,plain,
% 2.22/2.47 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[305, 11451])).
% 2.22/2.47 tff(11453,plain,
% 2.22/2.47 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[3398, 11449])).
% 2.22/2.47 tff(11454,plain,
% 2.22/2.47 (~(s(s(s(z))) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[109, 11449])).
% 2.22/2.47 tff(11455,plain,
% 2.22/2.47 (~(elem!1 = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10997, 11454])).
% 2.22/2.47 tff(11456,plain,
% 2.22/2.47 (~(s(elem!1) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1565, 11455, 11449])).
% 2.22/2.47 tff(11457,plain,
% 2.22/2.47 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11449])).
% 2.22/2.47 tff(11458,plain,
% 2.22/2.47 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[11457])).
% 2.22/2.47 tff(11459,plain,
% 2.22/2.47 (~(s(s(z)) = elem!1)),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[1446, 11458])).
% 2.22/2.47 tff(11460,plain,
% 2.22/2.47 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1508, 11459])).
% 2.22/2.47 tff(11461,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 1699])).
% 2.22/2.47 tff(11462,plain,
% 2.22/2.47 (b(elem!1, s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1538, 11455, 11461])).
% 2.22/2.47 tff(11463,plain,
% 2.22/2.47 (b(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2235, 11449, 123])).
% 2.22/2.47 tff(11464,plain,
% 2.22/2.47 (~b(s(z), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10692, 144, 11463, 11462, 4367])).
% 2.22/2.47 tff(11465,plain,
% 2.22/2.47 (r(s(z), s(s(s(z))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[172, 11464])).
% 2.22/2.48 tff(11466,plain,
% 2.22/2.48 (~b(s(s(s(z))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4375, 11463, 4367, 305])).
% 2.22/2.48 tff(11467,plain,
% 2.22/2.48 (r(s(s(s(z))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2794, 11466])).
% 2.22/2.48 tff(11468,plain,
% 2.22/2.48 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[5835, 509, 670, 1699])).
% 2.22/2.48 tff(11469,plain,
% 2.22/2.48 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[965, 11468, 960])).
% 2.22/2.48 tff(11470,plain,
% 2.22/2.48 (b(s(elem!1), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[448, 7135, 433])).
% 2.22/2.48 tff(11471,plain,
% 2.22/2.48 (((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11472,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11471])).
% 2.22/2.48 tff(11473,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11472, 10825])).
% 2.22/2.48 tff(11474,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11475,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11474, 11473])).
% 2.22/2.48 tff(11476,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11475, 144, 11470, 2082, 11469, 4367])).
% 2.22/2.48 tff(11477,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(11478,plain,
% 2.22/2.48 (~r(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11477, 11462, 4367, 11456, 11460, 11058, 408, 670, 1699])).
% 2.22/2.48 tff(11479,plain,
% 2.22/2.48 (b(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[507, 11478])).
% 2.22/2.48 tff(11480,plain,
% 2.22/2.48 (~b(s(elem!1), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[499, 11479, 490, 489])).
% 2.22/2.48 tff(11481,plain,
% 2.22/2.48 (r(s(elem!1), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[486, 11480, 1])).
% 2.22/2.48 tff(11482,plain,
% 2.22/2.48 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10910, 333, 11481, 11467, 11465])).
% 2.22/2.48 tff(11483,plain,
% 2.22/2.48 (b(s(elem!1), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[965, 11482, 11460])).
% 2.22/2.48 tff(11484,plain,
% 2.22/2.48 (~b(s(elem!1), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11475, 144, 11462, 11483, 4367])).
% 2.22/2.48 tff(11485,plain,
% 2.22/2.48 (r(s(elem!1), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[448, 11484, 11456])).
% 2.22/2.48 tff(11486,plain,
% 2.22/2.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2623, 11485, 11453])).
% 2.22/2.48 tff(11487,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2113, 11463, 3, 408, 123, 489])).
% 2.22/2.48 tff(11488,plain,
% 2.22/2.48 (~r(z, s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[940, 11486, 11058, 11487])).
% 2.22/2.48 tff(11489,plain,
% 2.22/2.48 (b(z, s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[583, 11488])).
% 2.22/2.48 tff(11490,plain,
% 2.22/2.48 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[7918, 11489, 11058, 860, 11479, 11487, 11486])).
% 2.22/2.48 tff(11491,plain,
% 2.22/2.48 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1451, 11490])).
% 2.22/2.48 tff(11492,plain,
% 2.22/2.48 (~b(s(s(z)), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1425, 11491, 123, 11452])).
% 2.22/2.48 tff(11493,plain,
% 2.22/2.48 (r(s(s(z)), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1429, 44, 11492, 1416])).
% 2.22/2.48 tff(11494,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11449])).
% 2.22/2.48 tff(11495,plain,
% 2.22/2.48 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.48 inference(symmetry,[status(thm)],[11494])).
% 2.22/2.48 tff(11496,plain,
% 2.22/2.48 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11495])).
% 2.22/2.48 tff(11497,plain,
% 2.22/2.48 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11461, 11496])).
% 2.22/2.48 tff(11498,plain,
% 2.22/2.48 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11449])).
% 2.22/2.48 tff(11499,plain,
% 2.22/2.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(symmetry,[status(thm)],[11498])).
% 2.22/2.48 tff(11500,plain,
% 2.22/2.48 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11499])).
% 2.22/2.48 tff(11501,plain,
% 2.22/2.48 (~r(s(s(s(z))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2079, 1699, 670, 408])).
% 2.22/2.48 tff(11502,plain,
% 2.22/2.48 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11501, 11500])).
% 2.22/2.48 tff(11503,plain,
% 2.22/2.48 (~b(s(s(z)), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[7952, 11491, 11502, 11497])).
% 2.22/2.48 tff(11504,plain,
% 2.22/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1473, 44, 11503, 217])).
% 2.22/2.48 tff(11505,plain,
% 2.22/2.48 (~b(s(z), s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2383, 11489, 489, 11479])).
% 2.22/2.48 tff(11506,plain,
% 2.22/2.48 (r(s(z), s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1244, 11505, 1229])).
% 2.22/2.48 tff(11507,plain,
% 2.22/2.48 (((~![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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11508,plain,
% 2.22/2.48 (((~r(s(z), s(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(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11509,plain,
% 2.22/2.48 (((~![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(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(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11508])).
% 2.22/2.48 tff(11510,plain,
% 2.22/2.48 (((~![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(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(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11509, 11507])).
% 2.22/2.48 tff(11511,plain,
% 2.22/2.48 ((~![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(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11512,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11511, 11510])).
% 2.22/2.48 tff(11513,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11512, 333, 11506, 11467, 11504, 11493])).
% 2.22/2.48 tff(11514,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(11515,plain,
% 2.22/2.48 (~r(s(s(s(z))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11514, 11446, 11374, 50, 10101, 1, 10977, 11354, 7265, 305, 3, 54])).
% 2.22/2.48 tff(11516,plain,
% 2.22/2.48 (b(s(s(s(z))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[396, 11515])).
% 2.22/2.48 tff(11517,plain,
% 2.22/2.48 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[7091, 144, 490, 489, 304])).
% 2.22/2.48 tff(11518,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[300, 44, 273, 11517])).
% 2.22/2.48 tff(11519,plain,
% 2.22/2.48 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2423, 333, 670, 408, 11518])).
% 2.22/2.48 tff(11520,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[130, 11519, 114])).
% 2.22/2.48 tff(11521,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11522,plain,
% 2.22/2.48 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11523,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11522])).
% 2.22/2.48 tff(11524,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11523, 11521])).
% 2.22/2.48 tff(11525,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11526,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11525, 11524])).
% 2.22/2.48 tff(11527,plain,
% 2.22/2.48 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11526, 144, 305, 304, 4367])).
% 2.22/2.48 tff(11528,plain,
% 2.22/2.48 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11527, 11520])).
% 2.22/2.48 tff(11529,plain,
% 2.22/2.48 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[2544])).
% 2.22/2.48 tff(11530,plain,
% 2.22/2.48 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[114, 11529])).
% 2.22/2.48 tff(11531,plain,
% 2.22/2.48 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3280, 333, 670, 408, 11518])).
% 2.22/2.48 tff(11532,plain,
% 2.22/2.48 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[121, 11531, 11530])).
% 2.22/2.48 tff(11533,plain,
% 2.22/2.48 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11534,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11533])).
% 2.22/2.48 tff(11535,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11534, 10103])).
% 2.22/2.48 tff(11536,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11537,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11536, 11535])).
% 2.22/2.48 tff(11538,plain,
% 2.22/2.48 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11537, 144, 11520, 11532, 4367])).
% 2.22/2.48 tff(11539,plain,
% 2.22/2.48 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[313, 11532, 305, 304])).
% 2.22/2.48 tff(11540,plain,
% 2.22/2.48 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[49, 11539])).
% 2.22/2.48 tff(11541,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.22/2.48 tff(11542,plain,
% 2.22/2.48 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1131, 1129])).
% 2.22/2.48 tff(11543,plain,
% 2.22/2.48 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1136, 11542, 11541])).
% 2.22/2.48 tff(11544,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 2.22/2.48 tff(11545,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[248, 1129, 11544])).
% 2.22/2.48 tff(11546,assumption,(r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.22/2.48 tff(11547,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11548,plain,
% 2.22/2.48 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11549,plain,
% 2.22/2.48 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11548])).
% 2.22/2.48 tff(11550,plain,
% 2.22/2.48 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11549, 11547])).
% 2.22/2.48 tff(11551,plain,
% 2.22/2.48 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11552,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11551, 11550])).
% 2.22/2.48 tff(11553,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11552, 333, 3193, 11546, 11545, 11543])).
% 2.22/2.48 tff(11554,plain,((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(11555,plain,
% 2.22/2.48 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11554, 11540, 7586, 11538, 11528])).
% 2.22/2.48 tff(11556,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11555])).
% 2.22/2.48 tff(11557,plain,
% 2.22/2.48 (b(s(s(s(z))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(symmetry,[status(thm)],[11556])).
% 2.22/2.48 tff(11558,plain,
% 2.22/2.48 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11557])).
% 2.22/2.48 tff(11559,plain,
% 2.22/2.48 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[2789, 11558])).
% 2.22/2.48 tff(11560,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[304, 11559])).
% 2.22/2.48 tff(11561,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(11562,plain,
% 2.22/2.48 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11561, 114, 4367, 670, 305, 490, 408, 11011, 489])).
% 2.22/2.48 tff(11563,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[319, 11562])).
% 2.22/2.48 tff(11564,plain,
% 2.22/2.48 (~r(s(z), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10422, 11120, 11012, 11563])).
% 2.22/2.48 tff(11565,plain,
% 2.22/2.48 (b(s(z), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[172, 11564])).
% 2.22/2.48 tff(11566,plain,
% 2.22/2.48 (~b(z, s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2156, 11565, 489, 285])).
% 2.22/2.48 tff(11567,plain,
% 2.22/2.48 (r(z, s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[619, 11566])).
% 2.22/2.48 tff(11568,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11569,plain,
% 2.22/2.48 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(11570,plain,
% 2.22/2.48 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11569])).
% 2.22/2.48 tff(11571,plain,
% 2.22/2.48 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[11570, 11568])).
% 2.22/2.48 tff(11572,plain,
% 2.22/2.48 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(11573,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[11572, 11571])).
% 2.22/2.48 tff(11574,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11573, 333, 11567, 11120, 11563, 51])).
% 2.22/2.48 tff(11575,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(11576,plain,
% 2.22/2.48 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[11575, 11446, 10955, 11516, 10101, 7265, 305, 10977, 11354, 3, 54])).
% 2.22/2.48 tff(11577,plain,
% 2.22/2.48 (b(s(z), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2235, 11576, 50])).
% 2.22/2.48 tff(11578,plain,
% 2.22/2.48 (~b(elem!1, z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[9125, 144, 10977, 11446, 305])).
% 2.22/2.48 tff(11579,plain,
% 2.22/2.48 (~(s(s(s(z))) = elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[380, 11516, 11578])).
% 2.22/2.48 tff(11580,plain,
% 2.22/2.48 (~(elem!1 = s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10997, 11579])).
% 2.22/2.48 tff(11581,plain,
% 2.22/2.48 (~(s(elem!1) = elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1565, 11576, 11580])).
% 2.22/2.48 tff(11582,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2113, 11577, 3, 11354, 50, 11446])).
% 2.22/2.48 tff(11583,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[11576])).
% 2.22/2.48 tff(11584,plain,
% 2.22/2.48 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(symmetry,[status(thm)],[11583])).
% 2.22/2.48 tff(11585,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[305, 11584])).
% 2.22/2.48 tff(11586,plain,
% 2.22/2.48 (~r(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[517, 435, 51, 408])).
% 2.22/2.48 tff(11587,plain,
% 2.22/2.48 (b(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[507, 11586])).
% 2.22/2.48 tff(11588,plain,
% 2.22/2.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2623, 435, 4854])).
% 2.22/2.48 tff(11589,plain,
% 2.22/2.48 (~r(z, s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[940, 11588, 51, 321])).
% 2.22/2.48 tff(11590,plain,
% 2.22/2.48 (b(z, s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[583, 11589])).
% 2.22/2.48 tff(11591,plain,
% 2.22/2.48 (~b(s(z), s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[2383, 11590, 489, 11587])).
% 2.22/2.48 tff(11592,plain,
% 2.22/2.48 (r(s(z), s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1244, 11591, 1237])).
% 2.22/2.48 tff(11593,plain,
% 2.22/2.48 (b(s(s(s(z))), s(elem!1))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3799, 11592, 489, 698, 81, 285, 304, 408, 435])).
% 2.22/2.48 tff(11594,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3170, 144, 11587, 11590, 285, 11593])).
% 2.22/2.49 tff(11595,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (s(s(s(z))) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11596,plain,
% 2.22/2.49 (~r(s(elem!1), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11595, 11516, 11446, 11579, 11576, 11585, 11354, 1229, 10955, 11582])).
% 2.22/2.49 tff(11597,plain,
% 2.22/2.49 (b(s(elem!1), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[448, 11596, 11581])).
% 2.22/2.49 tff(11598,plain,
% 2.22/2.49 (~b(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4344, 144, 11597, 11577, 305])).
% 2.22/2.49 tff(11599,plain,
% 2.22/2.49 (r(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[486, 11598, 1])).
% 2.22/2.49 tff(11600,plain,
% 2.22/2.49 (~(elem!1 = s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1569, 11581])).
% 2.22/2.49 tff(11601,plain,
% 2.22/2.49 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11576])).
% 2.22/2.49 tff(11602,plain,
% 2.22/2.49 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11601])).
% 2.22/2.49 tff(11603,plain,
% 2.22/2.49 (~(s(s(z)) = elem!1)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[1446, 11602])).
% 2.22/2.49 tff(11604,plain,
% 2.22/2.49 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1508, 11603])).
% 2.22/2.49 tff(11605,plain,
% 2.22/2.49 (~(s(s(s(z))) = s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1934, 11604])).
% 2.22/2.49 tff(11606,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2273, 11516, 11446, 10977])).
% 2.22/2.49 tff(11607,plain,
% 2.22/2.49 (r(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2794, 11606])).
% 2.22/2.49 tff(11608,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4819, 3745, 4367, 451])).
% 2.22/2.49 tff(11609,plain,
% 2.22/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 11608])).
% 2.22/2.49 tff(11610,plain,
% 2.22/2.49 (~b(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1732, 1725, 134, 902, 1727])).
% 2.22/2.49 tff(11611,plain,
% 2.22/2.49 (r(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1244, 11610, 1237])).
% 2.22/2.49 tff(11612,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3301, 333, 434, 11611, 3193, 11609])).
% 2.22/2.49 tff(11613,plain,(r(elem!1, s(elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11614,plain,
% 2.22/2.49 (r(elem!1, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11613, 11599, 11607, 11605, 10101, 11597, 1229, 11600, 11577, 11596])).
% 2.22/2.49 tff(11615,plain,
% 2.22/2.49 (~r(z, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2393, 11614, 7265, 11599])).
% 2.22/2.49 tff(11616,plain,
% 2.22/2.49 (b(z, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[583, 11615])).
% 2.22/2.49 tff(11617,plain,
% 2.22/2.49 (~r(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[678, 11614, 7265, 11354])).
% 2.22/2.49 tff(11618,plain,
% 2.22/2.49 (b(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[507, 11617])).
% 2.22/2.49 tff(11619,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3170, 144, 11618, 11616, 11516])).
% 2.22/2.49 tff(11620,plain,
% 2.22/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1951, 44, 11605, 11619])).
% 2.22/2.49 tff(11621,plain,
% 2.22/2.49 (~b(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2383, 11616, 11446, 11618])).
% 2.22/2.49 tff(11622,plain,
% 2.22/2.49 (r(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1244, 11621, 1229])).
% 2.22/2.49 tff(11623,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3301, 333, 11599, 11622, 11607, 11620])).
% 2.22/2.49 tff(11624,plain,((~b(elem!1, s(z))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11625,plain,
% 2.22/2.49 (~b(elem!1, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11624, 606, 3, 54, 1, 4])).
% 2.22/2.49 tff(11626,plain,
% 2.22/2.49 (r(elem!1, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[720, 11625, 11373])).
% 2.22/2.49 tff(11627,plain,
% 2.22/2.49 (~r(elem!1, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11018, 333, 11356, 11626, 11371])).
% 2.22/2.49 tff(11628,plain,
% 2.22/2.49 (b(elem!1, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1538, 11627, 11370])).
% 2.22/2.49 tff(11629,plain,
% 2.22/2.49 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11026, 144, 11628, 452, 10101])).
% 2.22/2.49 tff(11630,plain,
% 2.22/2.49 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[249, 11629])).
% 2.22/2.49 tff(11631,plain,
% 2.22/2.49 (~r(elem!1, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11018, 333, 409, 722, 3193])).
% 2.22/2.49 tff(11632,plain,
% 2.22/2.49 (b(elem!1, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1538, 11631, 1524])).
% 2.22/2.49 tff(11633,plain,
% 2.22/2.49 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11026, 144, 11632, 452, 4367])).
% 2.22/2.49 tff(11634,plain,
% 2.22/2.49 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[249, 11633])).
% 2.22/2.49 tff(11635,plain,
% 2.22/2.49 (~r(s(s(z)), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1458, 333, 2671, 224, 51])).
% 2.22/2.49 tff(11636,plain,
% 2.22/2.49 (b(s(s(z)), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1462, 44, 164, 11635])).
% 2.22/2.49 tff(11637,plain,
% 2.22/2.49 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1469, 333, 2671, 224, 6107])).
% 2.22/2.49 tff(11638,plain,
% 2.22/2.49 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1473, 44, 11637, 217])).
% 2.22/2.49 tff(11639,plain,
% 2.22/2.49 (~r(z, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1480, 333, 224, 6107, 51])).
% 2.22/2.49 tff(11640,plain,
% 2.22/2.49 (b(z, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[619, 11639])).
% 2.22/2.49 tff(11641,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1490, 144, 285, 11640, 11638, 11636])).
% 2.22/2.49 tff(11642,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11643,plain,
% 2.22/2.49 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11642, 285, 11634, 11058, 11120])).
% 2.22/2.49 tff(11644,plain,
% 2.22/2.49 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1451, 11643])).
% 2.22/2.49 tff(11645,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11646,plain,
% 2.22/2.49 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11647,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11646])).
% 2.22/2.49 tff(11648,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[11647, 11645])).
% 2.22/2.49 tff(11649,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(11650,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[11649, 11648])).
% 2.22/2.49 tff(11651,plain,
% 2.22/2.49 (~b(s(s(z)), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11650, 144, 11644, 452, 454])).
% 2.22/2.49 tff(11652,plain,
% 2.22/2.49 (~r(z, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1480, 333, 11634, 11120, 11058])).
% 2.22/2.49 tff(11653,plain,
% 2.22/2.49 (b(z, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[619, 11652])).
% 2.22/2.49 tff(11654,plain,
% 2.22/2.49 (~b(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2156, 11653, 489, 285])).
% 2.22/2.49 tff(11655,plain,
% 2.22/2.49 (r(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[172, 11654])).
% 2.22/2.49 tff(11656,plain,
% 2.22/2.49 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10422, 11655, 11120, 3193])).
% 2.22/2.49 tff(11657,plain,
% 2.22/2.49 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[319, 11656])).
% 2.22/2.49 tff(11658,plain,
% 2.22/2.49 (~b(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1425, 11644, 123, 11657])).
% 2.22/2.49 tff(11659,plain,
% 2.22/2.49 (r(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1429, 44, 11658, 1416])).
% 2.22/2.49 tff(11660,plain,
% 2.22/2.49 (~r(s(s(z)), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7974, 333, 409, 722, 11659])).
% 2.22/2.49 tff(11661,plain,
% 2.22/2.49 (s(s(z)) = elem!1),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7970, 11660, 11651])).
% 2.22/2.49 tff(11662,plain,
% 2.22/2.49 ((s(s(z)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11661])).
% 2.22/2.49 tff(11663,plain,
% 2.22/2.49 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.22/2.49 inference(transitivity,[status(thm)],[11662, 199])).
% 2.22/2.49 tff(11664,plain,
% 2.22/2.49 ((~(s(s(z)) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11663])).
% 2.22/2.49 tff(11665,plain,
% 2.22/2.49 (~(s(elem!1) = elem!1)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[860, 11664])).
% 2.22/2.49 tff(11666,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 2.22/2.49 tff(11667,plain,
% 2.22/2.49 (s(s(s(z))) = s(elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11666])).
% 2.22/2.49 tff(11668,plain,
% 2.22/2.49 (s(elem!1) = s(s(s(z)))),
% 2.22/2.49 inference(symmetry,[status(thm)],[11667])).
% 2.22/2.49 tff(11669,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[960, 11668])).
% 2.22/2.49 tff(11670,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11671,plain,
% 2.22/2.49 (s(elem!1) = s(s(s(z)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11670, 11661])).
% 2.22/2.49 tff(11672,plain,
% 2.22/2.49 (s(s(s(z))) = s(elem!1)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[11671, 998])).
% 2.22/2.49 tff(11673,plain,
% 2.22/2.49 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11671])).
% 2.22/2.49 tff(11674,plain,
% 2.22/2.49 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.22/2.49 inference(symmetry,[status(thm)],[11673])).
% 2.22/2.49 tff(11675,plain,
% 2.22/2.49 (b(s(elem!1), z)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[285, 11674])).
% 2.22/2.49 tff(11676,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11104, 11675, 11672, 722, 123, 489, 670, 11665, 409, 54, 114, 3, 1])).
% 2.22/2.49 tff(11677,plain,((~b(s(s(s(z))), z)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11678,plain,
% 2.22/2.49 (~b(s(s(s(z))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11677, 11358, 50, 11626, 7265, 11356, 54, 114, 3, 1, 11374, 11371, 10101, 11370])).
% 2.22/2.49 tff(11679,plain,
% 2.22/2.49 (r(s(s(s(z))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[396, 11678])).
% 2.22/2.49 tff(11680,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1340, 333, 11679, 11630, 10957, 10955])).
% 2.22/2.49 tff(11681,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11682,plain,
% 2.22/2.49 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11681, 606, 3, 1, 54, 4])).
% 2.22/2.49 tff(11683,plain,
% 2.22/2.49 (~(s(s(s(z))) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[109, 11682])).
% 2.22/2.49 tff(11684,plain,
% 2.22/2.49 (~(elem!1 = s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10997, 11683])).
% 2.22/2.49 tff(11685,plain,
% 2.22/2.49 (b(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2235, 11682, 50])).
% 2.22/2.49 tff(11686,plain,
% 2.22/2.49 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[735, 11682, 11625])).
% 2.22/2.49 tff(11687,plain,
% 2.22/2.49 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[319, 11686])).
% 2.22/2.49 tff(11688,plain,
% 2.22/2.49 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11682])).
% 2.22/2.49 tff(11689,plain,
% 2.22/2.49 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.49 inference(symmetry,[status(thm)],[11688])).
% 2.22/2.49 tff(11690,plain,
% 2.22/2.49 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[11354, 11689])).
% 2.22/2.49 tff(11691,plain,
% 2.22/2.49 (~r(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[341, 11690, 10955, 11687])).
% 2.22/2.49 tff(11692,plain,
% 2.22/2.49 (b(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[348, 11691])).
% 2.22/2.49 tff(11693,plain,
% 2.22/2.49 (~(s(elem!1) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1565, 11684, 11682])).
% 2.22/2.49 tff(11694,plain,
% 2.22/2.49 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11682])).
% 2.22/2.49 tff(11695,plain,
% 2.22/2.49 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11694])).
% 2.22/2.49 tff(11696,plain,
% 2.22/2.49 (~(s(s(z)) = elem!1)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[1446, 11695])).
% 2.22/2.49 tff(11697,plain,
% 2.22/2.49 (~(s(elem!1) = s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1508, 11696])).
% 2.22/2.49 tff(11698,plain,
% 2.22/2.49 (b(elem!1, s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1538, 11461, 1524])).
% 2.22/2.49 tff(11699,plain,
% 2.22/2.49 (~b(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10692, 144, 134, 11698, 4367])).
% 2.22/2.49 tff(11700,plain,
% 2.22/2.49 (r(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[172, 11699])).
% 2.22/2.49 tff(11701,plain,
% 2.22/2.49 (~r(s(elem!1), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7731, 11700, 670, 1, 722, 489, 490])).
% 2.22/2.49 tff(11702,plain,
% 2.22/2.49 (b(s(elem!1), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[448, 11701, 433])).
% 2.22/2.49 tff(11703,plain,
% 2.22/2.49 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10830, 144, 11702, 11698, 4367])).
% 2.22/2.49 tff(11704,plain,
% 2.22/2.49 (r(s(elem!1), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[965, 11703, 960])).
% 2.22/2.49 tff(11705,plain,
% 2.22/2.49 (~r(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11477, 11698, 4367, 433, 960, 51, 408, 670, 1699])).
% 2.22/2.49 tff(11706,plain,
% 2.22/2.49 (b(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[507, 11705])).
% 2.22/2.49 tff(11707,plain,
% 2.22/2.49 (~b(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[499, 11706, 490, 489])).
% 2.22/2.49 tff(11708,plain,
% 2.22/2.49 (r(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[486, 11707, 1])).
% 2.22/2.49 tff(11709,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11335, 333, 11708, 1699, 11704, 11700])).
% 2.22/2.49 tff(11710,plain,((~r(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11711,plain,
% 2.22/2.49 (~r(s(s(s(z))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11710, 11697, 10101, 11693, 7265, 1, 11626, 11692, 10977, 11685, 10955, 11354, 11684])).
% 2.22/2.49 tff(11712,plain,
% 2.22/2.49 (b(s(s(s(z))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[396, 11711])).
% 2.22/2.49 tff(11713,plain,
% 2.22/2.49 (~(s(s(s(z))) = s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1934, 11697])).
% 2.22/2.49 tff(11714,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2273, 11712, 11692, 10977])).
% 2.22/2.49 tff(11715,plain,
% 2.22/2.49 (r(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2794, 11714])).
% 2.22/2.49 tff(11716,plain,
% 2.22/2.49 (b(elem!1, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[560, 2896, 1722])).
% 2.22/2.49 tff(11717,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4819, 11716, 4367, 11470])).
% 2.22/2.49 tff(11718,plain,
% 2.22/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 11717])).
% 2.22/2.49 tff(11719,plain,
% 2.22/2.49 (~b(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1732, 2896, 134, 1722, 7135])).
% 2.22/2.49 tff(11720,plain,
% 2.22/2.49 (r(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1244, 11719, 1237])).
% 2.22/2.49 tff(11721,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11323, 333, 509, 11720, 3193, 11718])).
% 2.22/2.49 tff(11722,plain,((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11723,plain,
% 2.22/2.49 (~r(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11722, 11715, 11713, 1229, 10101, 11685, 11693, 7265, 11354, 10955])).
% 2.22/2.49 tff(11724,plain,
% 2.22/2.49 (b(s(elem!1), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[507, 11723])).
% 2.22/2.49 tff(11725,plain,
% 2.22/2.49 (~(elem!1 = s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1569, 11693])).
% 2.22/2.49 tff(11726,plain,
% 2.22/2.49 (~b(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[499, 11724, 10977, 11692])).
% 2.22/2.49 tff(11727,plain,
% 2.22/2.49 (r(s(elem!1), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[486, 11726, 1])).
% 2.22/2.49 tff(11728,plain,
% 2.22/2.49 (~r(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7799, 563, 722, 434])).
% 2.22/2.49 tff(11729,plain,
% 2.22/2.49 (b(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1244, 11728, 1237])).
% 2.22/2.49 tff(11730,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2383, 2775, 11729, 489, 491])).
% 2.22/2.49 tff(11731,plain,((~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11732,plain,
% 2.22/2.49 (~r(elem!1, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11731, 11692, 11724, 1229, 7265, 11727, 11626])).
% 2.22/2.49 tff(11733,plain,
% 2.22/2.49 (b(elem!1, s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[560, 11732, 11725])).
% 2.22/2.49 tff(11734,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11735,plain,
% 2.22/2.49 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11736,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11735])).
% 2.22/2.49 tff(11737,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.49 inference(transitivity,[status(thm)],[11736, 11734])).
% 2.22/2.49 tff(11738,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(11739,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[11738, 11737])).
% 2.22/2.49 tff(11740,plain,
% 2.22/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11739, 144, 11733, 11724, 11712, 10101])).
% 2.22/2.49 tff(11741,plain,
% 2.22/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1951, 44, 11713, 11740])).
% 2.22/2.49 tff(11742,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11743,plain,
% 2.22/2.49 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(11744,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[11743])).
% 2.22/2.49 tff(11745,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.22/2.49 inference(transitivity,[status(thm)],[11744, 11742])).
% 2.22/2.49 tff(11746,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(11747,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[11746, 11745])).
% 2.22/2.49 tff(11748,plain,
% 2.22/2.49 (~b(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11747, 144, 11733, 11724, 11685, 11692])).
% 2.22/2.49 tff(11749,plain,
% 2.22/2.49 (r(s(z), s(elem!1))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1244, 11748, 1229])).
% 2.22/2.49 tff(11750,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3301, 333, 11727, 11749, 11715, 11741])).
% 2.22/2.49 tff(11751,plain,(b(z, elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11752,plain,
% 2.22/2.49 (b(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11751, 54, 3, 1, 4])).
% 2.22/2.49 tff(11753,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2251, 333, 1699, 6107, 321, 51])).
% 2.22/2.49 tff(11754,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11755,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11754, 9397, 11120, 10570, 51])).
% 2.22/2.49 tff(11756,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11757,plain,
% 2.22/2.49 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11756, 624, 251, 51, 4367, 3, 54])).
% 2.22/2.49 tff(11758,plain,
% 2.22/2.49 (b(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2235, 11757, 123])).
% 2.22/2.49 tff(11759,plain,
% 2.22/2.49 (~b(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1602, 11758, 251, 624])).
% 2.22/2.49 tff(11760,plain,
% 2.22/2.49 (~(s(z) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3965, 11759, 624])).
% 2.22/2.49 tff(11761,plain,
% 2.22/2.49 (~(elem!1 = s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[712, 11760])).
% 2.22/2.49 tff(11762,plain,
% 2.22/2.49 ((~r(z, elem!1)) <=> (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[2301])).
% 2.22/2.49 tff(11763,plain,
% 2.22/2.49 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[1575, 11762])).
% 2.22/2.49 tff(11764,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[51, 11763])).
% 2.22/2.49 tff(11765,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(11766,plain,
% 2.22/2.49 (r(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11765, 11757, 51])).
% 2.22/2.49 tff(11767,plain,
% 2.22/2.49 (r(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[348, 11759])).
% 2.22/2.49 tff(11768,plain,
% 2.22/2.49 (~r(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11212, 11767, 11766, 10570])).
% 2.22/2.49 tff(11769,plain,
% 2.22/2.49 (b(s(s(s(z))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2794, 11768])).
% 2.22/2.49 tff(11770,plain,
% 2.22/2.49 (r(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11765, 81, 51])).
% 2.22/2.49 tff(11771,plain,
% 2.22/2.49 (~b(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1602, 7071, 251, 624])).
% 2.22/2.49 tff(11772,plain,
% 2.22/2.49 (r(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[348, 11771])).
% 2.22/2.49 tff(11773,plain,
% 2.22/2.49 (~b(z, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[11261, 11772, 81, 56, 123, 11770, 7071, 4367])).
% 2.32/2.50 tff(11774,plain,
% 2.32/2.50 (~b(elem!1, s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4375, 7071, 4367, 56])).
% 2.32/2.50 tff(11775,plain,
% 2.32/2.50 (r(elem!1, s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[720, 11774, 714])).
% 2.32/2.50 tff(11776,plain,
% 2.32/2.50 (~r(z, s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[727, 11772, 11770, 11775])).
% 2.32/2.50 tff(11777,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[372, 11776, 11773])).
% 2.32/2.50 tff(11778,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11779,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11778, 11769, 11761, 123, 4367, 11757, 251, 624, 51])).
% 2.32/2.50 tff(11780,plain,((~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11781,plain,
% 2.32/2.50 (~b(elem!1, z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11780, 4367, 123, 251, 11058, 3, 54])).
% 2.32/2.50 tff(11782,plain,
% 2.32/2.50 (~b(elem!1, z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10565, 285, 4367, 251])).
% 2.32/2.50 tff(11783,plain,
% 2.32/2.50 (r(elem!1, z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[653, 11782, 1368])).
% 2.32/2.50 tff(11784,plain,
% 2.32/2.50 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[2495])).
% 2.32/2.50 tff(11785,plain,
% 2.32/2.50 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11784])).
% 2.32/2.50 tff(11786,plain,
% 2.32/2.50 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[217, 11785])).
% 2.32/2.50 tff(11787,plain,
% 2.32/2.50 (b(s(elem!1), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[448, 7135, 2681])).
% 2.32/2.50 tff(11788,plain,
% 2.32/2.50 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[7622, 11787, 51, 408, 133, 509, 2483, 2698])).
% 2.32/2.50 tff(11789,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[3934, 11788, 11787, 123, 57, 133])).
% 2.32/2.50 tff(11790,plain,((~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11791,plain,
% 2.32/2.50 (~r(s(elem!1), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11790, 57, 123, 133, 51, 408])).
% 2.32/2.50 tff(11792,plain,
% 2.32/2.50 (b(s(elem!1), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[507, 11791])).
% 2.32/2.50 tff(11793,plain,
% 2.32/2.50 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[6107, 2767])).
% 2.32/2.50 tff(11794,plain,
% 2.32/2.50 (b(s(s(elem!1)), elem!1)),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[4367, 6760])).
% 2.32/2.50 tff(11795,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11796,plain,
% 2.32/2.50 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11797,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11796])).
% 2.32/2.50 tff(11798,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(transitivity,[status(thm)],[11797, 11795])).
% 2.32/2.50 tff(11799,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(11800,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11799, 11798])).
% 2.32/2.50 tff(11801,plain,
% 2.32/2.50 (~b(s(s(elem!1)), s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11800, 144, 251, 11792, 11794, 2498])).
% 2.32/2.50 tff(11802,plain,
% 2.32/2.50 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1283, 11801, 2507])).
% 2.32/2.50 tff(11803,plain,
% 2.32/2.50 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10010, 144, 251, 133, 2498])).
% 2.32/2.50 tff(11804,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11803, 286])).
% 2.32/2.50 tff(11805,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2758, 11804, 10047])).
% 2.32/2.50 tff(11806,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[542, 9999, 2698])).
% 2.32/2.50 tff(11807,plain,
% 2.32/2.50 (~r(s(elem!1), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[5258, 11806, 2737, 11805])).
% 2.32/2.50 tff(11808,plain,
% 2.32/2.50 (b(s(elem!1), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[965, 11807, 11786])).
% 2.32/2.50 tff(11809,plain,
% 2.32/2.50 (~b(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1802, 11808, 285, 491])).
% 2.32/2.50 tff(11810,plain,
% 2.32/2.50 (r(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[619, 11809])).
% 2.32/2.50 tff(11811,plain,
% 2.32/2.50 (r(z, s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2836, 11810, 57])).
% 2.32/2.50 tff(11812,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4331, 333, 2737, 11805, 51, 11811])).
% 2.32/2.50 tff(11813,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11814,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11813, 11802, 51, 57, 285, 11792, 251, 133])).
% 2.32/2.50 tff(11815,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[302, 11814])).
% 2.32/2.50 tff(11816,plain,
% 2.32/2.50 (~r(z, s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2843, 333, 11815, 51, 11793])).
% 2.32/2.50 tff(11817,plain,
% 2.32/2.50 (~r(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2836, 11816, 57])).
% 2.32/2.50 tff(11818,plain,
% 2.32/2.50 (b(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[619, 11817])).
% 2.32/2.50 tff(11819,plain,
% 2.32/2.50 (~b(s(elem!1), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1802, 11818, 285, 11792])).
% 2.32/2.50 tff(11820,plain,
% 2.32/2.50 (r(s(elem!1), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[965, 11819, 11786])).
% 2.32/2.50 tff(11821,plain,
% 2.32/2.50 (r(s(elem!1), s(s(elem!1)))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11820, 2849])).
% 2.32/2.50 tff(11822,plain,
% 2.32/2.50 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[3934, 451, 123, 57, 133])).
% 2.32/2.50 tff(11823,plain,
% 2.32/2.50 (~r(elem!1, s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[8472, 11822, 2857, 10047, 451, 2737, 4575, 2462, 133])).
% 2.32/2.50 tff(11824,plain,
% 2.32/2.50 (b(elem!1, s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[560, 11823, 2483])).
% 2.32/2.50 tff(11825,plain,
% 2.32/2.50 (~b(z, s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1642, 11824, 251, 451])).
% 2.32/2.50 tff(11826,plain,
% 2.32/2.50 (r(z, s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[583, 11825])).
% 2.32/2.50 tff(11827,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[555, 11824, 133, 451])).
% 2.32/2.50 tff(11828,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[542, 11827, 2698])).
% 2.32/2.50 tff(11829,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[3607, 11828, 11826, 51, 11822])).
% 2.32/2.50 tff(11830,plain,((~b(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11831,plain,
% 2.32/2.50 (~b(s(elem!1), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11830, 11802, 133, 251, 51, 123, 57])).
% 2.32/2.50 tff(11832,plain,
% 2.32/2.50 (r(s(elem!1), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[448, 11831, 2681])).
% 2.32/2.50 tff(11833,plain,
% 2.32/2.50 (b(z, s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2828, 11818, 57])).
% 2.32/2.50 tff(11834,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11835,plain,
% 2.32/2.50 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11836,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11835])).
% 2.32/2.50 tff(11837,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.50 inference(transitivity,[status(thm)],[11836, 11834])).
% 2.32/2.50 tff(11838,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(11839,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11838, 11837])).
% 2.32/2.50 tff(11840,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11839, 144, 251, 2812, 2811, 4972])).
% 2.32/2.50 tff(11841,plain,((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11842,plain,
% 2.32/2.50 (~b(elem!1, s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11841, 11833, 251, 11794])).
% 2.32/2.50 tff(11843,plain,
% 2.32/2.50 (r(elem!1, s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2522, 11842, 2462])).
% 2.32/2.50 tff(11844,plain,
% 2.32/2.50 (~r(s(elem!1), s(s(elem!1)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[5242, 11843, 11802, 11832])).
% 2.32/2.50 tff(11845,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11844, 11821])).
% 2.32/2.50 tff(11846,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11847,plain,
% 2.32/2.50 (~(s(z) = elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11846, 285, 251, 51, 133, 123, 11783, 4367, 6107])).
% 2.32/2.50 tff(11848,plain,
% 2.32/2.50 (r(s(z), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[406, 11847, 350])).
% 2.32/2.50 tff(11849,plain,
% 2.32/2.50 (~r(s(z), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[417, 11848, 51, 11783])).
% 2.32/2.50 tff(11850,plain,
% 2.32/2.50 (b(s(z), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[348, 11849])).
% 2.32/2.50 tff(11851,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11852,plain,
% 2.32/2.50 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11853,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11852])).
% 2.32/2.50 tff(11854,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.32/2.50 inference(transitivity,[status(thm)],[11853, 11851])).
% 2.32/2.50 tff(11855,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(11856,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11855, 11854])).
% 2.32/2.50 tff(11857,plain,
% 2.32/2.50 (~b(s(s(s(z))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11856, 144, 251, 11850, 285, 4367])).
% 2.32/2.50 tff(11858,plain,
% 2.32/2.50 (r(s(s(s(z))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2794, 11857])).
% 2.32/2.50 tff(11859,plain,
% 2.32/2.50 (~(s(s(s(z))) = elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[380, 11782, 285])).
% 2.32/2.50 tff(11860,plain,
% 2.32/2.50 (~(elem!1 = s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10997, 11859])).
% 2.32/2.50 tff(11861,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11026, 144, 2082, 133, 4367])).
% 2.32/2.50 tff(11862,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[249, 11861])).
% 2.32/2.50 tff(11863,plain,
% 2.32/2.50 (~b(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10684, 144, 251, 2082, 4367])).
% 2.32/2.50 tff(11864,plain,
% 2.32/2.50 (r(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[619, 11863])).
% 2.32/2.50 tff(11865,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11040, 333, 11864, 3193, 11862, 51])).
% 2.32/2.50 tff(11866,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11867,plain,
% 2.32/2.50 (~b(elem!1, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11866, 11858, 51, 133, 4367, 251])).
% 2.32/2.50 tff(11868,plain,
% 2.32/2.50 (r(elem!1, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1538, 11867, 11860])).
% 2.32/2.50 tff(11869,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), 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), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11870,plain,
% 2.32/2.50 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11871,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11870])).
% 2.32/2.50 tff(11872,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[11871, 11869])).
% 2.32/2.50 tff(11873,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(11874,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11873, 11872])).
% 2.32/2.50 tff(11875,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11874, 333, 409, 1525, 3193, 353])).
% 2.32/2.50 tff(11876,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11877,plain,
% 2.32/2.50 (~r(s(z), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11876, 11848, 11868, 11858])).
% 2.32/2.50 tff(11878,plain,
% 2.32/2.50 (b(s(z), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[172, 11877])).
% 2.32/2.50 tff(11879,plain,
% 2.32/2.50 (~b(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2156, 11878, 11850, 285])).
% 2.32/2.50 tff(11880,plain,
% 2.32/2.50 (r(z, s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[619, 11879])).
% 2.32/2.50 tff(11881,plain,
% 2.32/2.50 (((~![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(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, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11882,plain,
% 2.32/2.50 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(11883,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[11882])).
% 2.32/2.50 tff(11884,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[11883, 11881])).
% 2.32/2.50 tff(11885,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(11886,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[11885, 11884])).
% 2.32/2.50 tff(11887,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11886, 333, 11783, 11868, 11880, 11858])).
% 2.32/2.50 tff(11888,plain,((~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11889,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11888, 11120, 9956, 51, 4367, 251, 285, 123, 452, 1368])).
% 2.32/2.50 tff(11890,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(11891,plain,
% 2.32/2.50 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[11890, 285, 4367, 251, 11058, 123, 77, 3, 54])).
% 2.32/2.50 tff(11892,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[787, 11891, 11781])).
% 2.32/2.50 tff(11893,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[302, 11892])).
% 2.32/2.50 tff(11894,plain,
% 2.32/2.50 (b(s(z), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2235, 11891, 123])).
% 2.32/2.50 tff(11895,plain,
% 2.32/2.50 (~b(s(s(s(z))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[695, 78, 1, 54, 3, 123])).
% 2.32/2.50 tff(11896,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[8040, 11895, 78, 1, 54, 3, 123])).
% 2.32/2.50 tff(11897,plain,((~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11898,plain,
% 2.32/2.51 (~(s(s(s(z))) = elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11897, 54, 1, 3, 123])).
% 2.32/2.51 tff(11899,plain,
% 2.32/2.51 (~(elem!1 = s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10997, 11898])).
% 2.32/2.51 tff(11900,plain,
% 2.32/2.51 (~r(s(elem!1), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11722, 3193, 7071, 1229, 4367, 3785, 7082, 11770, 2322, 51])).
% 2.32/2.51 tff(11901,plain,
% 2.32/2.51 (b(s(elem!1), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[507, 11900])).
% 2.32/2.51 tff(11902,plain,
% 2.32/2.51 (~(s(s(elem!1)) = s(elem!1))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1196, 7083])).
% 2.32/2.51 tff(11903,plain,
% 2.32/2.51 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[81])).
% 2.32/2.51 tff(11904,plain,
% 2.32/2.51 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(symmetry,[status(thm)],[11903])).
% 2.32/2.51 tff(11905,plain,
% 2.32/2.51 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[251, 11904])).
% 2.32/2.51 tff(11906,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[341, 323, 51, 321])).
% 2.32/2.51 tff(11907,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[319, 11906])).
% 2.32/2.51 tff(11908,plain,
% 2.32/2.51 (~b(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[757, 11907, 123, 11905])).
% 2.32/2.51 tff(11909,plain,
% 2.32/2.51 (r(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[372, 11908])).
% 2.32/2.51 tff(11910,plain,
% 2.32/2.51 (~b(s(elem!1), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10696, 11909, 1682, 4367, 251, 1524, 7071, 323, 491, 7083, 1, 5609, 408])).
% 2.32/2.51 tff(11911,plain,
% 2.32/2.51 (r(s(elem!1), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[448, 11910, 7082])).
% 2.32/2.51 tff(11912,plain,
% 2.32/2.51 (~b(z, s(elem!1))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[5751, 11911, 51, 81, 1229, 11909, 11770, 408, 285, 7071, 11902])).
% 2.32/2.51 tff(11913,plain,
% 2.32/2.51 (~r(z, s(elem!1))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6950, 11911, 11770, 1, 81, 7083, 11909, 51])).
% 2.32/2.51 tff(11914,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[583, 11913, 11912])).
% 2.32/2.51 tff(11915,plain,((~r(s(z), z)) | (s(elem!1) = s(z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11916,plain,
% 2.32/2.51 (~r(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11915, 11901, 81, 51, 2322, 285, 4367, 251, 1524, 1, 123, 3730])).
% 2.32/2.51 tff(11917,plain,
% 2.32/2.51 (b(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[348, 11916])).
% 2.32/2.51 tff(11918,plain,
% 2.32/2.51 (~r(s(elem!1), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10741, 354, 81, 251, 491, 4367, 489, 134, 321, 1229])).
% 2.32/2.51 tff(11919,plain,
% 2.32/2.51 (~b(s(elem!1), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10726, 354, 251, 4367, 134, 491, 81, 321, 1])).
% 2.32/2.51 tff(11920,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[448, 11919, 11918, 433])).
% 2.32/2.51 tff(11921,plain,((~r(z, s(z))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11922,plain,
% 2.32/2.51 (~r(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11921, 11901, 251, 4367, 7071, 7082, 81, 3730, 1, 11917])).
% 2.32/2.51 tff(11923,plain,
% 2.32/2.51 (b(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[372, 11922])).
% 2.32/2.51 tff(11924,plain,
% 2.32/2.51 (~b(elem!1, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[7079, 11923, 251, 7071])).
% 2.32/2.51 tff(11925,plain,
% 2.32/2.51 (~r(elem!1, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10937, 11923, 4367, 251, 285, 377, 1, 7071, 1682, 11917, 2322, 7082, 3193, 1524])).
% 2.32/2.51 tff(11926,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[720, 11925, 11924, 5609])).
% 2.32/2.51 tff(11927,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | b(elem!1, z) | (s(elem!1) = s(z)) | (elem!1 = s(s(s(z)))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11928,plain,
% 2.32/2.51 (~r(s(s(s(z))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11927, 285, 251, 4367, 11781, 1, 11899, 11891, 11058, 123])).
% 2.32/2.51 tff(11929,plain,
% 2.32/2.51 (b(s(s(s(z))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2794, 11928])).
% 2.32/2.51 tff(11930,plain,
% 2.32/2.51 (~b(elem!1, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4375, 11929, 4367, 11894])).
% 2.32/2.51 tff(11931,plain,
% 2.32/2.51 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[735, 11930, 11891])).
% 2.32/2.51 tff(11932,plain,
% 2.32/2.51 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[319, 11931])).
% 2.32/2.51 tff(11933,plain,
% 2.32/2.51 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11891])).
% 2.32/2.51 tff(11934,plain,
% 2.32/2.51 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(z) = elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11933])).
% 2.32/2.51 tff(11935,plain,
% 2.32/2.51 (~(s(z) = elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[34, 11934])).
% 2.32/2.51 tff(11936,plain,
% 2.32/2.51 (~r(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[824, 11929, 71, 123, 11781, 3, 54, 11935, 11930])).
% 2.32/2.51 tff(11937,plain,
% 2.32/2.51 (b(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[348, 11936])).
% 2.32/2.51 tff(11938,plain,
% 2.32/2.51 ((~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2144, 144, 251, 11894, 285])).
% 2.32/2.51 tff(11939,plain,
% 2.32/2.51 (~b(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11938, 11937])).
% 2.32/2.51 tff(11940,plain,
% 2.32/2.51 (r(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[172, 11939])).
% 2.32/2.51 tff(11941,plain,
% 2.32/2.51 (~b(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2273, 11937, 285, 11929])).
% 2.32/2.51 tff(11942,plain,
% 2.32/2.51 (r(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[372, 11941])).
% 2.32/2.51 tff(11943,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[362, 11942, 11940, 11932, 11893])).
% 2.32/2.51 tff(11944,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11945,plain,
% 2.32/2.51 (~b(s(s(s(z))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11944, 11752, 50, 3, 54, 10101, 1])).
% 2.32/2.51 tff(11946,plain,
% 2.32/2.51 (r(s(s(s(z))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[396, 11945])).
% 2.32/2.51 tff(11947,plain,
% 2.32/2.51 (~(s(s(s(z))) = elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11897, 54, 1, 3, 50])).
% 2.32/2.51 tff(11948,plain,
% 2.32/2.51 (~(elem!1 = s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10997, 11947])).
% 2.32/2.51 tff(11949,plain,
% 2.32/2.51 (~b(elem!1, z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11780, 10101, 50, 11752, 10955, 3, 54])).
% 2.32/2.51 tff(11950,plain,
% 2.32/2.51 (r(elem!1, z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[653, 11949, 77])).
% 2.32/2.51 tff(11951,plain,
% 2.32/2.51 (((~![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(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, 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(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11952,plain,
% 2.32/2.51 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11953,plain,
% 2.32/2.51 (((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, 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, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11952])).
% 2.32/2.51 tff(11954,plain,
% 2.32/2.51 (((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, 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, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[11953, 11951])).
% 2.32/2.51 tff(11955,plain,
% 2.32/2.51 ((~![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(z))))))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(11956,plain,
% 2.32/2.51 ((~![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(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[11955, 11954])).
% 2.32/2.51 tff(11957,plain,
% 2.32/2.51 (~r(elem!1, s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11956, 333, 11950, 11946, 10955])).
% 2.32/2.51 tff(11958,plain,
% 2.32/2.51 (b(elem!1, s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1538, 11957, 11948])).
% 2.32/2.51 tff(11959,plain,
% 2.32/2.51 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11960,plain,
% 2.32/2.51 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11961,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11960])).
% 2.32/2.51 tff(11962,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[11961, 11959])).
% 2.32/2.51 tff(11963,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(11964,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[11963, 11962])).
% 2.32/2.51 tff(11965,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11964, 333, 1699, 11864, 11862, 51])).
% 2.32/2.51 tff(11966,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(11967,plain,
% 2.32/2.51 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11966, 11958, 10955, 11946, 10101, 11752])).
% 2.32/2.51 tff(11968,plain,
% 2.32/2.51 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[130, 11967, 54])).
% 2.32/2.51 tff(11969,plain,
% 2.32/2.51 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11968])).
% 2.32/2.51 tff(11970,plain,
% 2.32/2.51 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(z))),
% 2.32/2.51 inference(transitivity,[status(thm)],[11969, 53])).
% 2.32/2.51 tff(11971,plain,
% 2.32/2.51 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11970])).
% 2.32/2.51 tff(11972,plain,
% 2.32/2.51 (~(elem!1 = s(z))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[34, 11971])).
% 2.32/2.51 tff(11973,plain,
% 2.32/2.51 (b(s(z), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2235, 11968, 50])).
% 2.32/2.51 tff(11974,plain,
% 2.32/2.51 (~b(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10692, 144, 11973, 11958, 10101])).
% 2.32/2.51 tff(11975,plain,
% 2.32/2.51 (r(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[172, 11974])).
% 2.32/2.51 tff(11976,plain,
% 2.32/2.51 (~b(z, s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10684, 144, 11752, 11958, 10101])).
% 2.32/2.51 tff(11977,plain,
% 2.32/2.51 (r(z, s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[619, 11976])).
% 2.32/2.51 tff(11978,plain,
% 2.32/2.51 (((~![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(z))))) | (~r(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11979,plain,
% 2.32/2.51 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11980,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11979])).
% 2.32/2.51 tff(11981,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[11980, 11978])).
% 2.32/2.51 tff(11982,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(11983,plain,
% 2.32/2.51 ((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[11982, 11981])).
% 2.32/2.51 tff(11984,plain,
% 2.32/2.51 (~r(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11983, 333, 11946, 11977, 11975])).
% 2.32/2.51 tff(11985,plain,
% 2.32/2.51 (b(z, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[372, 11984])).
% 2.32/2.51 tff(11986,plain,
% 2.32/2.51 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11968])).
% 2.32/2.51 tff(11987,plain,
% 2.32/2.51 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11986])).
% 2.32/2.51 tff(11988,plain,
% 2.32/2.51 (~(s(s(z)) = elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[1446, 11987])).
% 2.32/2.51 tff(11989,plain,
% 2.32/2.51 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1508, 11988])).
% 2.32/2.51 tff(11990,plain,
% 2.32/2.51 (r(z, elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11765, 11968, 10955])).
% 2.32/2.51 tff(11991,plain,
% 2.32/2.51 (~(s(elem!1) = elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1565, 11968, 11948])).
% 2.32/2.51 tff(11992,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(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(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11993,plain,
% 2.32/2.51 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(11994,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[11993])).
% 2.32/2.51 tff(11995,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[11994, 11992])).
% 2.32/2.51 tff(11996,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(11997,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[11996, 11995])).
% 2.32/2.51 tff(11998,plain,
% 2.32/2.51 (~r(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11997, 333, 11946, 11977, 11975])).
% 2.32/2.51 tff(11999,plain,
% 2.32/2.51 (b(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[348, 11998])).
% 2.32/2.51 tff(12000,plain,
% 2.32/2.51 (~r(elem!1, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[11710, 11999, 10101, 11946, 11991, 1, 11990, 11989, 11985, 11973, 10955, 11950, 11948])).
% 2.32/2.51 tff(12001,plain,
% 2.32/2.51 (~b(elem!1, s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[7079, 11985, 11752, 11973])).
% 2.32/2.51 tff(12002,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[720, 12001, 12000, 11972])).
% 2.32/2.51 tff(12003,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(12004,plain,
% 2.32/2.51 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[12003, 4, 3, 1])).
% 2.32/2.51 tff(12005,plain,
% 2.32/2.51 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.32/2.51 inference(symmetry,[status(thm)],[112])).
% 2.32/2.51 tff(12006,plain,
% 2.32/2.51 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(elem!1, elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[12005])).
% 2.32/2.51 tff(12007,plain,
% 2.32/2.51 (r(elem!1, elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(symmetry,[status(thm)],[12006])).
% 2.32/2.51 tff(12008,plain,
% 2.32/2.51 ((~r(elem!1, elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[12007])).
% 2.32/2.51 tff(12009,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[9917, 12008])).
% 2.32/2.51 tff(12010,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2484, 12009])).
% 2.32/2.51 tff(12011,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(12012,plain,
% 2.32/2.51 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[12011, 12004])).
% 2.32/2.51 tff(12013,plain,
% 2.32/2.51 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[121, 12012, 3])).
% 2.32/2.51 tff(12014,plain,
% 2.32/2.51 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[12011, 2484])).
% 2.32/2.51 tff(12015,plain,
% 2.32/2.51 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[121, 12014, 3])).
% 2.32/2.51 tff(12016,plain,
% 2.32/2.51 (~r(z, elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2938, 408, 2484, 51])).
% 2.32/2.51 tff(12017,plain,
% 2.32/2.51 (b(z, elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[658, 12016, 74])).
% 2.32/2.51 tff(12018,plain,
% 2.32/2.51 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(12019,plain,
% 2.32/2.51 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(12020,plain,
% 2.32/2.51 (((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[12019])).
% 2.32/2.51 tff(12021,plain,
% 2.32/2.51 (((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[12020, 12018])).
% 2.32/2.51 tff(12022,plain,
% 2.32/2.51 ((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(12023,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[12022, 12021])).
% 2.32/2.51 tff(12024,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[12023, 333, 408, 2484, 321, 51])).
% 2.32/2.51 tff(12025,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(12026,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[12025, 408, 2484, 51])).
% 2.32/2.51 tff(12027,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[302, 12026])).
% 2.32/2.51 tff(12028,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, 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(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12029,plain,
% 2.32/2.52 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12030,plain,
% 2.32/2.52 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12029])).
% 2.32/2.52 tff(12031,plain,
% 2.32/2.52 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12030, 12028])).
% 2.32/2.52 tff(12032,plain,
% 2.32/2.52 ((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12033,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12032, 12031])).
% 2.32/2.52 tff(12034,plain,
% 2.32/2.52 (~r(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12033, 333, 408, 509, 51])).
% 2.32/2.52 tff(12035,plain,
% 2.32/2.52 (b(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[560, 12034, 902])).
% 2.32/2.52 tff(12036,plain,
% 2.32/2.52 (b(s(elem!1), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[448, 7135, 907])).
% 2.32/2.52 tff(12037,plain,
% 2.32/2.52 (~b(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1642, 12035, 251, 12036])).
% 2.32/2.52 tff(12038,plain,
% 2.32/2.52 (r(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[583, 12037])).
% 2.32/2.52 tff(12039,plain,
% 2.32/2.52 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12040,plain,
% 2.32/2.52 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12041,plain,
% 2.32/2.52 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12040])).
% 2.32/2.52 tff(12042,plain,
% 2.32/2.52 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, 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(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12041, 12039])).
% 2.32/2.52 tff(12043,plain,
% 2.32/2.52 ((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12044,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12043, 12042])).
% 2.32/2.52 tff(12045,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12044, 333, 509, 562, 51, 524])).
% 2.32/2.52 tff(12046,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12047,plain,
% 2.32/2.52 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12046, 509, 12038, 51])).
% 2.32/2.52 tff(12048,plain,
% 2.32/2.52 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5467, 12047, 132, 537, 12035])).
% 2.32/2.52 tff(12049,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3827, 333, 509, 2484, 51, 12048])).
% 2.32/2.52 tff(12050,plain,((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12051,plain,
% 2.32/2.52 (~r(s(elem!1), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12050, 2698, 51, 132, 2484, 251, 2483, 408])).
% 2.32/2.52 tff(12052,plain,
% 2.32/2.52 (b(s(elem!1), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[507, 12051])).
% 2.32/2.52 tff(12053,plain,
% 2.32/2.52 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[472, 466, 432])).
% 2.32/2.52 tff(12054,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12055,plain,
% 2.32/2.52 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12056,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12055])).
% 2.32/2.52 tff(12057,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12056, 12054])).
% 2.32/2.52 tff(12058,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12059,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12058, 12057])).
% 2.32/2.52 tff(12060,plain,
% 2.32/2.52 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12059, 144, 491, 132, 286])).
% 2.32/2.52 tff(12061,plain,
% 2.32/2.52 (~b(s(elem!1), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12060, 12053])).
% 2.32/2.52 tff(12062,plain,
% 2.32/2.52 (r(s(elem!1), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[448, 12061, 907])).
% 2.32/2.52 tff(12063,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12064,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12065,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12064, 12063])).
% 2.32/2.52 tff(12066,plain,
% 2.32/2.52 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12065, 333, 12062, 408, 2484])).
% 2.32/2.52 tff(12067,plain,
% 2.32/2.52 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[542, 12066, 537])).
% 2.32/2.52 tff(12068,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1668, 144, 491, 585, 286, 546])).
% 2.32/2.52 tff(12069,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12070,plain,
% 2.32/2.52 (~b(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12069, 12067, 286, 491])).
% 2.32/2.52 tff(12071,plain,
% 2.32/2.52 (r(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[583, 12070])).
% 2.32/2.52 tff(12072,plain,
% 2.32/2.52 (~b(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5467, 12066, 132, 537, 466])).
% 2.32/2.52 tff(12073,plain,
% 2.32/2.52 (r(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[560, 12072, 902])).
% 2.32/2.52 tff(12074,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12075,plain,
% 2.32/2.52 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12076,plain,
% 2.32/2.52 (((~![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(elem!1, s(elem!1))) | (~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, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12075])).
% 2.32/2.52 tff(12077,plain,
% 2.32/2.52 (((~![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(elem!1, s(elem!1))) | (~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, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12076, 12074])).
% 2.32/2.52 tff(12078,plain,
% 2.32/2.52 ((~![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(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12079,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12078, 12077])).
% 2.32/2.52 tff(12080,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12079, 333, 12073, 12062, 408, 12071])).
% 2.32/2.52 tff(12081,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12082,plain,
% 2.32/2.52 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12081, 12052, 286, 408, 2483, 132, 2698, 2484, 4762])).
% 2.32/2.52 tff(12083,plain,
% 2.32/2.52 (~r(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3818, 333, 2484, 51, 12082])).
% 2.32/2.52 tff(12084,plain,
% 2.32/2.52 (b(z, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[583, 12083])).
% 2.32/2.52 tff(12085,plain,
% 2.32/2.52 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12069, 12084, 286, 12052])).
% 2.32/2.52 tff(12086,plain,
% 2.32/2.52 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[542, 12085, 2698])).
% 2.32/2.52 tff(12087,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[8495, 333, 563, 2484, 525, 524])).
% 2.32/2.52 tff(12088,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12089,plain,
% 2.32/2.52 (~r(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12088, 12082, 2484, 12086])).
% 2.32/2.52 tff(12090,plain,
% 2.32/2.52 (b(elem!1, s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[560, 12089, 2483])).
% 2.32/2.52 tff(12091,plain,
% 2.32/2.52 (~b(s(elem!1), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1642, 12090, 251, 12084])).
% 2.32/2.52 tff(12092,plain,
% 2.32/2.52 (r(s(elem!1), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[448, 12091, 2681])).
% 2.32/2.52 tff(12093,plain,
% 2.32/2.52 (((~![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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12094,plain,
% 2.32/2.52 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12095,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12094])).
% 2.32/2.52 tff(12096,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12095, 12093])).
% 2.32/2.52 tff(12097,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12098,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12097, 12096])).
% 2.32/2.52 tff(12099,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12098, 333, 12092, 408, 2484, 12082])).
% 2.32/2.52 tff(12100,plain,((~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12101,plain,
% 2.32/2.52 (~(s(z) = elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12100, 286, 2484, 251, 408, 51, 132])).
% 2.32/2.52 tff(12102,plain,
% 2.32/2.52 (~(elem!1 = s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[712, 12101])).
% 2.32/2.52 tff(12103,plain,
% 2.32/2.52 (~r(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[417, 409, 51, 408])).
% 2.32/2.52 tff(12104,plain,
% 2.32/2.52 (b(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[348, 12103])).
% 2.32/2.52 tff(12105,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12106,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12107,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12106, 12105])).
% 2.32/2.52 tff(12108,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12107, 333, 409, 408, 2484, 322])).
% 2.32/2.52 tff(12109,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12110,plain,
% 2.32/2.52 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12109, 409, 2484, 408])).
% 2.32/2.52 tff(12111,plain,
% 2.32/2.52 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[319, 12110])).
% 2.32/2.52 tff(12112,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[7093, 12111, 12104, 490, 286])).
% 2.32/2.52 tff(12113,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(12114,plain,
% 2.32/2.52 (~r(s(z), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12113, 286, 490, 2484, 408, 51])).
% 2.32/2.52 tff(12115,plain,
% 2.32/2.52 (b(s(z), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[406, 12101, 12114])).
% 2.32/2.52 tff(12116,plain,
% 2.32/2.52 (~b(elem!1, s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[7079, 12115, 251, 490])).
% 2.32/2.52 tff(12117,plain,
% 2.32/2.52 (r(elem!1, s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[720, 12116, 12102])).
% 2.32/2.52 tff(12118,plain,
% 2.32/2.52 (~b(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2105, 12115, 132, 123, 286])).
% 2.32/2.52 tff(12119,plain,
% 2.32/2.52 (r(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[348, 12118])).
% 2.32/2.52 tff(12120,plain,
% 2.32/2.52 (((~![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(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, 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(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12121,plain,
% 2.32/2.52 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(12122,plain,
% 2.32/2.52 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[12121])).
% 2.32/2.52 tff(12123,plain,
% 2.32/2.52 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[12122, 12120])).
% 2.32/2.52 tff(12124,plain,
% 2.32/2.52 ((~![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(z))))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(12125,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[12124, 12123])).
% 2.32/2.52 tff(12126,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[12125, 333, 12119, 408, 12117, 51])).
% 2.32/2.52 tff(12127,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12128,plain,
% 2.32/2.53 (~b(z, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12127, 12027, 51, 12017, 408, 12015, 123, 2484])).
% 2.32/2.53 tff(12129,plain,
% 2.32/2.53 (~(s(z) = elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12100, 12027, 2484, 12017, 408, 51, 12015])).
% 2.32/2.53 tff(12130,plain,
% 2.32/2.53 (~(elem!1 = s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[712, 12129])).
% 2.32/2.53 tff(12131,plain,
% 2.32/2.53 (r(z, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[372, 12128])).
% 2.32/2.53 tff(12132,plain,
% 2.32/2.53 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[313, 10659, 123, 132])).
% 2.32/2.53 tff(12133,plain,
% 2.32/2.53 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[319, 12132])).
% 2.32/2.53 tff(12134,plain,
% 2.32/2.53 (((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12135,plain,
% 2.32/2.53 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12136,plain,
% 2.32/2.53 (((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12135])).
% 2.32/2.53 tff(12137,plain,
% 2.32/2.53 (((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[12136, 12134])).
% 2.32/2.53 tff(12138,plain,
% 2.32/2.53 ((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12139,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12138, 12137])).
% 2.32/2.53 tff(12140,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12139, 333, 354, 323, 12133, 51])).
% 2.32/2.53 tff(12141,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12142,plain,
% 2.32/2.53 (~r(s(z), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12141, 12131, 51, 123, 12015, 12130, 408])).
% 2.32/2.53 tff(12143,plain,
% 2.32/2.53 (b(s(z), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[348, 12142])).
% 2.32/2.53 tff(12144,plain,
% 2.32/2.53 (~b(s(z), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[2113, 12143, 3, 12026, 123, 408])).
% 2.32/2.53 tff(12145,plain,
% 2.32/2.53 (r(s(z), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[406, 12144, 12129])).
% 2.32/2.53 tff(12146,plain,
% 2.32/2.53 (r(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[9374, 9362, 51, 251, 123, 132, 350])).
% 2.32/2.53 tff(12147,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[2063, 333, 409, 9363, 408, 12146])).
% 2.32/2.53 tff(12148,plain,(b(z, s(z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12149,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12148, 12145, 12144, 51, 408, 12017, 123, 12015, 12128])).
% 2.32/2.53 tff(12150,plain,((~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12151,plain,
% 2.32/2.53 (~r(elem!1, z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12150, 51, 50, 3, 12004, 71])).
% 2.32/2.53 tff(12152,plain,
% 2.32/2.53 (b(elem!1, z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1380, 12151, 77])).
% 2.32/2.53 tff(12153,plain,
% 2.32/2.53 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[302, 296])).
% 2.32/2.53 tff(12154,plain,
% 2.32/2.53 (~r(z, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10975, 606, 51, 1, 3, 4])).
% 2.32/2.53 tff(12155,plain,
% 2.32/2.53 (b(z, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[372, 12154])).
% 2.32/2.53 tff(12156,plain,
% 2.32/2.53 (~b(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10115, 12155, 12013, 50, 12152])).
% 2.32/2.53 tff(12157,plain,
% 2.32/2.53 (~(s(z) = elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[8102, 12155, 606])).
% 2.32/2.53 tff(12158,plain,
% 2.32/2.53 (~(elem!1 = s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[712, 12157])).
% 2.32/2.53 tff(12159,plain,
% 2.32/2.53 (r(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[720, 12158, 12156])).
% 2.32/2.53 tff(12160,plain,
% 2.32/2.53 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12161,plain,
% 2.32/2.53 ((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12162,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12161, 12160])).
% 2.32/2.53 tff(12163,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12162, 333, 7265, 12159, 12004, 321])).
% 2.32/2.53 tff(12164,plain,(b(z, elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12165,plain,
% 2.32/2.53 (b(z, elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12164, 12153, 51, 1, 3, 4])).
% 2.32/2.53 tff(12166,plain,
% 2.32/2.53 (~b(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10991, 2169, 51, 123, 624, 132])).
% 2.32/2.53 tff(12167,plain,
% 2.32/2.53 (r(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[720, 12166, 713])).
% 2.32/2.53 tff(12168,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12169,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12170,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12169, 12168])).
% 2.32/2.53 tff(12171,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12170, 333, 409, 722, 2484, 322])).
% 2.32/2.53 tff(12172,plain,((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12173,plain,
% 2.32/2.53 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12172, 12167, 2484, 2169])).
% 2.32/2.53 tff(12174,plain,
% 2.32/2.53 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[319, 12173])).
% 2.32/2.53 tff(12175,plain,
% 2.32/2.53 (((~![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(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12176,plain,
% 2.32/2.53 ((~![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(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12177,plain,
% 2.32/2.53 ((~![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(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12176, 12175])).
% 2.32/2.53 tff(12178,plain,
% 2.32/2.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12177, 333, 722, 707, 2484])).
% 2.32/2.53 tff(12179,plain,
% 2.32/2.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[249, 12178])).
% 2.32/2.53 tff(12180,plain,
% 2.32/2.53 (((~![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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12181,plain,
% 2.32/2.53 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12182,plain,
% 2.32/2.53 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(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(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12181])).
% 2.32/2.53 tff(12183,plain,
% 2.32/2.53 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(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(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[12182, 12180])).
% 2.32/2.53 tff(12184,plain,
% 2.32/2.53 ((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12185,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12184, 12183])).
% 2.32/2.53 tff(12186,plain,
% 2.32/2.53 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12185, 333, 722, 707, 2484])).
% 2.32/2.53 tff(12187,plain,
% 2.32/2.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1137, 12186])).
% 2.32/2.53 tff(12188,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[2262, 893, 12187, 123, 12179])).
% 2.32/2.53 tff(12189,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12190,plain,
% 2.32/2.53 (~r(s(s(s(z))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12189, 12167, 123, 2484, 2169])).
% 2.32/2.53 tff(12191,plain,
% 2.32/2.53 (r(s(elem!1), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[507, 502])).
% 2.32/2.53 tff(12192,plain,
% 2.32/2.53 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[7702, 333, 12191, 321, 51])).
% 2.32/2.53 tff(12193,plain,
% 2.32/2.53 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[601, 333, 12191, 321, 51])).
% 2.32/2.53 tff(12194,plain,
% 2.32/2.53 (b(s(elem!1), z) <=> b(elem!1, z)),
% 2.32/2.53 inference(symmetry,[status(thm)],[4134])).
% 2.32/2.53 tff(12195,plain,
% 2.32/2.53 ((~b(s(elem!1), z)) <=> (~b(elem!1, z))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12194])).
% 2.32/2.53 tff(12196,plain,
% 2.32/2.53 (~b(elem!1, z)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[502, 12195])).
% 2.32/2.53 tff(12197,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[624, 12196])).
% 2.32/2.53 tff(12198,plain,((~(elem!1 = s(elem!1))) | (~b(elem!1, z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12199,plain,
% 2.32/2.53 (~(elem!1 = s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12198, 502, 624])).
% 2.32/2.53 tff(12200,plain,
% 2.32/2.53 (~b(elem!1, s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5467, 537, 132, 535, 466])).
% 2.32/2.53 tff(12201,plain,
% 2.32/2.53 (r(elem!1, s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[560, 12200, 902])).
% 2.32/2.53 tff(12202,plain,
% 2.32/2.53 (~b(s(z), s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3388, 144, 123, 5463, 5465])).
% 2.32/2.53 tff(12203,plain,
% 2.32/2.53 (r(s(z), s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1244, 12202, 1229])).
% 2.32/2.53 tff(12204,plain,
% 2.32/2.53 (~b(s(elem!1), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3040, 144, 123, 304, 5465])).
% 2.32/2.53 tff(12205,plain,
% 2.32/2.53 (r(s(elem!1), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[486, 12204, 1])).
% 2.32/2.53 tff(12206,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[7799, 12205, 12203, 722, 12201])).
% 2.32/2.53 tff(12207,plain,((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12208,plain,
% 2.32/2.53 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12207, 12199, 1, 123, 304, 722, 12193, 132, 12192])).
% 2.32/2.53 tff(12209,plain,
% 2.32/2.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12208])).
% 2.32/2.53 tff(12210,plain,
% 2.32/2.53 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12208, 175])).
% 2.32/2.53 tff(12211,plain,
% 2.32/2.53 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[78, 1193, 6163, 20])).
% 2.32/2.53 tff(12212,plain,
% 2.32/2.53 (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12211])).
% 2.32/2.53 tff(12213,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[196, 12212])).
% 2.32/2.53 tff(12214,plain,((~(s(s(s(z))) = elem!1)) | (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(12215,plain,
% 2.32/2.53 (~(s(s(s(z))) = elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12214, 12210])).
% 2.32/2.53 tff(12216,plain,
% 2.32/2.53 (b(s(s(s(z))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[704, 12215, 699])).
% 2.32/2.53 tff(12217,plain,
% 2.32/2.53 (~b(s(s(s(z))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10565, 12216, 624, 251])).
% 2.32/2.53 tff(12218,plain,
% 2.32/2.53 (r(s(s(s(z))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[396, 12217])).
% 2.32/2.53 tff(12219,plain,
% 2.32/2.53 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[11754, 12218, 51, 321])).
% 2.32/2.53 tff(12220,plain,
% 2.32/2.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1137, 12219])).
% 2.32/2.53 tff(12221,plain,
% 2.32/2.53 (b(s(s(s(z))), s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12220, 12209])).
% 2.32/2.53 tff(12222,plain,
% 2.32/2.53 (b(s(z), s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[2946, 12208, 123])).
% 2.32/2.53 tff(12223,plain,
% 2.32/2.53 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12208])).
% 2.32/2.53 tff(12224,plain,
% 2.32/2.53 (b(s(elem!1), s(z))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[304, 12223])).
% 2.32/2.53 tff(12225,plain,
% 2.32/2.53 (((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12226,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12225])).
% 2.32/2.53 tff(12227,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[12226, 1941])).
% 2.32/2.53 tff(12228,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12229,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12228, 12227])).
% 2.32/2.53 tff(12230,plain,
% 2.32/2.53 (~b(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12229, 144, 12224, 12222, 12221])).
% 2.32/2.53 tff(12231,plain,
% 2.32/2.53 (r(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[2794, 12230])).
% 2.32/2.53 tff(12232,plain,
% 2.32/2.53 (~(elem!1 = s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10997, 12215])).
% 2.32/2.53 tff(12233,plain,
% 2.32/2.53 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12208])).
% 2.32/2.53 tff(12234,plain,
% 2.32/2.53 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12233])).
% 2.32/2.53 tff(12235,plain,
% 2.32/2.53 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[244, 12234])).
% 2.32/2.53 tff(12236,plain,
% 2.32/2.53 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12208])).
% 2.32/2.53 tff(12237,plain,
% 2.32/2.53 (r(z, s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[51, 12236])).
% 2.32/2.53 tff(12238,plain,
% 2.32/2.53 (~r(s(elem!1), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[8134, 333, 12191, 12237, 12218])).
% 2.32/2.53 tff(12239,plain,
% 2.32/2.53 (b(s(elem!1), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[965, 12238, 12235])).
% 2.32/2.53 tff(12240,plain,
% 2.32/2.53 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12208])).
% 2.32/2.53 tff(12241,plain,
% 2.32/2.53 (b(elem!1, s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[132, 12240])).
% 2.32/2.53 tff(12242,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12243,plain,
% 2.32/2.53 (((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(12244,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[12243])).
% 2.32/2.53 tff(12245,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[12244, 12242])).
% 2.32/2.53 tff(12246,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(12247,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[12246, 12245])).
% 2.32/2.53 tff(12248,plain,
% 2.32/2.53 (~b(elem!1, s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[12247, 144, 12241, 12239, 12221])).
% 2.32/2.53 tff(12249,plain,
% 2.32/2.53 (r(elem!1, s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1538, 12248, 12232])).
% 2.32/2.53 tff(12250,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12251,plain,
% 2.32/2.54 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12252,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12251])).
% 2.32/2.54 tff(12253,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[12252, 12250])).
% 2.32/2.54 tff(12254,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12255,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12254, 12253])).
% 2.32/2.54 tff(12256,plain,
% 2.32/2.54 (~b(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12255, 144, 12222, 12239, 12221])).
% 2.32/2.54 tff(12257,plain,
% 2.32/2.54 (r(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[172, 12256])).
% 2.32/2.54 tff(12258,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[11876, 12257, 12249, 409, 12231])).
% 2.32/2.54 tff(12259,plain,(b(s(elem!1), z) | (~r(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12260,plain,
% 2.32/2.54 (b(s(elem!1), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12259, 2169, 51, 321, 624, 251, 12190, 12174, 132, 123, 1, 12167])).
% 2.32/2.54 tff(12261,plain,
% 2.32/2.54 (r(s(elem!1), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[448, 907, 7326])).
% 2.32/2.54 tff(12262,plain,
% 2.32/2.54 (~r(s(elem!1), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[7864, 333, 12261, 2169, 721])).
% 2.32/2.54 tff(12263,plain,
% 2.32/2.54 (b(s(elem!1), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[486, 12262, 1])).
% 2.32/2.54 tff(12264,plain,
% 2.32/2.54 (~r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12189, 721, 123, 2484, 2169])).
% 2.32/2.54 tff(12265,plain,
% 2.32/2.54 (((~![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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12266,plain,
% 2.32/2.54 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12267,plain,
% 2.32/2.54 (((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12266])).
% 2.32/2.54 tff(12268,plain,
% 2.32/2.54 (((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[12267, 12265])).
% 2.32/2.54 tff(12269,plain,
% 2.32/2.54 ((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12270,plain,
% 2.32/2.54 ((~![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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12269, 12268])).
% 2.32/2.54 tff(12271,plain,
% 2.32/2.54 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12270, 333, 12261, 721, 2484])).
% 2.32/2.54 tff(12272,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12172, 721, 2484, 2169])).
% 2.32/2.54 tff(12273,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[319, 12272])).
% 2.32/2.54 tff(12274,plain,
% 2.32/2.54 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[869, 144, 12263, 123, 12273])).
% 2.32/2.54 tff(12275,plain,
% 2.32/2.54 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[472, 12274, 12271])).
% 2.32/2.54 tff(12276,plain,
% 2.32/2.54 (~(s(s(s(z))) = elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12214, 12275])).
% 2.32/2.54 tff(12277,plain,
% 2.32/2.54 (b(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[704, 12276, 12264])).
% 2.32/2.54 tff(12278,plain,
% 2.32/2.54 (~b(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10565, 12277, 624, 251])).
% 2.32/2.54 tff(12279,plain,
% 2.32/2.54 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6057, 12278, 491])).
% 2.32/2.54 tff(12280,plain,
% 2.32/2.54 (r(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[396, 12278])).
% 2.32/2.54 tff(12281,plain,
% 2.32/2.54 (((~![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(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12282,plain,
% 2.32/2.54 ((~![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(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12283,plain,
% 2.32/2.54 ((~![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(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12282, 12281])).
% 2.32/2.54 tff(12284,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12283, 333, 12261, 721, 2484])).
% 2.32/2.54 tff(12285,plain,
% 2.32/2.54 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12207, 12271, 1, 123, 12273, 721, 902, 132, 12284])).
% 2.32/2.54 tff(12286,plain,
% 2.32/2.54 (r(s(elem!1), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[925, 12285, 321])).
% 2.32/2.54 tff(12287,plain,
% 2.32/2.54 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[472, 870, 466])).
% 2.32/2.54 tff(12288,plain,
% 2.32/2.54 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12287])).
% 2.32/2.54 tff(12289,plain,
% 2.32/2.54 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(elem!1))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12288])).
% 2.32/2.54 tff(12290,plain,
% 2.32/2.54 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(elem!1)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12289])).
% 2.32/2.54 tff(12291,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12292,plain,
% 2.32/2.54 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12293,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12292])).
% 2.32/2.54 tff(12294,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.54 inference(transitivity,[status(thm)],[12293, 12291])).
% 2.32/2.54 tff(12295,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12296,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12295, 12294])).
% 2.32/2.54 tff(12297,plain,
% 2.32/2.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12296, 333, 354, 1699, 321])).
% 2.32/2.54 tff(12298,plain,
% 2.32/2.54 (~r(s(s(s(z))), s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12297, 12290])).
% 2.32/2.54 tff(12299,plain,
% 2.32/2.54 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12287])).
% 2.32/2.54 tff(12300,plain,
% 2.32/2.54 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12299])).
% 2.32/2.54 tff(12301,plain,
% 2.32/2.54 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12300])).
% 2.32/2.54 tff(12302,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12303,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12304,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12303, 12302])).
% 2.32/2.54 tff(12305,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12304, 333, 354, 1699, 321])).
% 2.32/2.54 tff(12306,plain,
% 2.32/2.54 (~r(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12305, 12301])).
% 2.32/2.54 tff(12307,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6099, 12306, 12298, 488, 354, 466, 123, 304, 1699])).
% 2.32/2.54 tff(12308,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), s(z))) | (~r(z, s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12309,plain,
% 2.32/2.54 (~r(z, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12308, 12280, 12271, 12263, 123, 12273, 321])).
% 2.32/2.54 tff(12310,plain,
% 2.32/2.54 (b(z, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[372, 12309])).
% 2.32/2.54 tff(12311,plain,
% 2.32/2.54 (~b(s(z), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[499, 12310, 491, 12263])).
% 2.32/2.54 tff(12312,plain,
% 2.32/2.54 (r(s(z), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[348, 12311])).
% 2.32/2.54 tff(12313,plain,
% 2.32/2.54 (~r(s(z), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[7675, 12261, 706, 350, 708])).
% 2.32/2.54 tff(12314,plain,
% 2.32/2.54 (b(s(z), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1244, 12313, 1229])).
% 2.32/2.54 tff(12315,plain,
% 2.32/2.54 (~b(z, s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1853, 12310, 12263, 12314])).
% 2.32/2.54 tff(12316,plain,
% 2.32/2.54 (r(z, s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[583, 12315])).
% 2.32/2.54 tff(12317,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[8142, 12316, 12312, 12286, 12280, 12279, 12263])).
% 2.32/2.54 tff(12318,plain,((elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12319,plain,
% 2.32/2.54 (elem!1 = s(elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12318, 12260, 123, 321, 624, 251, 1, 132, 2484, 706, 350, 12166])).
% 2.32/2.54 tff(12320,plain,
% 2.32/2.54 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12319])).
% 2.32/2.54 tff(12321,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[132, 12320])).
% 2.32/2.54 tff(12322,plain,
% 2.32/2.54 (s(elem!1) = elem!1),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1569, 12319])).
% 2.32/2.54 tff(12323,plain,
% 2.32/2.54 (elem!1 = s(s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5813, 12322])).
% 2.32/2.54 tff(12324,plain,
% 2.32/2.54 (s(s(elem!1)) = elem!1),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5603, 12323])).
% 2.32/2.54 tff(12325,plain,
% 2.32/2.54 (~(s(s(s(z))) = elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[7595, 12324, 863])).
% 2.32/2.54 tff(12326,plain,
% 2.32/2.54 (b(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[704, 12325, 12190])).
% 2.32/2.54 tff(12327,plain,
% 2.32/2.54 (~b(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10565, 12326, 624, 251])).
% 2.32/2.54 tff(12328,plain,
% 2.32/2.54 (r(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[396, 12327])).
% 2.32/2.54 tff(12329,plain,
% 2.32/2.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[11754, 12328, 51, 321])).
% 2.32/2.54 tff(12330,plain,
% 2.32/2.54 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1137, 12329])).
% 2.32/2.54 tff(12331,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2199, 333, 12328, 321, 51])).
% 2.32/2.54 tff(12332,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[249, 12331])).
% 2.32/2.54 tff(12333,plain,
% 2.32/2.54 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12319])).
% 2.32/2.54 tff(12334,plain,
% 2.32/2.54 (s(s(s(elem!1))) = elem!1),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2482, 12319])).
% 2.32/2.54 tff(12335,plain,
% 2.32/2.54 (s(elem!1) = s(s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2584, 12334, 12319])).
% 2.32/2.54 tff(12336,plain,
% 2.32/2.54 (s(s(s(elem!1))) = s(elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3254, 12335])).
% 2.32/2.54 tff(12337,plain,
% 2.32/2.54 (~(elem!1 = s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3246, 12336, 706])).
% 2.32/2.54 tff(12338,plain,
% 2.32/2.54 (~b(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6004, 144, 123, 12330, 12174])).
% 2.32/2.54 tff(12339,plain,
% 2.32/2.54 (r(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2794, 12338])).
% 2.32/2.54 tff(12340,plain,
% 2.32/2.54 (~b(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2262, 12332, 123, 12330])).
% 2.32/2.54 tff(12341,plain,
% 2.32/2.54 (r(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[172, 12340])).
% 2.32/2.54 tff(12342,plain,
% 2.32/2.54 (~r(elem!1, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[11876, 12341, 2169, 12339])).
% 2.32/2.54 tff(12343,plain,
% 2.32/2.54 (b(elem!1, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1538, 12342, 12337])).
% 2.32/2.54 tff(12344,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12343, 12333])).
% 2.32/2.54 tff(12345,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[9088, 144, 12344, 12332, 12330, 12321])).
% 2.32/2.54 tff(12346,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12347,plain,
% 2.32/2.54 (b(s(z), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12346, 706, 12153, 51, 132, 624, 251, 123, 1, 2484])).
% 2.32/2.54 tff(12348,plain,
% 2.32/2.54 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(12349,plain,
% 2.32/2.54 (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12348, 14])).
% 2.32/2.54 tff(12350,plain,
% 2.32/2.54 (~b(s(z), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1602, 134, 624, 251])).
% 2.32/2.54 tff(12351,plain,
% 2.32/2.54 (r(s(z), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[348, 12350])).
% 2.32/2.54 tff(12352,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[341, 12351, 51, 321])).
% 2.32/2.54 tff(12353,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[319, 12352])).
% 2.32/2.54 tff(12354,plain,
% 2.32/2.54 (r(elem!1, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[9106, 12350, 132, 123, 51, 624])).
% 2.32/2.54 tff(12355,plain,
% 2.32/2.54 (~(s(elem!1) = elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[906, 12199])).
% 2.32/2.54 tff(12356,plain,
% 2.32/2.54 (~r(s(elem!1), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1911, 12355, 624, 251, 12351, 12354])).
% 2.32/2.54 tff(12357,plain,
% 2.32/2.54 (b(s(elem!1), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[486, 12356, 1])).
% 2.32/2.54 tff(12358,plain,
% 2.32/2.54 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[869, 144, 12357, 123, 12353])).
% 2.32/2.54 tff(12359,plain,
% 2.32/2.54 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[472, 12358, 12193])).
% 2.32/2.54 tff(12360,plain,
% 2.32/2.54 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.54 tff(12361,plain,
% 2.32/2.54 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12360])).
% 2.32/2.54 tff(12362,plain,
% 2.32/2.54 (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(elem!1)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12361])).
% 2.32/2.54 tff(12363,plain,
% 2.32/2.54 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12362])).
% 2.32/2.54 tff(12364,plain,
% 2.32/2.54 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.54 tff(12365,plain,
% 2.32/2.54 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12364])).
% 2.32/2.54 tff(12366,plain,
% 2.32/2.54 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.32/2.54 inference(transitivity,[status(thm)],[12365, 998])).
% 2.32/2.54 tff(12367,plain,
% 2.32/2.54 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12366])).
% 2.32/2.54 tff(12368,plain,
% 2.32/2.54 (~(s(s(s(z))) = s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[244, 12367])).
% 2.32/2.54 tff(12369,plain,
% 2.32/2.54 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.54 tff(12370,plain,
% 2.32/2.54 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12369])).
% 2.32/2.54 tff(12371,plain,
% 2.32/2.54 (r(z, s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[51, 12370])).
% 2.32/2.54 tff(12372,plain,
% 2.32/2.54 (~(s(s(s(z))) = elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12214, 12359])).
% 2.32/2.54 tff(12373,plain,
% 2.32/2.54 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12365])).
% 2.32/2.54 tff(12374,plain,
% 2.32/2.54 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[244, 12373])).
% 2.32/2.54 tff(12375,plain,
% 2.32/2.54 (~r(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[8142, 12371, 12351, 12191, 12374, 12357])).
% 2.32/2.54 tff(12376,plain,
% 2.32/2.54 (b(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[396, 12375])).
% 2.32/2.54 tff(12377,plain,
% 2.32/2.54 (~b(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10565, 12376, 624, 251])).
% 2.32/2.54 tff(12378,plain,
% 2.32/2.54 (r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[704, 12377, 12372])).
% 2.32/2.54 tff(12379,plain,
% 2.32/2.54 (~r(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[8824, 12378, 12351, 12354])).
% 2.32/2.54 tff(12380,plain,
% 2.32/2.54 (b(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2794, 12379])).
% 2.32/2.54 tff(12381,plain,
% 2.32/2.54 (~r(z, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1960, 12380, 12351, 12191, 12371, 12357, 1229, 12368])).
% 2.32/2.54 tff(12382,plain,
% 2.32/2.54 (b(z, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[619, 12381])).
% 2.32/2.54 tff(12383,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.54 tff(12384,plain,
% 2.32/2.54 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12207, 12193, 1, 123, 12353, 12354, 12199, 132, 12192])).
% 2.32/2.54 tff(12385,plain,
% 2.32/2.54 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.32/2.54 inference(monotonicity,[status(thm)],[919])).
% 2.32/2.54 tff(12386,plain,
% 2.32/2.54 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.54 inference(symmetry,[status(thm)],[12385])).
% 2.32/2.54 tff(12387,plain,
% 2.32/2.54 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12386])).
% 2.32/2.54 tff(12388,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[1727, 12387])).
% 2.32/2.54 tff(12389,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2484, 12388])).
% 2.32/2.54 tff(12390,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12391,plain,
% 2.32/2.54 (r(s(elem!1), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12390, 12384, 2484])).
% 2.32/2.54 tff(12392,plain,
% 2.32/2.54 (~r(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1694, 12378, 12354, 12391])).
% 2.32/2.54 tff(12393,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[965, 12392, 12374])).
% 2.32/2.54 tff(12394,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[12393, 12383])).
% 2.32/2.54 tff(12395,plain,
% 2.32/2.54 (~b(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[846, 12394, 12353, 12380])).
% 2.32/2.54 tff(12396,plain,
% 2.32/2.54 (r(s(z), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[172, 12395])).
% 2.32/2.54 tff(12397,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.32/2.54 tff(12398,plain,
% 2.32/2.54 (~(elem!1 = s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10997, 698])).
% 2.32/2.54 tff(12399,plain,
% 2.32/2.54 (r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[704, 698, 55])).
% 2.32/2.54 tff(12400,plain,
% 2.32/2.54 (~r(elem!1, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1533, 12399, 722, 353])).
% 2.32/2.54 tff(12401,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1538, 12400, 12398, 12397])).
% 2.32/2.54 tff(12402,plain,((s(s(s(z))) = elem!1) | b(elem!1, s(s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(12403,plain,
% 2.32/2.54 (b(elem!1, s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[12402, 12396, 12354, 12372, 12377])).
% 2.32/2.54 tff(12404,plain,
% 2.32/2.54 (~b(z, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2090, 12403, 251, 134, 12382])).
% 2.32/2.54 tff(12405,plain,
% 2.32/2.54 (r(z, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[372, 12404])).
% 2.32/2.54 tff(12406,plain,
% 2.32/2.54 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.54 tff(12407,plain,
% 2.32/2.54 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 2.32/2.54 inference(symmetry,[status(thm)],[12406])).
% 2.32/2.54 tff(12408,plain,
% 2.32/2.54 (b(elem!1, s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[132, 12407])).
% 2.32/2.54 tff(12409,plain,
% 2.32/2.54 (~(elem!1 = s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10997, 12372])).
% 2.32/2.54 tff(12410,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, 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(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12411,plain,
% 2.32/2.54 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(12412,plain,
% 2.32/2.54 (((~![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(s(s(s(s(z))))))))) | (~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(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[12411])).
% 2.32/2.54 tff(12413,plain,
% 2.32/2.54 (((~![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(s(s(s(s(z))))))))) | (~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(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[12412, 12410])).
% 2.32/2.54 tff(12414,plain,
% 2.32/2.54 ((~![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(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12415,plain,
% 2.32/2.55 ((~![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(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12414, 12413])).
% 2.32/2.55 tff(12416,plain,
% 2.32/2.55 (~r(s(z), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12415, 333, 12351, 12191, 51])).
% 2.32/2.55 tff(12417,plain,
% 2.32/2.55 (b(s(z), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1244, 12416, 1229])).
% 2.32/2.55 tff(12418,plain,
% 2.32/2.55 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[978])).
% 2.32/2.55 tff(12419,plain,
% 2.32/2.55 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(symmetry,[status(thm)],[12418])).
% 2.32/2.55 tff(12420,plain,
% 2.32/2.55 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[978])).
% 2.32/2.55 tff(12421,plain,
% 2.32/2.55 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12420])).
% 2.32/2.55 tff(12422,plain,
% 2.32/2.55 (s(s(elem!1)) = elem!1),
% 2.32/2.55 inference(transitivity,[status(thm)],[1007, 980, 850])).
% 2.32/2.55 tff(12423,plain,
% 2.32/2.55 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12422])).
% 2.32/2.55 tff(12424,plain,
% 2.32/2.55 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.55 inference(symmetry,[status(thm)],[12423])).
% 2.32/2.55 tff(12425,plain,
% 2.32/2.55 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12424])).
% 2.32/2.55 tff(12426,plain,
% 2.32/2.55 (~r(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[8822, 333, 323, 722, 3193])).
% 2.32/2.55 tff(12427,plain,
% 2.32/2.55 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12426, 12425])).
% 2.32/2.55 tff(12428,plain,
% 2.32/2.55 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12422])).
% 2.32/2.55 tff(12429,plain,
% 2.32/2.55 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.55 inference(symmetry,[status(thm)],[12428])).
% 2.32/2.55 tff(12430,plain,
% 2.32/2.55 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12429])).
% 2.32/2.55 tff(12431,plain,
% 2.32/2.55 (~r(s(s(s(z))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6555, 3193, 323, 354])).
% 2.32/2.55 tff(12432,plain,
% 2.32/2.55 (b(s(s(s(z))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[396, 12431])).
% 2.32/2.55 tff(12433,plain,
% 2.32/2.55 (~b(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10565, 12432, 624, 251])).
% 2.32/2.55 tff(12434,plain,
% 2.32/2.55 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12433, 12430])).
% 2.32/2.55 tff(12435,plain,
% 2.32/2.55 (r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1301, 12434, 1184])).
% 2.32/2.55 tff(12436,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12435, 12427])).
% 2.32/2.55 tff(12437,plain,((~r(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12438,plain,
% 2.32/2.55 (~r(s(s(s(z))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12437, 722, 1184, 323, 978, 624, 251, 354])).
% 2.32/2.55 tff(12439,plain,
% 2.32/2.55 (b(s(s(s(z))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2794, 12438])).
% 2.32/2.55 tff(12440,plain,
% 2.32/2.55 (~b(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1946, 144, 488, 1262, 12439])).
% 2.32/2.55 tff(12441,plain,
% 2.32/2.55 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12440, 12421])).
% 2.32/2.55 tff(12442,plain,
% 2.32/2.55 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[9560, 12441, 9531])).
% 2.32/2.55 tff(12443,plain,
% 2.32/2.55 (r(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12442, 12419])).
% 2.32/2.55 tff(12444,plain,
% 2.32/2.55 (~r(s(s(s(z))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1716, 12439, 488, 960, 354, 509, 323])).
% 2.32/2.55 tff(12445,plain,
% 2.32/2.55 (b(s(s(s(z))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[396, 12444])).
% 2.32/2.55 tff(12446,plain,
% 2.32/2.55 (~b(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10565, 12445, 624, 251])).
% 2.32/2.55 tff(12447,plain,
% 2.32/2.55 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[4795])).
% 2.32/2.55 tff(12448,plain,
% 2.32/2.55 (~(s(s(s(z))) = elem!1)),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[1524, 12447])).
% 2.32/2.55 tff(12449,plain,
% 2.32/2.55 (r(s(s(s(z))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[704, 12448, 12446])).
% 2.32/2.55 tff(12450,plain,
% 2.32/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12451,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12452,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12451, 12450])).
% 2.32/2.55 tff(12453,plain,
% 2.32/2.55 (~r(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12452, 333, 435, 722, 12449])).
% 2.32/2.55 tff(12454,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12453, 12443])).
% 2.32/2.55 tff(12455,plain,((~r(elem!1, s(z))) | (~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (elem!1 = s(s(s(z)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12456,plain,
% 2.32/2.55 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12455, 12405, 12354, 12417, 9480, 12391, 12357, 624, 251, 12374, 12351, 12191, 12409, 1184])).
% 2.32/2.55 tff(12457,plain,
% 2.32/2.55 (s(elem!1) = s(s(s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[3235, 2476])).
% 2.32/2.55 tff(12458,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1056, 12457])).
% 2.32/2.55 tff(12459,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12460,plain,
% 2.32/2.55 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12459, 12456])).
% 2.32/2.55 tff(12461,plain,
% 2.32/2.55 (b(s(z), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1244, 4398, 1237])).
% 2.32/2.55 tff(12462,plain,
% 2.32/2.55 (~b(elem!1, s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4409, 12461, 547, 488])).
% 2.32/2.55 tff(12463,plain,
% 2.32/2.55 (r(elem!1, s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[720, 12462, 714])).
% 2.32/2.55 tff(12464,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.32/2.55 tff(12465,plain,
% 2.32/2.55 (((~![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(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(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(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12466,plain,
% 2.32/2.55 ((~![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(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12467,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12466, 12465])).
% 2.32/2.55 tff(12468,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12467, 333, 354, 509, 9749, 12464])).
% 2.32/2.55 tff(12469,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12470,plain,
% 2.32/2.55 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12469, 12464, 509, 354])).
% 2.32/2.55 tff(12471,plain,
% 2.32/2.55 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4697, 12470, 3127])).
% 2.32/2.55 tff(12472,plain,
% 2.32/2.55 (~b(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4692, 12471, 488, 1262])).
% 2.32/2.55 tff(12473,plain,
% 2.32/2.55 (r(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1101, 12472])).
% 2.32/2.55 tff(12474,plain,
% 2.32/2.55 (((~![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))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12475,plain,
% 2.32/2.55 ((~![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))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12476,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12475, 12474])).
% 2.32/2.55 tff(12477,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12476, 333, 354, 12473, 323, 12464])).
% 2.32/2.55 tff(12478,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12479,plain,
% 2.32/2.55 (~r(s(s(s(elem!1))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12478, 12461, 323, 488, 354, 3127, 509])).
% 2.32/2.55 tff(12480,plain,
% 2.32/2.55 (b(s(s(s(elem!1))), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 12479])).
% 2.32/2.55 tff(12481,plain,
% 2.32/2.55 (~b(s(s(s(elem!1))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1074, 144, 251, 624, 12480])).
% 2.32/2.55 tff(12482,plain,
% 2.32/2.55 (r(s(s(s(elem!1))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1079, 12481, 1012])).
% 2.32/2.55 tff(12483,plain,
% 2.32/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12484,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12485,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12484, 12483])).
% 2.32/2.55 tff(12486,plain,
% 2.32/2.55 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12485, 333, 435, 12482, 12463])).
% 2.32/2.55 tff(12487,plain,
% 2.32/2.55 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4697, 12486, 3127])).
% 2.32/2.55 tff(12488,plain,
% 2.32/2.55 (~b(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4692, 12487, 488, 12461])).
% 2.32/2.55 tff(12489,plain,
% 2.32/2.55 (r(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1101, 12488])).
% 2.32/2.55 tff(12490,plain,
% 2.32/2.55 (((~![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(s(s(s(elem!1))), s(z))) | (~r(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12491,plain,
% 2.32/2.55 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12492,plain,
% 2.32/2.55 (((~![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(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12491])).
% 2.32/2.55 tff(12493,plain,
% 2.32/2.55 (((~![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(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(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.32/2.55 inference(transitivity,[status(thm)],[12492, 12490])).
% 2.32/2.55 tff(12494,plain,
% 2.32/2.55 ((~![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(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12495,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12494, 12493])).
% 2.32/2.55 tff(12496,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12495, 333, 12482, 12489, 323, 12463])).
% 2.32/2.55 tff(12497,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (elem!1 = s(z)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12498,plain,
% 2.32/2.55 (s(s(s(elem!1))) = elem!1),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12497, 12460, 251, 12391, 12351, 12357, 12191, 624, 12408, 714, 12405, 1229])).
% 2.32/2.55 tff(12499,plain,
% 2.32/2.55 (elem!1 = s(s(s(elem!1)))),
% 2.32/2.55 inference(symmetry,[status(thm)],[12498])).
% 2.32/2.55 tff(12500,plain,
% 2.32/2.55 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12359])).
% 2.32/2.55 tff(12501,plain,
% 2.32/2.55 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 2.32/2.55 inference(symmetry,[status(thm)],[12500])).
% 2.32/2.55 tff(12502,plain,
% 2.32/2.55 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[21, 12501, 850, 12499, 12363])).
% 2.32/2.55 tff(12503,plain,
% 2.32/2.55 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12502])).
% 2.32/2.55 tff(12504,plain,
% 2.32/2.55 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[93, 12503, 12349])).
% 2.32/2.55 tff(12505,plain,
% 2.32/2.55 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12504])).
% 2.32/2.55 tff(12506,plain,
% 2.32/2.55 (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[239, 12505, 181])).
% 2.32/2.55 tff(12507,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[196, 12506])).
% 2.32/2.55 tff(12508,plain,(b(s(elem!1), z) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12509,plain,
% 2.32/2.55 (b(s(elem!1), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12508, 713, 624, 251, 863, 12347, 51, 132, 2484, 1, 123, 12153])).
% 2.32/2.55 tff(12510,plain,
% 2.32/2.55 (~b(s(elem!1), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[916, 12509, 624, 251])).
% 2.32/2.55 tff(12511,plain,
% 2.32/2.55 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[174])).
% 2.32/2.55 tff(12512,plain,
% 2.32/2.55 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.55 inference(monotonicity,[status(thm)],[927])).
% 2.32/2.55 tff(12513,plain,
% 2.32/2.55 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(elem!1), z)),
% 2.32/2.55 inference(symmetry,[status(thm)],[12512])).
% 2.32/2.55 tff(12514,plain,
% 2.32/2.55 ((~b(s(s(s(s(s(s(s(z))))))), z)) <=> (~b(s(elem!1), z))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12513])).
% 2.32/2.55 tff(12515,plain,
% 2.32/2.55 (~b(s(elem!1), z)),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[296, 12514])).
% 2.32/2.55 tff(12516,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[491, 12515])).
% 2.32/2.55 tff(12517,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | b(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12518,plain,
% 2.32/2.55 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12517, 12509, 296])).
% 2.32/2.55 tff(12519,plain,
% 2.32/2.55 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12518, 12511])).
% 2.32/2.55 tff(12520,plain,
% 2.32/2.55 (~b(s(z), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1602, 12347, 624, 251])).
% 2.32/2.55 tff(12521,plain,
% 2.32/2.55 (r(elem!1, s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[9106, 12520, 132, 123, 51, 624])).
% 2.32/2.55 tff(12522,plain,
% 2.32/2.55 (r(s(z), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[348, 12520])).
% 2.32/2.55 tff(12523,plain,
% 2.32/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[341, 12522, 51, 12153])).
% 2.32/2.55 tff(12524,plain,
% 2.32/2.55 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[319, 12523])).
% 2.32/2.55 tff(12525,plain,
% 2.32/2.55 (r(s(elem!1), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[448, 907, 3616])).
% 2.32/2.55 tff(12526,plain,
% 2.32/2.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12270, 333, 12525, 722, 2484])).
% 2.32/2.55 tff(12527,plain,
% 2.32/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12283, 333, 12525, 722, 2484])).
% 2.32/2.55 tff(12528,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12207, 12527, 12526, 1, 123, 304, 722, 537, 132, 902])).
% 2.32/2.55 tff(12529,plain,((elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(12530,plain,
% 2.32/2.55 (elem!1 = s(elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12529, 12524, 123, 1, 12521, 12519, 132, 2484, 12510])).
% 2.32/2.55 tff(12531,plain,
% 2.32/2.55 (s(elem!1) = elem!1),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1569, 12530])).
% 2.32/2.55 tff(12532,plain,
% 2.32/2.55 (elem!1 = s(s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[5813, 12531])).
% 2.32/2.55 tff(12533,plain,
% 2.32/2.55 (s(s(elem!1)) = elem!1),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[5603, 12532])).
% 2.32/2.55 tff(12534,plain,
% 2.32/2.55 (~(s(s(s(z))) = elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[7595, 12533, 863])).
% 2.32/2.55 tff(12535,plain,
% 2.32/2.55 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12530])).
% 2.32/2.55 tff(12536,plain,
% 2.32/2.55 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[2484, 12535])).
% 2.32/2.55 tff(12537,plain,
% 2.32/2.55 (~b(elem!1, s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[313, 12524, 123, 132])).
% 2.32/2.55 tff(12538,plain,
% 2.32/2.55 (~b(s(elem!1), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[890, 12530, 12537])).
% 2.32/2.55 tff(12539,plain,
% 2.32/2.55 (r(s(elem!1), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[486, 12538, 1])).
% 2.32/2.55 tff(12540,plain,
% 2.32/2.55 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12530])).
% 2.32/2.55 tff(12541,plain,
% 2.32/2.55 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[132, 12540])).
% 2.32/2.55 tff(12542,plain,
% 2.32/2.55 (s(s(s(elem!1))) = elem!1),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2482, 12530])).
% 2.32/2.55 tff(12543,plain,
% 2.32/2.55 (s(elem!1) = s(s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2584, 12542, 12530])).
% 2.32/2.55 tff(12544,plain,
% 2.32/2.55 (~(s(elem!1) = s(s(s(z))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[990, 12543, 1])).
% 2.32/2.55 tff(12545,plain,
% 2.32/2.55 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[885])).
% 2.32/2.55 tff(12546,plain,
% 2.32/2.55 (r(s(s(s(z))), s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[707, 12545])).
% 2.32/2.55 tff(12547,plain,
% 2.32/2.55 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12548,plain,
% 2.32/2.55 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(12549,plain,
% 2.32/2.55 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[12548])).
% 2.32/2.55 tff(12550,plain,
% 2.32/2.55 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[12549, 12547])).
% 2.32/2.55 tff(12551,plain,
% 2.32/2.55 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(12552,plain,
% 2.32/2.55 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[12551, 12550])).
% 2.32/2.55 tff(12553,plain,
% 2.32/2.55 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[12552, 333, 434, 3003, 524])).
% 2.32/2.55 tff(12554,plain,
% 2.32/2.55 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1137, 12553])).
% 2.32/2.55 tff(12555,plain,
% 2.32/2.55 (((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12556,plain,
% 2.32/2.56 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12557,plain,
% 2.32/2.56 ((~![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(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12556, 12555])).
% 2.32/2.56 tff(12558,plain,
% 2.32/2.56 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12557, 333, 434, 3003, 524])).
% 2.32/2.56 tff(12559,plain,
% 2.32/2.56 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[249, 12558])).
% 2.32/2.56 tff(12560,plain,
% 2.32/2.56 (~b(s(z), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2262, 12554, 123, 12559])).
% 2.32/2.56 tff(12561,plain,
% 2.32/2.56 (r(s(z), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[172, 12560])).
% 2.32/2.56 tff(12562,plain,
% 2.32/2.56 (~r(s(elem!1), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[7227, 12561, 707, 434])).
% 2.32/2.56 tff(12563,plain,
% 2.32/2.56 (b(s(elem!1), s(s(s(z))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[965, 12562, 960])).
% 2.32/2.56 tff(12564,plain,
% 2.32/2.56 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12565,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12564])).
% 2.32/2.56 tff(12566,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[12565, 9083])).
% 2.32/2.56 tff(12567,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12568,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12567, 12566])).
% 2.32/2.56 tff(12569,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12568, 144, 12563, 12559, 12554, 450])).
% 2.32/2.56 tff(12570,plain,((~r(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12571,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12570, 707, 960, 450, 434, 123, 524])).
% 2.32/2.56 tff(12572,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12571, 12546])).
% 2.32/2.56 tff(12573,plain,((~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12574,plain,
% 2.32/2.56 (~r(s(s(s(z))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12573, 12530, 12544, 12541, 12539, 123, 12536])).
% 2.32/2.56 tff(12575,plain,
% 2.32/2.56 (b(s(s(s(z))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[704, 12574, 12534])).
% 2.32/2.56 tff(12576,plain,
% 2.32/2.56 (~b(s(s(s(z))), z)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10565, 12575, 624, 251])).
% 2.32/2.56 tff(12577,plain,
% 2.32/2.56 (r(s(s(s(z))), z)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[396, 12576])).
% 2.32/2.56 tff(12578,plain,
% 2.32/2.56 (((~![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(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12579,plain,
% 2.32/2.56 (((~r(z, s(s(s(s(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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12580,plain,
% 2.32/2.56 (((~![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(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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12579])).
% 2.32/2.56 tff(12581,plain,
% 2.32/2.56 (((~![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(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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[12580, 12578])).
% 2.32/2.56 tff(12582,plain,
% 2.32/2.56 ((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12583,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12582, 12581])).
% 2.32/2.56 tff(12584,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12583, 333, 12522, 12577, 51])).
% 2.32/2.56 tff(12585,plain,
% 2.32/2.56 (s(s(s(elem!1))) = s(elem!1)),
% 2.32/2.56 inference(transitivity,[status(thm)],[12542, 12530])).
% 2.32/2.56 tff(12586,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12585])).
% 2.32/2.56 tff(12587,plain,
% 2.32/2.56 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.32/2.56 inference(monotonicity,[status(thm)],[1000])).
% 2.32/2.56 tff(12588,plain,
% 2.32/2.56 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.56 inference(symmetry,[status(thm)],[12587])).
% 2.32/2.56 tff(12589,plain,
% 2.32/2.56 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12588])).
% 2.32/2.56 tff(12590,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[699, 12589])).
% 2.32/2.56 tff(12591,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 2.32/2.56 tff(12592,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12591, 12590])).
% 2.32/2.56 tff(12593,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12594,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12593, 12574, 12542])).
% 2.32/2.56 tff(12595,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[9560, 12594, 9480])).
% 2.32/2.56 tff(12596,plain,
% 2.32/2.56 (b(s(s(s(z))), s(elem!1))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12595, 12586])).
% 2.32/2.56 tff(12597,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[11754, 12577, 51, 12153])).
% 2.32/2.56 tff(12598,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1137, 12597])).
% 2.32/2.56 tff(12599,plain,
% 2.32/2.56 (b(s(z), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3262, 12531, 12347])).
% 2.32/2.56 tff(12600,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12601,plain,
% 2.32/2.56 (((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12602,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12601])).
% 2.32/2.56 tff(12603,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[12602, 12600])).
% 2.32/2.56 tff(12604,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12605,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12604, 12603])).
% 2.32/2.56 tff(12606,plain,
% 2.32/2.56 (~b(s(s(s(z))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12605, 144, 12599, 12598, 12524, 12596])).
% 2.32/2.56 tff(12607,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2794, 12606, 12584])).
% 2.32/2.56 tff(12608,plain,((s(z) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12609,plain,
% 2.32/2.56 (s(z) = elem!1),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12608, 12165, 12152, 51, 50, 12013, 12004, 1, 296])).
% 2.32/2.56 tff(12610,plain,
% 2.32/2.56 (~(s(s(s(elem!1))) = elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2468, 12609])).
% 2.32/2.56 tff(12611,plain,
% 2.32/2.56 (~(elem!1 = s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2482, 12610])).
% 2.32/2.56 tff(12612,plain,
% 2.32/2.56 (~(s(elem!1) = elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[906, 12611])).
% 2.32/2.56 tff(12613,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[3525])).
% 2.32/2.56 tff(12614,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.56 inference(symmetry,[status(thm)],[12613])).
% 2.32/2.56 tff(12615,plain,
% 2.32/2.56 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12614])).
% 2.32/2.56 tff(12616,plain,
% 2.32/2.56 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[601, 333, 509, 321, 51])).
% 2.32/2.56 tff(12617,plain,
% 2.32/2.56 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[472, 12616, 4762])).
% 2.32/2.56 tff(12618,plain,
% 2.32/2.56 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[7702, 333, 509, 321, 51])).
% 2.32/2.56 tff(12619,plain,
% 2.32/2.56 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[542, 12618, 2698])).
% 2.32/2.56 tff(12620,plain,
% 2.32/2.56 (~b(elem!1, s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5467, 12618, 132, 2698, 12616])).
% 2.32/2.56 tff(12621,plain,
% 2.32/2.56 (r(elem!1, s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[560, 12620, 2483])).
% 2.32/2.56 tff(12622,plain,
% 2.32/2.56 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[57])).
% 2.32/2.56 tff(12623,plain,
% 2.32/2.56 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.32/2.56 inference(symmetry,[status(thm)],[12622])).
% 2.32/2.56 tff(12624,plain,
% 2.32/2.56 (r(s(z), s(elem!1))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[563, 12623])).
% 2.32/2.56 tff(12625,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[9754, 1024, 509, 12624])).
% 2.32/2.56 tff(12626,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[4697, 12625, 3523])).
% 2.32/2.56 tff(12627,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12626, 9504])).
% 2.32/2.56 tff(12628,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12629,plain,
% 2.32/2.56 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12630,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12629])).
% 2.32/2.56 tff(12631,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[12630, 12628])).
% 2.32/2.56 tff(12632,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12633,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12632, 12631])).
% 2.32/2.56 tff(12634,plain,
% 2.32/2.56 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12633, 333, 563, 4626, 2484])).
% 2.32/2.56 tff(12635,plain,
% 2.32/2.56 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.32/2.56 inference(transitivity,[status(thm)],[21, 186, 183, 2496])).
% 2.32/2.56 tff(12636,plain,
% 2.32/2.56 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12635])).
% 2.32/2.56 tff(12637,plain,
% 2.32/2.56 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.32/2.56 inference(symmetry,[status(thm)],[12636])).
% 2.32/2.56 tff(12638,plain,
% 2.32/2.56 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[102, 12637, 92])).
% 2.32/2.56 tff(12639,plain,
% 2.32/2.56 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12638])).
% 2.32/2.56 tff(12640,plain,
% 2.32/2.56 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.32/2.56 inference(symmetry,[status(thm)],[12639])).
% 2.32/2.56 tff(12641,plain,
% 2.32/2.56 (s(s(s(elem!1))) = elem!1),
% 2.32/2.56 inference(transitivity,[status(thm)],[3525, 239, 12640, 850])).
% 2.32/2.56 tff(12642,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2469, 12641])).
% 2.32/2.56 tff(12643,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12644,plain,
% 2.32/2.56 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12643, 57])).
% 2.32/2.56 tff(12645,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3556, 44, 12644, 12634])).
% 2.32/2.56 tff(12646,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12647,plain,
% 2.32/2.56 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12648,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[12647])).
% 2.32/2.56 tff(12649,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[12648, 12646])).
% 2.32/2.56 tff(12650,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(12651,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[12650, 12649])).
% 2.32/2.56 tff(12652,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12651, 144, 546, 450, 12645, 12627])).
% 2.32/2.56 tff(12653,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(12654,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[12653, 12621, 2484, 57, 509, 12619, 12617])).
% 2.32/2.56 tff(12655,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1101, 12654])).
% 2.32/2.56 tff(12656,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3588, 12655, 57])).
% 2.32/2.56 tff(12657,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(12658,plain,
% 2.32/2.56 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(12659,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[12658])).
% 2.32/2.57 tff(12660,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.32/2.57 inference(transitivity,[status(thm)],[12659, 12657])).
% 2.32/2.57 tff(12661,plain,
% 2.32/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(12662,plain,
% 2.32/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[12661, 12660])).
% 2.32/2.57 tff(12663,plain,
% 2.32/2.57 (~b(s(s(s(s(z)))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[12662, 144, 251, 624, 12656])).
% 2.32/2.57 tff(12664,plain,
% 2.32/2.57 (r(s(s(s(s(z)))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[4243, 44, 242, 12663])).
% 2.32/2.57 tff(12665,plain,
% 2.32/2.57 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(12666,plain,
% 2.32/2.57 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[12665])).
% 2.32/2.57 tff(12667,plain,
% 2.32/2.57 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[12666, 4234])).
% 2.32/2.57 tff(12668,plain,
% 2.32/2.57 ((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(12669,plain,
% 2.32/2.57 ((~![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(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[12668, 12667])).
% 2.32/2.57 tff(12670,plain,
% 2.32/2.57 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12669, 333, 321, 51, 12664])).
% 2.32/2.58 tff(12671,plain,
% 2.32/2.58 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[9761, 12670])).
% 2.32/2.58 tff(12672,plain,
% 2.32/2.58 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12651, 144, 12619, 12617, 12671])).
% 2.32/2.58 tff(12673,plain,
% 2.32/2.58 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[12672, 12615])).
% 2.32/2.58 tff(12674,plain,
% 2.32/2.58 (((~![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(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, 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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12675,plain,
% 2.32/2.58 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12676,plain,
% 2.32/2.58 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12675])).
% 2.32/2.58 tff(12677,plain,
% 2.32/2.58 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[12676, 12674])).
% 2.32/2.58 tff(12678,plain,
% 2.32/2.58 ((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(12679,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[12678, 12677])).
% 2.32/2.58 tff(12680,plain,
% 2.32/2.58 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12679, 333, 509, 51, 12664])).
% 2.32/2.58 tff(12681,plain,
% 2.32/2.58 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[12680, 4583])).
% 2.32/2.58 tff(12682,plain,
% 2.32/2.58 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4697, 12681, 3523])).
% 2.32/2.58 tff(12683,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12682, 12673])).
% 2.32/2.58 tff(12684,plain,((~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(12685,plain,
% 2.32/2.58 (~r(s(elem!1), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12684, 12609, 12153, 51, 12165, 12152, 12004, 12013])).
% 2.32/2.58 tff(12686,plain,
% 2.32/2.58 (b(s(elem!1), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[507, 12685])).
% 2.32/2.58 tff(12687,plain,
% 2.32/2.58 (~b(s(elem!1), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[916, 12686, 12152, 12165])).
% 2.32/2.58 tff(12688,plain,
% 2.32/2.58 (r(s(elem!1), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[448, 12687, 12612])).
% 2.32/2.58 tff(12689,plain,
% 2.32/2.58 (~r(z, s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[940, 525, 51, 321])).
% 2.32/2.58 tff(12690,plain,
% 2.32/2.58 (b(z, s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[583, 12689])).
% 2.32/2.58 tff(12691,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12692,plain,
% 2.32/2.58 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12693,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12692])).
% 2.32/2.58 tff(12694,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[12693, 12691])).
% 2.32/2.58 tff(12695,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(12696,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[12695, 12694])).
% 2.32/2.58 tff(12697,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12696, 333, 563, 435, 2484, 525])).
% 2.32/2.58 tff(12698,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(12699,plain,
% 2.32/2.58 (~r(elem!1, s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12698, 525, 2484, 435])).
% 2.32/2.58 tff(12700,plain,
% 2.32/2.58 (b(elem!1, s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[560, 12699, 902])).
% 2.32/2.58 tff(12701,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[949, 12700, 12690, 624, 491])).
% 2.32/2.58 tff(12702,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(12703,plain,
% 2.32/2.58 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[12702, 12686, 12152, 12611, 12004, 12688, 51, 12153])).
% 2.32/2.58 tff(12704,plain,
% 2.32/2.58 (s(s(z)) = s(elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12609])).
% 2.32/2.58 tff(12705,plain,
% 2.32/2.58 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12704])).
% 2.32/2.58 tff(12706,plain,
% 2.32/2.58 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.32/2.58 inference(transitivity,[status(thm)],[12705, 174])).
% 2.32/2.58 tff(12707,plain,
% 2.32/2.58 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12706])).
% 2.32/2.58 tff(12708,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[1446, 12707])).
% 2.32/2.58 tff(12709,plain,
% 2.32/2.58 (s(s(s(z))) = s(s(elem!1))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12704])).
% 2.32/2.58 tff(12710,plain,
% 2.32/2.58 (s(s(elem!1)) = s(s(s(z)))),
% 2.32/2.58 inference(symmetry,[status(thm)],[12709])).
% 2.32/2.58 tff(12711,plain,
% 2.32/2.58 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12710])).
% 2.32/2.58 tff(12712,plain,
% 2.32/2.58 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12711])).
% 2.32/2.58 tff(12713,plain,
% 2.32/2.58 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12609])).
% 2.32/2.58 tff(12714,plain,
% 2.32/2.58 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.32/2.58 inference(transitivity,[status(thm)],[12713, 12712])).
% 2.32/2.58 tff(12715,plain,
% 2.32/2.58 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[12706, 175])).
% 2.32/2.58 tff(12716,plain,
% 2.32/2.58 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12715])).
% 2.32/2.58 tff(12717,plain,
% 2.32/2.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[1446, 12716])).
% 2.32/2.58 tff(12718,plain,
% 2.32/2.58 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[472, 12703, 12717])).
% 2.32/2.58 tff(12719,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.32/2.58 tff(12720,plain,
% 2.32/2.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(commutativity,[status(thm)],[])).
% 2.32/2.58 tff(12721,plain,
% 2.32/2.58 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.32/2.58 inference(symmetry,[status(thm)],[12720])).
% 2.32/2.58 tff(12722,plain,
% 2.32/2.58 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12721])).
% 2.32/2.58 tff(12723,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[196, 12722])).
% 2.32/2.58 tff(12724,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12725,plain,
% 2.32/2.58 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(12726,plain,
% 2.32/2.58 (((~![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(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[12725])).
% 2.32/2.58 tff(12727,plain,
% 2.32/2.58 (((~![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(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[12726, 12724])).
% 2.32/2.59 tff(12728,plain,
% 2.32/2.59 ((~![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(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(12729,plain,
% 2.32/2.59 ((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[12728, 12727])).
% 2.32/2.59 tff(12730,plain,
% 2.32/2.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[12729, 333, 321, 51, 12719])).
% 2.32/2.59 tff(12731,plain,
% 2.32/2.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(12732,plain,
% 2.32/2.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(12733,plain,
% 2.32/2.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[12732, 12731])).
% 2.32/2.59 tff(12734,plain,
% 2.32/2.59 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[12733, 44, 12730])).
% 2.32/2.59 tff(12735,plain,
% 2.32/2.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[12734, 12723])).
% 2.32/2.59 tff(12736,plain,
% 2.32/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[12669, 333, 321, 51, 12719])).
% 2.32/2.59 tff(12737,plain,
% 2.32/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[9761, 12736])).
% 2.32/2.59 tff(12738,plain,
% 2.32/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(12739,plain,
% 2.32/2.59 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(12740,plain,
% 2.32/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.32/2.60 inference(monotonicity,[status(thm)],[12739])).
% 2.32/2.60 tff(12741,plain,
% 2.32/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.60 inference(transitivity,[status(thm)],[12740, 12738])).
% 2.32/2.60 tff(12742,plain,
% 2.32/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.60 inference(quant_inst,[status(thm)],[])).
% 2.32/2.60 tff(12743,plain,
% 2.32/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.60 inference(modus_ponens,[status(thm)],[12742, 12741])).
% 2.32/2.60 tff(12744,plain,
% 2.32/2.60 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[12743, 144, 450, 12737, 12735])).
% 2.32/2.60 tff(12745,plain,
% 2.32/2.60 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.32/2.60 inference(modus_ponens,[status(thm)],[12744, 3528])).
% 2.32/2.60 tff(12746,plain,
% 2.32/2.60 (r(s(elem!1), s(s(s(elem!1))))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[1067, 12745, 3524])).
% 2.32/2.60 tff(12747,plain,
% 2.32/2.60 (r(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[3545, 12746, 57])).
% 2.32/2.60 tff(12748,plain,
% 2.32/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.60 inference(rewrite,[status(thm)],[])).
% 2.32/2.60 tff(12749,plain,
% 2.32/2.60 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.60 inference(rewrite,[status(thm)],[])).
% 2.32/2.60 tff(12750,plain,
% 2.32/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.32/2.60 inference(monotonicity,[status(thm)],[12749])).
% 2.32/2.60 tff(12751,plain,
% 2.32/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[12750, 12748])).
% 2.42/2.60 tff(12752,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(12753,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[12752, 12751])).
% 2.42/2.60 tff(12754,plain,
% 2.42/2.60 (~b(elem!1, s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[12753, 144, 132, 12737, 12735])).
% 2.42/2.60 tff(12755,plain,
% 2.42/2.60 (r(elem!1, s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[6873, 12754, 6862])).
% 2.42/2.60 tff(12756,plain,
% 2.42/2.60 (((~![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(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(12757,plain,
% 2.42/2.60 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(12758,plain,
% 2.42/2.60 (((~![X0: $i, 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(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(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(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[12757])).
% 2.42/2.60 tff(12759,plain,
% 2.42/2.60 (((~![X0: $i, 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(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(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(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[12758, 12756])).
% 2.42/2.60 tff(12760,plain,
% 2.42/2.60 ((~![X0: $i, 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(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(12761,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[12760, 12759])).
% 2.42/2.60 tff(12762,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[12761, 333, 435, 12755, 12747, 12719])).
% 2.42/2.60 tff(12763,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(12764,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[12763, 12688, 12609, 12718, 12013, 12153, 51])).
% 2.42/2.61 tff(12765,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[4243, 44, 242, 12764])).
% 2.42/2.61 tff(12766,plain,
% 2.42/2.61 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(12767,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[12766])).
% 2.42/2.61 tff(12768,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.42/2.61 inference(transitivity,[status(thm)],[12767, 12657])).
% 2.42/2.61 tff(12769,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(12770,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[12769, 12768])).
% 2.42/2.61 tff(12771,plain,
% 2.42/2.61 (~b(s(s(s(s(z)))), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[12770, 144, 12165, 12152, 12765])).
% 2.42/2.61 tff(12772,plain,
% 2.42/2.61 (~b(s(s(s(elem!1))), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3588, 12771, 12609])).
% 2.42/2.61 tff(12773,plain,
% 2.42/2.61 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1101, 12772])).
% 2.42/2.61 tff(12774,plain,
% 2.42/2.61 (r(s(s(s(s(z)))), elem!1)),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[12773, 12714])).
% 2.42/2.61 tff(12775,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[12633, 333, 563, 9507, 2484])).
% 2.42/2.61 tff(12776,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3556, 44, 12644, 12775])).
% 2.42/2.61 tff(12777,plain,
% 2.42/2.61 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[2495])).
% 2.42/2.61 tff(12778,plain,
% 2.42/2.61 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.42/2.61 inference(symmetry,[status(thm)],[12777])).
% 2.42/2.61 tff(12779,plain,
% 2.42/2.61 (r(s(s(z)), elem!1)),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[435, 12778])).
% 2.42/2.61 tff(12780,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(12781,plain,
% 2.42/2.61 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(12782,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), 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(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[12781])).
% 2.42/2.62 tff(12783,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), 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(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.42/2.62 inference(transitivity,[status(thm)],[12782, 12780])).
% 2.42/2.62 tff(12784,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(12785,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[12784, 12783])).
% 2.42/2.62 tff(12786,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12785, 333, 563, 2671, 2484, 7155])).
% 2.42/2.62 tff(12787,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(12788,plain,
% 2.42/2.62 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12787, 2484, 12779, 563])).
% 2.42/2.62 tff(12789,plain,
% 2.42/2.62 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[1451, 12788])).
% 2.42/2.62 tff(12790,plain,
% 2.42/2.62 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[2689, 12789, 57])).
% 2.42/2.62 tff(12791,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(12792,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(12793,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[12792, 12791])).
% 2.42/2.62 tff(12794,plain,
% 2.42/2.62 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12793, 333, 563, 435, 2484])).
% 2.42/2.62 tff(12795,plain,
% 2.42/2.62 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[540, 44, 2698, 12794])).
% 2.42/2.62 tff(12796,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12651, 144, 12795, 12790, 12776, 9514])).
% 2.42/2.62 tff(12797,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(12798,plain,
% 2.42/2.62 (~r(elem!1, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12797, 12774, 12004, 12609, 12688])).
% 2.42/2.62 tff(12799,plain,
% 2.42/2.62 (b(elem!1, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[560, 12798, 12611])).
% 2.42/2.62 tff(12800,plain,
% 2.42/2.62 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[5467, 12799, 12013, 12708, 12703])).
% 2.42/2.62 tff(12801,plain,
% 2.42/2.62 (~b(z, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[949, 12799, 12152, 12686])).
% 2.42/2.62 tff(12802,plain,
% 2.42/2.62 (r(z, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[583, 12801])).
% 2.42/2.62 tff(12803,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[2655, 12802, 12800, 51, 12688])).
% 2.42/2.62 tff(12804,plain,(b(s(s(s(s(s(s(s(z))))))), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(12805,plain,
% 2.42/2.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12804, 51, 1, 3, 4])).
% 2.42/2.62 tff(12806,plain,
% 2.42/2.62 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[4003, 606, 77, 12004, 51, 7265])).
% 2.42/2.62 tff(12807,plain,
% 2.42/2.62 (~b(elem!1, s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[632, 12805, 12152, 50, 12013])).
% 2.42/2.62 tff(12808,plain,
% 2.42/2.62 (r(elem!1, s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[720, 12158, 12807])).
% 2.42/2.62 tff(12809,plain,
% 2.42/2.62 (~r(elem!1, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[2492, 7265, 12004, 51])).
% 2.42/2.62 tff(12810,plain,
% 2.42/2.62 (b(elem!1, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[560, 12809, 902])).
% 2.42/2.62 tff(12811,plain,
% 2.42/2.62 (~b(z, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[949, 12810, 12152, 491])).
% 2.42/2.62 tff(12812,plain,
% 2.42/2.62 (r(z, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[583, 12811])).
% 2.42/2.62 tff(12813,plain,
% 2.42/2.62 (~r(s(elem!1), elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[1863, 12812, 7265, 12808])).
% 2.42/2.62 tff(12814,plain,
% 2.42/2.62 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12390, 12813, 12004])).
% 2.42/2.62 tff(12815,plain,
% 2.42/2.62 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[930, 12814])).
% 2.42/2.62 tff(12816,plain,
% 2.42/2.62 (b(s(elem!1), elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[448, 12813, 907])).
% 2.42/2.62 tff(12817,plain,
% 2.42/2.62 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12059, 144, 491, 12013, 12805])).
% 2.42/2.62 tff(12818,plain,
% 2.42/2.62 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12817, 12816])).
% 2.42/2.62 tff(12819,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[472, 12818, 12815, 12806])).
% 2.42/2.62 tff(12820,plain,(b(z, elem!1) | (~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(12821,plain,
% 2.42/2.62 (b(z, elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12820, 491, 902, 51, 1, 3, 4])).
% 2.42/2.62 tff(12822,plain,
% 2.42/2.62 (~b(elem!1, s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[632, 286, 624, 123, 132])).
% 2.42/2.62 tff(12823,plain,
% 2.42/2.62 (r(elem!1, s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[720, 713, 12822])).
% 2.42/2.62 tff(12824,plain,
% 2.42/2.62 (~b(s(elem!1), elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[916, 251, 624, 491])).
% 2.42/2.62 tff(12825,plain,
% 2.42/2.62 (~r(s(z), elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[12172, 322, 2484, 722])).
% 2.42/2.62 tff(12826,plain,
% 2.42/2.62 (b(s(z), elem!1)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[406, 12825, 706])).
% 2.42/2.62 tff(12827,plain,
% 2.42/2.62 (~b(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[1602, 12826, 624, 251])).
% 2.42/2.62 tff(12828,plain,
% 2.42/2.62 (r(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[348, 12827])).
% 2.42/2.63 tff(12829,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[818, 333, 12828, 722, 2484, 322])).
% 2.42/2.63 tff(12830,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(12831,plain,
% 2.42/2.63 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[12830, 12823, 2484, 624, 251, 706])).
% 2.42/2.63 tff(12832,plain,
% 2.42/2.63 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[319, 12831])).
% 2.42/2.63 tff(12833,plain,
% 2.42/2.63 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[12529, 12832, 123, 1, 902, 12824, 132, 2484, 12823])).
% 2.42/2.63 tff(12834,plain,
% 2.42/2.63 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[12833])).
% 2.42/2.63 tff(12835,plain,
% 2.42/2.63 (r(z, s(elem!1))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[51, 12834])).
% 2.42/2.63 tff(12836,plain,
% 2.42/2.63 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[12833])).
% 2.42/2.63 tff(12837,plain,
% 2.42/2.63 (b(s(elem!1), s(z))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[12832, 12836])).
% 2.42/2.63 tff(12838,plain,
% 2.42/2.63 (r(s(elem!1), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[448, 12824, 907])).
% 2.42/2.63 tff(12839,plain,
% 2.42/2.63 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.63 tff(12840,plain,
% 2.42/2.63 (r(z, s(elem!1))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[51, 12839])).
% 2.42/2.63 tff(12841,plain,
% 2.42/2.63 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[919, 175])).
% 2.42/2.63 tff(12842,plain,
% 2.42/2.63 (~(s(s(s(z))) = elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[12214, 12841])).
% 2.42/2.63 tff(12843,plain,
% 2.42/2.63 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[12830, 722, 2484, 624, 251, 706])).
% 2.42/2.63 tff(12844,plain,
% 2.42/2.63 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[319, 12843])).
% 2.42/2.63 tff(12845,plain,
% 2.42/2.63 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.63 tff(12846,plain,
% 2.42/2.63 (b(s(elem!1), s(z))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[304, 12845])).
% 2.42/2.63 tff(12847,plain,
% 2.42/2.63 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.63 tff(12848,plain,
% 2.42/2.63 (b(elem!1, s(elem!1))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[132, 12847])).
% 2.42/2.63 tff(12849,plain,
% 2.42/2.63 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.42/2.63 inference(transitivity,[status(thm)],[1212, 998])).
% 2.42/2.63 tff(12850,plain,
% 2.42/2.63 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[12849])).
% 2.42/2.63 tff(12851,plain,
% 2.42/2.63 (~(s(s(s(z))) = s(elem!1))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[244, 12850])).
% 2.42/2.63 tff(12852,plain,
% 2.42/2.63 (~b(s(s(s(z))), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[10565, 4367, 624, 251])).
% 2.42/2.63 tff(12853,plain,
% 2.42/2.63 (r(s(s(s(z))), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[396, 12852])).
% 2.42/2.63 tff(12854,plain,
% 2.42/2.63 (~r(s(s(s(z))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[6555, 12853, 354, 323])).
% 2.42/2.63 tff(12855,plain,
% 2.42/2.63 (b(s(s(s(z))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[2794, 12854])).
% 2.42/2.63 tff(12856,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(12857,plain,
% 2.42/2.63 (((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(12858,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[12857])).
% 2.42/2.64 tff(12859,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.64 inference(transitivity,[status(thm)],[12858, 12856])).
% 2.42/2.64 tff(12860,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(12861,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[12860, 12859])).
% 2.42/2.64 tff(12862,plain,
% 2.42/2.64 (~b(s(s(s(z))), s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[12861, 144, 547, 488, 12855, 4367])).
% 2.42/2.64 tff(12863,plain,
% 2.42/2.64 (r(s(s(s(z))), s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 12862])).
% 2.42/2.64 tff(12864,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[10628, 333, 435, 562, 12853, 12863])).
% 2.42/2.64 tff(12865,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(12866,plain,
% 2.42/2.64 (~b(s(s(s(z))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[12865, 3922, 12840, 12851, 12848, 12846, 354, 435, 624, 251])).
% 2.42/2.64 tff(12867,plain,
% 2.42/2.64 (r(s(s(s(z))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[704, 12866, 12842])).
% 2.42/2.64 tff(12868,plain,
% 2.42/2.64 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1694, 12867, 435, 722])).
% 2.42/2.64 tff(12869,plain,
% 2.42/2.64 (b(s(elem!1), s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[965, 12868, 1214])).
% 2.42/2.64 tff(12870,plain,
% 2.42/2.64 (~r(s(s(s(z))), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[9360, 12867, 132, 51, 123, 624, 3921])).
% 2.42/2.64 tff(12871,plain,
% 2.42/2.64 (b(s(s(s(z))), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2794, 12870])).
% 2.42/2.64 tff(12872,plain,
% 2.42/2.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.64 tff(12873,plain,
% 2.42/2.64 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.42/2.64 inference(symmetry,[status(thm)],[12872])).
% 2.42/2.64 tff(12874,plain,
% 2.42/2.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[12869, 12873])).
% 2.42/2.64 tff(12875,plain,
% 2.42/2.64 (~b(s(z), s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[846, 12874, 304, 12871])).
% 2.42/2.64 tff(12876,plain,
% 2.42/2.64 (r(s(z), s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[172, 12875])).
% 2.42/2.64 tff(12877,plain,
% 2.42/2.64 (~r(s(s(s(z))), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7314, 12876, 354, 3922])).
% 2.42/2.64 tff(12878,plain,
% 2.42/2.64 (b(s(s(s(z))), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[396, 12877])).
% 2.42/2.64 tff(12879,plain,
% 2.42/2.64 (~r(z, s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1519, 12876, 354, 12867])).
% 2.42/2.64 tff(12880,plain,
% 2.42/2.64 (b(z, s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[619, 12879])).
% 2.42/2.64 tff(12881,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1802, 12880, 12878, 491, 12869])).
% 2.42/2.64 tff(12882,plain,(b(s(z), z) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(12883,plain,
% 2.42/2.64 (b(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[12882, 354, 491, 12844, 919, 132, 51, 123, 624, 435, 722, 251])).
% 2.42/2.64 tff(12884,plain,
% 2.42/2.64 (~b(s(z), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1602, 12883, 624, 251])).
% 2.42/2.64 tff(12885,plain,
% 2.42/2.64 (r(s(z), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[406, 12884, 706])).
% 2.42/2.64 tff(12886,plain,
% 2.42/2.64 (~r(s(s(s(z))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[12189, 12885, 123, 2484, 722])).
% 2.42/2.64 tff(12887,plain,
% 2.42/2.64 (b(s(s(s(z))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[704, 12886, 12842])).
% 2.42/2.64 tff(12888,plain,
% 2.42/2.64 (~b(s(s(s(z))), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[10565, 12887, 624, 251])).
% 2.42/2.64 tff(12889,plain,
% 2.42/2.64 (r(s(s(s(z))), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[396, 12888])).
% 2.42/2.64 tff(12890,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[10628, 333, 435, 562, 1699, 3003])).
% 2.42/2.64 tff(12891,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(12892,plain,
% 2.42/2.64 (~r(s(s(s(z))), s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[12891, 12889, 12840, 435])).
% 2.42/2.64 tff(12893,plain,
% 2.42/2.64 (b(s(s(s(z))), s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1951, 44, 12851, 12892])).
% 2.42/2.64 tff(12894,plain,
% 2.42/2.64 (r(s(elem!1), s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6014, 12892, 12841, 123, 12844, 354, 12889])).
% 2.42/2.64 tff(12895,plain,
% 2.42/2.64 (~(elem!1 = s(s(s(z))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[10997, 12842])).
% 2.42/2.64 tff(12896,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(12897,plain,
% 2.42/2.64 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(12898,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[12897])).
% 2.42/2.64 tff(12899,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[12898, 12896])).
% 2.42/2.65 tff(12900,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(12901,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[12900, 12899])).
% 2.42/2.65 tff(12902,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12901, 144, 547, 624, 491, 2082, 4811])).
% 2.42/2.65 tff(12903,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(12904,plain,
% 2.42/2.65 (~b(elem!1, s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12903, 12893, 624, 491, 12848])).
% 2.42/2.65 tff(12905,plain,
% 2.42/2.65 (r(elem!1, s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1538, 12904, 12895])).
% 2.42/2.65 tff(12906,plain,
% 2.42/2.65 (~r(s(s(s(z))), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[10761, 12905, 435, 12894])).
% 2.42/2.65 tff(12907,plain,
% 2.42/2.65 (b(s(s(s(z))), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[2794, 12906])).
% 2.42/2.65 tff(12908,plain,
% 2.42/2.65 (b(s(z), s(elem!1))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[2946, 919, 123])).
% 2.42/2.65 tff(12909,plain,
% 2.42/2.65 (b(s(elem!1), s(z))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[12844, 12845])).
% 2.42/2.65 tff(12910,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12229, 144, 12909, 12908, 12907, 12893])).
% 2.42/2.65 tff(12911,plain,((~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(12912,plain,
% 2.42/2.65 (~r(z, s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12911, 12823, 624, 491, 123, 251, 2484, 12838, 706, 12833, 132, 51])).
% 2.42/2.65 tff(12913,plain,
% 2.42/2.65 (b(z, s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[372, 12912])).
% 2.42/2.65 tff(12914,plain,
% 2.42/2.65 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12833])).
% 2.42/2.65 tff(12915,plain,
% 2.42/2.65 (b(elem!1, s(elem!1))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[132, 12914])).
% 2.42/2.65 tff(12916,plain,
% 2.42/2.65 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.65 tff(12917,plain,
% 2.42/2.65 (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(elem!1)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12916])).
% 2.42/2.65 tff(12918,plain,
% 2.42/2.65 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.65 inference(symmetry,[status(thm)],[12917])).
% 2.42/2.65 tff(12919,plain,
% 2.42/2.65 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[21, 1203, 850, 1001, 12918])).
% 2.42/2.65 tff(12920,plain,
% 2.42/2.65 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12919])).
% 2.42/2.65 tff(12921,plain,
% 2.42/2.65 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.42/2.65 inference(transitivity,[status(thm)],[93, 12920, 12349, 12916])).
% 2.42/2.65 tff(12922,plain,
% 2.42/2.65 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12921])).
% 2.42/2.65 tff(12923,plain,
% 2.42/2.65 (s(s(s(s(z)))) = s(elem!1)),
% 2.42/2.65 inference(transitivity,[status(thm)],[239, 12922, 101])).
% 2.42/2.65 tff(12924,plain,
% 2.42/2.65 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[919])).
% 2.42/2.65 tff(12925,plain,
% 2.42/2.65 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12924])).
% 2.42/2.65 tff(12926,plain,
% 2.42/2.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[196, 12925])).
% 2.42/2.65 tff(12927,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12926, 12923])).
% 2.42/2.65 tff(12928,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(12929,plain,
% 2.42/2.65 (~(s(s(s(elem!1))) = elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12928, 12833])).
% 2.42/2.65 tff(12930,plain,
% 2.42/2.65 (r(z, s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[619, 255])).
% 2.42/2.65 tff(12931,plain,
% 2.42/2.65 (~(s(s(s(z))) = elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[257, 255, 251])).
% 2.42/2.65 tff(12932,plain,
% 2.42/2.65 (~b(s(z), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[499, 491, 488, 490])).
% 2.42/2.65 tff(12933,plain,
% 2.42/2.65 (r(s(z), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[348, 12932])).
% 2.42/2.65 tff(12934,plain,
% 2.42/2.65 (~(s(elem!1) = s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[8633, 2789, 488])).
% 2.42/2.65 tff(12935,plain,
% 2.42/2.65 (~r(s(s(s(z))), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[8030, 7586, 562, 12933])).
% 2.42/2.65 tff(12936,plain,
% 2.42/2.65 (b(s(s(s(z))), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[396, 12935])).
% 2.42/2.65 tff(12937,plain,
% 2.42/2.65 (~b(s(elem!1), s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1997, 144, 491, 490, 488, 12936])).
% 2.42/2.65 tff(12938,plain,
% 2.42/2.65 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[963, 44, 12937])).
% 2.42/2.65 tff(12939,plain,
% 2.42/2.65 (r(s(elem!1), s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12938, 12934])).
% 2.42/2.65 tff(12940,plain,
% 2.42/2.65 (((~![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(z))))) | (~r(z, s(elem!1))) | (~r(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(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(12941,plain,
% 2.42/2.65 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(12942,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[12941])).
% 2.42/2.65 tff(12943,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(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(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[12942, 12940])).
% 2.42/2.65 tff(12944,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(12945,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[12944, 12943])).
% 2.42/2.65 tff(12946,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[12945, 333, 562, 623, 7586, 12939])).
% 2.42/2.65 tff(12947,plain,(b(s(s(s(z))), s(z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(12948,plain,
% 2.42/2.66 (b(s(s(s(z))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12947, 12930, 562, 488, 491, 490])).
% 2.42/2.66 tff(12949,plain,
% 2.42/2.66 (b(s(s(s(z))), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1990, 12930, 562, 491, 488, 12948, 12933])).
% 2.42/2.66 tff(12950,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(12951,plain,
% 2.42/2.66 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(12952,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12951])).
% 2.42/2.66 tff(12953,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.66 inference(transitivity,[status(thm)],[12952, 12950])).
% 2.42/2.66 tff(12954,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(12955,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[12954, 12953])).
% 2.42/2.66 tff(12956,plain,
% 2.42/2.66 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12955, 144, 624, 490, 12948])).
% 2.42/2.66 tff(12957,plain,
% 2.42/2.66 (~b(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12956, 12949])).
% 2.42/2.66 tff(12958,plain,
% 2.42/2.66 ((s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[702, 44, 12957])).
% 2.42/2.66 tff(12959,plain,
% 2.42/2.66 (r(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12958, 12931])).
% 2.42/2.66 tff(12960,plain,
% 2.42/2.66 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1929, 12959, 12930, 562])).
% 2.42/2.66 tff(12961,plain,
% 2.42/2.66 (~b(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1997, 144, 491, 490, 488, 12949])).
% 2.42/2.66 tff(12962,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[963, 44, 12961])).
% 2.42/2.66 tff(12963,plain,
% 2.42/2.66 (s(elem!1) = s(s(s(z)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12962, 12960])).
% 2.42/2.66 tff(12964,plain,
% 2.42/2.66 (~(elem!1 = s(s(s(z))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[12931, 65])).
% 2.42/2.66 tff(12965,plain,
% 2.42/2.66 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12963])).
% 2.42/2.66 tff(12966,plain,
% 2.42/2.66 (b(elem!1, s(s(s(z))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[547, 12965])).
% 2.42/2.66 tff(12967,plain,
% 2.42/2.66 (b(s(s(s(z))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12947, 623, 562, 488, 491, 490])).
% 2.42/2.66 tff(12968,plain,
% 2.42/2.66 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12955, 144, 624, 490, 12967])).
% 2.42/2.66 tff(12969,plain,
% 2.42/2.66 (~b(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12968, 285])).
% 2.42/2.66 tff(12970,plain,
% 2.42/2.66 ((s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[702, 44, 12969])).
% 2.42/2.66 tff(12971,plain,
% 2.42/2.66 (r(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12970, 12448])).
% 2.42/2.66 tff(12972,plain,
% 2.42/2.66 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1929, 12971, 623, 562])).
% 2.42/2.66 tff(12973,plain,
% 2.42/2.66 (~b(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1997, 144, 491, 490, 488, 285])).
% 2.42/2.66 tff(12974,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[963, 44, 12973])).
% 2.42/2.66 tff(12975,plain,
% 2.42/2.66 (s(elem!1) = s(s(s(z)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12974, 12972])).
% 2.42/2.66 tff(12976,plain,
% 2.42/2.66 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12975])).
% 2.42/2.66 tff(12977,plain,
% 2.42/2.66 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12976])).
% 2.42/2.66 tff(12978,plain,
% 2.42/2.66 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.42/2.66 inference(symmetry,[status(thm)],[12977])).
% 2.42/2.66 tff(12979,plain,
% 2.42/2.66 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12978])).
% 2.42/2.66 tff(12980,plain,
% 2.42/2.66 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[12979])).
% 2.42/2.66 tff(12981,plain,
% 2.42/2.66 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[972])).
% 2.42/2.66 tff(12982,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12975])).
% 2.42/2.66 tff(12983,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[12982, 972])).
% 2.42/2.66 tff(12984,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[12983, 12981])).
% 2.42/2.66 tff(12985,plain,
% 2.42/2.66 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12984])).
% 2.42/2.66 tff(12986,plain,
% 2.42/2.66 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[1056, 12985])).
% 2.42/2.66 tff(12987,plain,
% 2.42/2.66 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12978])).
% 2.42/2.66 tff(12988,plain,
% 2.42/2.66 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12987])).
% 2.42/2.66 tff(12989,plain,
% 2.42/2.66 (~(elem!1 = s(elem!1))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[2482, 1012])).
% 2.42/2.66 tff(12990,plain,
% 2.42/2.66 (~(s(elem!1) = elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[906, 12989])).
% 2.42/2.66 tff(12991,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(12992,plain,
% 2.42/2.66 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(12993,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12992])).
% 2.42/2.66 tff(12994,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[12993, 12991])).
% 2.42/2.66 tff(12995,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), z)) | (~b(s(elem!1), elem!1)))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(12996,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[12995, 12994])).
% 2.42/2.66 tff(12997,plain,
% 2.42/2.66 ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12996, 144, 624, 490, 488])).
% 2.42/2.66 tff(12998,plain,
% 2.42/2.66 (~b(s(elem!1), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[12997, 491])).
% 2.42/2.66 tff(12999,plain,
% 2.42/2.66 (r(s(elem!1), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[448, 12998, 12990])).
% 2.42/2.66 tff(13000,plain,
% 2.42/2.66 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1929, 707, 623, 562])).
% 2.42/2.66 tff(13001,plain,
% 2.42/2.66 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[963, 44, 901])).
% 2.42/2.66 tff(13002,plain,
% 2.42/2.66 (s(elem!1) = s(s(s(z)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[13001, 13000])).
% 2.42/2.66 tff(13003,plain,
% 2.42/2.66 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13002])).
% 2.42/2.66 tff(13004,plain,
% 2.42/2.66 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13003])).
% 2.42/2.66 tff(13005,plain,
% 2.42/2.66 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.42/2.66 inference(symmetry,[status(thm)],[13004])).
% 2.42/2.66 tff(13006,plain,
% 2.42/2.66 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13002])).
% 2.42/2.66 tff(13007,plain,
% 2.42/2.66 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.42/2.66 inference(symmetry,[status(thm)],[13006])).
% 2.42/2.66 tff(13008,plain,
% 2.42/2.66 (s(s(z)) = elem!1),
% 2.42/2.66 inference(transitivity,[status(thm)],[87, 13007, 850])).
% 2.42/2.66 tff(13009,plain,
% 2.42/2.66 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13008, 13005])).
% 2.42/2.66 tff(13010,plain,
% 2.42/2.66 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.42/2.66 inference(transitivity,[status(thm)],[13009, 6857])).
% 2.42/2.66 tff(13011,plain,
% 2.42/2.66 ((s(s(s(elem!1))) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[13010])).
% 2.42/2.66 tff(13012,plain,
% 2.42/2.66 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13011])).
% 2.42/2.66 tff(13013,plain,
% 2.42/2.66 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[1012, 13012])).
% 2.42/2.66 tff(13014,plain,
% 2.42/2.66 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13008, 13005])).
% 2.42/2.66 tff(13015,plain,
% 2.42/2.66 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[13014])).
% 2.42/2.66 tff(13016,plain,
% 2.42/2.66 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13015])).
% 2.42/2.66 tff(13017,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 2.42/2.66 tff(13018,plain,
% 2.42/2.66 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13005, 13008])).
% 2.42/2.67 tff(13019,plain,
% 2.42/2.67 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13018])).
% 2.42/2.67 tff(13020,plain,
% 2.42/2.67 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13008])).
% 2.42/2.67 tff(13021,plain,
% 2.42/2.67 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.42/2.67 inference(symmetry,[status(thm)],[13020])).
% 2.42/2.67 tff(13022,plain,
% 2.42/2.67 (b(s(s(z)), z)),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[624, 13021])).
% 2.42/2.67 tff(13023,plain,
% 2.42/2.67 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13008])).
% 2.42/2.67 tff(13024,plain,
% 2.42/2.67 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.42/2.67 inference(symmetry,[status(thm)],[13023])).
% 2.42/2.67 tff(13025,plain,
% 2.42/2.67 (b(z, s(s(z)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[251, 13024])).
% 2.42/2.67 tff(13026,plain,
% 2.42/2.67 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13005])).
% 2.42/2.67 tff(13027,plain,
% 2.42/2.67 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.42/2.67 inference(symmetry,[status(thm)],[13026])).
% 2.42/2.67 tff(13028,plain,
% 2.42/2.67 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13002])).
% 2.42/2.67 tff(13029,plain,
% 2.42/2.67 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[13028, 972])).
% 2.42/2.67 tff(13030,plain,
% 2.42/2.67 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13029])).
% 2.42/2.67 tff(13031,plain,
% 2.42/2.67 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[1056, 13030])).
% 2.42/2.67 tff(13032,plain,
% 2.42/2.67 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1116, 13017, 13031])).
% 2.42/2.67 tff(13033,plain,
% 2.42/2.67 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[13032, 13027])).
% 2.42/2.67 tff(13034,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13008])).
% 2.42/2.67 tff(13035,plain,
% 2.42/2.67 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 2.42/2.67 inference(symmetry,[status(thm)],[13034])).
% 2.42/2.67 tff(13036,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(z)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[707, 13035])).
% 2.42/2.67 tff(13037,plain,
% 2.42/2.67 (((~![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))))), z)) | (~r(z, s(s(s(z))))) | (~r(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(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(13038,plain,
% 2.42/2.67 (((~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(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(13039,plain,
% 2.42/2.67 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13038])).
% 2.42/2.67 tff(13040,plain,
% 2.42/2.67 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[13039, 13037])).
% 2.42/2.67 tff(13041,plain,
% 2.42/2.67 ((~![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(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)))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(13042,plain,
% 2.42/2.67 ((~![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))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[13041, 13040])).
% 2.42/2.67 tff(13043,plain,
% 2.42/2.67 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[13042, 333, 623])).
% 2.42/2.67 tff(13044,plain,
% 2.42/2.67 (~r(s(s(s(s(s(z))))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[13043, 13036, 13033])).
% 2.42/2.67 tff(13045,plain,
% 2.42/2.67 (((~![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))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(13046,plain,
% 2.42/2.67 ((~![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))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(13047,plain,
% 2.42/2.67 ((~![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)),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[13046, 13045])).
% 2.42/2.67 tff(13048,plain,
% 2.42/2.67 (b(s(s(s(s(s(z))))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 13044])).
% 2.42/2.67 tff(13049,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(13050,plain,
% 2.42/2.67 (((~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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(13051,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[13050])).
% 2.42/2.67 tff(13052,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[13051, 13049])).
% 2.42/2.67 tff(13053,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(13054,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13053, 13052])).
% 2.42/2.68 tff(13055,plain,
% 2.42/2.68 ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13054, 144, 13048])).
% 2.42/2.68 tff(13056,plain,
% 2.42/2.68 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13055, 13025, 13022])).
% 2.42/2.68 tff(13057,plain,
% 2.42/2.68 (~b(s(s(s(elem!1))), elem!1)),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13056, 13019])).
% 2.42/2.68 tff(13058,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1079, 13057, 1012])).
% 2.42/2.68 tff(13059,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 2.42/2.68 tff(13060,plain,
% 2.42/2.68 (((~![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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~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(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13061,plain,
% 2.42/2.68 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13062,plain,
% 2.42/2.68 (((~![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(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13061])).
% 2.42/2.68 tff(13063,plain,
% 2.42/2.68 (((~![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(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(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(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[13062, 13060])).
% 2.42/2.68 tff(13064,plain,
% 2.42/2.68 ((~![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(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(13065,plain,
% 2.42/2.68 ((~![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(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13064, 13063])).
% 2.42/2.68 tff(13066,plain,
% 2.42/2.68 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13065, 333, 435, 13059, 707])).
% 2.42/2.68 tff(13067,plain,
% 2.42/2.68 (s(elem!1) = s(s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13001, 13066])).
% 2.42/2.68 tff(13068,plain,
% 2.42/2.68 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13067])).
% 2.42/2.68 tff(13069,plain,
% 2.42/2.68 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[13068, 972])).
% 2.42/2.68 tff(13070,plain,
% 2.42/2.68 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.42/2.68 inference(symmetry,[status(thm)],[13069])).
% 2.42/2.68 tff(13071,plain,
% 2.42/2.68 (((~![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))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(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(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13072,plain,
% 2.42/2.68 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13073,plain,
% 2.42/2.68 (((~![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(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13072])).
% 2.42/2.68 tff(13074,plain,
% 2.42/2.68 (((~![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(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[13073, 13071])).
% 2.42/2.68 tff(13075,plain,
% 2.42/2.68 ((~![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(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(13076,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13075, 13074])).
% 2.42/2.68 tff(13077,plain,
% 2.42/2.68 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13076, 333, 3065, 13059, 707])).
% 2.42/2.68 tff(13078,plain,
% 2.42/2.68 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1116, 13077, 13017])).
% 2.42/2.68 tff(13079,plain,
% 2.42/2.68 (s(elem!1) = s(s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13078, 13070])).
% 2.42/2.68 tff(13080,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1056, 13079])).
% 2.42/2.68 tff(13081,plain,((~r(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(13082,plain,
% 2.42/2.68 (~r(elem!1, s(s(s(elem!1))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13081, 13058, 1056, 901, 13017, 707, 435])).
% 2.42/2.68 tff(13083,plain,
% 2.42/2.68 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13082, 13016])).
% 2.42/2.68 tff(13084,plain,
% 2.42/2.68 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.42/2.68 inference(commutativity,[status(thm)],[])).
% 2.42/2.68 tff(13085,plain,
% 2.42/2.68 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 2.42/2.68 inference(symmetry,[status(thm)],[13084])).
% 2.42/2.68 tff(13086,plain,
% 2.42/2.68 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13085])).
% 2.42/2.68 tff(13087,plain,
% 2.42/2.68 (~(z = s(s(s(s(s(z))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[1444, 13086])).
% 2.42/2.68 tff(13088,plain,
% 2.42/2.68 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13005])).
% 2.42/2.68 tff(13089,plain,
% 2.42/2.68 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 2.42/2.68 inference(symmetry,[status(thm)],[13088])).
% 2.42/2.68 tff(13090,plain,
% 2.42/2.68 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13089])).
% 2.42/2.68 tff(13091,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13002])).
% 2.42/2.68 tff(13092,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.68 inference(symmetry,[status(thm)],[13091])).
% 2.42/2.68 tff(13093,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13032, 13092])).
% 2.42/2.68 tff(13094,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.42/2.68 tff(13095,plain,
% 2.42/2.68 (((~![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(z, s(s(s(elem!1))))) | (~r(s(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(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13096,plain,
% 2.42/2.68 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13097,plain,
% 2.42/2.68 (((~![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(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(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(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[13096])).
% 2.42/2.68 tff(13098,plain,
% 2.42/2.68 (((~![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(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(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(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[13097, 13095])).
% 2.42/2.68 tff(13099,plain,
% 2.42/2.68 ((~![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(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(13100,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13099, 13098])).
% 2.42/2.68 tff(13101,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13100, 333, 435, 562, 13094, 9749])).
% 2.42/2.68 tff(13102,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(13103,plain,
% 2.42/2.68 (~r(z, s(s(s(elem!1))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[13102, 13093, 562, 435])).
% 2.42/2.68 tff(13104,plain,
% 2.42/2.68 (~r(z, s(s(s(s(s(z))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13103, 13090])).
% 2.42/2.68 tff(13105,plain,
% 2.42/2.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(13106,plain,
% 2.42/2.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(13107,plain,
% 2.42/2.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[13106, 13105])).
% 2.42/2.68 tff(13108,plain,
% 2.42/2.68 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13107, 44, 13104])).
% 2.42/2.69 tff(13109,plain,
% 2.42/2.69 (b(z, s(s(s(s(s(z))))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13108, 13087])).
% 2.42/2.69 tff(13110,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(13111,plain,
% 2.42/2.69 (((~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)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(13112,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z)))))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[13111])).
% 2.42/2.69 tff(13113,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[13112, 13110])).
% 2.42/2.69 tff(13114,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(13115,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(s(s(s(s(z)))))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[13114, 13113])).
% 2.42/2.69 tff(13116,plain,
% 2.42/2.69 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13115, 144, 13109, 13048, 13022])).
% 2.42/2.69 tff(13117,plain,
% 2.42/2.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(13118,plain,
% 2.42/2.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(13119,plain,
% 2.42/2.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[13118, 13117])).
% 2.42/2.69 tff(13120,plain,
% 2.42/2.69 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13119, 44, 13116])).
% 2.42/2.69 tff(13121,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13120, 13083, 13013])).
% 2.42/2.69 tff(13122,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(13123,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13122, 12973, 1056, 1012, 12971, 12999, 251, 624, 623, 562])).
% 2.42/2.69 tff(13124,plain,
% 2.42/2.69 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.42/2.69 inference(symmetry,[status(thm)],[6857])).
% 2.42/2.69 tff(13125,plain,
% 2.42/2.69 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[13124])).
% 2.42/2.69 tff(13126,plain,
% 2.42/2.69 (~(elem!1 = s(s(s(elem!1))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[1012, 13125])).
% 2.42/2.69 tff(13127,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 2.42/2.69 tff(13128,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(13129,plain,
% 2.42/2.69 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(13130,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[13129])).
% 2.42/2.69 tff(13131,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[13130, 13128])).
% 2.42/2.69 tff(13132,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(13133,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[13132, 13131])).
% 2.42/2.69 tff(13134,plain,
% 2.42/2.69 (~b(elem!1, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13133, 144, 624, 2082, 285, 13127])).
% 2.42/2.69 tff(13135,plain,
% 2.42/2.69 ((elem!1 = s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1054, 44, 13134])).
% 2.42/2.69 tff(13136,plain,
% 2.42/2.69 (r(elem!1, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13135, 13126])).
% 2.42/2.69 tff(13137,plain,
% 2.42/2.69 (~r(s(elem!1), s(s(s(z))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13065, 333, 435, 13136, 707])).
% 2.42/2.69 tff(13138,plain,
% 2.42/2.69 (s(elem!1) = s(s(s(z)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[13001, 13137])).
% 2.51/2.70 tff(13139,plain,
% 2.51/2.70 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13138])).
% 2.51/2.70 tff(13140,plain,
% 2.51/2.70 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13139])).
% 2.51/2.70 tff(13141,plain,
% 2.51/2.70 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.51/2.70 inference(symmetry,[status(thm)],[13140])).
% 2.51/2.70 tff(13142,plain,
% 2.51/2.70 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13141])).
% 2.51/2.70 tff(13143,plain,
% 2.51/2.70 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.51/2.70 inference(symmetry,[status(thm)],[13142])).
% 2.51/2.70 tff(13144,plain,
% 2.51/2.70 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13138])).
% 2.51/2.70 tff(13145,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13146,plain,
% 2.51/2.70 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13147,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13146])).
% 2.51/2.70 tff(13148,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(transitivity,[status(thm)],[13147, 13145])).
% 2.51/2.70 tff(13149,plain,
% 2.51/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.51/2.70 inference(quant_inst,[status(thm)],[])).
% 2.51/2.70 tff(13150,plain,
% 2.51/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[13149, 13148])).
% 2.51/2.70 tff(13151,plain,
% 2.51/2.70 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[13150, 144, 3584, 2082, 56])).
% 2.51/2.70 tff(13152,plain,
% 2.51/2.70 (~b(s(s(s(elem!1))), elem!1)),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[13151, 13127])).
% 2.51/2.70 tff(13153,plain,
% 2.51/2.70 (r(s(s(s(elem!1))), elem!1)),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[1079, 13152, 1012])).
% 2.51/2.70 tff(13154,plain,
% 2.51/2.70 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~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))))))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13155,plain,
% 2.51/2.70 (((~![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), elem!1)) | (~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), elem!1)) | (~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)))))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13154])).
% 2.51/2.70 tff(13156,plain,
% 2.51/2.70 (((~![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), elem!1)) | (~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), elem!1)) | (~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))))))),
% 2.51/2.70 inference(transitivity,[status(thm)],[13155, 1081])).
% 2.51/2.70 tff(13157,plain,
% 2.51/2.70 ((~![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), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.51/2.70 inference(quant_inst,[status(thm)],[])).
% 2.51/2.70 tff(13158,plain,
% 2.51/2.70 ((~![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(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[13157, 13156])).
% 2.51/2.70 tff(13159,plain,
% 2.51/2.70 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[13158, 333, 435, 13153, 13136])).
% 2.51/2.70 tff(13160,plain,
% 2.51/2.70 (b(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[1067, 13159, 1056])).
% 2.51/2.70 tff(13161,plain,
% 2.51/2.70 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[13160, 13144])).
% 2.51/2.70 tff(13162,plain,
% 2.51/2.70 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[13161, 13143])).
% 2.51/2.70 tff(13163,plain,
% 2.51/2.70 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13141])).
% 2.51/2.70 tff(13164,plain,
% 2.51/2.70 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.51/2.70 inference(symmetry,[status(thm)],[13163])).
% 2.51/2.70 tff(13165,plain,
% 2.51/2.70 (b(s(s(s(s(s(z))))), s(z))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[3584, 13164])).
% 2.51/2.70 tff(13166,plain,
% 2.51/2.70 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(elem!1))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13141])).
% 2.51/2.70 tff(13167,plain,
% 2.51/2.70 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.51/2.70 inference(symmetry,[status(thm)],[13166])).
% 2.51/2.70 tff(13168,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13169,plain,
% 2.51/2.70 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13170,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13169])).
% 2.51/2.70 tff(13171,plain,
% 2.51/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(transitivity,[status(thm)],[13170, 13168])).
% 2.51/2.70 tff(13172,plain,
% 2.51/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.51/2.70 inference(quant_inst,[status(thm)],[])).
% 2.51/2.70 tff(13173,plain,
% 2.51/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.51/2.70 inference(modus_ponens,[status(thm)],[13172, 13171])).
% 2.51/2.70 tff(13174,plain,
% 2.51/2.70 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[13173, 144, 490, 3584, 285])).
% 2.51/2.70 tff(13175,plain,
% 2.51/2.70 (~b(s(s(s(elem!1))), z)),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[13174, 13127])).
% 2.51/2.70 tff(13176,plain,
% 2.51/2.70 (r(s(s(s(elem!1))), z)),
% 2.51/2.70 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 13175])).
% 2.51/2.70 tff(13177,plain,
% 2.51/2.70 (((~![X0: $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), z)) | (~r(z, 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), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13178,plain,
% 2.51/2.70 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.51/2.70 inference(rewrite,[status(thm)],[])).
% 2.51/2.70 tff(13179,plain,
% 2.51/2.70 (((~![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(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), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))))),
% 2.51/2.70 inference(monotonicity,[status(thm)],[13178])).
% 2.51/2.70 tff(13180,plain,
% 2.51/2.70 (((~![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(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), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.51/2.70 inference(transitivity,[status(thm)],[13179, 13177])).
% 2.51/2.70 tff(13181,plain,
% 2.51/2.70 ((~![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(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.51/2.70 inference(quant_inst,[status(thm)],[])).
% 2.51/2.70 tff(13182,plain,
% 2.51/2.70 ((~![X0: $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), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))),
% 2.51/2.71 inference(modus_ponens,[status(thm)],[13181, 13180])).
% 2.51/2.71 tff(13183,plain,
% 2.51/2.71 (~r(s(z), s(s(s(elem!1))))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13182, 333, 323, 562, 13176])).
% 2.51/2.71 tff(13184,plain,
% 2.51/2.71 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[3089, 44, 13183])).
% 2.51/2.71 tff(13185,plain,
% 2.51/2.71 (b(s(z), s(s(s(elem!1))))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13184, 3064])).
% 2.51/2.71 tff(13186,plain,
% 2.51/2.71 (b(s(z), s(s(s(s(s(z))))))),
% 2.51/2.71 inference(modus_ponens,[status(thm)],[13185, 13167])).
% 2.51/2.71 tff(13187,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13188,plain,
% 2.51/2.71 (((~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(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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13189,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[13188])).
% 2.51/2.71 tff(13190,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.71 inference(transitivity,[status(thm)],[13189, 13187])).
% 2.51/2.71 tff(13191,plain,
% 2.51/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 2.51/2.71 inference(quant_inst,[status(thm)],[])).
% 2.51/2.71 tff(13192,plain,
% 2.51/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.51/2.71 inference(modus_ponens,[status(thm)],[13191, 13190])).
% 2.51/2.71 tff(13193,plain,
% 2.51/2.71 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13192, 144, 56])).
% 2.51/2.71 tff(13194,plain,
% 2.51/2.71 ($false),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13193, 13186, 13165, 13162])).
% 2.51/2.71 tff(13195,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.71 tff(13196,plain,
% 2.51/2.71 (~b(s(s(s(elem!1))), s(z))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13195, 13123, 12967, 12973, 1056, 12999, 12971, 1012, 12933, 562, 624, 2082, 285, 490])).
% 2.51/2.71 tff(13197,plain,
% 2.51/2.71 (r(s(s(s(elem!1))), s(z))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[1101, 13196])).
% 2.51/2.71 tff(13198,plain,
% 2.51/2.71 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[982])).
% 2.51/2.71 tff(13199,plain,
% 2.51/2.71 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[13198])).
% 2.51/2.71 tff(13200,plain,
% 2.51/2.71 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.51/2.71 inference(symmetry,[status(thm)],[13199])).
% 2.51/2.71 tff(13201,plain,
% 2.51/2.71 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[13200])).
% 2.51/2.71 tff(13202,plain,
% 2.51/2.71 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.51/2.71 inference(symmetry,[status(thm)],[13201])).
% 2.51/2.71 tff(13203,plain,
% 2.51/2.71 (r(s(s(s(s(s(z))))), s(z))),
% 2.51/2.71 inference(modus_ponens,[status(thm)],[1024, 13202])).
% 2.51/2.71 tff(13204,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.51/2.71 tff(13205,plain,
% 2.51/2.71 ($false),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13204, 13203])).
% 2.51/2.71 tff(13206,plain,(r(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(elem!1) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.71 tff(13207,plain,
% 2.51/2.71 (r(s(s(s(s(s(z))))), s(z))),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13206, 13197, 12975])).
% 2.51/2.71 tff(13208,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.51/2.71 tff(13209,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.51/2.71 tff(13210,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13211,plain,
% 2.51/2.71 (((~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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13212,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[13211])).
% 2.51/2.71 tff(13213,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.51/2.71 inference(transitivity,[status(thm)],[13212, 13210])).
% 2.51/2.71 tff(13214,plain,
% 2.51/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.51/2.71 inference(quant_inst,[status(thm)],[])).
% 2.51/2.71 tff(13215,plain,
% 2.51/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.51/2.71 inference(modus_ponens,[status(thm)],[13214, 13213])).
% 2.51/2.71 tff(13216,plain,
% 2.51/2.71 ($false),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13215, 333, 323, 623, 13209, 13208])).
% 2.51/2.71 tff(13217,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.71 tff(13218,plain,
% 2.51/2.71 (~r(s(s(s(s(s(z))))), z)),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13217, 13207, 623, 12933])).
% 2.51/2.71 tff(13219,plain,
% 2.51/2.71 (b(s(s(s(s(s(z))))), z)),
% 2.51/2.71 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 13218])).
% 2.51/2.71 tff(13220,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13221,plain,
% 2.51/2.71 (((~b(z, s(z))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.71 inference(rewrite,[status(thm)],[])).
% 2.51/2.71 tff(13222,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.51/2.71 inference(monotonicity,[status(thm)],[13221])).
% 2.51/2.71 tff(13223,plain,
% 2.51/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.72 inference(transitivity,[status(thm)],[13222, 13220])).
% 2.51/2.72 tff(13224,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.51/2.72 inference(quant_inst,[status(thm)],[])).
% 2.51/2.72 tff(13225,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13224, 13223])).
% 2.51/2.72 tff(13226,plain,
% 2.51/2.72 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13225, 144, 490, 285, 12967, 13219])).
% 2.51/2.72 tff(13227,plain,
% 2.51/2.72 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13226, 12988])).
% 2.51/2.72 tff(13228,plain,
% 2.51/2.72 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[9560, 13227, 12986])).
% 2.51/2.72 tff(13229,plain,
% 2.51/2.72 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13228, 12980])).
% 2.51/2.72 tff(13230,plain,
% 2.51/2.72 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[12975])).
% 2.51/2.72 tff(13231,plain,
% 2.51/2.72 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13230])).
% 2.51/2.72 tff(13232,plain,
% 2.51/2.72 (s(s(z)) = elem!1),
% 2.51/2.72 inference(transitivity,[status(thm)],[87, 13231, 850])).
% 2.51/2.72 tff(13233,plain,
% 2.51/2.72 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.51/2.72 inference(monotonicity,[status(thm)],[12978, 13232])).
% 2.51/2.72 tff(13234,plain,
% 2.51/2.72 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13233])).
% 2.51/2.72 tff(13235,plain,
% 2.51/2.72 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.51/2.72 inference(monotonicity,[status(thm)],[12978, 13232])).
% 2.51/2.72 tff(13236,plain,
% 2.51/2.72 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13235])).
% 2.51/2.72 tff(13237,plain,
% 2.51/2.72 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[12978])).
% 2.51/2.72 tff(13238,plain,
% 2.51/2.72 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13237])).
% 2.51/2.72 tff(13239,plain,
% 2.51/2.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13123, 13238])).
% 2.51/2.72 tff(13240,plain,
% 2.51/2.72 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13232])).
% 2.51/2.72 tff(13241,plain,
% 2.51/2.72 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13240])).
% 2.51/2.72 tff(13242,plain,
% 2.51/2.72 (b(z, s(s(z)))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[251, 13241])).
% 2.51/2.72 tff(13243,plain,
% 2.51/2.72 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13232])).
% 2.51/2.72 tff(13244,plain,
% 2.51/2.72 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13243])).
% 2.51/2.72 tff(13245,plain,
% 2.51/2.72 (b(s(s(z)), s(s(s(z))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[2082, 13244])).
% 2.51/2.72 tff(13246,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13247,plain,
% 2.51/2.72 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13248,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13247])).
% 2.51/2.72 tff(13249,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.51/2.72 inference(transitivity,[status(thm)],[13248, 13246])).
% 2.51/2.72 tff(13250,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.51/2.72 inference(quant_inst,[status(thm)],[])).
% 2.51/2.72 tff(13251,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13250, 13249])).
% 2.51/2.72 tff(13252,plain,
% 2.51/2.72 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13251, 144, 13245])).
% 2.51/2.72 tff(13253,plain,
% 2.51/2.72 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13252, 13219, 13242, 13239])).
% 2.51/2.72 tff(13254,plain,
% 2.51/2.72 (~b(s(s(s(elem!1))), elem!1)),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13253, 13236])).
% 2.51/2.72 tff(13255,plain,
% 2.51/2.72 (r(s(s(s(elem!1))), elem!1)),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[1079, 13254, 1012])).
% 2.51/2.72 tff(13256,plain,
% 2.51/2.72 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13255, 13234])).
% 2.51/2.72 tff(13257,plain,
% 2.51/2.72 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13232])).
% 2.51/2.72 tff(13258,plain,
% 2.51/2.72 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13257])).
% 2.51/2.72 tff(13259,plain,
% 2.51/2.72 (r(s(s(s(z))), s(s(z)))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[12971, 13258])).
% 2.51/2.72 tff(13260,plain,
% 2.51/2.72 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13232, 12978])).
% 2.51/2.72 tff(13261,plain,
% 2.51/2.72 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.51/2.72 inference(transitivity,[status(thm)],[13260, 6857])).
% 2.51/2.72 tff(13262,plain,
% 2.51/2.72 ((s(s(s(elem!1))) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.51/2.72 inference(symmetry,[status(thm)],[13261])).
% 2.51/2.72 tff(13263,plain,
% 2.51/2.72 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13262])).
% 2.51/2.72 tff(13264,plain,
% 2.51/2.72 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[1012, 13263])).
% 2.51/2.72 tff(13265,plain,
% 2.51/2.72 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13232])).
% 2.51/2.72 tff(13266,plain,
% 2.51/2.72 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.51/2.72 inference(symmetry,[status(thm)],[13265])).
% 2.51/2.72 tff(13267,plain,
% 2.51/2.72 (b(s(s(z)), z)),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[624, 13266])).
% 2.51/2.72 tff(13268,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13269,plain,
% 2.51/2.72 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), 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(s(z))), z)) | (~b(s(s(z)), s(s(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))))))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13270,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13269])).
% 2.51/2.72 tff(13271,plain,
% 2.51/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.51/2.72 inference(transitivity,[status(thm)],[13270, 13268])).
% 2.51/2.72 tff(13272,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), 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))))))))),
% 2.51/2.72 inference(quant_inst,[status(thm)],[])).
% 2.51/2.72 tff(13273,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13272, 13271])).
% 2.51/2.72 tff(13274,plain,
% 2.51/2.72 ((~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)))))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13273, 144, 285, 13245])).
% 2.51/2.72 tff(13275,plain,
% 2.51/2.72 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13274, 13239, 13267])).
% 2.51/2.72 tff(13276,plain,
% 2.51/2.72 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13119, 44, 13275])).
% 2.51/2.72 tff(13277,plain,
% 2.51/2.72 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13276, 13264])).
% 2.51/2.72 tff(13278,plain,
% 2.51/2.72 (((~![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(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))))))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13279,plain,
% 2.51/2.72 (((~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))))))))),
% 2.51/2.72 inference(rewrite,[status(thm)],[])).
% 2.51/2.72 tff(13280,plain,
% 2.51/2.72 (((~![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(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)))))))))),
% 2.51/2.72 inference(monotonicity,[status(thm)],[13279])).
% 2.51/2.72 tff(13281,plain,
% 2.51/2.72 (((~![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(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))))))))),
% 2.51/2.72 inference(transitivity,[status(thm)],[13280, 13278])).
% 2.51/2.72 tff(13282,plain,
% 2.51/2.72 ((~![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(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)))))),
% 2.51/2.72 inference(quant_inst,[status(thm)],[])).
% 2.51/2.72 tff(13283,plain,
% 2.51/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.51/2.72 inference(modus_ponens,[status(thm)],[13282, 13281])).
% 2.51/2.72 tff(13284,plain,
% 2.51/2.72 ($false),
% 2.51/2.72 inference(unit_resolution,[status(thm)],[13283, 333, 13277, 13259, 13256, 13229])).
% 2.51/2.72 tff(13285,plain,((~b(s(s(s(z))), z)) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.73 tff(13286,plain,
% 2.51/2.73 (s(elem!1) = s(s(s(elem!1)))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13285, 12966, 490, 12930, 251, 624, 1012, 562, 12949, 12964, 491, 488])).
% 2.51/2.73 tff(13287,plain,
% 2.51/2.73 (s(s(s(elem!1))) = s(elem!1)),
% 2.51/2.73 inference(symmetry,[status(thm)],[13286])).
% 2.51/2.73 tff(13288,plain,
% 2.51/2.73 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[12963])).
% 2.51/2.73 tff(13289,plain,
% 2.51/2.73 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.51/2.73 inference(symmetry,[status(thm)],[13288])).
% 2.51/2.73 tff(13290,plain,
% 2.51/2.73 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13289])).
% 2.51/2.73 tff(13291,plain,
% 2.51/2.73 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 2.51/2.73 inference(transitivity,[status(thm)],[13290, 13287, 12963])).
% 2.51/2.73 tff(13292,plain,
% 2.51/2.73 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13291])).
% 2.51/2.73 tff(13293,plain,
% 2.51/2.73 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 2.51/2.73 inference(symmetry,[status(thm)],[13292])).
% 2.51/2.73 tff(13294,plain,
% 2.51/2.73 (s(s(z)) = s(s(s(s(z))))),
% 2.51/2.73 inference(transitivity,[status(thm)],[87, 13293, 238])).
% 2.51/2.73 tff(13295,plain,
% 2.51/2.73 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13294])).
% 2.51/2.73 tff(13296,plain,
% 2.51/2.73 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 2.51/2.73 inference(symmetry,[status(thm)],[13295])).
% 2.51/2.73 tff(13297,plain,
% 2.51/2.73 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 2.51/2.73 inference(symmetry,[status(thm)],[183])).
% 2.51/2.73 tff(13298,plain,
% 2.51/2.73 (s(s(s(z))) = s(z)),
% 2.51/2.73 inference(transitivity,[status(thm)],[13297, 13296, 80])).
% 2.51/2.73 tff(13299,plain,
% 2.51/2.73 ($false),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[166, 13298])).
% 2.51/2.73 tff(13300,plain,(b(z, s(s(s(z)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.73 tff(13301,plain,
% 2.51/2.73 (b(z, s(s(s(z))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13300, 12929, 624, 251, 12915, 12913, 12837, 12835, 491])).
% 2.51/2.73 tff(13302,plain,
% 2.51/2.73 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[12833, 175])).
% 2.51/2.73 tff(13303,plain,
% 2.51/2.73 (~(s(s(s(z))) = elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[12214, 13302])).
% 2.51/2.73 tff(13304,plain,
% 2.51/2.73 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[12833])).
% 2.51/2.73 tff(13305,plain,
% 2.51/2.73 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13304])).
% 2.51/2.73 tff(13306,plain,
% 2.51/2.73 (~(s(elem!1) = s(s(s(z))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[244, 13305])).
% 2.51/2.73 tff(13307,plain,
% 2.51/2.73 (~b(s(s(s(z))), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[10565, 285, 624, 251])).
% 2.51/2.73 tff(13308,plain,
% 2.51/2.73 (r(s(s(s(z))), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[704, 13307, 698])).
% 2.51/2.73 tff(13309,plain,
% 2.51/2.73 (~b(s(elem!1), s(s(s(z))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[1802, 285, 491, 284])).
% 2.51/2.73 tff(13310,plain,
% 2.51/2.73 (r(s(elem!1), s(s(s(z))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[965, 13309, 960])).
% 2.51/2.73 tff(13311,plain,
% 2.51/2.73 ($false),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[1694, 13310, 13308, 435, 722])).
% 2.51/2.73 tff(13312,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.73 tff(13313,plain,
% 2.51/2.73 (~b(s(s(s(z))), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13312, 12823, 12838, 13306, 13303, 491, 13301, 624, 251])).
% 2.51/2.73 tff(13314,plain,
% 2.51/2.73 (r(s(s(s(z))), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[396, 13313])).
% 2.51/2.73 tff(13315,plain,
% 2.51/2.73 (~b(s(z), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[7093, 12913, 286, 12832])).
% 2.51/2.73 tff(13316,plain,
% 2.51/2.73 (r(s(z), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[348, 13315])).
% 2.51/2.73 tff(13317,plain,
% 2.51/2.73 (~r(s(z), s(s(s(z))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[1979, 333, 13316, 12835, 13314])).
% 2.51/2.73 tff(13318,plain,
% 2.51/2.73 (b(s(z), s(s(s(z))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[172, 13317])).
% 2.51/2.73 tff(13319,plain,
% 2.51/2.73 (~r(s(s(s(z))), s(z))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[8030, 13314, 12835, 13316])).
% 2.51/2.73 tff(13320,plain,
% 2.51/2.73 (b(s(s(s(z))), s(z))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[2794, 13319])).
% 2.51/2.73 tff(13321,plain,
% 2.51/2.73 ($false),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[2176, 144, 12913, 13301, 13320, 13318])).
% 2.51/2.73 tff(13322,plain,((s(z) = elem!1) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.73 tff(13323,plain,
% 2.51/2.73 (s(z) = elem!1),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13322, 491, 12152, 12821, 12805, 50, 12004, 12013, 51, 1, 902])).
% 2.51/2.73 tff(13324,plain,
% 2.51/2.73 (~b(s(elem!1), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[916, 12821, 12152, 491])).
% 2.51/2.73 tff(13325,plain,
% 2.51/2.73 (r(s(elem!1), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[448, 13324, 907])).
% 2.51/2.73 tff(13326,plain,
% 2.51/2.73 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[12698, 563, 2484, 435])).
% 2.51/2.73 tff(13327,plain,
% 2.51/2.73 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[472, 13326, 4762])).
% 2.51/2.73 tff(13328,plain,
% 2.51/2.73 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.51/2.73 inference(commutativity,[status(thm)],[])).
% 2.51/2.73 tff(13329,plain,
% 2.51/2.73 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(symmetry,[status(thm)],[13328])).
% 2.51/2.73 tff(13330,plain,
% 2.51/2.73 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(transitivity,[status(thm)],[10045, 13329])).
% 2.51/2.73 tff(13331,plain,
% 2.51/2.73 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13330])).
% 2.51/2.73 tff(13332,plain,
% 2.51/2.73 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[244, 13331])).
% 2.51/2.73 tff(13333,plain,
% 2.51/2.73 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[542, 12794, 2698])).
% 2.51/2.73 tff(13334,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.51/2.73 tff(13335,plain,
% 2.51/2.73 (~b(z, s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[12069, 546, 286, 491])).
% 2.51/2.73 tff(13336,plain,
% 2.51/2.73 (r(z, s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[583, 13335])).
% 2.51/2.73 tff(13337,plain,
% 2.51/2.73 (~r(s(s(elem!1)), s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[5505, 5497, 435, 13336])).
% 2.51/2.73 tff(13338,plain,
% 2.51/2.73 (b(s(s(elem!1)), s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[1283, 13337, 2854])).
% 2.51/2.73 tff(13339,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13340,plain,
% 2.51/2.73 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13341,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13340])).
% 2.51/2.73 tff(13342,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.73 inference(transitivity,[status(thm)],[13341, 13339])).
% 2.51/2.73 tff(13343,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.73 inference(quant_inst,[status(thm)],[])).
% 2.51/2.73 tff(13344,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[13343, 13342])).
% 2.51/2.73 tff(13345,plain,
% 2.51/2.73 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13344, 144, 13338, 546, 450])).
% 2.51/2.73 tff(13346,plain,
% 2.51/2.73 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[7819, 44, 13345, 13334])).
% 2.51/2.73 tff(13347,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13348,plain,
% 2.51/2.73 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13349,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13348])).
% 2.51/2.73 tff(13350,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(transitivity,[status(thm)],[13349, 13347])).
% 2.51/2.73 tff(13351,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(quant_inst,[status(thm)],[])).
% 2.51/2.73 tff(13352,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[13351, 13350])).
% 2.51/2.73 tff(13353,plain,
% 2.51/2.73 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13352, 144, 491, 13338, 286, 546])).
% 2.51/2.73 tff(13354,plain,
% 2.51/2.73 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[2758, 13353, 2725])).
% 2.51/2.73 tff(13355,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13356,plain,
% 2.51/2.73 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13357,plain,
% 2.51/2.73 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13356])).
% 2.51/2.73 tff(13358,plain,
% 2.51/2.73 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.73 inference(transitivity,[status(thm)],[13357, 13355])).
% 2.51/2.73 tff(13359,plain,
% 2.51/2.73 ((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)))),
% 2.51/2.73 inference(quant_inst,[status(thm)],[])).
% 2.51/2.73 tff(13360,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[13359, 13358])).
% 2.51/2.73 tff(13361,plain,
% 2.51/2.73 ($false),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13360, 333, 13354, 51, 5497, 13346])).
% 2.51/2.73 tff(13362,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.73 tff(13363,plain,
% 2.51/2.73 (~r(s(s(elem!1)), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13362, 13333, 13332, 10047, 51, 13327, 491, 286, 2854, 435])).
% 2.51/2.73 tff(13364,plain,
% 2.51/2.73 (b(s(s(elem!1)), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[5509, 13363])).
% 2.51/2.73 tff(13365,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13366,plain,
% 2.51/2.73 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.51/2.73 inference(rewrite,[status(thm)],[])).
% 2.51/2.73 tff(13367,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.51/2.73 inference(monotonicity,[status(thm)],[13366])).
% 2.51/2.73 tff(13368,plain,
% 2.51/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.51/2.73 inference(transitivity,[status(thm)],[13367, 13365])).
% 2.51/2.73 tff(13369,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.51/2.73 inference(quant_inst,[status(thm)],[])).
% 2.51/2.73 tff(13370,plain,
% 2.51/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.51/2.73 inference(modus_ponens,[status(thm)],[13369, 13368])).
% 2.51/2.73 tff(13371,plain,
% 2.51/2.73 (~b(s(s(elem!1)), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[13370, 144, 251, 624, 13364])).
% 2.51/2.73 tff(13372,plain,
% 2.51/2.73 (~r(s(s(s(z))), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[6447, 13363, 57])).
% 2.51/2.73 tff(13373,plain,
% 2.51/2.73 (b(s(s(s(z))), z)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[396, 13372])).
% 2.51/2.73 tff(13374,plain,
% 2.51/2.73 (~b(s(s(s(z))), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[10565, 13373, 624, 251])).
% 2.51/2.73 tff(13375,plain,
% 2.51/2.73 (r(s(s(s(z))), elem!1)),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[704, 13374, 4798])).
% 2.51/2.73 tff(13376,plain,
% 2.51/2.73 (~b(z, s(elem!1))),
% 2.51/2.73 inference(unit_resolution,[status(thm)],[12069, 13333, 286, 491])).
% 2.51/2.74 tff(13377,plain,
% 2.51/2.74 (r(z, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[583, 13376])).
% 2.51/2.74 tff(13378,plain,
% 2.51/2.74 (b(z, s(z))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[9366, 57, 251])).
% 2.51/2.74 tff(13379,plain,
% 2.51/2.74 (~b(z, s(s(s(z))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[9320, 13375, 1, 491, 13378, 6022, 11786, 13373])).
% 2.51/2.74 tff(13380,plain,
% 2.51/2.74 (r(z, s(s(s(z))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[619, 13379])).
% 2.51/2.74 tff(13381,plain,
% 2.51/2.74 (~r(s(elem!1), s(s(s(z))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[1929, 13380, 13377, 13375])).
% 2.51/2.74 tff(13382,plain,
% 2.51/2.74 (b(s(elem!1), s(s(s(z))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[965, 13381, 11786])).
% 2.51/2.74 tff(13383,plain,
% 2.51/2.74 (b(s(elem!1), s(s(elem!1)))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13382, 2501])).
% 2.51/2.74 tff(13384,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13385,plain,
% 2.51/2.74 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13386,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13385])).
% 2.51/2.74 tff(13387,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13386, 13384])).
% 2.51/2.74 tff(13388,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.51/2.74 inference(quant_inst,[status(thm)],[])).
% 2.51/2.74 tff(13389,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13388, 13387])).
% 2.51/2.74 tff(13390,plain,
% 2.51/2.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13389, 144, 286, 13383, 13333, 13364])).
% 2.51/2.74 tff(13391,plain,
% 2.51/2.74 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[2758, 13390, 10047])).
% 2.51/2.74 tff(13392,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13393,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.74 inference(quant_inst,[status(thm)],[])).
% 2.51/2.74 tff(13394,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13393, 13392])).
% 2.51/2.74 tff(13395,plain,
% 2.51/2.74 ($false),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13394, 333, 563, 4627, 3654, 2484])).
% 2.51/2.74 tff(13396,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.74 tff(13397,plain,
% 2.51/2.74 (~r(s(s(elem!1)), elem!1)),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13396, 13391, 2484, 563])).
% 2.51/2.74 tff(13398,plain,
% 2.51/2.74 ($false),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[1260, 44, 13397, 4575, 13371])).
% 2.51/2.74 tff(13399,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(z) = elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.74 tff(13400,plain,
% 2.51/2.74 (~r(elem!1, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13399, 12821, 12805, 12004, 12152, 13323, 1, 491, 51, 2727, 13325])).
% 2.51/2.74 tff(13401,plain,
% 2.51/2.74 (b(elem!1, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[560, 13400, 902])).
% 2.51/2.74 tff(13402,plain,
% 2.51/2.74 (elem!1 = s(z)),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13323, 53])).
% 2.51/2.74 tff(13403,plain,
% 2.51/2.74 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13323])).
% 2.51/2.74 tff(13404,plain,
% 2.51/2.74 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13403, 1218])).
% 2.51/2.74 tff(13405,plain,
% 2.51/2.74 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13404])).
% 2.51/2.74 tff(13406,plain,
% 2.51/2.74 (~(elem!1 = s(s(elem!1)))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[107, 13405])).
% 2.51/2.74 tff(13407,plain,
% 2.51/2.74 (s(s(z)) = s(elem!1)),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13323])).
% 2.51/2.74 tff(13408,plain,
% 2.51/2.74 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13407])).
% 2.51/2.74 tff(13409,plain,
% 2.51/2.74 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13408, 174])).
% 2.51/2.74 tff(13410,plain,
% 2.51/2.74 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13409, 175])).
% 2.51/2.74 tff(13411,plain,
% 2.51/2.74 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13410])).
% 2.51/2.74 tff(13412,plain,
% 2.51/2.74 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[1446, 13411])).
% 2.51/2.74 tff(13413,plain,
% 2.51/2.74 (b(s(z), z)),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[3965, 13323, 12152])).
% 2.51/2.74 tff(13414,plain,
% 2.51/2.74 (b(s(z), s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[4682, 13401, 13323])).
% 2.51/2.74 tff(13415,plain,
% 2.51/2.74 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[3222, 13414, 12805, 50, 13413])).
% 2.51/2.74 tff(13416,plain,
% 2.51/2.74 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[472, 13415, 13412])).
% 2.51/2.74 tff(13417,plain,
% 2.51/2.74 (~(s(elem!1) = elem!1)),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[5813, 1221])).
% 2.51/2.74 tff(13418,plain,
% 2.51/2.74 (~(elem!1 = s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[1569, 13417])).
% 2.51/2.74 tff(13419,plain,
% 2.51/2.74 (~r(elem!1, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[12698, 2484, 435, 525])).
% 2.51/2.74 tff(13420,plain,
% 2.51/2.74 (b(elem!1, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[560, 13419, 13418])).
% 2.51/2.74 tff(13421,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13422,plain,
% 2.51/2.74 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13423,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13422])).
% 2.51/2.74 tff(13424,plain,
% 2.51/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13423, 13421])).
% 2.51/2.74 tff(13425,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.51/2.74 inference(quant_inst,[status(thm)],[])).
% 2.51/2.74 tff(13426,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13425, 13424])).
% 2.51/2.74 tff(13427,plain,
% 2.51/2.74 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13426, 144, 624, 491, 1249])).
% 2.51/2.74 tff(13428,plain,
% 2.51/2.74 (~b(elem!1, s(s(elem!1)))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13427, 13420])).
% 2.51/2.74 tff(13429,plain,
% 2.51/2.74 (r(elem!1, s(s(elem!1)))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[2522, 13428, 1221])).
% 2.51/2.74 tff(13430,plain,
% 2.51/2.74 (((~![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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13431,plain,
% 2.51/2.74 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.74 inference(rewrite,[status(thm)],[])).
% 2.51/2.74 tff(13432,plain,
% 2.51/2.74 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[13431])).
% 2.51/2.74 tff(13433,plain,
% 2.51/2.74 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.74 inference(transitivity,[status(thm)],[13432, 13430])).
% 2.51/2.74 tff(13434,plain,
% 2.51/2.74 ((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.74 inference(quant_inst,[status(thm)],[])).
% 2.51/2.74 tff(13435,plain,
% 2.51/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[13434, 13433])).
% 2.51/2.74 tff(13436,plain,
% 2.51/2.74 ($false),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13435, 333, 435, 13429, 2484, 525])).
% 2.51/2.74 tff(13437,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.74 tff(13438,plain,
% 2.51/2.74 (~b(s(s(elem!1)), s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13437, 13416, 12004, 12152, 13406, 13325, 491])).
% 2.51/2.74 tff(13439,plain,
% 2.51/2.74 (r(s(s(elem!1)), s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[1283, 13438, 2727])).
% 2.51/2.74 tff(13440,plain,
% 2.51/2.74 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[9387])).
% 2.51/2.74 tff(13441,plain,
% 2.51/2.74 (r(s(s(s(z))), s(elem!1))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[2737, 13440])).
% 2.51/2.74 tff(13442,plain,
% 2.51/2.74 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 2.51/2.74 inference(monotonicity,[status(thm)],[9445])).
% 2.51/2.74 tff(13443,plain,
% 2.51/2.74 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.51/2.74 inference(symmetry,[status(thm)],[13442])).
% 2.51/2.74 tff(13444,plain,
% 2.51/2.74 (r(s(s(s(z))), s(s(z)))),
% 2.51/2.74 inference(modus_ponens,[status(thm)],[3003, 13443])).
% 2.51/2.74 tff(13445,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.51/2.74 tff(13446,plain,
% 2.51/2.74 ($false),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13445, 13444])).
% 2.51/2.74 tff(13447,plain,(r(s(s(s(z))), s(s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.74 tff(13448,plain,
% 2.51/2.74 (r(s(s(s(z))), s(s(z)))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[13447, 13441, 709])).
% 2.51/2.74 tff(13449,plain,
% 2.51/2.74 (~r(z, s(elem!1))),
% 2.51/2.74 inference(unit_resolution,[status(thm)],[5505, 9429, 435, 2737])).
% 2.51/2.74 tff(13450,plain,
% 2.51/2.75 (b(z, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[583, 13449])).
% 2.51/2.75 tff(13451,plain,
% 2.51/2.75 (~b(s(elem!1), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[949, 13450, 624, 547])).
% 2.51/2.75 tff(13452,plain,
% 2.51/2.75 (r(s(elem!1), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[507, 13451])).
% 2.51/2.75 tff(13453,plain,
% 2.51/2.75 (r(s(s(z)), z)),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13452, 9393])).
% 2.51/2.75 tff(13454,plain,
% 2.51/2.75 (((~![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))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13455,plain,
% 2.51/2.75 (((~r(z, s(s(s(s(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13456,plain,
% 2.51/2.75 (((~![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(s(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13455])).
% 2.51/2.75 tff(13457,plain,
% 2.51/2.75 (((~![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(s(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.51/2.75 inference(transitivity,[status(thm)],[13456, 13454])).
% 2.51/2.75 tff(13458,plain,
% 2.51/2.75 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.51/2.75 inference(quant_inst,[status(thm)],[])).
% 2.51/2.75 tff(13459,plain,
% 2.51/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13458, 13457])).
% 2.51/2.75 tff(13460,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13459, 333, 1699, 51, 13453, 13448])).
% 2.51/2.75 tff(13461,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13462,plain,
% 2.51/2.75 (~r(s(s(s(z))), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13461, 13439, 51, 12152, 13402, 13325, 13401])).
% 2.51/2.75 tff(13463,plain,
% 2.51/2.75 (b(s(s(s(z))), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[396, 13462])).
% 2.51/2.75 tff(13464,plain,
% 2.51/2.75 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13323])).
% 2.51/2.75 tff(13465,plain,
% 2.51/2.75 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.51/2.75 inference(transitivity,[status(thm)],[13464, 2])).
% 2.51/2.75 tff(13466,plain,
% 2.51/2.75 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.51/2.75 inference(transitivity,[status(thm)],[13465, 4795])).
% 2.51/2.75 tff(13467,plain,
% 2.51/2.75 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13466])).
% 2.51/2.75 tff(13468,plain,
% 2.51/2.75 (~(s(s(s(z))) = elem!1)),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[166, 13467])).
% 2.51/2.75 tff(13469,plain,
% 2.51/2.75 (~b(s(s(s(z))), elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[10565, 13463, 12152, 12821])).
% 2.51/2.75 tff(13470,plain,
% 2.51/2.75 (r(s(s(s(z))), elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[704, 13469, 13468])).
% 2.51/2.75 tff(13471,plain,
% 2.51/2.75 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13407])).
% 2.51/2.75 tff(13472,plain,
% 2.51/2.75 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13471])).
% 2.51/2.75 tff(13473,plain,
% 2.51/2.75 (~(s(elem!1) = s(s(s(z))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[217, 13472])).
% 2.51/2.75 tff(13474,plain,
% 2.51/2.75 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13465])).
% 2.51/2.75 tff(13475,plain,
% 2.51/2.75 (~(elem!1 = s(s(s(z))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[166, 13474])).
% 2.51/2.75 tff(13476,plain,
% 2.51/2.75 (~b(z, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[949, 13401, 12152, 491])).
% 2.51/2.75 tff(13477,plain,
% 2.51/2.75 (r(z, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[583, 13476])).
% 2.51/2.75 tff(13478,plain,
% 2.51/2.75 (~b(elem!1, s(s(elem!1)))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[5640, 13439, 13325, 13477, 12152])).
% 2.51/2.75 tff(13479,plain,
% 2.51/2.75 (~b(s(z), s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[5343, 13478, 13323])).
% 2.51/2.75 tff(13480,plain,
% 2.51/2.75 (b(s(z), s(s(s(z))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[2082, 5335])).
% 2.51/2.75 tff(13481,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[156, 13480])).
% 2.51/2.75 tff(13482,plain,((~b(elem!1, s(s(s(z))))) | b(s(z), s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13483,plain,
% 2.51/2.75 (~b(elem!1, s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13482, 13479, 13323])).
% 2.51/2.75 tff(13484,plain,
% 2.51/2.75 (r(elem!1, s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[1538, 13483, 13475])).
% 2.51/2.75 tff(13485,plain,
% 2.51/2.75 (~b(z, s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[7329, 13484, 12152, 491, 907, 12821, 13473, 13470, 13463])).
% 2.51/2.75 tff(13486,plain,
% 2.51/2.75 (r(z, s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[619, 13485])).
% 2.51/2.75 tff(13487,plain,
% 2.51/2.75 (r(z, s(s(elem!1)))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[2836, 13486, 13323])).
% 2.51/2.75 tff(13488,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[5627, 333, 13325, 13439, 13477, 13487])).
% 2.51/2.75 tff(13489,plain,((~b(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13490,plain,
% 2.51/2.75 (~b(s(elem!1), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13489, 902, 51, 1, 3, 4])).
% 2.51/2.75 tff(13491,plain,
% 2.51/2.75 (r(s(elem!1), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[507, 13490])).
% 2.51/2.75 tff(13492,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[3827, 333, 509, 2484, 51, 525])).
% 2.51/2.75 tff(13493,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13494,plain,
% 2.51/2.75 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13493, 509, 2484, 51])).
% 2.51/2.75 tff(13495,plain,
% 2.51/2.75 (~r(elem!1, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[2492, 8715, 2484, 51])).
% 2.51/2.75 tff(13496,plain,
% 2.51/2.75 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[4003, 606, 730, 2484, 51, 8715])).
% 2.51/2.75 tff(13497,plain,
% 2.51/2.75 (~b(elem!1, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[5467, 13496, 132, 537, 535])).
% 2.51/2.75 tff(13498,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[560, 13497, 13495, 902])).
% 2.51/2.75 tff(13499,plain,(b(z, elem!1) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13500,plain,
% 2.51/2.75 (b(z, elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13499, 535, 132, 537, 902, 2484, 51, 71])).
% 2.51/2.75 tff(13501,plain,
% 2.51/2.75 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[12207, 6065, 1, 123, 466, 535, 537, 132, 902])).
% 2.51/2.75 tff(13502,plain,
% 2.51/2.75 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[319, 13501])).
% 2.51/2.75 tff(13503,plain,
% 2.51/2.75 (~r(s(z), elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[12172, 13502, 2484, 6065])).
% 2.51/2.75 tff(13504,plain,
% 2.51/2.75 (b(s(z), elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[406, 13503, 706])).
% 2.51/2.75 tff(13505,plain,
% 2.51/2.75 (~b(s(z), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[1602, 13504, 624, 251])).
% 2.51/2.75 tff(13506,plain,
% 2.51/2.75 (r(s(z), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[348, 13505])).
% 2.51/2.75 tff(13507,plain,
% 2.51/2.75 ($false),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[818, 333, 13506, 6065, 2484, 13502])).
% 2.51/2.75 tff(13508,plain,((s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.75 tff(13509,plain,
% 2.51/2.75 (s(z) = elem!1),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13508, 466, 624, 13500, 1, 123, 2484, 535, 537, 132, 902, 12822])).
% 2.51/2.75 tff(13510,plain,
% 2.51/2.75 (s(s(z)) = s(elem!1)),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13509])).
% 2.51/2.75 tff(13511,plain,
% 2.51/2.75 (s(s(s(z))) = s(s(elem!1))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13510])).
% 2.51/2.75 tff(13512,plain,
% 2.51/2.75 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13511])).
% 2.51/2.75 tff(13513,plain,
% 2.51/2.75 (b(s(z), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[3965, 13509, 624])).
% 2.51/2.75 tff(13514,plain,
% 2.51/2.75 (b(z, s(z))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[9366, 13509, 13500])).
% 2.51/2.75 tff(13515,plain,
% 2.51/2.75 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[472, 466, 5464])).
% 2.51/2.75 tff(13516,plain,
% 2.51/2.75 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[542, 535, 537])).
% 2.51/2.75 tff(13517,plain,
% 2.51/2.75 (~b(elem!1, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[5467, 466, 132, 537, 535])).
% 2.51/2.75 tff(13518,plain,
% 2.51/2.75 (r(elem!1, s(elem!1))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[560, 13517, 902])).
% 2.51/2.75 tff(13519,plain,
% 2.51/2.75 (~r(s(s(s(elem!1))), s(z))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[12653, 13509, 2484, 509, 13518, 13516, 13515])).
% 2.51/2.75 tff(13520,plain,
% 2.51/2.75 (b(s(s(s(elem!1))), s(z))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[1101, 13519])).
% 2.51/2.75 tff(13521,plain,
% 2.51/2.75 (b(s(s(s(s(z)))), elem!1)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[3588, 13520, 13509])).
% 2.51/2.75 tff(13522,plain,
% 2.51/2.75 (~b(s(s(s(s(z)))), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[12662, 144, 13500, 624, 13521])).
% 2.51/2.75 tff(13523,plain,
% 2.51/2.75 (r(s(s(s(s(z)))), z)),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[4243, 44, 242, 13522])).
% 2.51/2.75 tff(13524,plain,
% 2.51/2.75 (((~![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(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, 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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13525,plain,
% 2.51/2.75 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13526,plain,
% 2.51/2.75 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13525])).
% 2.51/2.75 tff(13527,plain,
% 2.51/2.75 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(transitivity,[status(thm)],[13526, 13524])).
% 2.51/2.75 tff(13528,plain,
% 2.51/2.75 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.75 inference(quant_inst,[status(thm)],[])).
% 2.51/2.75 tff(13529,plain,
% 2.51/2.75 ((~![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(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13528, 13527])).
% 2.51/2.75 tff(13530,plain,
% 2.51/2.75 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13529, 333, 509, 51, 12719])).
% 2.51/2.75 tff(13531,plain,
% 2.51/2.75 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[3545, 13530, 57])).
% 2.51/2.75 tff(13532,plain,
% 2.51/2.75 (b(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[1067, 13531, 3524])).
% 2.51/2.75 tff(13533,plain,
% 2.51/2.75 (b(s(elem!1), s(s(s(s(z)))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13532, 9536])).
% 2.51/2.75 tff(13534,plain,
% 2.51/2.75 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[3525, 2496])).
% 2.51/2.75 tff(13535,plain,
% 2.51/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, 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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13536,plain,
% 2.51/2.75 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(rewrite,[status(thm)],[])).
% 2.51/2.75 tff(13537,plain,
% 2.51/2.75 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[13536])).
% 2.51/2.75 tff(13538,plain,
% 2.51/2.75 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.75 inference(transitivity,[status(thm)],[13537, 13535])).
% 2.51/2.75 tff(13539,plain,
% 2.51/2.75 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.51/2.75 inference(quant_inst,[status(thm)],[])).
% 2.51/2.75 tff(13540,plain,
% 2.51/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13539, 13538])).
% 2.51/2.75 tff(13541,plain,
% 2.51/2.75 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[13540, 333, 51, 5497, 12719])).
% 2.51/2.75 tff(13542,plain,
% 2.51/2.75 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13541, 4623])).
% 2.51/2.75 tff(13543,plain,
% 2.51/2.75 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[1116, 13542, 4621])).
% 2.51/2.75 tff(13544,plain,
% 2.51/2.75 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13543, 13534])).
% 2.51/2.75 tff(13545,plain,
% 2.51/2.75 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.51/2.75 inference(monotonicity,[status(thm)],[4296])).
% 2.51/2.75 tff(13546,plain,
% 2.51/2.75 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.51/2.75 inference(unit_resolution,[status(thm)],[9528, 333, 51, 5497, 12719])).
% 2.51/2.75 tff(13547,plain,
% 2.51/2.75 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.51/2.75 inference(modus_ponens,[status(thm)],[13546, 13545])).
% 2.51/2.75 tff(13548,plain,
% 2.51/2.75 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[4311, 13547, 4620])).
% 2.51/2.76 tff(13549,plain,
% 2.51/2.76 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13548, 4643])).
% 2.51/2.76 tff(13550,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, 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(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13551,plain,
% 2.51/2.76 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13552,plain,
% 2.51/2.76 (((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13551])).
% 2.51/2.76 tff(13553,plain,
% 2.51/2.76 (((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13552, 13550])).
% 2.51/2.76 tff(13554,plain,
% 2.51/2.76 ((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.51/2.76 inference(quant_inst,[status(thm)],[])).
% 2.51/2.76 tff(13555,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13554, 13553])).
% 2.51/2.76 tff(13556,plain,
% 2.51/2.76 (~r(s(elem!1), s(s(elem!1)))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13555, 333, 509, 51, 5497])).
% 2.51/2.76 tff(13557,plain,
% 2.51/2.76 (b(s(elem!1), s(s(elem!1)))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[2860, 44, 8456, 13556])).
% 2.51/2.76 tff(13558,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13559,plain,
% 2.51/2.76 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13560,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13559])).
% 2.51/2.76 tff(13561,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13560, 13558])).
% 2.51/2.76 tff(13562,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.51/2.76 inference(quant_inst,[status(thm)],[])).
% 2.51/2.76 tff(13563,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13562, 13561])).
% 2.51/2.76 tff(13564,plain,
% 2.51/2.76 ($false),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13563, 144, 13557, 13549, 13544, 13533])).
% 2.51/2.76 tff(13565,plain,((~r(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.76 tff(13566,plain,
% 2.51/2.76 (~r(s(s(elem!1)), z)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13565, 13509, 6691, 4007, 51, 13523, 509])).
% 2.51/2.76 tff(13567,plain,
% 2.51/2.76 (~r(s(s(s(z))), z)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[6447, 13566, 13509])).
% 2.51/2.76 tff(13568,plain,
% 2.51/2.76 (b(s(s(s(z))), z)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[396, 13567])).
% 2.51/2.76 tff(13569,plain,
% 2.51/2.76 (~b(s(s(s(z))), s(z))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[2273, 13568, 13514, 13513])).
% 2.51/2.76 tff(13570,plain,
% 2.51/2.76 (r(s(s(s(z))), s(z))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[2794, 13569])).
% 2.51/2.76 tff(13571,plain,
% 2.51/2.76 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[7093, 13513, 286, 13514])).
% 2.51/2.76 tff(13572,plain,
% 2.51/2.76 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[319, 13571])).
% 2.51/2.76 tff(13573,plain,
% 2.51/2.76 (b(s(s(elem!1)), z)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[5509, 13566])).
% 2.51/2.76 tff(13574,plain,
% 2.51/2.76 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13511])).
% 2.51/2.76 tff(13575,plain,
% 2.51/2.76 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13574])).
% 2.51/2.76 tff(13576,plain,
% 2.51/2.76 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[244, 13575])).
% 2.51/2.76 tff(13577,plain,
% 2.51/2.76 (~b(s(s(elem!1)), elem!1)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13370, 144, 13500, 624, 13573])).
% 2.51/2.76 tff(13578,plain,
% 2.51/2.76 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13509])).
% 2.51/2.76 tff(13579,plain,
% 2.51/2.76 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13578, 1218])).
% 2.51/2.76 tff(13580,plain,
% 2.51/2.76 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.51/2.76 inference(transitivity,[status(thm)],[13579, 4572])).
% 2.51/2.76 tff(13581,plain,
% 2.51/2.76 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13580])).
% 2.51/2.76 tff(13582,plain,
% 2.51/2.76 (~(s(s(elem!1)) = elem!1)),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[107, 13581])).
% 2.51/2.76 tff(13583,plain,
% 2.51/2.76 (r(s(s(elem!1)), elem!1)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[1260, 44, 13582, 13577])).
% 2.51/2.76 tff(13584,plain,
% 2.51/2.76 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13396, 13583, 2484, 13518])).
% 2.51/2.76 tff(13585,plain,
% 2.51/2.76 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[2758, 13584, 13576])).
% 2.51/2.76 tff(13586,plain,
% 2.51/2.76 (~b(elem!1, s(s(elem!1)))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[5306, 144, 624, 13585, 132, 13573])).
% 2.51/2.76 tff(13587,plain,
% 2.51/2.76 (~b(s(z), s(s(s(z))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[5343, 13586, 13509])).
% 2.51/2.76 tff(13588,plain,
% 2.51/2.76 (r(s(z), s(s(s(z))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[172, 13587])).
% 2.51/2.76 tff(13589,plain,
% 2.51/2.76 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[10422, 13588, 13572, 13570])).
% 2.51/2.76 tff(13590,plain,
% 2.51/2.76 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[1137, 13589])).
% 2.51/2.76 tff(13591,plain,
% 2.51/2.76 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13590, 13512])).
% 2.51/2.76 tff(13592,plain,
% 2.51/2.76 (s(s(elem!1)) = s(s(s(z)))),
% 2.51/2.76 inference(symmetry,[status(thm)],[13511])).
% 2.51/2.76 tff(13593,plain,
% 2.51/2.76 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13592])).
% 2.51/2.76 tff(13594,plain,
% 2.51/2.76 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.51/2.76 inference(symmetry,[status(thm)],[13593])).
% 2.51/2.76 tff(13595,plain,
% 2.51/2.76 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13594])).
% 2.51/2.76 tff(13596,plain,
% 2.51/2.76 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.51/2.76 inference(symmetry,[status(thm)],[13595])).
% 2.51/2.76 tff(13597,plain,
% 2.51/2.76 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13509])).
% 2.51/2.76 tff(13598,plain,
% 2.51/2.76 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13597, 2])).
% 2.51/2.76 tff(13599,plain,
% 2.51/2.76 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13598])).
% 2.51/2.76 tff(13600,plain,
% 2.51/2.76 (~(elem!1 = s(s(s(z))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[166, 13599])).
% 2.51/2.76 tff(13601,plain,
% 2.51/2.76 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[3522, 13511, 13600])).
% 2.51/2.76 tff(13602,plain,
% 2.51/2.76 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[3254, 13601])).
% 2.51/2.76 tff(13603,plain,
% 2.51/2.76 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13529, 333, 509, 51, 13523])).
% 2.51/2.76 tff(13604,plain,
% 2.51/2.76 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[3545, 13603, 13509])).
% 2.51/2.76 tff(13605,plain,
% 2.51/2.76 (b(s(elem!1), s(s(s(elem!1))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[1067, 13604, 13602])).
% 2.51/2.76 tff(13606,plain,
% 2.51/2.76 (b(s(elem!1), s(s(s(s(z)))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13605, 13596])).
% 2.51/2.76 tff(13607,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13608,plain,
% 2.51/2.76 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13609,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13608])).
% 2.51/2.76 tff(13610,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13609, 13607])).
% 2.51/2.76 tff(13611,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.51/2.76 inference(quant_inst,[status(thm)],[])).
% 2.51/2.76 tff(13612,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13611, 13610])).
% 2.51/2.76 tff(13613,plain,
% 2.51/2.76 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13612, 144, 13521, 132, 13515])).
% 2.51/2.76 tff(13614,plain,
% 2.51/2.76 (~b(s(elem!1), elem!1)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13613, 13606])).
% 2.51/2.76 tff(13615,plain,
% 2.51/2.76 (r(s(elem!1), elem!1)),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[448, 13614, 907])).
% 2.51/2.76 tff(13616,plain,
% 2.51/2.76 (~r(s(s(elem!1)), s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[8792, 333, 13518, 13615, 13583])).
% 2.51/2.76 tff(13617,plain,
% 2.51/2.76 (b(s(s(elem!1)), s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[1283, 13616, 2727])).
% 2.51/2.76 tff(13618,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13619,plain,
% 2.51/2.76 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(rewrite,[status(thm)],[])).
% 2.51/2.76 tff(13620,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.76 inference(monotonicity,[status(thm)],[13619])).
% 2.51/2.76 tff(13621,plain,
% 2.51/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.76 inference(transitivity,[status(thm)],[13620, 13618])).
% 2.51/2.76 tff(13622,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.76 inference(quant_inst,[status(thm)],[])).
% 2.51/2.76 tff(13623,plain,
% 2.51/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.76 inference(modus_ponens,[status(thm)],[13622, 13621])).
% 2.51/2.76 tff(13624,plain,
% 2.51/2.76 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13623, 144, 286, 13515, 13573])).
% 2.51/2.76 tff(13625,plain,
% 2.51/2.76 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13624, 13617])).
% 2.51/2.76 tff(13626,plain,
% 2.51/2.76 ($false),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13625, 13591])).
% 2.51/2.76 tff(13627,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.76 tff(13628,plain,
% 2.51/2.76 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[13627, 13494, 624, 132, 2484, 51, 509, 1, 123, 286, 2900, 902])).
% 2.51/2.76 tff(13629,plain,
% 2.51/2.76 (~r(z, s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[12046, 13628, 509, 51])).
% 2.51/2.76 tff(13630,plain,
% 2.51/2.76 (b(z, s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[583, 13629])).
% 2.51/2.76 tff(13631,plain,
% 2.51/2.76 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[472, 13494, 2901])).
% 2.51/2.76 tff(13632,plain,
% 2.51/2.76 (~b(elem!1, s(elem!1))),
% 2.51/2.76 inference(unit_resolution,[status(thm)],[2710, 144, 624, 132, 286, 13631])).
% 2.51/2.77 tff(13633,plain,
% 2.51/2.77 (r(elem!1, s(elem!1))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[560, 13632, 902])).
% 2.51/2.77 tff(13634,plain,
% 2.51/2.77 (~r(z, elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2492, 13633, 2484, 51])).
% 2.51/2.77 tff(13635,plain,
% 2.51/2.77 (b(z, elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[658, 13634, 71])).
% 2.51/2.77 tff(13636,plain,
% 2.51/2.77 (b(z, elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[658, 1575, 71])).
% 2.51/2.77 tff(13637,plain,
% 2.51/2.77 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[12830, 6065, 2484, 624, 13636, 706])).
% 2.51/2.77 tff(13638,plain,
% 2.51/2.77 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[319, 13637])).
% 2.51/2.77 tff(13639,plain,
% 2.51/2.77 (~b(s(elem!1), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[3040, 144, 123, 13638, 450])).
% 2.51/2.77 tff(13640,plain,
% 2.51/2.77 (~r(z, s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1653, 13639, 902, 706, 509, 1, 1575])).
% 2.51/2.77 tff(13641,plain,
% 2.51/2.77 (b(z, s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[372, 13640])).
% 2.51/2.77 tff(13642,plain,
% 2.51/2.77 (r(s(elem!1), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[486, 13639, 1])).
% 2.51/2.77 tff(13643,plain,
% 2.51/2.77 (~r(s(z), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1911, 13642, 624, 13636, 907, 6065])).
% 2.51/2.77 tff(13644,plain,
% 2.51/2.77 (b(s(z), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[348, 13643])).
% 2.51/2.77 tff(13645,plain,
% 2.51/2.77 ($false),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[7093, 13644, 13641, 286, 13638])).
% 2.51/2.77 tff(13646,plain,((s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | r(z, elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.77 tff(13647,plain,
% 2.51/2.77 (s(z) = elem!1),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13646, 509, 624, 902, 286, 1, 13634, 123, 13631, 2484, 12822])).
% 2.51/2.77 tff(13648,plain,
% 2.51/2.77 (b(z, s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[9366, 13647, 13635])).
% 2.51/2.77 tff(13649,plain,
% 2.51/2.77 (b(s(z), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[3965, 13647, 624])).
% 2.51/2.77 tff(13650,plain,
% 2.51/2.77 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[7093, 13649, 286, 13648])).
% 2.51/2.77 tff(13651,plain,
% 2.51/2.77 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[319, 13650])).
% 2.51/2.77 tff(13652,plain,
% 2.51/2.77 (~b(s(s(elem!1)), elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13370, 144, 251, 624, 2498])).
% 2.51/2.77 tff(13653,plain,
% 2.51/2.77 (r(s(s(elem!1)), elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1260, 44, 4575, 13652])).
% 2.51/2.77 tff(13654,plain,
% 2.51/2.77 (~b(s(s(s(z))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2273, 285, 13378, 6022])).
% 2.51/2.77 tff(13655,plain,
% 2.51/2.77 (r(s(s(s(z))), s(z))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2794, 13654])).
% 2.51/2.77 tff(13656,plain,
% 2.51/2.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13396, 13653, 2484, 563])).
% 2.51/2.77 tff(13657,plain,
% 2.51/2.77 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2758, 13656, 10047])).
% 2.51/2.77 tff(13658,plain,
% 2.51/2.77 (~b(elem!1, s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[5306, 144, 624, 13657, 132, 2498])).
% 2.51/2.77 tff(13659,plain,
% 2.51/2.77 (~b(s(z), s(s(s(z))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[5343, 13658, 57])).
% 2.51/2.77 tff(13660,plain,
% 2.51/2.77 (r(s(z), s(s(s(z))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[172, 13659])).
% 2.51/2.77 tff(13661,plain,
% 2.51/2.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[10422, 13660, 322, 13655])).
% 2.51/2.77 tff(13662,plain,
% 2.51/2.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1137, 13661])).
% 2.51/2.77 tff(13663,plain,
% 2.51/2.77 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13662, 4584])).
% 2.51/2.77 tff(13664,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13665,plain,
% 2.51/2.77 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13666,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.77 inference(monotonicity,[status(thm)],[13665])).
% 2.51/2.77 tff(13667,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(transitivity,[status(thm)],[13666, 13664])).
% 2.51/2.77 tff(13668,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.51/2.77 inference(quant_inst,[status(thm)],[])).
% 2.51/2.77 tff(13669,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13668, 13667])).
% 2.51/2.77 tff(13670,plain,
% 2.51/2.77 (~b(s(s(elem!1)), s(elem!1))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13669, 144, 585, 13663, 450, 2498])).
% 2.51/2.77 tff(13671,plain,
% 2.51/2.77 (r(s(s(elem!1)), s(elem!1))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1283, 13670, 2854])).
% 2.51/2.77 tff(13672,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13673,plain,
% 2.51/2.77 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13674,plain,
% 2.51/2.77 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))))),
% 2.51/2.77 inference(monotonicity,[status(thm)],[13673])).
% 2.51/2.77 tff(13675,plain,
% 2.51/2.77 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.51/2.77 inference(transitivity,[status(thm)],[13674, 13672])).
% 2.51/2.77 tff(13676,plain,
% 2.51/2.77 ((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.51/2.77 inference(quant_inst,[status(thm)],[])).
% 2.51/2.77 tff(13677,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13676, 13675])).
% 2.51/2.77 tff(13678,plain,
% 2.51/2.77 ($false),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13677, 333, 563, 13671, 509, 13653])).
% 2.51/2.77 tff(13679,plain,((~b(s(s(s(z))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.77 tff(13680,plain,
% 2.51/2.77 (~b(s(s(s(z))), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13679, 13633, 509, 2727, 13630, 13631, 13647, 13651, 624, 132, 2484, 13635])).
% 2.51/2.77 tff(13681,plain,
% 2.51/2.77 (r(s(s(s(z))), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[396, 13680])).
% 2.51/2.77 tff(13682,plain,
% 2.51/2.77 (r(s(s(elem!1)), z)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[6447, 1699, 57])).
% 2.51/2.77 tff(13683,plain,
% 2.51/2.77 (~r(s(elem!1), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13555, 333, 509, 51, 13682])).
% 2.51/2.77 tff(13684,plain,
% 2.51/2.77 (~(s(elem!1) = s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2856, 2854])).
% 2.51/2.77 tff(13685,plain,
% 2.51/2.77 (b(s(elem!1), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2860, 44, 13684, 13683])).
% 2.51/2.77 tff(13686,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, 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(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13687,plain,
% 2.51/2.77 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13688,plain,
% 2.51/2.77 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.77 inference(monotonicity,[status(thm)],[13687])).
% 2.51/2.77 tff(13689,plain,
% 2.51/2.77 (((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.77 inference(transitivity,[status(thm)],[13688, 13686])).
% 2.51/2.77 tff(13690,plain,
% 2.51/2.77 ((~![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(z))))))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.51/2.77 inference(quant_inst,[status(thm)],[])).
% 2.51/2.77 tff(13691,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13690, 13689])).
% 2.51/2.77 tff(13692,plain,
% 2.51/2.77 (~r(s(s(elem!1)), s(elem!1))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13691, 333, 509, 51, 13682])).
% 2.51/2.77 tff(13693,plain,
% 2.51/2.77 (b(s(s(elem!1)), s(elem!1))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[1283, 13692, 2854])).
% 2.51/2.77 tff(13694,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13695,plain,
% 2.51/2.77 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13696,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.51/2.77 inference(monotonicity,[status(thm)],[13695])).
% 2.51/2.77 tff(13697,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.51/2.77 inference(transitivity,[status(thm)],[13696, 13694])).
% 2.51/2.77 tff(13698,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 2.51/2.77 inference(quant_inst,[status(thm)],[])).
% 2.51/2.77 tff(13699,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13698, 13697])).
% 2.51/2.77 tff(13700,plain,
% 2.51/2.77 (~b(z, s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13699, 144, 451, 251, 585, 13693])).
% 2.51/2.77 tff(13701,plain,
% 2.51/2.77 (~b(z, s(s(s(z))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2828, 13700, 57])).
% 2.51/2.77 tff(13702,plain,
% 2.51/2.77 (r(z, s(s(s(z))))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[619, 13701])).
% 2.51/2.77 tff(13703,plain,
% 2.51/2.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[6811, 13702, 624, 132, 57, 1699])).
% 2.51/2.77 tff(13704,plain,
% 2.51/2.77 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[2758, 13703, 10047])).
% 2.51/2.77 tff(13705,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13706,plain,
% 2.51/2.77 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.77 inference(rewrite,[status(thm)],[])).
% 2.51/2.77 tff(13707,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.51/2.77 inference(monotonicity,[status(thm)],[13706])).
% 2.51/2.77 tff(13708,plain,
% 2.51/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.51/2.77 inference(transitivity,[status(thm)],[13707, 13705])).
% 2.51/2.77 tff(13709,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 2.51/2.77 inference(quant_inst,[status(thm)],[])).
% 2.51/2.77 tff(13710,plain,
% 2.51/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.51/2.77 inference(modus_ponens,[status(thm)],[13709, 13708])).
% 2.51/2.77 tff(13711,plain,
% 2.51/2.77 ($false),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13710, 144, 451, 13704, 132, 13685, 450])).
% 2.51/2.77 tff(13712,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.77 tff(13713,plain,
% 2.51/2.77 (~b(s(elem!1), elem!1)),
% 2.51/2.77 inference(unit_resolution,[status(thm)],[13712, 13681, 132, 13631, 624, 13647, 13635, 13630, 2727, 509, 51])).
% 2.51/2.77 tff(13714,plain,
% 2.51/2.77 (r(s(elem!1), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[448, 13713, 907])).
% 2.51/2.78 tff(13715,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12793, 333, 13633, 13714, 2484, 13628])).
% 2.51/2.78 tff(13716,plain,((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13717,plain,
% 2.51/2.78 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13716, 13491, 12013, 12152, 51, 12805, 902, 1, 50, 12004])).
% 2.51/2.78 tff(13718,plain,
% 2.51/2.78 (b(z, elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12164, 13717, 51, 1, 3, 4])).
% 2.51/2.78 tff(13719,plain,
% 2.51/2.78 (~(s(z) = elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12684, 13717, 13491, 51, 13718, 12152, 12004, 12013])).
% 2.51/2.78 tff(13720,plain,
% 2.51/2.78 (~(s(s(z)) = s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[855, 13719])).
% 2.51/2.78 tff(13721,plain,
% 2.51/2.78 (b(s(z), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12346, 13717, 13719, 51, 12013, 12152, 13718, 50, 1, 12004])).
% 2.51/2.78 tff(13722,plain,
% 2.51/2.78 (~(elem!1 = s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[712, 13719])).
% 2.51/2.78 tff(13723,plain,
% 2.51/2.78 (s(s(s(z))) = s(s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12508, 13722, 12152, 13490, 13718, 13717, 51, 12013, 12004, 1, 50, 13721])).
% 2.51/2.78 tff(13724,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[862, 13723, 13720])).
% 2.51/2.78 tff(13725,plain,((elem!1 = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13726,plain,
% 2.51/2.78 (elem!1 = s(elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13725, 51, 1, 3, 4])).
% 2.51/2.78 tff(13727,plain,
% 2.51/2.78 (s(s(s(elem!1))) = elem!1),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2482, 13726])).
% 2.51/2.78 tff(13728,plain,
% 2.51/2.78 (~(s(z) = elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2468, 13727])).
% 2.51/2.78 tff(13729,plain,
% 2.51/2.78 (~(elem!1 = s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[712, 13728])).
% 2.51/2.78 tff(13730,plain,
% 2.51/2.78 (r(elem!1, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[720, 13729, 12807])).
% 2.51/2.78 tff(13731,plain,
% 2.51/2.78 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.51/2.78 inference(monotonicity,[status(thm)],[13726])).
% 2.51/2.78 tff(13732,plain,
% 2.51/2.78 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.51/2.78 inference(modus_ponens,[status(thm)],[12004, 13731])).
% 2.51/2.78 tff(13733,plain,
% 2.51/2.78 (~b(s(elem!1), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[890, 13726, 12807])).
% 2.51/2.78 tff(13734,plain,
% 2.51/2.78 (r(s(elem!1), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[486, 13733, 1])).
% 2.51/2.78 tff(13735,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[3361, 333, 434, 562, 51, 524])).
% 2.51/2.78 tff(13736,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13737,plain,
% 2.51/2.78 (~r(z, s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13736, 13734, 51, 13732])).
% 2.51/2.78 tff(13738,plain,
% 2.51/2.78 (b(z, s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[583, 13737])).
% 2.51/2.78 tff(13739,plain,
% 2.51/2.78 (b(z, elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2974, 13738, 13726])).
% 2.51/2.78 tff(13740,plain,
% 2.51/2.78 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12830, 13739, 12004, 12152, 13730, 13728])).
% 2.51/2.78 tff(13741,plain,
% 2.51/2.78 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[319, 13740])).
% 2.51/2.78 tff(13742,plain,
% 2.51/2.78 (~(s(s(z)) = s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[855, 13728])).
% 2.51/2.78 tff(13743,plain,
% 2.51/2.78 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[862, 13742])).
% 2.51/2.78 tff(13744,plain,
% 2.51/2.78 (s(elem!1) = elem!1),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1569, 13726])).
% 2.51/2.78 tff(13745,plain,
% 2.51/2.78 (elem!1 = s(s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[5813, 13744])).
% 2.51/2.78 tff(13746,plain,
% 2.51/2.78 (s(s(elem!1)) = elem!1),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[5603, 13745])).
% 2.51/2.78 tff(13747,plain,
% 2.51/2.78 (~(s(s(s(z))) = elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[7595, 13746, 13743])).
% 2.51/2.78 tff(13748,plain,
% 2.51/2.78 (s(elem!1) = s(s(s(elem!1)))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2584, 13727, 13726])).
% 2.51/2.78 tff(13749,plain,
% 2.51/2.78 (~(s(elem!1) = s(s(s(z))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[990, 13748, 1])).
% 2.51/2.78 tff(13750,plain,
% 2.51/2.78 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(monotonicity,[status(thm)],[13726])).
% 2.51/2.78 tff(13751,plain,
% 2.51/2.78 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(modus_ponens,[status(thm)],[12013, 13750])).
% 2.51/2.78 tff(13752,plain,
% 2.51/2.78 (~r(s(s(s(z))), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12573, 13751, 13726, 13749, 13734, 50, 13732])).
% 2.51/2.78 tff(13753,plain,
% 2.51/2.78 (b(s(s(s(z))), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[704, 13752, 13747])).
% 2.51/2.78 tff(13754,plain,
% 2.51/2.78 (~b(s(s(s(z))), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[10565, 13739, 12152, 13753])).
% 2.51/2.78 tff(13755,plain,
% 2.51/2.78 (r(s(s(s(z))), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[396, 13754])).
% 2.51/2.78 tff(13756,plain,
% 2.51/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, 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(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(rewrite,[status(thm)],[])).
% 2.51/2.78 tff(13757,plain,
% 2.51/2.78 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(rewrite,[status(thm)],[])).
% 2.51/2.78 tff(13758,plain,
% 2.51/2.78 (((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.78 inference(monotonicity,[status(thm)],[13757])).
% 2.51/2.78 tff(13759,plain,
% 2.51/2.78 (((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(transitivity,[status(thm)],[13758, 13756])).
% 2.51/2.78 tff(13760,plain,
% 2.51/2.78 ((~![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(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))),
% 2.51/2.78 inference(quant_inst,[status(thm)],[])).
% 2.51/2.78 tff(13761,plain,
% 2.51/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.78 inference(modus_ponens,[status(thm)],[13760, 13759])).
% 2.51/2.78 tff(13762,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13761, 333, 1699, 6107, 51, 524])).
% 2.51/2.78 tff(13763,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13764,plain,
% 2.51/2.78 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13763, 13755, 51, 13732])).
% 2.51/2.78 tff(13765,plain,
% 2.51/2.78 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1137, 13764])).
% 2.51/2.78 tff(13766,plain,
% 2.51/2.78 (~r(s(s(s(z))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12583, 333, 323, 1699, 51])).
% 2.51/2.78 tff(13767,plain,
% 2.51/2.78 (b(s(s(s(z))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2794, 13766])).
% 2.51/2.78 tff(13768,plain,
% 2.51/2.78 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1124, 144, 13767, 123, 304])).
% 2.51/2.78 tff(13769,plain,
% 2.51/2.78 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1137, 13768])).
% 2.51/2.78 tff(13770,plain,
% 2.51/2.78 (((~![X0: $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))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, 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(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(rewrite,[status(thm)],[])).
% 2.51/2.78 tff(13771,plain,
% 2.51/2.78 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(rewrite,[status(thm)],[])).
% 2.51/2.78 tff(13772,plain,
% 2.51/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.78 inference(monotonicity,[status(thm)],[13771])).
% 2.51/2.78 tff(13773,plain,
% 2.51/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.78 inference(transitivity,[status(thm)],[13772, 13770])).
% 2.51/2.78 tff(13774,plain,
% 2.51/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.51/2.78 inference(quant_inst,[status(thm)],[])).
% 2.51/2.78 tff(13775,plain,
% 2.51/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.78 inference(modus_ponens,[status(thm)],[13774, 13773])).
% 2.51/2.78 tff(13776,plain,
% 2.51/2.78 (~r(s(z), s(s(s(z))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13775, 333, 323, 1699, 51])).
% 2.51/2.78 tff(13777,plain,
% 2.51/2.78 (b(s(z), s(s(s(z))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[172, 13776])).
% 2.51/2.78 tff(13778,plain,
% 2.51/2.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[846, 13777, 304, 13767])).
% 2.51/2.78 tff(13779,plain,
% 2.51/2.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[249, 13778])).
% 2.51/2.78 tff(13780,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1340, 333, 1699, 13779, 13769, 51])).
% 2.51/2.78 tff(13781,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13782,plain,
% 2.51/2.78 (~r(s(z), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13781, 13755, 51, 50, 13741])).
% 2.51/2.78 tff(13783,plain,
% 2.51/2.78 (b(s(z), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[348, 13782])).
% 2.51/2.78 tff(13784,plain,
% 2.51/2.78 (~b(s(z), s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[3222, 13783, 12805, 50, 13751])).
% 2.51/2.78 tff(13785,plain,
% 2.51/2.78 (r(s(z), s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[1244, 13784, 1229])).
% 2.51/2.78 tff(13786,plain,
% 2.51/2.78 (~b(z, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[7093, 13783, 12805, 13741])).
% 2.51/2.78 tff(13787,plain,
% 2.51/2.78 (r(z, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[372, 13786])).
% 2.51/2.78 tff(13788,plain,
% 2.51/2.78 (~r(s(s(s(z))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[6565, 13787, 13785, 13755])).
% 2.51/2.78 tff(13789,plain,
% 2.51/2.78 (b(s(s(s(z))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[2794, 13788])).
% 2.51/2.78 tff(13790,plain,
% 2.51/2.78 ($false),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[6004, 144, 13789, 50, 13765, 13741])).
% 2.51/2.78 tff(13791,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.78 tff(13792,plain,
% 2.51/2.78 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13791, 4, 3, 1])).
% 2.51/2.78 tff(13793,plain,
% 2.51/2.78 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[3398, 12014])).
% 2.51/2.78 tff(13794,plain,
% 2.51/2.78 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(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(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.51/2.78 inference(rewrite,[status(thm)],[])).
% 2.51/2.78 tff(13795,plain,
% 2.51/2.78 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.51/2.78 inference(quant_inst,[status(thm)],[])).
% 2.51/2.78 tff(13796,plain,
% 2.51/2.78 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.51/2.78 inference(modus_ponens,[status(thm)],[13795, 13794])).
% 2.51/2.78 tff(13797,plain,
% 2.51/2.78 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[13796, 333, 7265, 408, 2484])).
% 2.51/2.78 tff(13798,plain,
% 2.51/2.78 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[302, 13797])).
% 2.51/2.78 tff(13799,plain,
% 2.51/2.78 (~b(s(z), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[7741, 13798, 123, 8045])).
% 2.51/2.78 tff(13800,plain,
% 2.51/2.78 (r(s(z), z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[348, 13799])).
% 2.51/2.78 tff(13801,plain,
% 2.51/2.78 (~r(s(z), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[8094, 333, 7265, 13800, 408])).
% 2.51/2.78 tff(13802,plain,
% 2.51/2.78 (~r(elem!1, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[3944, 333, 7265, 13800, 408])).
% 2.51/2.78 tff(13803,plain,
% 2.51/2.78 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[757, 490, 123, 259])).
% 2.51/2.78 tff(13804,plain,
% 2.51/2.78 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[319, 13803])).
% 2.51/2.78 tff(13805,plain,
% 2.51/2.78 (~(s(z) = elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[8102, 490, 606])).
% 2.51/2.78 tff(13806,plain,
% 2.51/2.78 (~(elem!1 = s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[712, 13805])).
% 2.51/2.78 tff(13807,plain,
% 2.51/2.78 (~(s(s(z)) = s(elem!1))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[855, 13805])).
% 2.51/2.78 tff(13808,plain,
% 2.51/2.78 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[862, 13807])).
% 2.51/2.78 tff(13809,plain,
% 2.51/2.78 (r(s(z), elem!1)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[406, 13805, 350])).
% 2.51/2.78 tff(13810,plain,
% 2.51/2.78 (~r(elem!1, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12172, 13804, 2484, 13809])).
% 2.51/2.78 tff(13811,plain,
% 2.51/2.78 (b(elem!1, s(z))),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[720, 13810, 13806])).
% 2.51/2.78 tff(13812,plain,
% 2.51/2.78 (~r(elem!1, z)),
% 2.51/2.78 inference(unit_resolution,[status(thm)],[12109, 13804, 2484, 13809])).
% 2.51/2.78 tff(13813,plain,
% 2.51/2.78 (b(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1380, 13812, 1368])).
% 2.51/2.79 tff(13814,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10115, 13813, 13811, 132, 123, 490])).
% 2.51/2.79 tff(13815,plain,((~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(z), elem!1) | b(z, elem!1) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13816,plain,
% 2.51/2.79 (~b(z, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13815, 350, 123, 77, 2484, 132, 606, 259])).
% 2.51/2.79 tff(13817,plain,
% 2.51/2.79 (r(z, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[372, 13816])).
% 2.51/2.79 tff(13818,plain,
% 2.51/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.79 inference(rewrite,[status(thm)],[])).
% 2.51/2.79 tff(13819,plain,
% 2.51/2.79 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.79 inference(rewrite,[status(thm)],[])).
% 2.51/2.79 tff(13820,plain,
% 2.51/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.51/2.79 inference(monotonicity,[status(thm)],[13819])).
% 2.51/2.79 tff(13821,plain,
% 2.51/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.79 inference(transitivity,[status(thm)],[13820, 13818])).
% 2.51/2.79 tff(13822,plain,
% 2.51/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.51/2.79 inference(quant_inst,[status(thm)],[])).
% 2.51/2.79 tff(13823,plain,
% 2.51/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.51/2.79 inference(modus_ponens,[status(thm)],[13822, 13821])).
% 2.51/2.79 tff(13824,plain,
% 2.51/2.79 (~b(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13823, 144, 624, 489, 132, 259])).
% 2.51/2.79 tff(13825,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10960, 6065, 7670, 670, 354])).
% 2.51/2.79 tff(13826,plain,((s(z) = elem!1) | (~r(z, elem!1)) | (~r(z, s(z))) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13827,plain,
% 2.51/2.79 (s(z) = elem!1),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13826, 13824, 13817, 7265, 350])).
% 2.51/2.79 tff(13828,plain,
% 2.51/2.79 (~(s(s(s(elem!1))) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2468, 13827])).
% 2.51/2.79 tff(13829,plain,
% 2.51/2.79 (r(s(elem!1), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8651, 13827, 123, 259, 7265, 77, 1229, 114, 606])).
% 2.51/2.79 tff(13830,plain,
% 2.51/2.79 (~(elem!1 = s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2482, 13828])).
% 2.51/2.79 tff(13831,plain,
% 2.51/2.79 (~r(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8367, 8071, 2484, 7265])).
% 2.51/2.79 tff(13832,plain,
% 2.51/2.79 (b(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[560, 13830, 13831])).
% 2.51/2.79 tff(13833,plain,
% 2.51/2.79 (~b(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8787, 13832, 259, 132, 624])).
% 2.51/2.79 tff(13834,plain,
% 2.51/2.79 (r(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[507, 13833])).
% 2.51/2.79 tff(13835,plain,
% 2.51/2.79 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8783, 13834, 7265, 132, 8071, 13830, 13829])).
% 2.51/2.79 tff(13836,plain,
% 2.51/2.79 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.51/2.79 inference(monotonicity,[status(thm)],[96])).
% 2.51/2.79 tff(13837,plain,
% 2.51/2.79 (s(s(s(elem!1))) = elem!1),
% 2.51/2.79 inference(transitivity,[status(thm)],[13836, 21, 1203, 850])).
% 2.51/2.79 tff(13838,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1012, 13837])).
% 2.51/2.79 tff(13839,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13840,plain,
% 2.51/2.79 (~(s(s(s(z))) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13839, 13835, 13828])).
% 2.51/2.79 tff(13841,plain,
% 2.51/2.79 (r(s(s(s(z))), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[704, 13840, 55])).
% 2.51/2.79 tff(13842,plain,
% 2.51/2.79 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10189, 333, 670, 1964, 321])).
% 2.51/2.79 tff(13843,plain,
% 2.51/2.79 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1137, 13842])).
% 2.51/2.79 tff(13844,plain,
% 2.51/2.79 (((~![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(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.51/2.79 inference(rewrite,[status(thm)],[])).
% 2.51/2.79 tff(13845,plain,
% 2.51/2.79 ((~![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(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.51/2.79 inference(quant_inst,[status(thm)],[])).
% 2.51/2.79 tff(13846,plain,
% 2.51/2.79 ((~![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(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.51/2.79 inference(modus_ponens,[status(thm)],[13845, 13844])).
% 2.51/2.79 tff(13847,plain,
% 2.51/2.79 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13846, 333, 670, 1964, 321])).
% 2.51/2.79 tff(13848,plain,
% 2.51/2.79 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[249, 13847])).
% 2.51/2.79 tff(13849,plain,
% 2.51/2.79 (~b(elem!1, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8765, 144, 132, 13848, 13843])).
% 2.51/2.79 tff(13850,plain,
% 2.51/2.79 (~b(z, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[9071, 144, 13848, 13843, 259])).
% 2.51/2.79 tff(13851,plain,
% 2.51/2.79 (r(z, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[619, 13850])).
% 2.51/2.79 tff(13852,plain,
% 2.51/2.79 (~b(s(z), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2262, 13843, 123, 13848])).
% 2.51/2.79 tff(13853,plain,
% 2.51/2.79 (r(s(z), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[172, 13852])).
% 2.51/2.79 tff(13854,plain,
% 2.51/2.79 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[362, 13853, 354, 321])).
% 2.51/2.79 tff(13855,plain,
% 2.51/2.79 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[319, 13854])).
% 2.51/2.79 tff(13856,plain,
% 2.51/2.79 (~b(s(s(s(z))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[6004, 144, 123, 13843, 13855])).
% 2.51/2.79 tff(13857,plain,
% 2.51/2.79 (r(s(s(s(z))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2794, 13856])).
% 2.51/2.79 tff(13858,plain,
% 2.51/2.79 (~r(elem!1, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3201, 13857, 670, 13851])).
% 2.51/2.79 tff(13859,plain,
% 2.51/2.79 (elem!1 = s(s(s(z)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1538, 13858, 13849])).
% 2.51/2.79 tff(13860,plain,
% 2.51/2.79 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.51/2.79 inference(monotonicity,[status(thm)],[13859])).
% 2.51/2.79 tff(13861,plain,
% 2.51/2.79 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 2.51/2.79 inference(symmetry,[status(thm)],[13860])).
% 2.51/2.79 tff(13862,plain,
% 2.51/2.79 ((~b(s(s(s(z))), z)) <=> (~b(elem!1, z))),
% 2.51/2.79 inference(monotonicity,[status(thm)],[13861])).
% 2.51/2.79 tff(13863,plain,
% 2.51/2.79 (~b(elem!1, z)),
% 2.51/2.79 inference(modus_ponens,[status(thm)],[1963, 13862])).
% 2.51/2.79 tff(13864,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[624, 13863])).
% 2.51/2.79 tff(13865,plain,(b(s(s(s(z))), z) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13866,plain,
% 2.51/2.79 (b(s(s(s(z))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13865, 8071, 7265, 259, 132, 123, 13817, 624])).
% 2.51/2.79 tff(13867,plain,
% 2.51/2.79 (~b(s(z), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10462, 144, 489, 13866, 123, 259])).
% 2.51/2.79 tff(13868,plain,
% 2.51/2.79 (r(s(z), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[172, 13867])).
% 2.51/2.79 tff(13869,plain,
% 2.51/2.79 (~b(s(elem!1), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8082, 13834, 7265, 13827, 123, 114, 8071])).
% 2.51/2.79 tff(13870,plain,
% 2.51/2.79 (~b(s(elem!1), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3619, 13869, 13827])).
% 2.51/2.79 tff(13871,plain,
% 2.51/2.79 (r(s(elem!1), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[486, 13870, 1])).
% 2.51/2.79 tff(13872,plain,
% 2.51/2.79 (~r(s(elem!1), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[7227, 13871, 13868, 13841])).
% 2.51/2.79 tff(13873,plain,
% 2.51/2.79 (~(elem!1 = s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10997, 13840])).
% 2.51/2.79 tff(13874,plain,
% 2.51/2.79 (~(elem!1 = s(s(elem!1)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1216, 13835])).
% 2.51/2.79 tff(13875,plain,
% 2.51/2.79 (~r(z, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1519, 13841, 13817, 13868])).
% 2.51/2.79 tff(13876,plain,
% 2.51/2.79 (b(z, s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[619, 13875])).
% 2.51/2.79 tff(13877,plain,
% 2.51/2.79 (b(z, s(s(elem!1)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2828, 13876, 13827])).
% 2.51/2.79 tff(13878,plain,
% 2.51/2.79 (~b(elem!1, s(s(elem!1)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2821, 13877, 624, 13827, 13866])).
% 2.51/2.79 tff(13879,plain,
% 2.51/2.79 (r(elem!1, s(s(elem!1)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2522, 13878, 13874])).
% 2.51/2.79 tff(13880,plain,
% 2.51/2.79 (~r(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[5359, 13879, 7265, 13829])).
% 2.51/2.79 tff(13881,plain,
% 2.51/2.79 (b(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[583, 13880])).
% 2.51/2.79 tff(13882,plain,
% 2.51/2.79 (~b(s(elem!1), s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3897, 13881, 624, 13829, 7265, 13832, 13873, 13866])).
% 2.51/2.79 tff(13883,plain,
% 2.51/2.79 (s(elem!1) = s(s(s(z)))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[965, 13882, 13872])).
% 2.51/2.79 tff(13884,plain,
% 2.51/2.79 (s(s(z)) = s(elem!1)),
% 2.51/2.79 inference(monotonicity,[status(thm)],[13827])).
% 2.51/2.79 tff(13885,plain,
% 2.51/2.79 (s(s(z)) = s(s(s(z)))),
% 2.51/2.79 inference(transitivity,[status(thm)],[13884, 13883])).
% 2.51/2.79 tff(13886,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[217, 13885])).
% 2.51/2.79 tff(13887,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (s(elem!1) = s(z)) | b(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | b(s(z), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13888,plain,
% 2.51/2.79 (~b(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13887, 4833, 1, 55, 123, 114, 132, 259, 606, 350, 2484])).
% 2.51/2.79 tff(13889,plain,
% 2.51/2.79 (r(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[348, 13888])).
% 2.51/2.79 tff(13890,plain,
% 2.51/2.79 (~(s(z) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3965, 13888, 4833])).
% 2.51/2.79 tff(13891,plain,
% 2.51/2.79 (r(s(z), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[406, 13890, 350])).
% 2.51/2.79 tff(13892,plain,
% 2.51/2.79 (~r(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10119, 13891, 7265, 13817])).
% 2.51/2.79 tff(13893,plain,
% 2.51/2.79 (b(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13826, 13890, 13817, 7265, 350])).
% 2.51/2.79 tff(13894,plain,
% 2.51/2.79 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[313, 132, 123, 305])).
% 2.51/2.79 tff(13895,plain,
% 2.51/2.79 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[319, 13894])).
% 2.51/2.79 tff(13896,plain,
% 2.51/2.79 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8274, 13895, 562, 323])).
% 2.51/2.79 tff(13897,plain,
% 2.51/2.79 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[302, 13896])).
% 2.51/2.79 tff(13898,plain,
% 2.51/2.79 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.51/2.79 inference(rewrite,[status(thm)],[])).
% 2.51/2.79 tff(13899,plain,
% 2.51/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.51/2.79 inference(monotonicity,[status(thm)],[13898])).
% 2.51/2.79 tff(13900,plain,
% 2.51/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.51/2.79 inference(transitivity,[status(thm)],[13899, 6804])).
% 2.51/2.79 tff(13901,plain,
% 2.51/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.51/2.79 inference(quant_inst,[status(thm)],[])).
% 2.51/2.79 tff(13902,plain,
% 2.51/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.51/2.79 inference(modus_ponens,[status(thm)],[13901, 13900])).
% 2.51/2.79 tff(13903,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13902, 144, 624, 132, 13897, 259])).
% 2.51/2.79 tff(13904,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13905,plain,
% 2.51/2.79 (~r(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13904, 13893, 259, 132, 4833, 123, 13889])).
% 2.51/2.79 tff(13906,plain,
% 2.51/2.79 (b(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[583, 13905])).
% 2.51/2.79 tff(13907,plain,
% 2.51/2.79 (~(elem!1 = s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2974, 13906, 606])).
% 2.51/2.79 tff(13908,plain,
% 2.51/2.79 (b(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[560, 13907, 13892])).
% 2.51/2.79 tff(13909,plain,
% 2.51/2.79 (~b(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8787, 13908, 259, 132, 4833])).
% 2.51/2.79 tff(13910,plain,
% 2.51/2.79 (r(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[507, 13909])).
% 2.51/2.79 tff(13911,plain,
% 2.51/2.79 (b(s(elem!1), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8704, 13907, 13891, 71, 13817, 606, 1378])).
% 2.51/2.79 tff(13912,plain,
% 2.51/2.79 (~b(s(z), s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[4409, 13908, 13893, 13911])).
% 2.51/2.79 tff(13913,plain,
% 2.51/2.79 (r(s(z), s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1244, 13912, 1229])).
% 2.51/2.79 tff(13914,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1235, 13913, 13910, 13889, 13817])).
% 2.51/2.79 tff(13915,plain,(r(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (s(elem!1) = s(z)) | b(s(s(s(z))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13916,plain,
% 2.51/2.79 (r(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13915, 350, 132, 606, 123, 259, 1, 55, 114, 2484])).
% 2.51/2.79 tff(13917,plain,
% 2.51/2.79 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13796, 333, 7265, 13916, 2484])).
% 2.51/2.79 tff(13918,plain,
% 2.51/2.79 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[302, 13917])).
% 2.51/2.79 tff(13919,plain,
% 2.51/2.79 (~b(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[7741, 13918, 123, 259])).
% 2.51/2.79 tff(13920,plain,
% 2.51/2.79 (r(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[348, 13919])).
% 2.51/2.79 tff(13921,plain,
% 2.51/2.79 (~r(s(z), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1376, 13920, 13817, 13916])).
% 2.51/2.79 tff(13922,plain,
% 2.51/2.79 (s(z) = elem!1),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[406, 13921, 350])).
% 2.51/2.79 tff(13923,plain,
% 2.51/2.79 (~b(s(s(s(z))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[63, 13922, 55])).
% 2.51/2.79 tff(13924,plain,
% 2.51/2.79 (~r(s(s(s(z))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[11212, 323, 1699, 7265])).
% 2.51/2.79 tff(13925,plain,
% 2.51/2.79 (b(s(s(s(z))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2794, 13924])).
% 2.51/2.79 tff(13926,plain,
% 2.51/2.79 (~(s(z) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[63, 13925, 55])).
% 2.51/2.79 tff(13927,plain,
% 2.51/2.79 (r(s(z), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[406, 13926, 350])).
% 2.51/2.79 tff(13928,plain,
% 2.51/2.79 (~r(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1376, 354, 323, 409])).
% 2.51/2.79 tff(13929,plain,
% 2.51/2.79 (~(elem!1 = s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[712, 13926])).
% 2.51/2.79 tff(13930,plain,
% 2.51/2.79 (~r(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10960, 354, 7265, 409])).
% 2.51/2.79 tff(13931,plain,
% 2.51/2.79 (b(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[720, 13930, 13929])).
% 2.51/2.79 tff(13932,plain,
% 2.51/2.79 (b(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1380, 13928, 77])).
% 2.51/2.79 tff(13933,plain,
% 2.51/2.79 (~r(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13904, 13932, 259, 132, 323, 123, 13931])).
% 2.51/2.79 tff(13934,plain,
% 2.51/2.79 (b(z, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[583, 13933])).
% 2.51/2.79 tff(13935,plain,
% 2.51/2.79 (~(elem!1 = s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2974, 13934, 606])).
% 2.51/2.79 tff(13936,plain,
% 2.51/2.79 (b(s(elem!1), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8704, 13935, 409, 71, 354, 606, 13928])).
% 2.51/2.79 tff(13937,plain,
% 2.51/2.79 (~r(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10119, 354, 7265, 409])).
% 2.51/2.79 tff(13938,plain,
% 2.51/2.79 (b(elem!1, s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[560, 13935, 13937])).
% 2.51/2.79 tff(13939,plain,
% 2.51/2.79 (~b(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[949, 13938, 13932, 13934])).
% 2.51/2.79 tff(13940,plain,
% 2.51/2.79 (r(s(elem!1), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[507, 13939])).
% 2.51/2.79 tff(13941,plain,
% 2.51/2.79 (~(s(elem!1) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[906, 13935])).
% 2.51/2.79 tff(13942,plain,
% 2.51/2.79 (~r(s(elem!1), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[5456, 13938, 1, 354, 13926, 13931, 323, 13932, 13935, 7265])).
% 2.51/2.79 tff(13943,plain,
% 2.51/2.79 (b(s(elem!1), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[448, 13942, 13941])).
% 2.51/2.79 tff(13944,plain,
% 2.51/2.79 (~(s(elem!1) = s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8316, 13943, 55])).
% 2.51/2.79 tff(13945,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8561, 13944, 13940, 1699, 323, 354, 13936])).
% 2.51/2.79 tff(13946,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | b(z, elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13947,plain,
% 2.51/2.79 (~r(z, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13946, 323, 1699, 55, 1, 13927, 606, 259, 132, 123])).
% 2.51/2.79 tff(13948,plain,
% 2.51/2.79 (b(z, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[372, 13947])).
% 2.51/2.79 tff(13949,plain,
% 2.51/2.79 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[757, 13948, 123, 259])).
% 2.51/2.79 tff(13950,plain,
% 2.51/2.79 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[319, 13949])).
% 2.51/2.79 tff(13951,plain,
% 2.51/2.79 (~r(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[12172, 13950, 2484, 13927])).
% 2.51/2.79 tff(13952,plain,
% 2.51/2.79 (b(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[720, 13951, 13929])).
% 2.51/2.79 tff(13953,plain,
% 2.51/2.79 (~r(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[12109, 13950, 2484, 13927])).
% 2.51/2.79 tff(13954,plain,
% 2.51/2.79 (b(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[1380, 13953, 77])).
% 2.51/2.79 tff(13955,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10115, 13954, 13952, 132, 123, 13948])).
% 2.51/2.79 tff(13956,plain,((~r(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | b(z, elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13957,plain,
% 2.51/2.79 (~r(s(s(s(z))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13956, 13920, 123, 2484, 259, 132, 55, 1, 606, 350])).
% 2.51/2.79 tff(13958,plain,
% 2.51/2.79 (b(s(s(s(z))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[396, 13957])).
% 2.51/2.79 tff(13959,plain,
% 2.51/2.79 (~b(elem!1, z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3965, 13922, 13919])).
% 2.51/2.79 tff(13960,plain,
% 2.51/2.79 (~(s(s(s(z))) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[380, 13959, 13958])).
% 2.51/2.79 tff(13961,plain,
% 2.51/2.79 (~(elem!1 = s(s(s(z))))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[10997, 13960])).
% 2.51/2.79 tff(13962,plain,
% 2.51/2.79 (~(s(s(s(elem!1))) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2468, 13922])).
% 2.51/2.79 tff(13963,plain,
% 2.51/2.79 (~(elem!1 = s(elem!1))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2482, 13962])).
% 2.51/2.79 tff(13964,plain,
% 2.51/2.79 (~(s(elem!1) = elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[906, 13963])).
% 2.51/2.79 tff(13965,plain,
% 2.51/2.79 (r(s(s(s(z))), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[704, 13960, 55])).
% 2.51/2.79 tff(13966,plain,
% 2.51/2.79 ($false),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[8658, 13965, 13964, 259, 123, 114, 13916, 606, 13961, 1, 13923, 350])).
% 2.51/2.79 tff(13967,plain,(b(s(z), elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(z, elem!1) | (s(elem!1) = s(z)) | b(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.79 tff(13968,plain,
% 2.51/2.79 (b(s(z), elem!1)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[13967, 114, 123, 259, 606, 1, 55, 2484, 454])).
% 2.51/2.79 tff(13969,plain,
% 2.51/2.79 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[9297, 2322, 670, 114, 123, 134])).
% 2.51/2.79 tff(13970,plain,
% 2.51/2.79 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[302, 13969])).
% 2.51/2.79 tff(13971,plain,
% 2.51/2.79 (~b(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[2113, 2322, 3, 134, 123, 13969])).
% 2.51/2.79 tff(13972,plain,
% 2.51/2.79 (r(s(z), z)),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[348, 13971])).
% 2.51/2.79 tff(13973,plain,
% 2.51/2.79 (~r(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[3944, 333, 670, 13972, 2322])).
% 2.51/2.79 tff(13974,plain,
% 2.51/2.79 (b(elem!1, s(z))),
% 2.51/2.79 inference(unit_resolution,[status(thm)],[720, 13973, 714])).
% 2.51/2.79 tff(13975,plain,
% 2.51/2.79 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[152, 134, 123, 454])).
% 2.61/2.80 tff(13976,plain,
% 2.61/2.80 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[7595, 78, 1184])).
% 2.61/2.80 tff(13977,plain,
% 2.61/2.80 (~(elem!1 = s(s(elem!1)))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[5603, 13976])).
% 2.61/2.80 tff(13978,plain,
% 2.61/2.80 (~(s(elem!1) = elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[5813, 13977])).
% 2.61/2.80 tff(13979,plain,
% 2.61/2.80 (~(elem!1 = s(elem!1))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[1569, 13978])).
% 2.61/2.80 tff(13980,plain,
% 2.61/2.80 (~r(s(elem!1), z)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[7112, 13979, 490, 323, 305, 1, 670])).
% 2.61/2.80 tff(13981,plain,
% 2.61/2.80 (b(s(elem!1), z)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[507, 13980])).
% 2.61/2.80 tff(13982,plain,
% 2.61/2.80 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[10345, 144, 13981, 286, 259])).
% 2.61/2.80 tff(13983,plain,
% 2.61/2.80 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[472, 197, 13982])).
% 2.61/2.80 tff(13984,plain,
% 2.61/2.80 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[787, 377, 286])).
% 2.61/2.80 tff(13985,plain,
% 2.61/2.80 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[130, 13984, 2545])).
% 2.61/2.80 tff(13986,plain,
% 2.61/2.80 (r(elem!1, z)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[1380, 377, 1368])).
% 2.61/2.80 tff(13987,plain,
% 2.61/2.80 ($false),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[12098, 333, 435, 13986, 13985, 525])).
% 2.61/2.80 tff(13988,plain,(b(elem!1, z) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.80 tff(13989,plain,
% 2.61/2.80 (~r(s(elem!1), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[13988, 13983, 2545, 377, 286, 77])).
% 2.61/2.80 tff(13990,plain,
% 2.61/2.80 (b(s(elem!1), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[448, 13989, 13978])).
% 2.61/2.80 tff(13991,plain,
% 2.61/2.80 (~b(s(elem!1), s(z))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[1820, 13990, 134, 13981, 490])).
% 2.61/2.80 tff(13992,plain,
% 2.61/2.80 (r(s(elem!1), s(z))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[486, 13991, 1])).
% 2.61/2.80 tff(13993,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(13994,plain,
% 2.61/2.80 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(13995,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.80 inference(monotonicity,[status(thm)],[13994])).
% 2.61/2.80 tff(13996,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(transitivity,[status(thm)],[13995, 13993])).
% 2.61/2.80 tff(13997,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(quant_inst,[status(thm)],[])).
% 2.61/2.80 tff(13998,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.80 inference(modus_ponens,[status(thm)],[13997, 13996])).
% 2.61/2.80 tff(13999,plain,
% 2.61/2.80 ($false),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[13998, 333, 323, 13992, 322, 13983])).
% 2.61/2.80 tff(14000,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.80 tff(14001,plain,
% 2.61/2.80 (~(s(s(s(z))) = elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14000, 13972, 13804, 1, 134, 490, 13975, 377, 13970, 259, 13974, 670, 1184])).
% 2.61/2.80 tff(14002,plain,
% 2.61/2.80 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[152, 132, 123, 134])).
% 2.61/2.80 tff(14003,plain,
% 2.61/2.80 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[130, 14002, 114])).
% 2.61/2.80 tff(14004,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14005,plain,
% 2.61/2.80 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(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(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14006,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.80 inference(monotonicity,[status(thm)],[14005])).
% 2.61/2.80 tff(14007,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(transitivity,[status(thm)],[14006, 14004])).
% 2.61/2.80 tff(14008,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.61/2.80 inference(quant_inst,[status(thm)],[])).
% 2.61/2.80 tff(14009,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.80 inference(modus_ponens,[status(thm)],[14008, 14007])).
% 2.61/2.80 tff(14010,plain,
% 2.61/2.80 (~b(s(z), s(s(s(z))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14009, 144, 134, 123, 132, 4367])).
% 2.61/2.80 tff(14011,plain,
% 2.61/2.80 (r(s(z), s(s(s(z))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[172, 14010])).
% 2.61/2.80 tff(14012,plain,
% 2.61/2.80 (~b(s(s(s(z))), s(z))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[4375, 4367, 305, 134])).
% 2.61/2.80 tff(14013,plain,
% 2.61/2.80 (r(s(s(s(z))), s(z))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[2794, 14012])).
% 2.61/2.80 tff(14014,plain,
% 2.61/2.80 ($false),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[10420, 333, 14013, 14011, 6107, 13895])).
% 2.61/2.80 tff(14015,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.80 tff(14016,plain,
% 2.61/2.80 (~b(s(s(s(z))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14015, 132, 134, 123, 6107, 305])).
% 2.61/2.80 tff(14017,plain,
% 2.61/2.80 (r(s(s(s(z))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[704, 14016, 698])).
% 2.61/2.80 tff(14018,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14019,plain,
% 2.61/2.80 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14020,plain,
% 2.61/2.80 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), 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(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.61/2.80 inference(monotonicity,[status(thm)],[14019])).
% 2.61/2.80 tff(14021,plain,
% 2.61/2.80 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), 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(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.80 inference(transitivity,[status(thm)],[14020, 14018])).
% 2.61/2.80 tff(14022,plain,
% 2.61/2.80 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(quant_inst,[status(thm)],[])).
% 2.61/2.80 tff(14023,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.61/2.80 inference(modus_ponens,[status(thm)],[14022, 14021])).
% 2.61/2.80 tff(14024,plain,
% 2.61/2.80 ($false),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14023, 333, 408, 14017, 14003, 6107])).
% 2.61/2.80 tff(14025,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.80 tff(14026,plain,
% 2.61/2.80 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14025, 14001, 454, 134, 2322, 123, 13974, 114])).
% 2.61/2.80 tff(14027,plain,
% 2.61/2.80 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[1137, 14026])).
% 2.61/2.80 tff(14028,plain,
% 2.61/2.80 (r(s(s(s(z))), elem!1)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[704, 14001, 55])).
% 2.61/2.80 tff(14029,plain,
% 2.61/2.80 (~r(s(s(s(z))), z)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[2079, 14028, 670, 2322])).
% 2.61/2.80 tff(14030,plain,
% 2.61/2.80 (b(s(s(s(z))), z)),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[396, 14029])).
% 2.61/2.80 tff(14031,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14032,plain,
% 2.61/2.80 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.80 inference(rewrite,[status(thm)],[])).
% 2.61/2.80 tff(14033,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.61/2.80 inference(monotonicity,[status(thm)],[14032])).
% 2.61/2.80 tff(14034,plain,
% 2.61/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.80 inference(transitivity,[status(thm)],[14033, 14031])).
% 2.61/2.80 tff(14035,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.80 inference(quant_inst,[status(thm)],[])).
% 2.61/2.80 tff(14036,plain,
% 2.61/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.61/2.80 inference(modus_ponens,[status(thm)],[14035, 14034])).
% 2.61/2.80 tff(14037,plain,
% 2.61/2.80 ($false),
% 2.61/2.80 inference(unit_resolution,[status(thm)],[14036, 144, 14030, 14027, 13970, 259])).
% 2.61/2.80 tff(14038,plain,(b(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (elem!1 = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.81 tff(14039,plain,
% 2.61/2.81 (b(elem!1, z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14038, 490, 7265, 13968, 123, 114, 55, 1, 259, 13808, 13806, 3])).
% 2.61/2.81 tff(14040,plain,
% 2.61/2.81 (~b(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[10115, 14039, 454, 123, 490])).
% 2.61/2.81 tff(14041,plain,
% 2.61/2.81 (r(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[720, 14040, 13806])).
% 2.61/2.81 tff(14042,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14043,plain,
% 2.61/2.81 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14044,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[14043])).
% 2.61/2.81 tff(14045,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(transitivity,[status(thm)],[14044, 14042])).
% 2.61/2.81 tff(14046,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.61/2.81 inference(quant_inst,[status(thm)],[])).
% 2.61/2.81 tff(14047,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.81 inference(modus_ponens,[status(thm)],[14046, 14045])).
% 2.61/2.81 tff(14048,plain,
% 2.61/2.81 (~b(s(z), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14047, 144, 14039, 13968, 123, 259])).
% 2.61/2.81 tff(14049,plain,
% 2.61/2.81 (r(s(z), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[348, 14048])).
% 2.61/2.81 tff(14050,plain,
% 2.61/2.81 ($false),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[818, 333, 14049, 14041, 2484, 13804])).
% 2.61/2.81 tff(14051,plain,((~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.81 tff(14052,plain,
% 2.61/2.81 (~b(z, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14051, 8049, 123, 8045, 2484, 55, 1, 3, 606])).
% 2.61/2.81 tff(14053,plain,
% 2.61/2.81 (r(z, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[372, 14052])).
% 2.61/2.81 tff(14054,plain,
% 2.61/2.81 (b(s(z), elem!1)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[13967, 8049, 123, 8045, 606, 1, 55, 2484, 8052])).
% 2.61/2.81 tff(14055,plain,
% 2.61/2.81 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[52])).
% 2.61/2.81 tff(14056,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14057,plain,
% 2.61/2.81 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14058,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[14057])).
% 2.61/2.81 tff(14059,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.81 inference(transitivity,[status(thm)],[14058, 14056])).
% 2.61/2.81 tff(14060,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(z))))),
% 2.61/2.81 inference(quant_inst,[status(thm)],[])).
% 2.61/2.81 tff(14061,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.81 inference(modus_ponens,[status(thm)],[14060, 14059])).
% 2.61/2.81 tff(14062,plain,
% 2.61/2.81 (~b(s(z), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14061, 144, 134, 123, 454])).
% 2.61/2.81 tff(14063,plain,
% 2.61/2.81 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[709])).
% 2.61/2.81 tff(14064,plain,
% 2.61/2.81 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 2.61/2.81 inference(symmetry,[status(thm)],[14063])).
% 2.61/2.81 tff(14065,plain,
% 2.61/2.81 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[14064])).
% 2.61/2.81 tff(14066,assumption,(~b(s(z), s(z))), introduced(assumption)).
% 2.61/2.81 tff(14067,plain,
% 2.61/2.81 (~b(s(z), elem!1)),
% 2.61/2.81 inference(modus_ponens,[status(thm)],[14066, 14065])).
% 2.61/2.81 tff(14068,plain,
% 2.61/2.81 ($false),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[134, 14067])).
% 2.61/2.81 tff(14069,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1)) | b(s(z), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.81 tff(14070,plain,
% 2.61/2.81 (~(elem!1 = s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14069, 134, 14062])).
% 2.61/2.81 tff(14071,plain,
% 2.61/2.81 (~(s(z) = elem!1)),
% 2.61/2.81 inference(modus_ponens,[status(thm)],[14070, 14055])).
% 2.61/2.81 tff(14072,plain,
% 2.61/2.81 (~r(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[727, 13972, 670, 354])).
% 2.61/2.81 tff(14073,plain,
% 2.61/2.81 (b(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[720, 14072, 14070])).
% 2.61/2.81 tff(14074,plain,
% 2.61/2.81 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[7595, 78, 863])).
% 2.61/2.81 tff(14075,plain,
% 2.61/2.81 (~(elem!1 = s(s(elem!1)))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[5603, 14074])).
% 2.61/2.81 tff(14076,plain,
% 2.61/2.81 (~(s(elem!1) = elem!1)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[5813, 14075])).
% 2.61/2.81 tff(14077,plain,
% 2.61/2.81 (~(elem!1 = s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1569, 14076])).
% 2.61/2.81 tff(14078,plain,
% 2.61/2.81 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[9297, 114, 408, 670, 123, 134])).
% 2.61/2.81 tff(14079,plain,
% 2.61/2.81 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[302, 14078])).
% 2.61/2.81 tff(14080,plain,
% 2.61/2.81 (~b(s(z), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[7741, 14079, 123, 259])).
% 2.61/2.81 tff(14081,plain,
% 2.61/2.81 (r(s(z), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[348, 14080])).
% 2.61/2.81 tff(14082,plain,
% 2.61/2.81 (~r(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[727, 14081, 354, 670])).
% 2.61/2.81 tff(14083,plain,
% 2.61/2.81 (b(elem!1, s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[720, 14082, 713])).
% 2.61/2.81 tff(14084,plain,
% 2.61/2.81 (~b(s(elem!1), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[4344, 144, 1728, 134, 14083])).
% 2.61/2.81 tff(14085,plain,
% 2.61/2.81 (r(s(elem!1), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[486, 14084, 1])).
% 2.61/2.81 tff(14086,plain,
% 2.61/2.81 (~r(z, s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1355, 333, 354, 14081, 14085])).
% 2.61/2.81 tff(14087,plain,
% 2.61/2.81 (b(z, s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[583, 14086])).
% 2.61/2.81 tff(14088,plain,
% 2.61/2.81 (~r(s(elem!1), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1365, 14085, 354, 14081])).
% 2.61/2.81 tff(14089,plain,
% 2.61/2.81 (b(s(elem!1), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[507, 14088])).
% 2.61/2.81 tff(14090,plain,
% 2.61/2.81 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1668, 144, 14089, 14087, 14079])).
% 2.61/2.81 tff(14091,plain,
% 2.61/2.81 (~b(s(elem!1), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[4344, 144, 451, 134, 14083])).
% 2.61/2.81 tff(14092,plain,
% 2.61/2.81 (r(s(elem!1), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[486, 14091, 1])).
% 2.61/2.81 tff(14093,plain,
% 2.61/2.81 (~r(s(elem!1), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1365, 14092, 354, 14081])).
% 2.61/2.81 tff(14094,plain,
% 2.61/2.81 (b(s(elem!1), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[507, 14093])).
% 2.61/2.81 tff(14095,plain,
% 2.61/2.81 (~r(z, s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1355, 333, 354, 14081, 14092])).
% 2.61/2.81 tff(14096,plain,
% 2.61/2.81 (b(z, s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[583, 14095])).
% 2.61/2.81 tff(14097,plain,
% 2.61/2.81 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1668, 144, 14094, 14096, 14079])).
% 2.61/2.81 tff(14098,plain,
% 2.61/2.81 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[542, 2947, 14097])).
% 2.61/2.81 tff(14099,plain,
% 2.61/2.81 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[10345, 144, 14094, 14079, 259])).
% 2.61/2.81 tff(14100,plain,
% 2.61/2.81 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[472, 2951, 14099])).
% 2.61/2.81 tff(14101,plain,
% 2.61/2.81 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1670, 2947, 354, 14081, 14092, 14094])).
% 2.61/2.81 tff(14102,plain,
% 2.61/2.81 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[319, 14101])).
% 2.61/2.81 tff(14103,plain,
% 2.61/2.81 (b(s(s(elem!1)), z)),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[5056, 11096, 670, 408, 134, 323, 305])).
% 2.61/2.81 tff(14104,plain,
% 2.61/2.81 (~b(s(s(elem!1)), s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[5572, 14103, 585, 491])).
% 2.61/2.81 tff(14105,plain,
% 2.61/2.81 (r(s(s(elem!1)), s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[1283, 14104, 2854])).
% 2.61/2.81 tff(14106,plain,
% 2.61/2.81 (~r(s(s(elem!1)), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[4994, 333, 14105, 434, 1230])).
% 2.61/2.81 tff(14107,plain,
% 2.61/2.81 (b(s(s(elem!1)), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[4983, 14106])).
% 2.61/2.81 tff(14108,plain,
% 2.61/2.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[3662, 14105, 525, 524])).
% 2.61/2.81 tff(14109,plain,
% 2.61/2.81 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[2758, 14108, 11085])).
% 2.61/2.81 tff(14110,plain,
% 2.61/2.81 (~r(s(z), s(s(elem!1)))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[7828, 333, 14105, 434, 1230])).
% 2.61/2.81 tff(14111,plain,
% 2.61/2.81 (b(s(z), s(s(elem!1)))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[5484, 14110])).
% 2.61/2.81 tff(14112,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14113,plain,
% 2.61/2.81 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.81 inference(rewrite,[status(thm)],[])).
% 2.61/2.81 tff(14114,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.61/2.81 inference(monotonicity,[status(thm)],[14113])).
% 2.61/2.81 tff(14115,plain,
% 2.61/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.81 inference(transitivity,[status(thm)],[14114, 14112])).
% 2.61/2.81 tff(14116,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.81 inference(quant_inst,[status(thm)],[])).
% 2.61/2.81 tff(14117,plain,
% 2.61/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.61/2.81 inference(modus_ponens,[status(thm)],[14116, 14115])).
% 2.61/2.81 tff(14118,plain,
% 2.61/2.81 ($false),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14117, 144, 14111, 14109, 304, 14107])).
% 2.61/2.81 tff(14119,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.81 tff(14120,plain,
% 2.61/2.81 (~(s(s(s(z))) = s(elem!1))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[14119, 14102, 14092, 2950, 14100, 14098, 2854, 14096, 14094, 670, 408, 134, 14081, 14083, 1])).
% 2.61/2.81 tff(14121,plain,
% 2.61/2.81 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[3953, 144, 134, 305, 133])).
% 2.61/2.81 tff(14122,plain,
% 2.61/2.81 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.81 inference(unit_resolution,[status(thm)],[319, 14121])).
% 2.61/2.82 tff(14123,plain,
% 2.61/2.82 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1497, 333, 354, 323, 14122])).
% 2.61/2.82 tff(14124,plain,
% 2.61/2.82 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[300, 44, 273, 14123])).
% 2.61/2.82 tff(14125,plain,
% 2.61/2.82 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1658, 333, 323, 434, 14122])).
% 2.61/2.82 tff(14126,plain,
% 2.61/2.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[540, 44, 537, 14125])).
% 2.61/2.82 tff(14127,plain,
% 2.61/2.82 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[591, 144, 451, 1357, 133])).
% 2.61/2.82 tff(14128,plain,
% 2.61/2.82 ($false),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14127, 14126, 14124])).
% 2.61/2.82 tff(14129,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.82 tff(14130,plain,
% 2.61/2.82 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14129, 2947, 14083, 14081, 14092, 354, 134, 451])).
% 2.61/2.82 tff(14131,plain,
% 2.61/2.82 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[130, 14130, 114])).
% 2.61/2.82 tff(14132,plain,
% 2.61/2.82 (~b(s(s(s(z))), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[3170, 144, 491, 585, 285])).
% 2.61/2.82 tff(14133,plain,
% 2.61/2.82 (r(s(s(s(z))), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1951, 44, 1948, 14132])).
% 2.61/2.82 tff(14134,plain,
% 2.61/2.82 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14135,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14134])).
% 2.61/2.82 tff(14136,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.82 inference(transitivity,[status(thm)],[14135, 14031])).
% 2.61/2.82 tff(14137,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.61/2.82 inference(quant_inst,[status(thm)],[])).
% 2.61/2.82 tff(14138,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14137, 14136])).
% 2.61/2.82 tff(14139,plain,
% 2.61/2.82 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14138, 144, 285, 286, 259])).
% 2.61/2.82 tff(14140,plain,
% 2.61/2.82 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1137, 14139])).
% 2.61/2.82 tff(14141,plain,
% 2.61/2.82 (((~![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(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), 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(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14142,plain,
% 2.61/2.82 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14143,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14142])).
% 2.61/2.82 tff(14144,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.82 inference(transitivity,[status(thm)],[14143, 14141])).
% 2.61/2.82 tff(14145,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.61/2.82 inference(quant_inst,[status(thm)],[])).
% 2.61/2.82 tff(14146,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14145, 14144])).
% 2.61/2.82 tff(14147,plain,
% 2.61/2.82 ($false),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14146, 333, 2484, 14140, 14133, 525])).
% 2.61/2.82 tff(14148,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.82 tff(14149,plain,
% 2.61/2.82 (~b(s(s(s(z))), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14148, 14131, 14100, 14120, 14079, 259, 14094, 14096])).
% 2.61/2.82 tff(14150,plain,
% 2.61/2.82 (r(s(s(s(z))), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[396, 14149])).
% 2.61/2.82 tff(14151,plain,
% 2.61/2.82 (~r(s(s(s(z))), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[2079, 14150, 670, 408])).
% 2.61/2.82 tff(14152,plain,
% 2.61/2.82 (~r(s(s(s(z))), s(z))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[6565, 14150, 354, 2950])).
% 2.61/2.82 tff(14153,plain,
% 2.61/2.82 (b(s(s(s(z))), s(z))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[2794, 14152])).
% 2.61/2.82 tff(14154,plain,
% 2.61/2.82 (~b(s(s(s(z))), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[4375, 14153, 14083, 134])).
% 2.61/2.82 tff(14155,plain,
% 2.61/2.82 (s(s(s(z))) = elem!1),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[704, 14154, 14151])).
% 2.61/2.82 tff(14156,plain,
% 2.61/2.82 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[7595, 14155, 863])).
% 2.61/2.82 tff(14157,plain,
% 2.61/2.82 (b(s(s(elem!1)), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5056, 14156, 670, 408, 134, 14081, 14083])).
% 2.61/2.82 tff(14158,plain,
% 2.61/2.82 (~b(s(s(elem!1)), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5572, 14157, 14096, 14094])).
% 2.61/2.82 tff(14159,plain,
% 2.61/2.82 (r(s(s(elem!1)), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1283, 14158, 2854])).
% 2.61/2.82 tff(14160,plain,
% 2.61/2.82 (~r(s(s(elem!1)), s(z))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[4994, 333, 14159, 14092, 2950])).
% 2.61/2.82 tff(14161,plain,
% 2.61/2.82 (b(s(s(elem!1)), s(z))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[4983, 14160])).
% 2.61/2.82 tff(14162,plain,
% 2.61/2.82 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[7608, 14155, 706])).
% 2.61/2.82 tff(14163,plain,
% 2.61/2.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[3662, 14159, 14100, 14098])).
% 2.61/2.82 tff(14164,plain,
% 2.61/2.82 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[2758, 14163, 14162])).
% 2.61/2.82 tff(14165,plain,
% 2.61/2.82 (~r(s(z), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[7828, 333, 14159, 14092, 2950])).
% 2.61/2.82 tff(14166,plain,
% 2.61/2.82 (b(s(z), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5484, 14165])).
% 2.61/2.82 tff(14167,plain,
% 2.61/2.82 ($false),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14117, 144, 14166, 14164, 14102, 14161])).
% 2.61/2.82 tff(14168,plain,(b(s(z), s(elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (s(z) = elem!1) | (~r(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.82 tff(14169,plain,
% 2.61/2.82 (b(s(z), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14168, 114, 670, 408, 134, 706, 354, 259, 1, 2727, 1728, 123])).
% 2.61/2.82 tff(14170,plain,
% 2.61/2.82 (~b(s(s(elem!1)), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5570, 144, 491, 585, 1249])).
% 2.61/2.82 tff(14171,plain,
% 2.61/2.82 (r(s(s(elem!1)), z)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5041, 44, 1094, 14170])).
% 2.61/2.82 tff(14172,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14173,plain,
% 2.61/2.82 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14174,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14173])).
% 2.61/2.82 tff(14175,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(transitivity,[status(thm)],[14174, 14172])).
% 2.61/2.82 tff(14176,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 2.61/2.82 inference(quant_inst,[status(thm)],[])).
% 2.61/2.82 tff(14177,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14176, 14175])).
% 2.61/2.82 tff(14178,plain,
% 2.61/2.82 (~b(s(z), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14177, 144, 451, 134, 1249, 1262])).
% 2.61/2.82 tff(14179,plain,
% 2.61/2.82 (r(s(z), s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[5484, 14178])).
% 2.61/2.82 tff(14180,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~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(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14181,plain,
% 2.61/2.82 (((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14182,plain,
% 2.61/2.82 (((~![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(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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14181])).
% 2.61/2.82 tff(14183,plain,
% 2.61/2.82 (((~![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(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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 2.61/2.82 inference(transitivity,[status(thm)],[14182, 14180])).
% 2.61/2.82 tff(14184,plain,
% 2.61/2.82 ((~![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(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.61/2.82 inference(quant_inst,[status(thm)],[])).
% 2.61/2.82 tff(14185,plain,
% 2.61/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14184, 14183])).
% 2.61/2.82 tff(14186,plain,
% 2.61/2.82 ($false),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14185, 333, 354, 323, 14179, 14171])).
% 2.61/2.82 tff(14187,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.82 tff(14188,plain,
% 2.61/2.82 (~b(s(s(elem!1)), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14187, 14169, 1728, 14089, 134, 14081, 14087, 354])).
% 2.61/2.82 tff(14189,plain,
% 2.61/2.82 (r(s(s(elem!1)), s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1283, 14188, 2727])).
% 2.61/2.82 tff(14190,plain,
% 2.61/2.82 (r(elem!1, s(elem!1))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1732, 14169, 1727, 902, 134])).
% 2.61/2.82 tff(14191,plain,
% 2.61/2.82 (((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14192,plain,
% 2.61/2.82 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(rewrite,[status(thm)],[])).
% 2.61/2.82 tff(14193,plain,
% 2.61/2.82 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14192])).
% 2.61/2.82 tff(14194,plain,
% 2.61/2.82 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.82 inference(transitivity,[status(thm)],[14193, 14191])).
% 2.61/2.82 tff(14195,plain,
% 2.61/2.82 ((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.61/2.82 inference(quant_inst,[status(thm)],[])).
% 2.61/2.82 tff(14196,plain,
% 2.61/2.82 ((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14195, 14194])).
% 2.61/2.82 tff(14197,plain,
% 2.61/2.82 (~r(s(s(elem!1)), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14196, 333, 14190, 14189, 14085])).
% 2.61/2.82 tff(14198,plain,
% 2.61/2.82 (elem!1 = s(s(s(s(s(s(z))))))),
% 2.61/2.82 inference(transitivity,[status(thm)],[1193, 6163, 20])).
% 2.61/2.82 tff(14199,plain,
% 2.61/2.82 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14198])).
% 2.61/2.82 tff(14200,plain,
% 2.61/2.82 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[134, 14199])).
% 2.61/2.82 tff(14201,plain,
% 2.61/2.82 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[6102, 14198])).
% 2.61/2.82 tff(14202,plain,
% 2.61/2.82 (~(elem!1 = s(s(elem!1)))),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1216, 3326])).
% 2.61/2.82 tff(14203,plain,
% 2.61/2.82 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1223, 14202])).
% 2.61/2.82 tff(14204,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.61/2.82 tff(14205,plain,
% 2.61/2.82 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[1260, 44, 14204])).
% 2.61/2.82 tff(14206,plain,
% 2.61/2.82 (b(s(s(elem!1)), elem!1)),
% 2.61/2.82 inference(unit_resolution,[status(thm)],[14205, 14203])).
% 2.61/2.82 tff(14207,plain,
% 2.61/2.82 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[14206, 14201])).
% 2.61/2.82 tff(14208,plain,
% 2.61/2.82 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 2.61/2.82 inference(monotonicity,[status(thm)],[14198])).
% 2.61/2.82 tff(14209,plain,
% 2.61/2.82 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.61/2.82 inference(modus_ponens,[status(thm)],[305, 14208])).
% 2.61/2.82 tff(14210,plain,
% 2.61/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14211,plain,
% 2.61/2.83 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14212,plain,
% 2.61/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))))))),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14211])).
% 2.61/2.83 tff(14213,plain,
% 2.61/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 2.61/2.83 inference(transitivity,[status(thm)],[14212, 14210])).
% 2.61/2.83 tff(14214,plain,
% 2.61/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 2.61/2.83 inference(quant_inst,[status(thm)],[])).
% 2.61/2.83 tff(14215,plain,
% 2.61/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14214, 14213])).
% 2.61/2.83 tff(14216,plain,
% 2.61/2.83 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14215, 144, 14209, 14207, 14200])).
% 2.61/2.83 tff(14217,plain,
% 2.61/2.83 (~b(s(s(elem!1)), s(z))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14216, 6144])).
% 2.61/2.83 tff(14218,plain,
% 2.61/2.83 (r(s(s(elem!1)), s(z))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[4983, 14217])).
% 2.61/2.83 tff(14219,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14218, 6142])).
% 2.61/2.83 tff(14220,plain,
% 2.61/2.83 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.83 inference(monotonicity,[status(thm)],[927])).
% 2.61/2.83 tff(14221,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[434, 14220])).
% 2.61/2.83 tff(14222,plain,
% 2.61/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14223,plain,
% 2.61/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.83 inference(quant_inst,[status(thm)],[])).
% 2.61/2.83 tff(14224,plain,
% 2.61/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14223, 14222])).
% 2.61/2.83 tff(14225,plain,
% 2.61/2.83 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14224, 333, 323, 14221, 14219])).
% 2.61/2.83 tff(14226,plain,
% 2.61/2.83 ($false),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14225, 6225])).
% 2.61/2.83 tff(14227,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14228,plain,
% 2.61/2.83 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14227, 14081, 14083, 134, 14085, 14189, 14197])).
% 2.61/2.83 tff(14229,plain,
% 2.61/2.83 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14228, 12511])).
% 2.61/2.83 tff(14230,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[542, 14229, 14090])).
% 2.61/2.83 tff(14231,plain,
% 2.61/2.83 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14129, 14229, 14083, 14081, 14085, 354, 134, 1728])).
% 2.61/2.83 tff(14232,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[130, 14231, 114])).
% 2.61/2.83 tff(14233,plain,
% 2.61/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14234,plain,
% 2.61/2.83 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14235,plain,
% 2.61/2.83 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14234])).
% 2.61/2.83 tff(14236,plain,
% 2.61/2.83 (((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.61/2.83 inference(transitivity,[status(thm)],[14235, 14233])).
% 2.61/2.83 tff(14237,plain,
% 2.61/2.83 ((~![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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.83 inference(quant_inst,[status(thm)],[])).
% 2.61/2.83 tff(14238,plain,
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% 2.61/2.83 inference(modus_ponens,[status(thm)],[14237, 14236])).
% 2.61/2.83 tff(14239,plain,
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% 2.61/2.83 tff(14240,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(z))) | (~b(s(z), elem!1)) | r(s(elem!1), elem!1) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(z) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14241,plain,
% 2.61/2.83 (r(s(elem!1), elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14240, 14077, 670, 114, 134, 354, 2322, 706, 259, 1, 123])).
% 2.61/2.83 tff(14242,plain,
% 2.61/2.83 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[13988, 14241, 2545, 377, 13970, 77])).
% 2.61/2.83 tff(14243,plain,
% 2.61/2.83 (~r(s(elem!1), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[4411, 14241, 1, 670, 305, 14077, 323, 354])).
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% 2.61/2.83 (b(s(elem!1), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[507, 14243])).
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% 2.61/2.83 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[10345, 144, 14244, 13970, 259])).
% 2.61/2.83 tff(14246,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[472, 14245, 197, 14242])).
% 2.61/2.83 tff(14247,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, z) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), elem!1)) | (s(z) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14248,plain,
% 2.61/2.83 (~(s(s(s(z))) = elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14247, 14073, 1, 670, 259, 13972, 354, 13975, 377, 114, 134, 14071, 123])).
% 2.61/2.83 tff(14249,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[704, 14248, 55])).
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% 2.61/2.83 (~r(s(s(s(z))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[2079, 707, 670, 408])).
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% 2.61/2.83 (b(s(s(s(z))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[396, 14250])).
% 2.61/2.83 tff(14252,plain,
% 2.61/2.83 (~r(z, s(s(s(z))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[2136, 707, 670, 408])).
% 2.61/2.83 tff(14253,plain,
% 2.61/2.83 (b(z, s(s(s(z))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[619, 14252])).
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[294, 14253, 14251, 283, 286])).
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% 2.61/2.83 tff(14256,plain,
% 2.61/2.83 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14255, 14249, 670, 2322, 13970])).
% 2.61/2.83 tff(14257,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[249, 14256])).
% 2.61/2.83 tff(14258,plain,
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% 2.61/2.83 inference(rewrite,[status(thm)],[])).
% 2.61/2.83 tff(14259,plain,
% 2.61/2.83 ((~![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(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.61/2.83 inference(quant_inst,[status(thm)],[])).
% 2.61/2.83 tff(14260,plain,
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% 2.61/2.83 inference(modus_ponens,[status(thm)],[14259, 14258])).
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[14260, 333, 2322, 14249, 2484, 14257])).
% 2.61/2.83 tff(14262,plain,(b(elem!1, z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14263,plain,
% 2.61/2.83 (b(elem!1, z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14262, 7265, 2484, 55, 1, 8045, 14053, 8049, 14054, 123, 3])).
% 2.61/2.83 tff(14264,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[14047, 144, 14263, 14054, 123, 8045])).
% 2.61/2.83 tff(14265,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[348, 14264])).
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% 2.61/2.83 (~b(s(z), s(z))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14061, 144, 14054, 123, 8052])).
% 2.61/2.83 tff(14267,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[14069, 14054, 14266])).
% 2.61/2.83 tff(14268,plain,
% 2.61/2.83 (~r(elem!1, s(z))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[727, 14265, 7265, 14053])).
% 2.61/2.83 tff(14269,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[720, 14268, 14267])).
% 2.61/2.83 tff(14270,plain,
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% 2.61/2.83 tff(14271,plain,
% 2.61/2.83 (b(z, s(elem!1))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[583, 14270])).
% 2.61/2.83 tff(14272,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[2974, 14271, 606])).
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% 2.61/2.83 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[632, 14269, 8052, 123, 14263])).
% 2.61/2.83 tff(14274,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[302, 14273])).
% 2.61/2.83 tff(14275,plain,
% 2.61/2.83 (~r(elem!1, s(elem!1))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[8367, 14274, 2484, 7265])).
% 2.61/2.83 tff(14276,plain,
% 2.61/2.83 (b(elem!1, s(elem!1))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[560, 14275, 14272])).
% 2.61/2.83 tff(14277,plain,
% 2.61/2.83 (~b(s(elem!1), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[8787, 14276, 8045, 8052, 14263])).
% 2.61/2.83 tff(14278,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[507, 14277])).
% 2.61/2.83 tff(14279,plain,
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% 2.61/2.83 inference(modus_ponens,[status(thm)],[14267, 14055])).
% 2.61/2.83 tff(14280,plain,
% 2.61/2.83 (~r(s(elem!1), elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[5456, 14276, 1, 14053, 14279, 14263, 14265, 14269, 14272, 7265])).
% 2.61/2.83 tff(14281,plain,
% 2.61/2.83 (~b(s(z), s(elem!1))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[1732, 14280, 14054, 14272, 14275])).
% 2.61/2.83 tff(14282,plain,
% 2.61/2.83 (r(s(z), s(elem!1))),
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[1235, 14282, 14278, 14265, 14053])).
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% 2.61/2.83 tff(14285,plain,
% 2.61/2.83 (b(s(s(s(z))), elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14284, 606, 2484, 123, 1, 3, 2303])).
% 2.61/2.83 tff(14286,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[720, 713, 715])).
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% 2.61/2.83 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
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% 2.61/2.83 tff(14288,plain,
% 2.61/2.83 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[1137, 14287])).
% 2.61/2.83 tff(14289,plain,
% 2.61/2.83 (~b(s(s(s(z))), s(z))),
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% 2.61/2.83 tff(14290,plain,
% 2.61/2.83 (r(s(s(s(z))), s(z))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[2794, 14289])).
% 2.61/2.83 tff(14291,plain,
% 2.61/2.83 (~r(s(s(s(z))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[11212, 14290, 670, 10280])).
% 2.61/2.83 tff(14292,plain,
% 2.61/2.83 (b(s(s(s(z))), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[396, 14291])).
% 2.61/2.83 tff(14293,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[14036, 144, 14292, 14288, 286, 259])).
% 2.61/2.83 tff(14294,plain,((s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14295,plain,
% 2.61/2.83 (s(z) = elem!1),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14294, 13798, 8045, 7265, 12015, 123, 14285, 13802, 13801])).
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% 2.61/2.83 (r(s(elem!1), elem!1)),
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% 2.61/2.83 tff(14297,plain,
% 2.61/2.83 (~r(s(elem!1), z)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[10296, 333, 14296, 7265, 408])).
% 2.61/2.83 tff(14298,plain,
% 2.61/2.83 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14295])).
% 2.61/2.83 tff(14299,plain,
% 2.61/2.83 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
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% 2.61/2.83 tff(14300,plain,
% 2.61/2.83 (r(s(elem!1), s(z))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14296, 14299])).
% 2.61/2.83 tff(14301,plain,
% 2.61/2.83 (s(s(z)) = s(elem!1)),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14295])).
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% 2.61/2.83 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14301])).
% 2.61/2.83 tff(14303,plain,
% 2.61/2.83 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
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% 2.61/2.83 tff(14304,plain,
% 2.61/2.83 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14303])).
% 2.61/2.83 tff(14305,plain,
% 2.61/2.83 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[1446, 14304])).
% 2.61/2.83 tff(14306,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[8102, 14295, 606])).
% 2.61/2.83 tff(14307,plain,
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[372, 14306])).
% 2.61/2.83 tff(14308,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.83 inference(monotonicity,[status(thm)],[14295])).
% 2.61/2.83 tff(14309,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
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% 2.61/2.83 tff(14310,plain,
% 2.61/2.83 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[2484, 14309])).
% 2.61/2.83 tff(14311,plain,
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% 2.61/2.83 tff(14313,plain,(b(z, elem!1) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.83 tff(14314,plain,
% 2.61/2.83 (b(z, elem!1)),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[14313, 2322, 2484, 123, 1, 3, 2303])).
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% 2.61/2.83 inference(unit_resolution,[status(thm)],[63, 57, 55])).
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% 2.61/2.83 (r(s(s(elem!1)), elem!1)),
% 2.61/2.83 inference(modus_ponens,[status(thm)],[14317, 2770])).
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% 2.61/2.83 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
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% 2.61/2.83 tff(14320,plain,
% 2.61/2.83 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.83 inference(unit_resolution,[status(thm)],[7819, 44, 14319, 13332])).
% 2.61/2.83 tff(14321,plain,
% 2.61/2.83 (((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.84 inference(rewrite,[status(thm)],[])).
% 2.61/2.84 tff(14322,plain,
% 2.61/2.84 ((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.84 inference(quant_inst,[status(thm)],[])).
% 2.61/2.84 tff(14323,plain,
% 2.61/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14322, 14321])).
% 2.61/2.84 tff(14324,plain,
% 2.61/2.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14323, 333, 408, 14318, 2484])).
% 2.61/2.84 tff(14325,plain,
% 2.61/2.84 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2758, 14324, 10047])).
% 2.61/2.84 tff(14326,plain,
% 2.61/2.84 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14325, 4019])).
% 2.61/2.84 tff(14327,plain,
% 2.61/2.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14319, 4024])).
% 2.61/2.84 tff(14328,plain,
% 2.61/2.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[1137, 14327])).
% 2.61/2.84 tff(14329,plain,
% 2.61/2.84 (~b(s(z), s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2262, 14328, 123, 14326])).
% 2.61/2.84 tff(14330,plain,
% 2.61/2.84 (~b(elem!1, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[13482, 14329, 57])).
% 2.61/2.84 tff(14331,plain,
% 2.61/2.84 (r(elem!1, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[1538, 14330, 3516])).
% 2.61/2.84 tff(14332,plain,
% 2.61/2.84 (~r(z, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[7510, 14331, 408, 14317])).
% 2.61/2.84 tff(14333,plain,
% 2.61/2.84 (b(z, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[619, 14332])).
% 2.61/2.84 tff(14334,plain,
% 2.61/2.84 (b(z, s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2828, 14333, 57])).
% 2.61/2.84 tff(14335,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[8617, 144, 14334, 14325, 14320, 259])).
% 2.61/2.84 tff(14336,plain,((~(s(z) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14337,plain,
% 2.61/2.84 (~(s(z) = elem!1)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14336, 4414, 259, 123, 2484, 55])).
% 2.61/2.84 tff(14338,plain,
% 2.61/2.84 (r(s(z), elem!1)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[406, 14337, 350])).
% 2.61/2.84 tff(14339,plain,
% 2.61/2.84 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[12109, 14338, 2484, 4414])).
% 2.61/2.84 tff(14340,plain,
% 2.61/2.84 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[319, 14339])).
% 2.61/2.84 tff(14341,plain,
% 2.61/2.84 (((~![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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.84 inference(rewrite,[status(thm)],[])).
% 2.61/2.84 tff(14342,plain,
% 2.61/2.84 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.84 inference(rewrite,[status(thm)],[])).
% 2.61/2.84 tff(14343,plain,
% 2.61/2.84 (((~![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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14342])).
% 2.61/2.84 tff(14344,plain,
% 2.61/2.84 (((~![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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.61/2.84 inference(transitivity,[status(thm)],[14343, 14341])).
% 2.61/2.84 tff(14345,plain,
% 2.61/2.84 ((~![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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.84 inference(quant_inst,[status(thm)],[])).
% 2.61/2.84 tff(14346,plain,
% 2.61/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14345, 14344])).
% 2.61/2.84 tff(14347,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14346, 333, 354, 408, 2484, 321])).
% 2.61/2.84 tff(14348,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14349,plain,
% 2.61/2.84 (~r(z, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14348, 8071, 2484, 408])).
% 2.61/2.84 tff(14350,plain,
% 2.61/2.84 (b(z, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[372, 14349])).
% 2.61/2.84 tff(14351,plain,
% 2.61/2.84 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[757, 14350, 123, 259])).
% 2.61/2.84 tff(14352,plain,
% 2.61/2.84 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[319, 14351])).
% 2.61/2.84 tff(14353,plain,
% 2.61/2.84 (~r(s(z), elem!1)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[12109, 14352, 2484, 408])).
% 2.61/2.84 tff(14354,plain,
% 2.61/2.84 (s(z) = elem!1),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[406, 14353, 350])).
% 2.61/2.84 tff(14355,plain,
% 2.61/2.84 (b(s(z), z) <=> b(elem!1, z)),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14354])).
% 2.61/2.84 tff(14356,plain,
% 2.61/2.84 (b(elem!1, z) <=> b(s(z), z)),
% 2.61/2.84 inference(symmetry,[status(thm)],[14355])).
% 2.61/2.84 tff(14357,plain,
% 2.61/2.84 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14356])).
% 2.61/2.84 tff(14358,plain,
% 2.61/2.84 (~b(s(z), z)),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[377, 14357])).
% 2.61/2.84 tff(14359,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[489, 14358])).
% 2.61/2.84 tff(14360,plain,((~b(s(z), z)) | b(elem!1, z) | b(s(z), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14361,plain,
% 2.61/2.84 (~b(s(z), z)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14360, 377, 350, 2484, 4414, 123, 259])).
% 2.61/2.84 tff(14362,plain,
% 2.61/2.84 (r(s(z), z)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[348, 14361])).
% 2.61/2.84 tff(14363,plain,
% 2.61/2.84 (~r(z, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[1376, 14338, 4414, 14362])).
% 2.61/2.84 tff(14364,plain,
% 2.61/2.84 (b(z, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[372, 14363])).
% 2.61/2.84 tff(14365,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[757, 14364, 14340, 123, 259])).
% 2.61/2.84 tff(14366,plain,(b(elem!1, z) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14367,plain,
% 2.61/2.84 (b(elem!1, z)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14366, 350, 259, 2484, 123, 55, 77])).
% 2.61/2.84 tff(14368,plain,
% 2.61/2.84 (~b(elem!1, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[813, 490, 123, 251, 259])).
% 2.61/2.84 tff(14369,plain,
% 2.61/2.84 (r(elem!1, s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[720, 14368, 714])).
% 2.61/2.84 tff(14370,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[12172, 14369, 13804, 2484, 409])).
% 2.61/2.84 tff(14371,plain,((~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14372,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14371, 7670, 713, 2484, 490, 123, 251, 259])).
% 2.61/2.84 tff(14373,plain,((s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14374,plain,
% 2.61/2.84 (s(z) = elem!1),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14373, 490, 2484, 123, 251, 259, 350])).
% 2.61/2.84 tff(14375,plain,
% 2.61/2.84 (s(s(z)) = s(elem!1)),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14374])).
% 2.61/2.84 tff(14376,plain,
% 2.61/2.84 (s(s(s(z))) = s(s(elem!1))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14375])).
% 2.61/2.84 tff(14377,plain,
% 2.61/2.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14376])).
% 2.61/2.84 tff(14378,plain,
% 2.61/2.84 (~b(s(s(s(z))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[63, 14374, 55])).
% 2.61/2.84 tff(14379,plain,
% 2.61/2.84 (r(s(s(s(z))), s(z))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2794, 14378])).
% 2.61/2.84 tff(14380,plain,
% 2.61/2.84 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[2495])).
% 2.61/2.84 tff(14381,plain,
% 2.61/2.84 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.61/2.84 inference(symmetry,[status(thm)],[14380])).
% 2.61/2.84 tff(14382,plain,
% 2.61/2.84 (~b(s(z), s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[5343, 5340, 57])).
% 2.61/2.84 tff(14383,plain,
% 2.61/2.84 (r(s(z), s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[172, 14382])).
% 2.61/2.84 tff(14384,plain,
% 2.61/2.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[10422, 14383, 322, 3193])).
% 2.61/2.84 tff(14385,plain,
% 2.61/2.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[1137, 14384])).
% 2.61/2.84 tff(14386,plain,
% 2.61/2.84 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14385, 4584])).
% 2.61/2.84 tff(14387,plain,
% 2.61/2.84 (r(elem!1, s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2522, 5340, 2462])).
% 2.61/2.84 tff(14388,plain,
% 2.61/2.84 (r(s(s(s(z))), elem!1)),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[3193, 2768])).
% 2.61/2.84 tff(14389,plain,
% 2.61/2.84 (r(s(s(elem!1)), elem!1)),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14388, 2770])).
% 2.61/2.84 tff(14390,plain,
% 2.61/2.84 (((~![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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.84 inference(rewrite,[status(thm)],[])).
% 2.61/2.84 tff(14391,plain,
% 2.61/2.84 ((~![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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.84 inference(quant_inst,[status(thm)],[])).
% 2.61/2.84 tff(14392,plain,
% 2.61/2.84 ((~![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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14391, 14390])).
% 2.61/2.84 tff(14393,plain,
% 2.61/2.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14392, 333, 14389, 14387, 2484])).
% 2.61/2.84 tff(14394,plain,
% 2.61/2.84 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2758, 14393, 10047])).
% 2.61/2.84 tff(14395,plain,
% 2.61/2.84 (((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.84 inference(rewrite,[status(thm)],[])).
% 2.61/2.84 tff(14396,plain,
% 2.61/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14395])).
% 2.61/2.84 tff(14397,plain,
% 2.61/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.84 inference(transitivity,[status(thm)],[14396, 8612])).
% 2.61/2.84 tff(14398,plain,
% 2.61/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.84 inference(quant_inst,[status(thm)],[])).
% 2.61/2.84 tff(14399,plain,
% 2.61/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14398, 14397])).
% 2.61/2.84 tff(14400,plain,
% 2.61/2.84 (~b(z, s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14399, 144, 14394, 14386, 259])).
% 2.61/2.84 tff(14401,plain,
% 2.61/2.84 (~b(z, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2828, 14400, 57])).
% 2.61/2.84 tff(14402,plain,
% 2.61/2.84 (r(z, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[619, 14401])).
% 2.61/2.84 tff(14403,plain,
% 2.61/2.84 (r(z, s(s(elem!1)))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[2836, 14402, 57])).
% 2.61/2.84 tff(14404,plain,
% 2.61/2.84 ($false),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[13902, 144, 624, 132, 286, 259])).
% 2.61/2.84 tff(14405,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.84 tff(14406,plain,
% 2.61/2.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[14405, 624, 132, 259])).
% 2.61/2.84 tff(14407,plain,
% 2.61/2.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[302, 14406])).
% 2.61/2.84 tff(14408,plain,
% 2.61/2.84 (~b(elem!1, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[13482, 14382, 57])).
% 2.61/2.84 tff(14409,plain,
% 2.61/2.84 (r(elem!1, s(s(s(z))))),
% 2.61/2.84 inference(unit_resolution,[status(thm)],[1538, 14408, 3516])).
% 2.61/2.84 tff(14410,plain,
% 2.61/2.84 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.84 inference(symmetry,[status(thm)],[8165])).
% 2.61/2.84 tff(14411,plain,
% 2.61/2.84 ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.61/2.84 inference(monotonicity,[status(thm)],[14410])).
% 2.61/2.84 tff(14412,plain,
% 2.61/2.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.84 inference(modus_ponens,[status(thm)],[14393, 14411])).
% 2.61/2.85 tff(14413,plain,
% 2.61/2.85 (r(s(elem!1), elem!1)),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[448, 7436, 2681])).
% 2.61/2.85 tff(14414,plain,
% 2.61/2.85 (~r(s(elem!1), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[10761, 14413, 3193, 1525])).
% 2.61/2.85 tff(14415,plain,
% 2.61/2.85 (b(s(elem!1), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[965, 14414, 11786])).
% 2.61/2.85 tff(14416,plain,
% 2.61/2.85 (b(s(s(z)), s(s(s(z))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14415, 14381])).
% 2.61/2.85 tff(14417,plain,
% 2.61/2.85 (~b(elem!1, s(elem!1))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[8787, 491, 259, 132, 624])).
% 2.61/2.85 tff(14418,plain,
% 2.61/2.85 (r(elem!1, s(elem!1))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[560, 14417, 2483])).
% 2.61/2.85 tff(14419,plain,
% 2.61/2.85 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[12698, 14413, 2484, 14418])).
% 2.61/2.85 tff(14420,plain,
% 2.61/2.85 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[2674, 14419, 57])).
% 2.61/2.85 tff(14421,plain,
% 2.61/2.85 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[1451, 14420])).
% 2.61/2.85 tff(14422,plain,
% 2.61/2.85 (~b(s(s(z)), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[7952, 14421, 7927, 7926])).
% 2.61/2.85 tff(14423,plain,
% 2.61/2.85 ($false),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14422, 14416])).
% 2.61/2.85 tff(14424,plain,((~b(s(elem!1), z)) | (~(s(z) = elem!1)) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.85 tff(14425,plain,
% 2.61/2.85 (~b(s(elem!1), z)),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14424, 14384, 57, 14412, 3193, 14409, 2484, 251, 624, 259, 132])).
% 2.61/2.85 tff(14426,plain,
% 2.61/2.85 (r(s(elem!1), z)),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[507, 14425])).
% 2.61/2.85 tff(14427,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14428,plain,
% 2.61/2.85 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14429,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14428])).
% 2.61/2.85 tff(14430,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(transitivity,[status(thm)],[14429, 14427])).
% 2.61/2.85 tff(14431,plain,
% 2.61/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(quant_inst,[status(thm)],[])).
% 2.61/2.85 tff(14432,plain,
% 2.61/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14431, 14430])).
% 2.61/2.85 tff(14433,plain,
% 2.61/2.85 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14432, 333, 14426, 14407, 14403])).
% 2.61/2.85 tff(14434,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14435,plain,
% 2.61/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.61/2.85 inference(quant_inst,[status(thm)],[])).
% 2.61/2.85 tff(14436,plain,
% 2.61/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14435, 14434])).
% 2.61/2.85 tff(14437,plain,
% 2.61/2.85 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14436, 333, 14426, 14407, 14403])).
% 2.61/2.85 tff(14438,plain,
% 2.61/2.85 (~b(z, s(elem!1))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[8386, 14437, 259, 2698, 14433])).
% 2.61/2.85 tff(14439,plain,
% 2.61/2.85 (r(z, s(elem!1))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[583, 14438])).
% 2.61/2.85 tff(14440,plain,
% 2.61/2.85 (~r(s(elem!1), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[1929, 14439, 14388, 14402])).
% 2.61/2.85 tff(14441,plain,
% 2.61/2.85 (b(s(elem!1), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[965, 14440, 11786])).
% 2.61/2.85 tff(14442,plain,
% 2.61/2.85 (b(s(s(z)), s(s(s(z))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14441, 14381])).
% 2.61/2.85 tff(14443,plain,
% 2.61/2.85 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[2674, 14433, 57])).
% 2.61/2.85 tff(14444,plain,
% 2.61/2.85 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[1451, 14443])).
% 2.61/2.85 tff(14445,plain,
% 2.61/2.85 (~b(s(s(z)), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[7952, 14444, 14384, 14412])).
% 2.61/2.85 tff(14446,plain,
% 2.61/2.85 ($false),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14445, 14442])).
% 2.61/2.85 tff(14447,plain,(b(elem!1, s(s(elem!1))) | (~(s(z) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.85 tff(14448,plain,
% 2.61/2.85 (b(elem!1, s(s(elem!1)))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14447, 14374, 259, 14379, 2484, 251, 624, 132, 13804])).
% 2.61/2.85 tff(14449,plain,
% 2.61/2.85 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14376])).
% 2.61/2.85 tff(14450,plain,
% 2.61/2.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14374])).
% 2.61/2.85 tff(14451,plain,
% 2.61/2.85 (r(s(s(s(z))), elem!1)),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14379, 14450])).
% 2.61/2.85 tff(14452,plain,
% 2.61/2.85 (r(s(s(elem!1)), elem!1)),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14451, 14449])).
% 2.61/2.85 tff(14453,plain,
% 2.61/2.85 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[2254, 4584])).
% 2.61/2.85 tff(14454,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14455,plain,
% 2.61/2.85 (((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14456,plain,
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% 2.61/2.85 inference(monotonicity,[status(thm)],[14455])).
% 2.61/2.85 tff(14457,plain,
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% 2.61/2.85 inference(modus_ponens,[status(thm)],[14458, 14457])).
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% 2.61/2.85 (~b(z, s(s(elem!1)))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[14459, 144, 251, 2812, 14453, 259])).
% 2.61/2.85 tff(14461,plain,
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% 2.61/2.85 inference(unit_resolution,[status(thm)],[2828, 14460, 57])).
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% 2.61/2.85 (b(s(z), s(s(s(z))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[2812, 5338])).
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% 2.61/2.85 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[2262, 2254, 123, 14462])).
% 2.61/2.85 tff(14464,plain,
% 2.61/2.85 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[249, 14463])).
% 2.61/2.85 tff(14465,plain,
% 2.61/2.85 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14464, 8165])).
% 2.61/2.85 tff(14466,plain,
% 2.61/2.85 (~r(z, s(s(elem!1)))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[9411, 14465, 321, 4627])).
% 2.61/2.85 tff(14467,plain,
% 2.61/2.85 (~r(z, s(s(s(z))))),
% 2.61/2.85 inference(unit_resolution,[status(thm)],[2836, 14466, 57])).
% 2.61/2.85 tff(14468,plain,
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% 2.61/2.85 inference(unit_resolution,[status(thm)],[619, 14467, 14461])).
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% 2.61/2.85 tff(14470,plain,
% 2.61/2.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
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% 2.61/2.85 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
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% 2.61/2.85 tff(14472,plain,
% 2.61/2.85 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[14471, 14377])).
% 2.61/2.85 tff(14473,plain,
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% 2.61/2.85 inference(unit_resolution,[status(thm)],[2468, 14374])).
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% 2.61/2.85 inference(unit_resolution,[status(thm)],[2482, 14473])).
% 2.61/2.85 tff(14475,plain,
% 2.61/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14376])).
% 2.61/2.85 tff(14476,plain,
% 2.61/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14475])).
% 2.61/2.85 tff(14477,plain,
% 2.61/2.85 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.61/2.85 inference(modus_ponens,[status(thm)],[244, 14476])).
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% 2.61/2.85 tff(14479,plain,
% 2.61/2.85 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
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% 2.61/2.85 inference(monotonicity,[status(thm)],[14479])).
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% 2.61/2.85 inference(modus_ponens,[status(thm)],[14482, 14481])).
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% 2.61/2.85 tff(14486,plain,
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% 2.61/2.85 tff(14487,plain,
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% 2.61/2.85 tff(14488,plain,
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% 2.61/2.85 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.85 inference(monotonicity,[status(thm)],[14375])).
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% 2.61/2.85 inference(monotonicity,[status(thm)],[14491])).
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% 2.61/2.85 inference(unit_resolution,[status(thm)],[5467, 14503, 132, 14493, 14489])).
% 2.61/2.85 tff(14505,plain,
% 2.61/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14506,plain,
% 2.61/2.85 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.85 inference(rewrite,[status(thm)],[])).
% 2.61/2.85 tff(14507,plain,
% 2.61/2.85 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14506])).
% 2.61/2.86 tff(14508,plain,
% 2.61/2.86 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.61/2.86 inference(transitivity,[status(thm)],[14507, 14505])).
% 2.61/2.86 tff(14509,plain,
% 2.61/2.86 ((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.86 inference(quant_inst,[status(thm)],[])).
% 2.61/2.86 tff(14510,plain,
% 2.61/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.61/2.86 inference(modus_ponens,[status(thm)],[14509, 14508])).
% 2.61/2.86 tff(14511,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14510, 333, 14502, 14487, 14504, 14472])).
% 2.61/2.86 tff(14512,plain,((~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14513,plain,
% 2.61/2.86 (~b(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14512, 2241, 14367, 259, 2484, 251, 123, 55, 350])).
% 2.61/2.86 tff(14514,plain,
% 2.61/2.86 (~(s(z) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[9366, 14513, 251])).
% 2.61/2.86 tff(14515,plain,
% 2.61/2.86 (r(s(z), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[406, 14514, 350])).
% 2.61/2.86 tff(14516,plain,
% 2.61/2.86 (~(elem!1 = s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[712, 14514])).
% 2.61/2.86 tff(14517,plain,
% 2.61/2.86 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14405, 14367, 2241, 259])).
% 2.61/2.86 tff(14518,plain,
% 2.61/2.86 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[302, 14517])).
% 2.61/2.86 tff(14519,plain,
% 2.61/2.86 (r(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[372, 14513])).
% 2.61/2.86 tff(14520,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[2209, 333, 409, 354, 322, 321])).
% 2.61/2.86 tff(14521,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14522,plain,
% 2.61/2.86 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14521, 14515, 14519, 14518])).
% 2.61/2.86 tff(14523,plain,
% 2.61/2.86 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[319, 14522])).
% 2.61/2.86 tff(14524,plain,
% 2.61/2.86 (~b(elem!1, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[313, 14523, 123, 2241])).
% 2.61/2.86 tff(14525,plain,
% 2.61/2.86 (r(elem!1, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[720, 14524, 14516])).
% 2.61/2.86 tff(14526,plain,
% 2.61/2.86 (~r(s(s(s(z))), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[12189, 14525, 123, 2484, 14515])).
% 2.61/2.86 tff(14527,plain,
% 2.61/2.86 (s(s(s(z))) = elem!1),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[704, 14526, 55])).
% 2.61/2.86 tff(14528,plain,
% 2.61/2.86 (s(s(s(s(z)))) = s(elem!1)),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14527])).
% 2.61/2.86 tff(14529,plain,
% 2.61/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14528])).
% 2.61/2.86 tff(14530,plain,
% 2.61/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.86 inference(transitivity,[status(thm)],[14529, 174])).
% 2.61/2.86 tff(14531,plain,
% 2.61/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(transitivity,[status(thm)],[14530, 175])).
% 2.61/2.86 tff(14532,plain,
% 2.61/2.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14531])).
% 2.61/2.86 tff(14533,plain,
% 2.61/2.86 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(modus_ponens,[status(thm)],[196, 14532])).
% 2.61/2.86 tff(14534,plain,
% 2.61/2.86 (~(s(s(z)) = s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[855, 14514])).
% 2.61/2.86 tff(14535,plain,
% 2.61/2.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[862, 14534])).
% 2.61/2.86 tff(14536,plain,
% 2.61/2.86 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[7595, 14527, 14535])).
% 2.61/2.86 tff(14537,plain,
% 2.61/2.86 (~(elem!1 = s(s(elem!1)))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[5603, 14536])).
% 2.61/2.86 tff(14538,plain,
% 2.61/2.86 (~(s(elem!1) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[5813, 14537])).
% 2.61/2.86 tff(14539,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1177, 333, 354, 509, 321, 525])).
% 2.61/2.86 tff(14540,plain,((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14541,plain,
% 2.61/2.86 (~r(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14540, 525, 14407, 354])).
% 2.61/2.86 tff(14542,plain,
% 2.61/2.86 (b(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[507, 14541])).
% 2.61/2.86 tff(14543,plain,
% 2.61/2.86 (~b(elem!1, s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[8787, 14542, 259, 132, 624])).
% 2.61/2.86 tff(14544,plain,
% 2.61/2.86 (r(elem!1, s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[560, 14543, 1722])).
% 2.61/2.86 tff(14545,plain,
% 2.61/2.86 (~b(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[916, 14542, 251, 624])).
% 2.61/2.86 tff(14546,plain,
% 2.61/2.86 (r(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[448, 14545, 433])).
% 2.61/2.86 tff(14547,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[12698, 14546, 14544, 2484, 525])).
% 2.61/2.86 tff(14548,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14549,plain,
% 2.61/2.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14548, 14538, 2484, 251, 14367, 259, 2241, 14519])).
% 2.61/2.86 tff(14550,plain,
% 2.61/2.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[472, 14549, 14533])).
% 2.61/2.86 tff(14551,plain,
% 2.61/2.86 (~b(s(elem!1), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[3040, 144, 123, 14523, 14550])).
% 2.61/2.86 tff(14552,plain,
% 2.61/2.86 (r(s(elem!1), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[486, 14551, 1])).
% 2.61/2.86 tff(14553,plain,
% 2.61/2.86 (~(elem!1 = s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1569, 14538])).
% 2.61/2.86 tff(14554,plain,
% 2.61/2.86 (~r(z, elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[13826, 14524, 350, 14519, 14514])).
% 2.61/2.86 tff(14555,plain,
% 2.61/2.86 (~r(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1653, 14551, 14514, 14554, 14553, 1, 14519])).
% 2.61/2.86 tff(14556,plain,
% 2.61/2.86 (b(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[507, 14555])).
% 2.61/2.86 tff(14557,plain,
% 2.61/2.86 (~b(elem!1, s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[8787, 14556, 259, 2241, 14367])).
% 2.61/2.86 tff(14558,plain,
% 2.61/2.86 (r(elem!1, s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[560, 14557, 14553])).
% 2.61/2.86 tff(14559,plain,
% 2.61/2.86 (~b(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[916, 14556, 251, 14367])).
% 2.61/2.86 tff(14560,plain,
% 2.61/2.86 (r(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[448, 14559, 14538])).
% 2.61/2.86 tff(14561,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1390, 14560, 14558, 14515, 14552])).
% 2.61/2.86 tff(14562,plain,(b(s(z), elem!1) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(s(s(z))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14563,plain,
% 2.61/2.86 (b(s(z), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14562, 251, 259, 1, 123, 2484, 55, 3])).
% 2.61/2.86 tff(14564,plain,
% 2.61/2.86 (~(s(z) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14336, 2322, 259, 123, 2484, 55])).
% 2.61/2.86 tff(14565,plain,
% 2.61/2.86 (~(elem!1 = s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[712, 14564])).
% 2.61/2.86 tff(14566,plain,
% 2.61/2.86 (~b(s(z), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[2113, 297, 3, 14563, 123, 2322])).
% 2.61/2.86 tff(14567,plain,
% 2.61/2.86 (r(s(z), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[348, 14566])).
% 2.61/2.86 tff(14568,plain,
% 2.61/2.86 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[787, 2097, 377])).
% 2.61/2.86 tff(14569,plain,
% 2.61/2.86 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[116, 14568])).
% 2.61/2.86 tff(14570,plain,
% 2.61/2.86 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[121, 14569, 3])).
% 2.61/2.86 tff(14571,plain,
% 2.61/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.86 inference(rewrite,[status(thm)],[])).
% 2.61/2.86 tff(14572,plain,
% 2.61/2.86 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.86 inference(rewrite,[status(thm)],[])).
% 2.61/2.86 tff(14573,plain,
% 2.61/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14572])).
% 2.61/2.86 tff(14574,plain,
% 2.61/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.86 inference(transitivity,[status(thm)],[14573, 14571])).
% 2.61/2.86 tff(14575,plain,
% 2.61/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.61/2.86 inference(quant_inst,[status(thm)],[])).
% 2.61/2.86 tff(14576,plain,
% 2.61/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.86 inference(modus_ponens,[status(thm)],[14575, 14574])).
% 2.61/2.86 tff(14577,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14576, 144, 251, 134, 490, 132, 259])).
% 2.61/2.86 tff(14578,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14579,plain,
% 2.61/2.86 (~b(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14578, 14570, 259, 251, 14563])).
% 2.61/2.86 tff(14580,plain,
% 2.61/2.86 (r(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[372, 14579])).
% 2.61/2.86 tff(14581,plain,
% 2.61/2.86 (~r(elem!1, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[747, 14580, 2322, 14567])).
% 2.61/2.86 tff(14582,plain,
% 2.61/2.86 (b(elem!1, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[720, 14581, 14565])).
% 2.61/2.86 tff(14583,plain,
% 2.61/2.86 (~(s(s(z)) = s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[855, 14564])).
% 2.61/2.86 tff(14584,plain,
% 2.61/2.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[862, 14583])).
% 2.61/2.86 tff(14585,plain,
% 2.61/2.86 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14025, 698, 134, 408, 132, 123, 305, 114])).
% 2.61/2.86 tff(14586,plain,
% 2.61/2.86 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1137, 14585])).
% 2.61/2.86 tff(14587,plain,
% 2.61/2.86 (~r(s(s(s(z))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[2122, 12399, 408, 354])).
% 2.61/2.86 tff(14588,plain,
% 2.61/2.86 (b(s(s(s(z))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[396, 14587])).
% 2.61/2.86 tff(14589,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14036, 144, 14588, 14586, 286, 259])).
% 2.61/2.86 tff(14590,plain,((s(s(s(z))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14591,plain,
% 2.61/2.86 (s(s(s(z))) = elem!1),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14590, 2097, 259, 2322, 14580, 14563, 14570, 123, 14582, 14568, 55])).
% 2.61/2.86 tff(14592,plain,
% 2.61/2.86 (~(s(s(elem!1)) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[7595, 14591, 14584])).
% 2.61/2.86 tff(14593,plain,
% 2.61/2.86 (~(elem!1 = s(s(elem!1)))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[5603, 14592])).
% 2.61/2.86 tff(14594,plain,
% 2.61/2.86 (~(s(elem!1) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[5813, 14593])).
% 2.61/2.86 tff(14595,plain,
% 2.61/2.86 (~(elem!1 = s(elem!1))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1569, 14594])).
% 2.61/2.86 tff(14596,plain,
% 2.61/2.86 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[313, 14582, 123, 14570])).
% 2.61/2.86 tff(14597,plain,
% 2.61/2.86 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[319, 14596])).
% 2.61/2.86 tff(14598,plain,
% 2.61/2.86 (~r(z, elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14262, 14580, 2484, 55, 1, 259, 377, 14568, 14563, 123, 3])).
% 2.61/2.86 tff(14599,plain,
% 2.61/2.86 (s(s(s(s(z)))) = s(elem!1)),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14591])).
% 2.61/2.86 tff(14600,plain,
% 2.61/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14599])).
% 2.61/2.86 tff(14601,plain,
% 2.61/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.86 inference(transitivity,[status(thm)],[14600, 174])).
% 2.61/2.86 tff(14602,plain,
% 2.61/2.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14601])).
% 2.61/2.86 tff(14603,plain,
% 2.61/2.86 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.86 inference(modus_ponens,[status(thm)],[196, 14602])).
% 2.61/2.86 tff(14604,plain,
% 2.61/2.86 (b(s(elem!1), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1673, 14603, 14580, 14598, 14567, 14597, 14564, 14595, 1])).
% 2.61/2.86 tff(14605,plain,
% 2.61/2.86 (~b(s(s(s(z))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[380, 14591, 377])).
% 2.61/2.86 tff(14606,plain,
% 2.61/2.86 (r(s(s(s(z))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[396, 14605])).
% 2.61/2.86 tff(14607,plain,
% 2.61/2.86 (s(s(z)) = s(s(s(z)))),
% 2.61/2.86 inference(transitivity,[status(thm)],[11666, 7929])).
% 2.61/2.86 tff(14608,plain,
% 2.61/2.86 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14607])).
% 2.61/2.86 tff(14609,plain,
% 2.61/2.86 (s(z) = elem!1),
% 2.61/2.86 inference(transitivity,[status(thm)],[193, 14608, 86, 11666])).
% 2.61/2.86 tff(14610,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[706, 14609])).
% 2.61/2.86 tff(14611,plain,((~(s(s(z)) = elem!1)) | (s(z) = elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14612,plain,
% 2.61/2.86 (~(s(s(z)) = elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14611, 14591, 14564])).
% 2.61/2.86 tff(14613,plain,
% 2.61/2.86 (~(s(elem!1) = s(s(s(z))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[1508, 14612])).
% 2.61/2.86 tff(14614,plain,
% 2.61/2.86 (~r(s(s(s(z))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[6555, 14606, 14580, 14567])).
% 2.61/2.86 tff(14615,plain,
% 2.61/2.86 (b(s(s(s(z))), s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[2794, 14614])).
% 2.61/2.86 tff(14616,plain,
% 2.61/2.86 (~r(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[7383, 14615, 14567, 14598, 1, 14564, 14580, 14595, 14613, 14606])).
% 2.61/2.86 tff(14617,plain,
% 2.61/2.86 (b(s(elem!1), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[507, 14616])).
% 2.61/2.86 tff(14618,plain,
% 2.61/2.86 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[267, 14570, 259, 251])).
% 2.61/2.86 tff(14619,plain,
% 2.61/2.86 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[12214, 14591])).
% 2.61/2.86 tff(14620,plain,
% 2.61/2.86 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[10345, 144, 14617, 2097, 259])).
% 2.61/2.86 tff(14621,plain,
% 2.61/2.86 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[472, 14620, 14619])).
% 2.61/2.86 tff(14622,plain,
% 2.61/2.86 (~r(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[13988, 14621, 377, 14618, 2097, 77])).
% 2.61/2.86 tff(14623,plain,
% 2.61/2.86 (b(s(elem!1), elem!1)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[448, 14622, 14594])).
% 2.61/2.86 tff(14624,plain,
% 2.61/2.86 ($false),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[7294, 144, 14623, 251, 14617, 14604, 14582])).
% 2.61/2.86 tff(14625,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~b(z, elem!1)) | b(elem!1, z) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.86 tff(14626,plain,
% 2.61/2.86 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14625, 377, 251, 1, 259, 123, 55, 2484, 3])).
% 2.61/2.86 tff(14627,plain,
% 2.61/2.86 (~r(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14348, 14626, 2484, 2322])).
% 2.61/2.86 tff(14628,plain,
% 2.61/2.86 (b(z, s(z))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[372, 14627])).
% 2.61/2.86 tff(14629,plain,
% 2.61/2.86 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[14578, 14628, 259, 251, 14563])).
% 2.61/2.86 tff(14630,plain,
% 2.61/2.86 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.61/2.86 inference(unit_resolution,[status(thm)],[121, 14629, 3])).
% 2.61/2.86 tff(14631,plain,
% 2.61/2.86 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14630])).
% 2.61/2.86 tff(14632,plain,
% 2.61/2.86 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.86 inference(symmetry,[status(thm)],[14631])).
% 2.61/2.86 tff(14633,plain,
% 2.61/2.86 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.61/2.86 inference(monotonicity,[status(thm)],[14632])).
% 2.61/2.86 tff(14634,plain,
% 2.61/2.86 (((~![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(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.86 inference(rewrite,[status(thm)],[])).
% 2.61/2.86 tff(14635,plain,
% 2.61/2.86 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.86 inference(rewrite,[status(thm)],[])).
% 2.61/2.86 tff(14636,plain,
% 2.61/2.86 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14635])).
% 2.61/2.87 tff(14637,plain,
% 2.61/2.87 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.61/2.87 inference(transitivity,[status(thm)],[14636, 14634])).
% 2.61/2.87 tff(14638,plain,
% 2.61/2.87 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(quant_inst,[status(thm)],[])).
% 2.61/2.87 tff(14639,plain,
% 2.61/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14638, 14637])).
% 2.61/2.87 tff(14640,plain,
% 2.61/2.87 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14639, 333, 2322, 2484])).
% 2.61/2.87 tff(14641,plain,
% 2.61/2.87 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14640, 14633])).
% 2.61/2.87 tff(14642,plain,
% 2.61/2.87 ($false),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[2484, 14641])).
% 2.61/2.87 tff(14643,plain,(b(elem!1, z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.87 tff(14644,plain,
% 2.61/2.87 (b(s(s(s(z))), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14643, 14314, 3, 8045, 2484, 1, 123, 377])).
% 2.61/2.87 tff(14645,plain,
% 2.61/2.87 (~b(s(z), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14578, 490, 132, 259, 251])).
% 2.61/2.87 tff(14646,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[14373, 14645, 490, 2484, 123, 259, 251, 706])).
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% 2.61/2.87 tff(14648,plain,
% 2.61/2.87 (~b(z, s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14647, 706, 123, 259, 251, 2484, 132])).
% 2.61/2.87 tff(14649,plain,
% 2.61/2.87 (r(z, s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[372, 14648])).
% 2.61/2.87 tff(14650,plain,
% 2.61/2.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14348, 14649, 2484, 408])).
% 2.61/2.87 tff(14651,plain,
% 2.61/2.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[302, 14650])).
% 2.61/2.87 tff(14652,plain,
% 2.61/2.87 (~b(s(z), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[7741, 14651, 123, 259])).
% 2.61/2.87 tff(14653,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[348, 14652])).
% 2.61/2.87 tff(14654,plain,
% 2.61/2.87 (~r(s(z), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[1376, 14653, 408, 14649])).
% 2.61/2.87 tff(14655,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[406, 14654, 706])).
% 2.61/2.87 tff(14656,plain,
% 2.61/2.87 (~r(elem!1, s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[747, 14653, 408, 14649])).
% 2.61/2.87 tff(14657,plain,
% 2.61/2.87 (b(elem!1, s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[720, 14656, 713])).
% 2.61/2.87 tff(14658,plain,
% 2.61/2.87 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14015, 14657, 132, 123, 14655, 4367])).
% 2.61/2.87 tff(14659,plain,
% 2.61/2.87 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[1137, 14658])).
% 2.61/2.87 tff(14660,plain,
% 2.61/2.87 (~b(s(s(s(z))), s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[4375, 14657, 4367, 14655])).
% 2.61/2.87 tff(14661,plain,
% 2.61/2.87 (r(s(s(s(z))), s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[2794, 14660])).
% 2.61/2.87 tff(14662,plain,
% 2.61/2.87 (~r(s(s(s(z))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[6555, 14661, 14653, 14649])).
% 2.61/2.87 tff(14663,plain,
% 2.61/2.87 (b(s(s(s(z))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[396, 14662])).
% 2.61/2.87 tff(14664,plain,
% 2.61/2.87 ($false),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14036, 144, 14663, 14659, 14651, 259])).
% 2.61/2.87 tff(14665,plain,((s(z) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.87 tff(14666,plain,
% 2.61/2.87 (s(z) = elem!1),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14665, 14644, 12015, 123, 8045, 2322, 2484, 14314])).
% 2.61/2.87 tff(14667,plain,
% 2.61/2.87 (s(s(z)) = s(elem!1)),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14666])).
% 2.61/2.87 tff(14668,plain,
% 2.61/2.87 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14667])).
% 2.61/2.87 tff(14669,plain,
% 2.61/2.87 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.87 inference(transitivity,[status(thm)],[14668, 174])).
% 2.61/2.87 tff(14670,plain,
% 2.61/2.87 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(transitivity,[status(thm)],[14669, 175])).
% 2.61/2.87 tff(14671,plain,
% 2.61/2.87 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14670])).
% 2.61/2.87 tff(14672,plain,
% 2.61/2.87 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[1446, 14671])).
% 2.61/2.87 tff(14673,plain,
% 2.61/2.87 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14669])).
% 2.61/2.87 tff(14674,plain,
% 2.61/2.87 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[1446, 14673])).
% 2.61/2.87 tff(14675,plain,
% 2.61/2.87 (~(s(s(s(elem!1))) = elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[2468, 14666])).
% 2.61/2.87 tff(14676,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[2482, 14675])).
% 2.61/2.87 tff(14677,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[9366, 14666, 14314])).
% 2.61/2.87 tff(14678,plain,
% 2.61/2.87 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[757, 14677, 123, 8045])).
% 2.61/2.87 tff(14679,plain,
% 2.61/2.87 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[319, 14678])).
% 2.61/2.87 tff(14680,plain,
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% 2.61/2.87 inference(unit_resolution,[status(thm)],[14578, 14677, 12015, 8045, 14314])).
% 2.61/2.87 tff(14681,plain,
% 2.61/2.87 (~b(s(z), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14360, 14680, 8045, 2484, 2322, 123, 377])).
% 2.61/2.87 tff(14682,plain,
% 2.61/2.87 (r(s(z), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[348, 14681])).
% 2.61/2.87 tff(14683,plain,
% 2.61/2.87 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14666])).
% 2.61/2.87 tff(14684,plain,
% 2.61/2.87 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.61/2.87 inference(symmetry,[status(thm)],[14683])).
% 2.61/2.87 tff(14685,plain,
% 2.61/2.87 (b(s(s(s(z))), s(z))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14644, 14684])).
% 2.61/2.87 tff(14686,plain,
% 2.61/2.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[779, 14685, 14682, 123, 14677, 14679])).
% 2.61/2.87 tff(14687,plain,
% 2.61/2.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[302, 14686])).
% 2.61/2.87 tff(14688,plain,
% 2.61/2.87 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[267, 14314, 12015, 8045])).
% 2.61/2.87 tff(14689,plain,
% 2.61/2.87 (~(s(elem!1) = elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[906, 14676])).
% 2.61/2.87 tff(14690,plain,
% 2.61/2.87 (s(s(s(z))) = s(s(elem!1))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14667])).
% 2.61/2.87 tff(14691,plain,
% 2.61/2.87 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14690])).
% 2.61/2.87 tff(14692,plain,
% 2.61/2.87 (b(s(s(elem!1)), elem!1)),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14644, 14691])).
% 2.61/2.87 tff(14693,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(rewrite,[status(thm)],[])).
% 2.61/2.87 tff(14694,plain,
% 2.61/2.87 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(rewrite,[status(thm)],[])).
% 2.61/2.87 tff(14695,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14694])).
% 2.61/2.87 tff(14696,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(transitivity,[status(thm)],[14695, 14693])).
% 2.61/2.87 tff(14697,plain,
% 2.61/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.61/2.87 inference(quant_inst,[status(thm)],[])).
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% 2.61/2.87 inference(modus_ponens,[status(thm)],[14697, 14696])).
% 2.61/2.87 tff(14699,plain,
% 2.61/2.87 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14698, 144, 132, 286, 4972, 2498])).
% 2.61/2.87 tff(14700,plain,
% 2.61/2.87 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[7819, 44, 14699, 13332])).
% 2.61/2.87 tff(14701,plain,
% 2.61/2.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[294, 284, 286, 285])).
% 2.61/2.87 tff(14702,plain,
% 2.61/2.87 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[249, 14701])).
% 2.61/2.87 tff(14703,plain,
% 2.61/2.87 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14702, 8165])).
% 2.61/2.87 tff(14704,plain,
% 2.61/2.87 (b(z, s(s(elem!1)))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[2828, 284, 57])).
% 2.61/2.87 tff(14705,plain,
% 2.61/2.87 (~b(elem!1, s(s(elem!1)))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[11841, 14704, 251, 4972])).
% 2.61/2.87 tff(14706,plain,
% 2.61/2.87 (r(elem!1, s(s(elem!1)))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[2522, 14705, 2462])).
% 2.61/2.87 tff(14707,plain,
% 2.61/2.87 ($false),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[8182, 333, 14706, 14703, 2484, 8162])).
% 2.61/2.87 tff(14708,plain,((~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.87 tff(14709,plain,
% 2.61/2.87 (~b(z, s(s(s(z))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14708, 14700, 2484, 57, 251, 4972, 286, 285])).
% 2.61/2.87 tff(14710,plain,
% 2.61/2.87 (r(z, s(s(s(z))))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[619, 14709])).
% 2.61/2.87 tff(14711,plain,
% 2.61/2.87 (~r(s(elem!1), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[10865, 509, 408, 623])).
% 2.61/2.87 tff(14712,plain,
% 2.61/2.87 (b(s(elem!1), elem!1)),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[448, 14711, 2681])).
% 2.61/2.87 tff(14713,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(rewrite,[status(thm)],[])).
% 2.61/2.87 tff(14714,plain,
% 2.61/2.87 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(rewrite,[status(thm)],[])).
% 2.61/2.87 tff(14715,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14714])).
% 2.61/2.87 tff(14716,plain,
% 2.61/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.87 inference(transitivity,[status(thm)],[14715, 14713])).
% 2.61/2.87 tff(14717,plain,
% 2.61/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.61/2.87 inference(quant_inst,[status(thm)],[])).
% 2.61/2.87 tff(14718,plain,
% 2.61/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[14717, 14716])).
% 2.61/2.87 tff(14719,plain,
% 2.61/2.87 (~b(z, s(elem!1))),
% 2.61/2.87 inference(unit_resolution,[status(thm)],[14718, 144, 14712, 251, 132, 259])).
% 2.61/2.87 tff(14720,plain,
% 2.61/2.87 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.61/2.87 inference(transitivity,[status(thm)],[11784, 998])).
% 2.61/2.87 tff(14721,plain,
% 2.61/2.87 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.61/2.87 inference(monotonicity,[status(thm)],[14720])).
% 2.61/2.87 tff(14722,plain,
% 2.61/2.87 (~(s(s(s(z))) = s(elem!1))),
% 2.61/2.87 inference(modus_ponens,[status(thm)],[217, 14721])).
% 2.61/2.88 tff(14723,plain,
% 2.61/2.88 (b(s(elem!1), s(z))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[14712, 2662])).
% 2.61/2.88 tff(14724,plain,
% 2.61/2.88 (~r(z, s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1960, 14723, 323, 56, 623, 509, 1237, 14722])).
% 2.61/2.88 tff(14725,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[583, 14724, 14719])).
% 2.61/2.88 tff(14726,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14727,plain,
% 2.61/2.88 (~r(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14726, 14710, 56, 323, 1237, 251, 132, 259, 57, 4414])).
% 2.61/2.88 tff(14728,plain,
% 2.61/2.88 (b(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[507, 14727])).
% 2.61/2.88 tff(14729,plain,
% 2.61/2.88 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12081, 14728, 4414, 286, 2483, 132, 2698, 2484, 4762])).
% 2.61/2.88 tff(14730,plain,
% 2.61/2.88 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[267, 251, 132, 259])).
% 2.61/2.88 tff(14731,plain,
% 2.61/2.88 (~r(s(elem!1), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13988, 14729, 377, 14730, 286, 1368])).
% 2.61/2.88 tff(14732,plain,
% 2.61/2.88 (b(s(elem!1), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[448, 14731, 2681])).
% 2.61/2.88 tff(14733,plain,
% 2.61/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14734,plain,
% 2.61/2.88 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14735,plain,
% 2.61/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 2.61/2.88 inference(monotonicity,[status(thm)],[14734])).
% 2.61/2.88 tff(14736,plain,
% 2.61/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.61/2.88 inference(transitivity,[status(thm)],[14735, 14733])).
% 2.61/2.88 tff(14737,plain,
% 2.61/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.61/2.88 inference(quant_inst,[status(thm)],[])).
% 2.61/2.88 tff(14738,plain,
% 2.61/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[14737, 14736])).
% 2.61/2.88 tff(14739,plain,
% 2.61/2.88 (~b(s(elem!1), s(s(elem!1)))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14738, 144, 14732, 251, 14728, 2498])).
% 2.61/2.88 tff(14740,plain,
% 2.61/2.88 (r(s(elem!1), s(s(elem!1)))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2860, 44, 14739, 2857])).
% 2.61/2.88 tff(14741,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[8545, 333, 2484, 14740, 14729, 14700])).
% 2.61/2.88 tff(14742,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14743,plain,
% 2.61/2.88 (~b(s(s(s(z))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14742, 14314, 2484, 377, 14687, 77, 12015, 14685, 14682, 1229, 8045, 14666, 14692])).
% 2.61/2.88 tff(14744,plain,
% 2.61/2.88 (r(s(s(elem!1)), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[6447, 1964, 57])).
% 2.61/2.88 tff(14745,plain,
% 2.61/2.88 (~b(z, s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14718, 144, 451, 251, 132, 259])).
% 2.61/2.88 tff(14746,plain,
% 2.61/2.88 (r(z, s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[583, 14745])).
% 2.61/2.88 tff(14747,plain,
% 2.61/2.88 (~r(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[8142, 14746, 323, 1964, 11786, 3924])).
% 2.61/2.88 tff(14748,plain,
% 2.61/2.88 (b(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[507, 14747])).
% 2.61/2.88 tff(14749,plain,
% 2.61/2.88 (~r(z, s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1990, 14748, 56, 1963, 3924, 14746, 323])).
% 2.61/2.88 tff(14750,plain,
% 2.61/2.88 (b(z, s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[619, 14749])).
% 2.61/2.88 tff(14751,plain,
% 2.61/2.88 (b(z, s(s(elem!1)))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2828, 14750, 57])).
% 2.61/2.88 tff(14752,plain,
% 2.61/2.88 (~b(elem!1, s(s(elem!1)))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[11841, 14751, 251, 4972])).
% 2.61/2.88 tff(14753,plain,
% 2.61/2.88 (r(elem!1, s(s(elem!1)))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2522, 14752, 2462])).
% 2.61/2.88 tff(14754,plain,
% 2.61/2.88 (((~![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)), z)) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14755,plain,
% 2.61/2.88 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14756,plain,
% 2.61/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 2.61/2.88 inference(monotonicity,[status(thm)],[14755])).
% 2.61/2.88 tff(14757,plain,
% 2.61/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 2.61/2.88 inference(transitivity,[status(thm)],[14756, 14754])).
% 2.61/2.88 tff(14758,plain,
% 2.61/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.61/2.88 inference(quant_inst,[status(thm)],[])).
% 2.61/2.88 tff(14759,plain,
% 2.61/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[14758, 14757])).
% 2.61/2.88 tff(14760,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14759, 333, 408, 14746, 14753, 14744])).
% 2.61/2.88 tff(14761,plain,((~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), z) | (~r(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14762,plain,
% 2.61/2.88 (~b(s(elem!1), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14761, 2322, 14314, 14692, 14666, 14685, 14743, 14682, 12015, 8045])).
% 2.61/2.88 tff(14763,plain,
% 2.61/2.88 (r(s(elem!1), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[448, 14762, 14689])).
% 2.61/2.88 tff(14764,plain,
% 2.61/2.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13988, 14763, 377, 14688, 14687, 77])).
% 2.61/2.88 tff(14765,plain,
% 2.61/2.88 (~b(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12081, 14764, 2322, 14687, 14676, 12015, 14674, 2484, 14672])).
% 2.61/2.88 tff(14766,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.88 inference(monotonicity,[status(thm)],[72])).
% 2.61/2.88 tff(14767,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.88 inference(symmetry,[status(thm)],[14766])).
% 2.61/2.88 tff(14768,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[286, 14767])).
% 2.61/2.88 tff(14769,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2545, 14768])).
% 2.61/2.88 tff(14770,plain,((~(elem!1 = z)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14771,plain,
% 2.61/2.88 (~(elem!1 = z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14770, 2545, 286])).
% 2.61/2.88 tff(14772,plain,
% 2.61/2.88 (r(elem!1, z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1380, 14771, 377])).
% 2.61/2.88 tff(14773,plain,
% 2.61/2.88 (~r(z, s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[9017, 14772, 435, 509])).
% 2.61/2.88 tff(14774,plain,
% 2.61/2.88 (b(z, s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[583, 14773])).
% 2.61/2.88 tff(14775,plain,
% 2.61/2.88 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[517, 14772, 435, 509])).
% 2.61/2.88 tff(14776,plain,
% 2.61/2.88 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[278, 14775, 274])).
% 2.61/2.88 tff(14777,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[8386, 14776, 537, 466, 14774])).
% 2.61/2.88 tff(14778,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[130, 2545, 2333])).
% 2.61/2.88 tff(14779,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12065, 333, 435, 14772, 14778, 14777])).
% 2.61/2.88 tff(14780,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), z)) | b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14781,plain,
% 2.61/2.88 (~r(s(elem!1), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14780, 14764, 377, 14674, 14687, 14688, 14763])).
% 2.61/2.88 tff(14782,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[507, 14781, 14765])).
% 2.61/2.88 tff(14783,plain,(b(elem!1, z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14784,plain,
% 2.61/2.88 (b(elem!1, z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14783, 12004, 50, 3, 1, 13792])).
% 2.61/2.88 tff(14785,plain,
% 2.61/2.88 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[279, 13792])).
% 2.61/2.88 tff(14786,plain,
% 2.61/2.88 (~b(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13815, 350, 123, 1368, 2484, 259, 132, 606])).
% 2.61/2.88 tff(14787,plain,
% 2.61/2.88 (r(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[372, 14786])).
% 2.61/2.88 tff(14788,plain,
% 2.61/2.88 (b(elem!1, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13826, 14787, 670, 706, 350])).
% 2.61/2.88 tff(14789,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14521, 2169, 14787, 321])).
% 2.61/2.88 tff(14790,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[319, 14789])).
% 2.61/2.88 tff(14791,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[313, 14790, 14788, 123, 132])).
% 2.61/2.88 tff(14792,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14793,plain,
% 2.61/2.88 (b(s(z), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14792, 706, 132, 670, 123, 14407, 1368, 2484, 259, 606])).
% 2.61/2.88 tff(14794,plain,
% 2.61/2.88 ((~b(s(z), z)) | (~b(s(z), elem!1))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14047, 144, 624, 123, 259])).
% 2.61/2.88 tff(14795,plain,
% 2.61/2.88 (~b(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14794, 14793])).
% 2.61/2.88 tff(14796,plain,
% 2.61/2.88 (r(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[348, 14795])).
% 2.61/2.88 tff(14797,plain,
% 2.61/2.88 (((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14798,plain,
% 2.61/2.88 ((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.61/2.88 inference(quant_inst,[status(thm)],[])).
% 2.61/2.88 tff(14799,plain,
% 2.61/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[14798, 14797])).
% 2.61/2.88 tff(14800,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14799, 333, 670, 14796, 14407])).
% 2.61/2.88 tff(14801,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[319, 14800])).
% 2.61/2.88 tff(14802,plain,
% 2.61/2.88 (~b(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[757, 14801, 123, 259])).
% 2.61/2.88 tff(14803,plain,
% 2.61/2.88 (r(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[372, 14802])).
% 2.61/2.88 tff(14804,plain,
% 2.61/2.88 (~b(elem!1, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[313, 14801, 123, 132])).
% 2.61/2.88 tff(14805,plain,
% 2.61/2.88 (r(elem!1, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[720, 14804, 713])).
% 2.61/2.88 tff(14806,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[727, 14805, 14803, 670, 14796])).
% 2.61/2.88 tff(14807,plain,((s(z) = elem!1) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14808,plain,
% 2.61/2.88 (s(z) = elem!1),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14807, 8715, 123, 132, 259, 624, 730, 2484, 606])).
% 2.61/2.88 tff(14809,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.61/2.88 inference(monotonicity,[status(thm)],[14808])).
% 2.61/2.88 tff(14810,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(symmetry,[status(thm)],[14809])).
% 2.61/2.88 tff(14811,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[2484, 14810])).
% 2.61/2.88 tff(14812,plain,
% 2.61/2.88 (b(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[3965, 14808, 624])).
% 2.61/2.88 tff(14813,plain,
% 2.61/2.88 (~r(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13865, 1963, 259, 14407, 132, 123, 670, 624])).
% 2.61/2.88 tff(14814,plain,
% 2.61/2.88 (b(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[372, 14813])).
% 2.61/2.88 tff(14815,plain,
% 2.61/2.88 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[757, 14814, 123, 259])).
% 2.61/2.88 tff(14816,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[319, 14815])).
% 2.61/2.88 tff(14817,plain,
% 2.61/2.88 (b(s(z), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[13815, 14814, 123, 1368, 2484, 259, 132, 606])).
% 2.61/2.88 tff(14818,plain,
% 2.61/2.88 (~b(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14794, 14817])).
% 2.61/2.88 tff(14819,plain,
% 2.61/2.88 (r(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[348, 14818])).
% 2.61/2.88 tff(14820,plain,
% 2.61/2.88 (~b(s(s(s(z))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[779, 14819, 14407, 123, 14814, 14816])).
% 2.61/2.88 tff(14821,plain,
% 2.61/2.88 (~r(s(s(s(z))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[11212, 14819, 670, 1964])).
% 2.61/2.88 tff(14822,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2794, 14821, 14820])).
% 2.61/2.88 tff(14823,plain,(b(s(s(s(z))), z) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14824,plain,
% 2.61/2.88 (b(s(s(s(z))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14823, 8715, 123, 624, 259, 730, 2484, 132, 606])).
% 2.61/2.88 tff(14825,plain,
% 2.61/2.88 ((~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[10462, 144, 14824, 123, 259])).
% 2.61/2.88 tff(14826,plain,
% 2.61/2.88 (~b(s(z), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14825, 14812])).
% 2.61/2.88 tff(14827,plain,
% 2.61/2.88 (r(s(z), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[172, 14826])).
% 2.61/2.88 tff(14828,plain,
% 2.61/2.88 (~b(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[8102, 14808, 606])).
% 2.61/2.88 tff(14829,plain,
% 2.61/2.88 (r(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[372, 14828])).
% 2.61/2.88 tff(14830,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[362, 14829, 14407, 14827])).
% 2.61/2.88 tff(14831,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14830, 14811])).
% 2.61/2.88 tff(14832,plain,(b(z, elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14833,plain,
% 2.61/2.88 (b(z, elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14832, 2484, 123, 259, 624, 12015, 71])).
% 2.61/2.88 tff(14834,plain,
% 2.61/2.88 (~b(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14647, 706, 123, 259, 14833, 2484, 12015])).
% 2.61/2.88 tff(14835,plain,
% 2.61/2.88 (r(z, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[372, 14834])).
% 2.61/2.88 tff(14836,plain,
% 2.61/2.88 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12296, 333, 354, 1699, 14407])).
% 2.61/2.88 tff(14837,plain,
% 2.61/2.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1137, 14836])).
% 2.61/2.88 tff(14838,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12304, 333, 354, 1699, 14407])).
% 2.61/2.88 tff(14839,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[249, 14838])).
% 2.61/2.88 tff(14840,plain,
% 2.61/2.88 (~b(elem!1, s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[8765, 144, 132, 14839, 14837])).
% 2.61/2.88 tff(14841,plain,
% 2.61/2.88 (~b(s(z), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2262, 14839, 123, 14837])).
% 2.61/2.88 tff(14842,plain,
% 2.61/2.88 (r(s(z), s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[172, 14841])).
% 2.61/2.88 tff(14843,plain,
% 2.61/2.88 (~r(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[7314, 14842, 1699, 354])).
% 2.61/2.88 tff(14844,plain,
% 2.61/2.88 (b(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[348, 14843])).
% 2.61/2.88 tff(14845,plain,
% 2.61/2.88 (~b(s(z), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1602, 14844, 624, 251])).
% 2.61/2.88 tff(14846,plain,
% 2.61/2.88 (r(s(z), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[406, 14845, 706])).
% 2.61/2.88 tff(14847,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[362, 14842, 14407, 354])).
% 2.61/2.88 tff(14848,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[319, 14847])).
% 2.61/2.88 tff(14849,plain,
% 2.61/2.88 (~b(s(s(s(z))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[6004, 144, 123, 14837, 14848])).
% 2.61/2.88 tff(14850,plain,
% 2.61/2.88 (r(s(s(s(z))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[2794, 14849])).
% 2.61/2.88 tff(14851,plain,
% 2.61/2.88 (~r(elem!1, s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[11876, 14850, 14846, 14842])).
% 2.61/2.88 tff(14852,plain,
% 2.61/2.88 (~b(z, s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[9071, 144, 14839, 14837, 259])).
% 2.61/2.88 tff(14853,plain,
% 2.61/2.88 (~(s(s(s(z))) = elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[257, 14852, 251])).
% 2.61/2.88 tff(14854,plain,
% 2.61/2.88 (~(elem!1 = s(s(s(z))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[10997, 14853])).
% 2.61/2.88 tff(14855,plain,
% 2.61/2.88 ($false),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[1538, 14854, 14851, 14840])).
% 2.61/2.88 tff(14856,plain,((~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.88 tff(14857,plain,
% 2.61/2.88 (~r(s(s(s(z))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14856, 706, 259, 12015, 123, 14833, 624, 14835])).
% 2.61/2.88 tff(14858,plain,
% 2.61/2.88 (b(s(s(s(z))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[396, 14857])).
% 2.61/2.88 tff(14859,plain,
% 2.61/2.88 (~b(s(s(s(z))), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[10565, 14858, 624, 14833])).
% 2.61/2.88 tff(14860,plain,
% 2.61/2.88 (b(s(z), elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14562, 14859, 259, 1, 123, 2484, 14833, 3])).
% 2.61/2.88 tff(14861,plain,
% 2.61/2.88 (~b(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14794, 14860])).
% 2.61/2.88 tff(14862,plain,
% 2.61/2.88 (r(s(z), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[348, 14861])).
% 2.61/2.88 tff(14863,plain,
% 2.61/2.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14405, 624, 12015, 259])).
% 2.61/2.88 tff(14864,plain,
% 2.61/2.88 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[302, 14863])).
% 2.61/2.88 tff(14865,plain,
% 2.61/2.88 (((~![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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.61/2.88 inference(rewrite,[status(thm)],[])).
% 2.61/2.88 tff(14866,plain,
% 2.61/2.88 ((~![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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.61/2.88 inference(quant_inst,[status(thm)],[])).
% 2.61/2.88 tff(14867,plain,
% 2.61/2.88 ((~![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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.61/2.88 inference(modus_ponens,[status(thm)],[14866, 14865])).
% 2.61/2.88 tff(14868,plain,
% 2.61/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14867, 333, 14835, 14862, 14864])).
% 2.61/2.88 tff(14869,plain,
% 2.61/2.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[319, 14868])).
% 2.61/2.88 tff(14870,plain,
% 2.61/2.88 (~b(elem!1, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[313, 14869, 123, 12015])).
% 2.61/2.88 tff(14871,plain,
% 2.61/2.88 (r(elem!1, s(z))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[720, 14870, 713])).
% 2.61/2.88 tff(14872,plain,
% 2.61/2.88 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[12214, 78])).
% 2.61/2.88 tff(14873,plain,
% 2.61/2.88 (b(z, elem!1)),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14832, 2484, 123, 259, 624, 132, 71])).
% 2.61/2.88 tff(14874,plain,
% 2.61/2.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[14548, 13978, 2484, 132, 259, 624, 14873, 354])).
% 2.61/2.88 tff(14875,plain,
% 2.61/2.88 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.88 inference(unit_resolution,[status(thm)],[472, 14874, 14872])).
% 2.61/2.89 tff(14876,plain,
% 2.61/2.89 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14867, 333, 354, 323, 14407])).
% 2.61/2.89 tff(14877,plain,
% 2.61/2.89 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[319, 14876])).
% 2.61/2.89 tff(14878,plain,
% 2.61/2.89 (~r(s(elem!1), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[1911, 13978, 624, 14873, 323, 722])).
% 2.61/2.89 tff(14879,plain,
% 2.61/2.89 (b(s(elem!1), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[486, 14878, 1])).
% 2.61/2.89 tff(14880,plain,
% 2.61/2.89 ($false),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[869, 144, 14879, 123, 14877, 14875])).
% 2.61/2.89 tff(14881,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.89 tff(14882,plain,
% 2.61/2.89 (~(s(s(s(z))) = elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14881, 14835, 1, 2484, 12015, 259, 624, 123, 14862, 14871, 863])).
% 2.61/2.89 tff(14883,plain,
% 2.61/2.89 (r(s(s(s(z))), elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[704, 14882, 14859])).
% 2.61/2.89 tff(14884,plain,
% 2.61/2.89 (~r(s(s(s(z))), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[8824, 14883, 14871, 14862])).
% 2.61/2.89 tff(14885,plain,
% 2.61/2.89 (b(s(s(s(z))), s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[2794, 14884])).
% 2.61/2.89 tff(14886,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14887,plain,
% 2.61/2.89 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14888,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14887])).
% 2.61/2.89 tff(14889,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(transitivity,[status(thm)],[14888, 14886])).
% 2.61/2.89 tff(14890,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.61/2.89 inference(quant_inst,[status(thm)],[])).
% 2.61/2.89 tff(14891,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14890, 14889])).
% 2.61/2.89 tff(14892,plain,
% 2.61/2.89 (~b(elem!1, s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14891, 144, 624, 14858, 12015, 259])).
% 2.61/2.89 tff(14893,plain,
% 2.61/2.89 (~r(s(z), s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[12402, 14882, 14859, 14892, 14871])).
% 2.61/2.89 tff(14894,plain,
% 2.61/2.89 (b(s(z), s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[172, 14893])).
% 2.61/2.89 tff(14895,plain,
% 2.61/2.89 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[846, 14894, 14869, 14885])).
% 2.61/2.89 tff(14896,plain,
% 2.61/2.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[249, 14895])).
% 2.61/2.89 tff(14897,plain,
% 2.61/2.89 (~(elem!1 = s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[10997, 14882])).
% 2.61/2.89 tff(14898,plain,
% 2.61/2.89 (r(elem!1, s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[1538, 14897, 14892])).
% 2.61/2.89 tff(14899,plain,
% 2.61/2.89 (((~![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(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14900,plain,
% 2.61/2.89 ((~![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(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.61/2.89 inference(quant_inst,[status(thm)],[])).
% 2.61/2.89 tff(14901,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14900, 14899])).
% 2.61/2.89 tff(14902,plain,
% 2.61/2.89 ($false),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14901, 333, 14898, 14883, 2484, 14896])).
% 2.61/2.89 tff(14903,plain,((s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.89 tff(14904,plain,
% 2.61/2.89 (s(z) = elem!1),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14903, 12004, 1, 14785, 14784, 50, 3])).
% 2.61/2.89 tff(14905,plain,
% 2.61/2.89 (s(s(z)) = s(elem!1)),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14904])).
% 2.61/2.89 tff(14906,plain,
% 2.61/2.89 (s(s(s(z))) = s(s(elem!1))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14905])).
% 2.61/2.89 tff(14907,plain,
% 2.61/2.89 (s(s(elem!1)) = s(s(s(z)))),
% 2.61/2.89 inference(symmetry,[status(thm)],[14906])).
% 2.61/2.89 tff(14908,plain,
% 2.61/2.89 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14907])).
% 2.61/2.89 tff(14909,plain,
% 2.61/2.89 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14908])).
% 2.61/2.89 tff(14910,plain,
% 2.61/2.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14905])).
% 2.61/2.89 tff(14911,plain,
% 2.61/2.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.61/2.89 inference(transitivity,[status(thm)],[14910, 174])).
% 2.61/2.89 tff(14912,plain,
% 2.61/2.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(transitivity,[status(thm)],[14911, 175])).
% 2.61/2.89 tff(14913,plain,
% 2.61/2.89 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14912])).
% 2.61/2.89 tff(14914,plain,
% 2.61/2.89 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[1446, 14913])).
% 2.61/2.89 tff(14915,plain,
% 2.61/2.89 (~(s(s(s(elem!1))) = elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[2468, 14904])).
% 2.61/2.89 tff(14916,plain,
% 2.61/2.89 (~(elem!1 = s(elem!1))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[2482, 14915])).
% 2.61/2.89 tff(14917,plain,
% 2.61/2.89 (~(s(elem!1) = elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[906, 14916])).
% 2.61/2.89 tff(14918,plain,
% 2.61/2.89 (b(z, elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14832, 12004, 50, 14785, 14784, 12013, 71])).
% 2.61/2.89 tff(14919,plain,
% 2.61/2.89 (b(s(z), z)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[3965, 14904, 14784])).
% 2.61/2.89 tff(14920,plain,
% 2.61/2.89 (~b(s(z), elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[1602, 14919, 14784, 14918])).
% 2.61/2.89 tff(14921,plain,
% 2.61/2.89 (b(z, s(z))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[9366, 14904, 14918])).
% 2.61/2.89 tff(14922,plain,
% 2.61/2.89 (b(s(s(s(z))), elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14512, 14921, 12013, 14785, 12004, 14784, 50, 14918, 14920])).
% 2.61/2.89 tff(14923,plain,
% 2.61/2.89 (~b(s(s(s(z))), z)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[10565, 14922, 14784, 14918])).
% 2.61/2.89 tff(14924,plain,
% 2.61/2.89 (r(s(s(s(z))), z)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[396, 14923])).
% 2.61/2.89 tff(14925,plain,
% 2.61/2.89 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14906])).
% 2.61/2.89 tff(14926,plain,
% 2.61/2.89 (b(s(s(elem!1)), elem!1)),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14922, 14925])).
% 2.61/2.89 tff(14927,plain,
% 2.61/2.89 (~b(s(elem!1), z)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[916, 451, 624, 251])).
% 2.61/2.89 tff(14928,plain,
% 2.61/2.89 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[10450, 14746, 321, 1699])).
% 2.61/2.89 tff(14929,plain,
% 2.61/2.89 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[1137, 14928])).
% 2.61/2.89 tff(14930,plain,
% 2.61/2.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14929, 4584])).
% 2.61/2.89 tff(14931,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14932,plain,
% 2.61/2.89 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14933,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.61/2.89 inference(monotonicity,[status(thm)],[14932])).
% 2.61/2.89 tff(14934,plain,
% 2.61/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.61/2.89 inference(transitivity,[status(thm)],[14933, 14931])).
% 2.61/2.89 tff(14935,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.61/2.89 inference(quant_inst,[status(thm)],[])).
% 2.61/2.89 tff(14936,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14935, 14934])).
% 2.61/2.89 tff(14937,plain,
% 2.61/2.89 (~b(s(s(elem!1)), s(elem!1))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14936, 144, 451, 132, 4972, 14930])).
% 2.61/2.89 tff(14938,plain,
% 2.61/2.89 (((~![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), z)) | (~r(s(s(elem!1)), z)) | (~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(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.89 inference(rewrite,[status(thm)],[])).
% 2.61/2.89 tff(14939,plain,
% 2.61/2.89 ((~![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), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.61/2.89 inference(quant_inst,[status(thm)],[])).
% 2.61/2.89 tff(14940,plain,
% 2.61/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.61/2.89 inference(modus_ponens,[status(thm)],[14939, 14938])).
% 2.61/2.89 tff(14941,plain,
% 2.61/2.89 (~r(s(s(elem!1)), s(elem!1))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14940, 333, 509, 14746, 13682])).
% 2.61/2.89 tff(14942,plain,
% 2.61/2.89 ($false),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[1283, 14941, 14937, 2507])).
% 2.61/2.89 tff(14943,plain,((~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.89 tff(14944,plain,
% 2.61/2.89 (~r(s(elem!1), z)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14943, 451, 132, 4972, 57, 14407, 1699, 251, 259])).
% 2.61/2.89 tff(14945,plain,
% 2.61/2.89 ($false),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[507, 14944, 14927])).
% 2.61/2.89 tff(14946,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.61/2.89 tff(14947,plain,
% 2.61/2.89 (~b(s(elem!1), elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[14946, 12013, 14926, 14904, 14924, 14918, 14785, 14784])).
% 2.61/2.89 tff(14948,plain,
% 2.61/2.89 (r(s(elem!1), elem!1)),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[448, 14947, 14917])).
% 2.61/2.89 tff(14949,plain,
% 2.61/2.89 (~r(z, s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[6811, 3654, 624, 132, 57, 1699])).
% 2.61/2.89 tff(14950,plain,
% 2.61/2.89 (b(z, s(s(s(z))))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[619, 14949])).
% 2.61/2.89 tff(14951,plain,
% 2.61/2.89 (b(z, s(s(elem!1)))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[2828, 14950, 57])).
% 2.61/2.89 tff(14952,plain,
% 2.61/2.89 (~b(elem!1, s(s(elem!1)))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[11841, 14951, 251, 4972])).
% 2.61/2.89 tff(14953,plain,
% 2.61/2.89 (r(elem!1, s(s(elem!1)))),
% 2.61/2.89 inference(unit_resolution,[status(thm)],[2522, 14952, 2462])).
% 2.61/2.89 tff(14954,plain,
% 2.61/2.89 (((~![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(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14955,plain,
% 2.70/2.90 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14956,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[14955])).
% 2.70/2.90 tff(14957,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[14956, 14954])).
% 2.70/2.90 tff(14958,plain,
% 2.70/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.70/2.90 inference(quant_inst,[status(thm)],[])).
% 2.70/2.90 tff(14959,plain,
% 2.70/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[14958, 14957])).
% 2.70/2.90 tff(14960,plain,
% 2.70/2.90 ($false),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14959, 333, 14953, 3654, 2484, 13682])).
% 2.70/2.90 tff(14961,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.90 tff(14962,plain,
% 2.70/2.90 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14961, 12004, 14918, 14926, 14904, 14784, 12013, 14924])).
% 2.70/2.90 tff(14963,plain,
% 2.70/2.90 (r(s(s(elem!1)), z)),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[6447, 14924, 14904])).
% 2.70/2.90 tff(14964,plain,
% 2.70/2.90 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14405, 14784, 12013, 14785])).
% 2.70/2.90 tff(14965,plain,
% 2.70/2.90 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[302, 14964])).
% 2.70/2.90 tff(14966,plain,
% 2.70/2.90 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[2499])).
% 2.70/2.90 tff(14967,plain,
% 2.70/2.90 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[14966, 997])).
% 2.70/2.90 tff(14968,plain,
% 2.70/2.90 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[14967])).
% 2.70/2.90 tff(14969,plain,
% 2.70/2.90 (~(s(elem!1) = s(s(s(z))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[2507, 14968])).
% 2.70/2.90 tff(14970,plain,
% 2.70/2.90 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[2848])).
% 2.70/2.90 tff(14971,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 2.70/2.90 tff(14972,plain,
% 2.70/2.90 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[2758, 14971, 2704])).
% 2.70/2.90 tff(14973,plain,
% 2.70/2.90 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[2499])).
% 2.70/2.90 tff(14974,plain,
% 2.70/2.90 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(symmetry,[status(thm)],[14973])).
% 2.70/2.90 tff(14975,plain,
% 2.70/2.90 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[6460, 562, 57, 321, 5497])).
% 2.70/2.90 tff(14976,plain,
% 2.70/2.90 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[1136, 14975, 1132])).
% 2.70/2.90 tff(14977,plain,
% 2.70/2.90 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[14976, 14974])).
% 2.70/2.90 tff(14978,plain,
% 2.70/2.90 (~r(s(s(elem!1)), s(elem!1))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[5505, 562, 435, 5497])).
% 2.70/2.90 tff(14979,plain,
% 2.70/2.90 (b(s(s(elem!1)), s(elem!1))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[1283, 14978, 2507])).
% 2.70/2.90 tff(14980,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14981,plain,
% 2.70/2.90 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14982,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[14981])).
% 2.70/2.90 tff(14983,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[14982, 14980])).
% 2.70/2.90 tff(14984,plain,
% 2.70/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(quant_inst,[status(thm)],[])).
% 2.70/2.90 tff(14985,plain,
% 2.70/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[14984, 14983])).
% 2.70/2.90 tff(14986,plain,
% 2.70/2.90 ($false),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14985, 144, 547, 1249, 133, 4972, 6147])).
% 2.70/2.90 tff(14987,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.90 tff(14988,plain,
% 2.70/2.90 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14987, 14979, 547, 4972, 14977])).
% 2.70/2.90 tff(14989,plain,
% 2.70/2.90 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[130, 14988, 4182])).
% 2.70/2.90 tff(14990,plain,
% 2.70/2.90 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[4180, 2544])).
% 2.70/2.90 tff(14991,plain,
% 2.70/2.90 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[14990])).
% 2.70/2.90 tff(14992,plain,
% 2.70/2.90 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[34, 14991])).
% 2.70/2.90 tff(14993,plain,
% 2.70/2.90 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[2669])).
% 2.70/2.90 tff(14994,plain,
% 2.70/2.90 (((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14995,plain,
% 2.70/2.90 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(14996,plain,
% 2.70/2.90 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[14995])).
% 2.70/2.90 tff(14997,plain,
% 2.70/2.90 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[14996, 14994])).
% 2.70/2.90 tff(14998,plain,
% 2.70/2.90 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(quant_inst,[status(thm)],[])).
% 2.70/2.90 tff(14999,plain,
% 2.70/2.90 ((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[14998, 14997])).
% 2.70/2.90 tff(15000,plain,
% 2.70/2.90 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[14999, 333, 435, 2484, 2323])).
% 2.70/2.90 tff(15001,plain,
% 2.70/2.90 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[15000, 14993])).
% 2.70/2.90 tff(15002,plain,
% 2.70/2.90 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[1451, 15001])).
% 2.70/2.90 tff(15003,plain,
% 2.70/2.90 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[15002, 2686])).
% 2.70/2.90 tff(15004,plain,
% 2.70/2.90 (((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(15005,plain,
% 2.70/2.90 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(15006,plain,
% 2.70/2.90 (((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.70/2.90 inference(monotonicity,[status(thm)],[15005])).
% 2.70/2.90 tff(15007,plain,
% 2.70/2.90 (((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.90 inference(transitivity,[status(thm)],[15006, 15004])).
% 2.70/2.90 tff(15008,plain,
% 2.70/2.90 ((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.90 inference(quant_inst,[status(thm)],[])).
% 2.70/2.90 tff(15009,plain,
% 2.70/2.90 ((~![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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.70/2.90 inference(modus_ponens,[status(thm)],[15008, 15007])).
% 2.70/2.90 tff(15010,plain,
% 2.70/2.90 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[15009, 333, 435, 2484, 2323])).
% 2.70/2.90 tff(15011,plain,
% 2.70/2.90 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.90 inference(unit_resolution,[status(thm)],[540, 44, 2698, 15010])).
% 2.70/2.90 tff(15012,plain,
% 2.70/2.90 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.90 inference(rewrite,[status(thm)],[])).
% 2.70/2.90 tff(15013,plain,
% 2.70/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.91 inference(monotonicity,[status(thm)],[15012])).
% 2.70/2.91 tff(15014,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(transitivity,[status(thm)],[15013, 13339])).
% 2.70/2.91 tff(15015,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(quant_inst,[status(thm)],[])).
% 2.70/2.91 tff(15016,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15015, 15014])).
% 2.70/2.91 tff(15017,plain,
% 2.70/2.91 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15016, 144, 1249, 6147, 15011])).
% 2.70/2.91 tff(15018,plain,
% 2.70/2.91 ($false),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15017, 15003])).
% 2.70/2.91 tff(15019,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.91 tff(15020,plain,
% 2.70/2.91 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15019, 14979, 57, 14977, 435, 14989])).
% 2.70/2.91 tff(15021,plain,
% 2.70/2.91 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[121, 15020, 14992])).
% 2.70/2.91 tff(15022,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15023,plain,
% 2.70/2.91 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15024,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.70/2.91 inference(monotonicity,[status(thm)],[15023])).
% 2.70/2.91 tff(15025,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.70/2.91 inference(transitivity,[status(thm)],[15024, 15022])).
% 2.70/2.91 tff(15026,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(quant_inst,[status(thm)],[])).
% 2.70/2.91 tff(15027,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15026, 15025])).
% 2.70/2.91 tff(15028,plain,
% 2.70/2.91 ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15027, 144, 547, 14979, 5659])).
% 2.70/2.91 tff(15029,plain,
% 2.70/2.91 (~b(elem!1, s(s(elem!1)))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15028, 15021])).
% 2.70/2.91 tff(15030,plain,
% 2.70/2.91 (r(elem!1, s(s(elem!1)))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[2522, 15029, 2462])).
% 2.70/2.91 tff(15031,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), 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), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15032,plain,
% 2.70/2.91 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15033,plain,
% 2.70/2.91 (((~![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(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.70/2.91 inference(monotonicity,[status(thm)],[15032])).
% 2.70/2.91 tff(15034,plain,
% 2.70/2.91 (((~![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(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.91 inference(transitivity,[status(thm)],[15033, 15031])).
% 2.70/2.91 tff(15035,plain,
% 2.70/2.91 ((~![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(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.70/2.91 inference(quant_inst,[status(thm)],[])).
% 2.70/2.91 tff(15036,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15035, 15034])).
% 2.70/2.91 tff(15037,plain,
% 2.70/2.91 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15036, 333, 435, 15030, 14989])).
% 2.70/2.91 tff(15038,plain,
% 2.70/2.91 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[540, 44, 2698, 15037])).
% 2.70/2.91 tff(15039,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15040,plain,
% 2.70/2.91 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15041,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.91 inference(monotonicity,[status(thm)],[15040])).
% 2.70/2.91 tff(15042,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.91 inference(transitivity,[status(thm)],[15041, 15039])).
% 2.70/2.91 tff(15043,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.70/2.91 inference(quant_inst,[status(thm)],[])).
% 2.70/2.91 tff(15044,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15043, 15042])).
% 2.70/2.91 tff(15045,plain,
% 2.70/2.91 ($false),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15044, 144, 14979, 15021, 4972, 14977, 15038])).
% 2.70/2.91 tff(15046,plain,((~r(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.91 tff(15047,plain,
% 2.70/2.91 (~r(z, s(elem!1))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15046, 321, 435, 547, 14972, 57, 4972, 5497])).
% 2.70/2.91 tff(15048,plain,
% 2.70/2.91 (b(z, s(elem!1))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[583, 15047])).
% 2.70/2.91 tff(15049,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15050,plain,
% 2.70/2.91 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.70/2.91 inference(rewrite,[status(thm)],[])).
% 2.70/2.91 tff(15051,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 2.70/2.91 inference(monotonicity,[status(thm)],[15050])).
% 2.70/2.91 tff(15052,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.70/2.91 inference(transitivity,[status(thm)],[15051, 15049])).
% 2.70/2.91 tff(15053,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.70/2.91 inference(quant_inst,[status(thm)],[])).
% 2.70/2.91 tff(15054,plain,
% 2.70/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15053, 15052])).
% 2.70/2.91 tff(15055,plain,
% 2.70/2.91 (~b(z, s(s(elem!1)))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[15054, 144, 547, 251, 15048, 4972])).
% 2.70/2.91 tff(15056,plain,
% 2.70/2.91 (~b(z, s(s(s(z))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[2828, 15055, 57])).
% 2.70/2.91 tff(15057,plain,
% 2.70/2.91 (r(z, s(s(s(z))))),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[619, 15056])).
% 2.70/2.91 tff(15058,plain,
% 2.70/2.91 (r(z, s(s(elem!1)))),
% 2.70/2.91 inference(modus_ponens,[status(thm)],[15057, 2832])).
% 2.70/2.91 tff(15059,plain,
% 2.70/2.91 (~b(s(elem!1), z)),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[949, 15048, 547, 624])).
% 2.70/2.91 tff(15060,plain,
% 2.70/2.91 (r(s(elem!1), z)),
% 2.70/2.91 inference(unit_resolution,[status(thm)],[507, 15059])).
% 2.70/2.91 tff(15061,plain,
% 2.70/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.70/2.92 inference(rewrite,[status(thm)],[])).
% 2.70/2.92 tff(15062,plain,
% 2.70/2.92 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.70/2.92 inference(rewrite,[status(thm)],[])).
% 2.70/2.92 tff(15063,plain,
% 2.70/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 2.70/2.92 inference(monotonicity,[status(thm)],[15062])).
% 2.70/2.92 tff(15064,plain,
% 2.70/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.70/2.92 inference(transitivity,[status(thm)],[15063, 15061])).
% 2.70/2.92 tff(15065,plain,
% 2.70/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.70/2.92 inference(quant_inst,[status(thm)],[])).
% 2.70/2.92 tff(15066,plain,
% 2.70/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15065, 15064])).
% 2.70/2.92 tff(15067,plain,
% 2.70/2.92 (~r(s(elem!1), s(s(elem!1)))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[15066, 333, 15060, 15058, 5497])).
% 2.70/2.92 tff(15068,plain,
% 2.70/2.92 (~r(s(elem!1), s(s(s(z))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15067, 14970])).
% 2.70/2.92 tff(15069,plain,
% 2.70/2.92 (b(s(elem!1), s(s(s(z))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[965, 15068, 14969])).
% 2.70/2.92 tff(15070,plain,
% 2.70/2.92 (b(s(s(z)), s(s(s(z))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15069, 14381])).
% 2.70/2.92 tff(15071,plain,
% 2.70/2.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[14971, 14411])).
% 2.70/2.92 tff(15072,plain,
% 2.70/2.92 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.92 inference(monotonicity,[status(thm)],[6449])).
% 2.70/2.92 tff(15073,plain,
% 2.70/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.92 inference(rewrite,[status(thm)],[])).
% 2.70/2.92 tff(15074,plain,
% 2.70/2.92 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.92 inference(rewrite,[status(thm)],[])).
% 2.70/2.92 tff(15075,plain,
% 2.70/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.92 inference(monotonicity,[status(thm)],[15074])).
% 2.70/2.92 tff(15076,plain,
% 2.70/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.92 inference(transitivity,[status(thm)],[15075, 15073])).
% 2.70/2.92 tff(15077,plain,
% 2.70/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.92 inference(quant_inst,[status(thm)],[])).
% 2.70/2.92 tff(15078,plain,
% 2.70/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15077, 15076])).
% 2.70/2.92 tff(15079,plain,
% 2.70/2.92 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[15078, 333, 321, 15058, 5497])).
% 2.70/2.92 tff(15080,plain,
% 2.70/2.92 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15079, 15072])).
% 2.70/2.92 tff(15081,plain,
% 2.70/2.92 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[14432, 333, 15060, 321, 15058])).
% 2.70/2.92 tff(15082,plain,
% 2.70/2.92 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[15081, 14993])).
% 2.70/2.92 tff(15083,plain,
% 2.70/2.92 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[1451, 15082])).
% 2.70/2.92 tff(15084,plain,
% 2.70/2.92 (~b(s(s(z)), s(s(s(z))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[7951, 15083, 244, 15080, 15071])).
% 2.70/2.92 tff(15085,plain,
% 2.70/2.92 ($false),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[15084, 15070])).
% 2.70/2.92 tff(15086,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.92 tff(15087,plain,
% 2.70/2.92 (~b(elem!1, s(elem!1))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[15086, 14948, 14965, 14918, 14963, 14926, 14962, 14784, 14904])).
% 2.70/2.92 tff(15088,plain,
% 2.70/2.92 (r(elem!1, s(elem!1))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[560, 15087, 14916])).
% 2.70/2.92 tff(15089,plain,
% 2.70/2.92 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[12698, 15088, 12004, 14948])).
% 2.70/2.92 tff(15090,plain,
% 2.70/2.92 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[472, 15089, 14914])).
% 2.70/2.92 tff(15091,plain,
% 2.70/2.92 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.92 inference(monotonicity,[status(thm)],[14906])).
% 2.70/2.92 tff(15092,plain,
% 2.70/2.92 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.70/2.92 inference(monotonicity,[status(thm)],[14911])).
% 2.70/2.92 tff(15093,plain,
% 2.70/2.92 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.70/2.92 inference(modus_ponens,[status(thm)],[1446, 15092])).
% 2.70/2.92 tff(15094,plain,
% 2.70/2.92 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[8386, 466, 259, 537, 585])).
% 2.70/2.92 tff(15095,plain,
% 2.70/2.92 (~b(elem!1, s(elem!1))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[5287, 144, 624, 585, 132, 12053])).
% 2.70/2.92 tff(15096,plain,
% 2.70/2.92 (r(elem!1, s(elem!1))),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[560, 15095, 902])).
% 2.70/2.92 tff(15097,plain,
% 2.70/2.92 ($false),
% 2.70/2.92 inference(unit_resolution,[status(thm)],[12793, 333, 15096, 435, 2484, 15094])).
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% 2.70/2.93 inference(monotonicity,[status(thm)],[15188])).
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% 2.70/2.93 inference(symmetry,[status(thm)],[15190])).
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% 2.70/2.94 inference(quant_inst,[status(thm)],[])).
% 2.70/2.94 tff(15293,plain,
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% 2.70/2.94 inference(modus_ponens,[status(thm)],[15292, 15291])).
% 2.70/2.94 tff(15294,plain,
% 2.70/2.94 ((s(z) = s(s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[15293, 44, 15290])).
% 2.70/2.94 tff(15295,plain,
% 2.70/2.94 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[15294, 15286])).
% 2.70/2.94 tff(15296,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(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(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.94 inference(rewrite,[status(thm)],[])).
% 2.70/2.94 tff(15297,plain,
% 2.70/2.94 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z)))) <=> ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.94 inference(rewrite,[status(thm)],[])).
% 2.70/2.94 tff(15298,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.70/2.94 inference(monotonicity,[status(thm)],[15297])).
% 2.70/2.94 tff(15299,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.94 inference(transitivity,[status(thm)],[15298, 15296])).
% 2.70/2.94 tff(15300,plain,
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% 2.70/2.94 tff(15301,plain,
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% 2.70/2.94 inference(modus_ponens,[status(thm)],[15300, 15299])).
% 2.70/2.94 tff(15302,plain,
% 2.70/2.94 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z)))),
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% 2.70/2.94 tff(15303,plain,
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% 2.70/2.94 inference(unit_resolution,[status(thm)],[15302, 15259])).
% 2.70/2.94 tff(15304,plain,
% 2.70/2.94 (~r(s(s(elem!1)), s(z))),
% 2.70/2.94 inference(modus_ponens,[status(thm)],[15303, 15281])).
% 2.70/2.94 tff(15305,plain,
% 2.70/2.94 (b(s(s(elem!1)), s(z))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[4983, 15304])).
% 2.70/2.94 tff(15306,plain,
% 2.70/2.94 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.70/2.94 inference(modus_ponens,[status(thm)],[15305, 15279])).
% 2.70/2.94 tff(15307,plain,
% 2.70/2.94 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[3868, 15217, 2358])).
% 2.70/2.94 tff(15308,plain,
% 2.70/2.94 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[472, 15307, 15144])).
% 2.70/2.94 tff(15309,plain,
% 2.70/2.94 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.94 inference(modus_ponens,[status(thm)],[15308, 2547])).
% 2.70/2.94 tff(15310,plain,
% 2.70/2.94 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
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% 2.70/2.94 tff(15311,plain,
% 2.70/2.94 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.94 inference(unit_resolution,[status(thm)],[1137, 15310])).
% 2.70/2.94 tff(15312,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.94 inference(rewrite,[status(thm)],[])).
% 2.70/2.94 tff(15313,plain,
% 2.70/2.94 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.94 inference(rewrite,[status(thm)],[])).
% 2.70/2.94 tff(15314,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.70/2.94 inference(monotonicity,[status(thm)],[15313])).
% 2.70/2.94 tff(15315,plain,
% 2.70/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.94 inference(transitivity,[status(thm)],[15314, 15312])).
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% 2.70/2.94 tff(15317,plain,
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% 2.70/2.94 tff(15318,plain,
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% 2.70/2.94 tff(15319,plain,
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% 2.70/2.94 tff(15320,plain,
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% 2.70/2.94 tff(15321,plain,
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% 2.70/2.94 tff(15322,plain,
% 2.70/2.94 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
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% 2.70/2.94 tff(15323,plain,
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% 2.70/2.94 tff(15324,plain,
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% 2.70/2.94 tff(15325,assumption,(~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 2.70/2.94 tff(15326,plain,
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% 2.70/2.94 tff(15327,plain,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | (~r(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.94 tff(15328,plain,
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% 2.70/2.94 tff(15329,plain,
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% 2.70/2.94 tff(15330,plain,
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% 2.70/2.94 tff(15332,plain,
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% 2.70/2.95 tff(15333,plain,
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% 2.70/2.95 inference(unit_resolution,[status(thm)],[4518, 44, 15332])).
% 2.70/2.95 tff(15334,plain,
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% 2.70/2.95 tff(15335,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
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% 2.70/2.95 tff(15337,plain,
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% 2.70/2.95 inference(unit_resolution,[status(thm)],[15337, 15286])).
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% 2.70/2.95 inference(monotonicity,[status(thm)],[15340])).
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% 2.70/2.95 inference(unit_resolution,[status(thm)],[15344, 333, 353, 15338, 15335, 15334])).
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% 2.70/2.95 tff(15347,plain,
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% 2.70/2.95 tff(15365,plain,
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% 2.70/2.95 tff(15380,plain,
% 2.70/2.95 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.95 inference(modus_ponens,[status(thm)],[15379, 15227])).
% 2.70/2.95 tff(15381,plain,
% 2.70/2.95 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.95 inference(unit_resolution,[status(thm)],[4518, 44, 15380])).
% 2.70/2.95 tff(15382,plain,
% 2.70/2.95 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.95 inference(unit_resolution,[status(thm)],[15381, 15224])).
% 2.70/2.95 tff(15383,plain,
% 2.70/2.95 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.70/2.95 inference(symmetry,[status(thm)],[15148])).
% 2.70/2.95 tff(15384,plain,
% 2.70/2.95 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.70/2.95 inference(modus_ponens,[status(thm)],[15376, 15383])).
% 2.70/2.95 tff(15385,assumption,(r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.70/2.95 tff(15386,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), z)), introduced(assumption)).
% 2.70/2.95 tff(15387,plain,
% 2.70/2.95 (((~![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(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, 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(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.95 inference(rewrite,[status(thm)],[])).
% 2.70/2.95 tff(15388,plain,
% 2.70/2.95 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.95 inference(rewrite,[status(thm)],[])).
% 2.70/2.95 tff(15389,plain,
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% 2.70/2.95 inference(monotonicity,[status(thm)],[15388])).
% 2.70/2.95 tff(15390,plain,
% 2.70/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(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(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.95 inference(transitivity,[status(thm)],[15389, 15387])).
% 2.70/2.95 tff(15391,plain,
% 2.70/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(z))))),
% 2.70/2.95 inference(quant_inst,[status(thm)],[])).
% 2.70/2.95 tff(15392,plain,
% 2.70/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.95 inference(modus_ponens,[status(thm)],[15391, 15390])).
% 2.70/2.95 tff(15393,plain,
% 2.70/2.95 ($false),
% 2.70/2.95 inference(unit_resolution,[status(thm)],[15392, 333, 3193, 2340, 15386, 15385])).
% 2.70/2.95 tff(15394,plain,((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.95 tff(15395,plain,
% 2.70/2.95 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15394, 15384, 15370, 15382])).
% 2.70/2.96 tff(15396,plain,
% 2.70/2.96 ($false),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1230, 2370])).
% 2.70/2.96 tff(15397,plain,(r(s(z), s(s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.96 tff(15398,plain,
% 2.70/2.96 (~r(s(z), s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15397, 15395, 112])).
% 2.70/2.96 tff(15399,plain,
% 2.70/2.96 (b(s(z), s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1244, 15398, 1229])).
% 2.70/2.96 tff(15400,plain,
% 2.70/2.96 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(z))),
% 2.70/2.96 inference(transitivity,[status(thm)],[15170, 53])).
% 2.70/2.96 tff(15401,plain,
% 2.70/2.96 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(z)))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15400])).
% 2.70/2.96 tff(15402,plain,
% 2.70/2.96 (~(elem!1 = s(z))),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[34, 15401])).
% 2.70/2.96 tff(15403,plain,
% 2.70/2.96 (~b(elem!1, s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[4409, 15399, 488, 15378])).
% 2.70/2.96 tff(15404,plain,
% 2.70/2.96 (r(elem!1, s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[720, 15403, 15402])).
% 2.70/2.96 tff(15405,plain,
% 2.70/2.96 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15188])).
% 2.70/2.96 tff(15406,plain,
% 2.70/2.96 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.70/2.96 inference(symmetry,[status(thm)],[15405])).
% 2.70/2.96 tff(15407,plain,
% 2.70/2.96 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15406])).
% 2.70/2.96 tff(15408,plain,
% 2.70/2.96 (~b(s(s(s(z))), s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[2273, 285, 490, 15200])).
% 2.70/2.96 tff(15409,plain,
% 2.70/2.96 (r(s(s(s(z))), s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[2794, 15408])).
% 2.70/2.96 tff(15410,plain,
% 2.70/2.96 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[509, 15383])).
% 2.70/2.96 tff(15411,plain,
% 2.70/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15412,plain,
% 2.70/2.96 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15413,plain,
% 2.70/2.96 (((~![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(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15412])).
% 2.70/2.96 tff(15414,plain,
% 2.70/2.96 (((~![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(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(transitivity,[status(thm)],[15413, 15411])).
% 2.70/2.96 tff(15415,plain,
% 2.70/2.96 ((~![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(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.70/2.96 inference(quant_inst,[status(thm)],[])).
% 2.70/2.96 tff(15416,plain,
% 2.70/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[15415, 15414])).
% 2.70/2.96 tff(15417,plain,
% 2.70/2.96 ($false),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15416, 333, 623, 3193, 15335, 15386])).
% 2.70/2.96 tff(15418,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.96 tff(15419,plain,
% 2.70/2.96 (~r(z, s(s(s(z))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15418, 15410, 15335, 15409])).
% 2.70/2.96 tff(15420,plain,
% 2.70/2.96 (b(z, s(s(s(z))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[619, 15419])).
% 2.70/2.96 tff(15421,plain,
% 2.70/2.96 (r(s(s(s(s(s(s(s(s(s(z))))))))), z) <=> r(s(s(elem!1)), z)),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15188])).
% 2.70/2.96 tff(15422,plain,
% 2.70/2.96 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) <=> (~r(s(s(elem!1)), z))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15421])).
% 2.70/2.96 tff(15423,plain,
% 2.70/2.96 (~b(s(z), s(s(s(z))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[2156, 15420, 15200, 285])).
% 2.70/2.96 tff(15424,plain,
% 2.70/2.96 (r(s(z), s(s(s(z))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[172, 15423])).
% 2.70/2.96 tff(15425,plain,
% 2.70/2.96 (((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15426,plain,
% 2.70/2.96 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15427,plain,
% 2.70/2.96 (((~![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(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15426])).
% 2.70/2.96 tff(15428,plain,
% 2.70/2.96 (((~![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(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(transitivity,[status(thm)],[15427, 15425])).
% 2.70/2.96 tff(15429,plain,
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% 2.70/2.96 inference(quant_inst,[status(thm)],[])).
% 2.70/2.96 tff(15430,plain,
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% 2.70/2.96 inference(modus_ponens,[status(thm)],[15429, 15428])).
% 2.70/2.96 tff(15431,plain,
% 2.70/2.96 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15430, 333, 15409, 15424, 15335])).
% 2.70/2.96 tff(15432,plain,
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% 2.70/2.96 inference(modus_ponens,[status(thm)],[15431, 2368])).
% 2.70/2.96 tff(15433,plain,
% 2.70/2.96 (b(s(z), s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1244, 15432, 1229])).
% 2.70/2.96 tff(15434,plain,
% 2.70/2.96 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15234])).
% 2.70/2.96 tff(15435,plain,
% 2.70/2.96 (((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15436,plain,
% 2.70/2.96 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15437,plain,
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% 2.70/2.96 inference(monotonicity,[status(thm)],[15436])).
% 2.70/2.96 tff(15438,plain,
% 2.70/2.96 (((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.96 inference(transitivity,[status(thm)],[15437, 15435])).
% 2.70/2.96 tff(15439,plain,
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% 2.70/2.96 inference(quant_inst,[status(thm)],[])).
% 2.70/2.96 tff(15440,plain,
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% 2.70/2.96 inference(modus_ponens,[status(thm)],[15439, 15438])).
% 2.70/2.96 tff(15441,plain,
% 2.70/2.96 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15440, 333, 15409, 15424, 15335])).
% 2.70/2.96 tff(15442,plain,
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% 2.70/2.96 inference(modus_ponens,[status(thm)],[15441, 15434])).
% 2.70/2.96 tff(15443,plain,
% 2.70/2.96 (b(s(elem!1), s(z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[486, 15442, 1])).
% 2.70/2.96 tff(15444,plain,
% 2.70/2.96 (~b(z, s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1853, 15443, 15433, 490])).
% 2.70/2.96 tff(15445,plain,
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% 2.70/2.96 inference(unit_resolution,[status(thm)],[583, 15444])).
% 2.70/2.96 tff(15446,plain,
% 2.70/2.96 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[15445, 15136])).
% 2.70/2.96 tff(15447,plain,
% 2.70/2.96 (b(elem!1, s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[560, 2896, 15143])).
% 2.70/2.96 tff(15448,plain,
% 2.70/2.96 (~b(s(s(elem!1)), s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1278, 15433, 722, 451, 15443, 15252, 15447, 409])).
% 2.70/2.96 tff(15449,plain,
% 2.70/2.96 (r(s(s(elem!1)), s(elem!1))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[1283, 15448, 15198])).
% 2.70/2.96 tff(15450,plain,
% 2.70/2.96 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[15449, 15197])).
% 2.70/2.96 tff(15451,plain,
% 2.70/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15452,plain,
% 2.70/2.96 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))) <=> ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.70/2.96 inference(rewrite,[status(thm)],[])).
% 2.70/2.96 tff(15453,plain,
% 2.70/2.96 (((~![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(s(s(s(s(z)))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))))),
% 2.70/2.96 inference(monotonicity,[status(thm)],[15452])).
% 2.70/2.96 tff(15454,plain,
% 2.70/2.96 (((~![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(s(s(s(s(z)))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.70/2.96 inference(transitivity,[status(thm)],[15453, 15451])).
% 2.70/2.96 tff(15455,plain,
% 2.70/2.96 ((~![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(s(s(s(s(z)))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.70/2.96 inference(quant_inst,[status(thm)],[])).
% 2.70/2.96 tff(15456,plain,
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% 2.70/2.96 inference(modus_ponens,[status(thm)],[15455, 15454])).
% 2.70/2.96 tff(15457,plain,
% 2.70/2.96 ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15456, 333, 15410])).
% 2.70/2.96 tff(15458,plain,
% 2.70/2.96 (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[15457, 15450, 15446])).
% 2.70/2.96 tff(15459,plain,
% 2.70/2.96 (~r(s(s(elem!1)), z)),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[15458, 15422])).
% 2.70/2.96 tff(15460,plain,
% 2.70/2.96 (b(s(s(elem!1)), z)),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[5509, 15459])).
% 2.70/2.96 tff(15461,plain,
% 2.70/2.96 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.70/2.96 inference(unit_resolution,[status(thm)],[5708, 15460, 15420, 285])).
% 2.70/2.96 tff(15462,plain,
% 2.70/2.96 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.70/2.96 inference(modus_ponens,[status(thm)],[15461, 15407])).
% 2.70/2.96 tff(15463,plain,
% 2.70/2.96 (~r(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[9952, 15409, 409, 408])).
% 2.70/2.97 tff(15464,plain,
% 2.70/2.97 (b(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[704, 15463, 15140])).
% 2.70/2.97 tff(15465,plain,
% 2.70/2.97 (~b(s(s(s(z))), s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[4819, 15447, 451, 15464])).
% 2.70/2.97 tff(15466,plain,
% 2.70/2.97 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15465, 15227])).
% 2.70/2.97 tff(15467,plain,
% 2.70/2.97 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[4518, 44, 15466])).
% 2.70/2.97 tff(15468,plain,
% 2.70/2.97 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15467, 15224])).
% 2.70/2.97 tff(15469,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(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(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15470,plain,
% 2.70/2.97 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15471,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))))),
% 2.70/2.97 inference(monotonicity,[status(thm)],[15470])).
% 2.70/2.97 tff(15472,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.70/2.97 inference(transitivity,[status(thm)],[15471, 15469])).
% 2.70/2.97 tff(15473,plain,
% 2.70/2.97 ((~![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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.70/2.97 inference(quant_inst,[status(thm)],[])).
% 2.70/2.97 tff(15474,plain,
% 2.70/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15473, 15472])).
% 2.70/2.97 tff(15475,plain,
% 2.70/2.97 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15474, 333, 15410, 15468])).
% 2.70/2.97 tff(15476,plain,
% 2.70/2.97 (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15475, 15450])).
% 2.70/2.97 tff(15477,plain,
% 2.70/2.97 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15275, 44, 15476])).
% 2.70/2.97 tff(15478,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15477, 15462, 15195])).
% 2.70/2.97 tff(15479,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15480,plain,
% 2.70/2.97 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15479, 15404, 285, 490, 15376, 15374, 15166, 1, 112, 670, 408])).
% 2.70/2.97 tff(15481,plain,
% 2.70/2.97 (~r(s(elem!1), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15327, 15480, 112])).
% 2.70/2.97 tff(15482,plain,
% 2.70/2.97 (b(s(elem!1), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[965, 15481, 15156])).
% 2.70/2.97 tff(15483,plain,
% 2.70/2.97 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.97 inference(monotonicity,[status(thm)],[112])).
% 2.70/2.97 tff(15484,plain,
% 2.70/2.97 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(symmetry,[status(thm)],[15483])).
% 2.70/2.97 tff(15485,plain,
% 2.70/2.97 (r(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[6107, 15484])).
% 2.70/2.97 tff(15486,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[699, 15485])).
% 2.70/2.97 tff(15487,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), elem!1) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15488,plain,
% 2.70/2.97 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15487, 15371, 112])).
% 2.70/2.97 tff(15489,plain,
% 2.70/2.97 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[1137, 15488])).
% 2.70/2.97 tff(15490,plain,
% 2.70/2.97 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15317, 144, 283, 2254])).
% 2.70/2.97 tff(15491,plain,
% 2.70/2.97 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15490, 15147])).
% 2.70/2.97 tff(15492,plain,
% 2.70/2.97 (~b(s(elem!1), s(s(s(z))))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15491, 2355])).
% 2.70/2.97 tff(15493,plain,
% 2.70/2.97 (r(s(elem!1), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[965, 15492, 15156])).
% 2.70/2.97 tff(15494,plain,
% 2.70/2.97 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15327, 15493, 112])).
% 2.70/2.97 tff(15495,plain,
% 2.70/2.97 (b(s(elem!1), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[448, 1727, 15142])).
% 2.70/2.97 tff(15496,plain,
% 2.70/2.97 (~r(s(elem!1), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15479, 15495, 285, 490, 722, 112, 15166, 1, 15494, 670, 408])).
% 2.70/2.97 tff(15497,plain,
% 2.70/2.97 (b(s(elem!1), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[507, 15496])).
% 2.70/2.97 tff(15498,plain,
% 2.70/2.97 (~b(s(elem!1), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[499, 15497, 15368, 490])).
% 2.70/2.97 tff(15499,plain,
% 2.70/2.97 (r(s(elem!1), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[486, 15498, 1])).
% 2.70/2.97 tff(15500,plain,
% 2.70/2.97 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15499, 15235])).
% 2.70/2.97 tff(15501,plain,
% 2.70/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15502,plain,
% 2.70/2.97 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15503,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.70/2.97 inference(monotonicity,[status(thm)],[15502])).
% 2.70/2.97 tff(15504,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(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(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.97 inference(transitivity,[status(thm)],[15503, 15501])).
% 2.70/2.97 tff(15505,plain,
% 2.70/2.97 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.97 inference(quant_inst,[status(thm)],[])).
% 2.70/2.97 tff(15506,plain,
% 2.70/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15505, 15504])).
% 2.70/2.97 tff(15507,plain,
% 2.70/2.97 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15506, 333, 15370, 11546, 15494])).
% 2.70/2.97 tff(15508,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15507, 15500])).
% 2.70/2.97 tff(15509,plain,(r(s(elem!1), elem!1) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15510,plain,
% 2.70/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15509, 15404, 11546, 1, 490, 15373, 112, 670, 408, 285, 15489])).
% 2.70/2.97 tff(15511,plain,
% 2.70/2.97 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[249, 15510])).
% 2.70/2.97 tff(15512,plain,
% 2.70/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15513,plain,
% 2.70/2.97 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15514,plain,
% 2.70/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.97 inference(monotonicity,[status(thm)],[15513])).
% 2.70/2.97 tff(15515,plain,
% 2.70/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.97 inference(transitivity,[status(thm)],[15514, 15512])).
% 2.70/2.97 tff(15516,plain,
% 2.70/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.97 inference(quant_inst,[status(thm)],[])).
% 2.70/2.97 tff(15517,plain,
% 2.70/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15516, 15515])).
% 2.70/2.97 tff(15518,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15517, 333, 3193, 353, 11546, 224])).
% 2.70/2.97 tff(15519,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15520,plain,
% 2.70/2.97 (~r(s(z), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15519, 15511, 11546, 15370])).
% 2.70/2.97 tff(15521,plain,
% 2.70/2.97 (b(s(z), s(s(s(z))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[172, 15520])).
% 2.70/2.97 tff(15522,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[2631, 15521, 15482, 15368, 285, 15399])).
% 2.70/2.97 tff(15523,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15524,plain,
% 2.70/2.97 (~b(s(elem!1), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15523, 15366, 11546, 112, 15185, 1, 670, 2322])).
% 2.70/2.97 tff(15525,plain,
% 2.70/2.97 (r(s(elem!1), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[486, 15524, 1])).
% 2.70/2.97 tff(15526,plain,
% 2.70/2.97 (~r(s(z), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[417, 2322, 15173, 15166])).
% 2.70/2.97 tff(15527,plain,
% 2.70/2.97 (b(s(z), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[348, 15526])).
% 2.70/2.97 tff(15528,plain,
% 2.70/2.97 (~b(s(s(s(z))), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[2273, 15366, 15185, 15527])).
% 2.70/2.97 tff(15529,plain,
% 2.70/2.97 (r(s(s(s(z))), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[2794, 15528])).
% 2.70/2.97 tff(15530,plain,
% 2.70/2.97 (~r(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[9952, 15529, 15166, 2322])).
% 2.70/2.97 tff(15531,plain,
% 2.70/2.97 (b(s(s(s(z))), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[704, 15530, 15140])).
% 2.70/2.97 tff(15532,plain,
% 2.70/2.97 (~r(s(elem!1), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15216, 15185, 1, 15166, 2322, 15173])).
% 2.70/2.97 tff(15533,plain,
% 2.70/2.97 (b(s(elem!1), elem!1)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[448, 15532, 15142])).
% 2.70/2.97 tff(15534,plain,
% 2.70/2.97 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15239, 15525, 112])).
% 2.70/2.97 tff(15535,plain,
% 2.70/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(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(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15536,plain,
% 2.70/2.97 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.97 inference(rewrite,[status(thm)],[])).
% 2.70/2.97 tff(15537,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.70/2.97 inference(monotonicity,[status(thm)],[15536])).
% 2.70/2.97 tff(15538,plain,
% 2.70/2.97 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.70/2.97 inference(transitivity,[status(thm)],[15537, 15535])).
% 2.70/2.97 tff(15539,plain,
% 2.70/2.97 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.97 inference(quant_inst,[status(thm)],[])).
% 2.70/2.97 tff(15540,plain,
% 2.70/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15539, 15538])).
% 2.70/2.97 tff(15541,plain,
% 2.70/2.97 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15540, 333, 15529, 11546, 15534])).
% 2.70/2.97 tff(15542,plain,
% 2.70/2.97 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[4518, 44, 15541])).
% 2.70/2.97 tff(15543,plain,
% 2.70/2.97 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[15542, 15224])).
% 2.70/2.97 tff(15544,plain,
% 2.70/2.97 (b(s(s(s(z))), s(elem!1))),
% 2.70/2.97 inference(modus_ponens,[status(thm)],[15543, 15225])).
% 2.70/2.97 tff(15545,plain,
% 2.70/2.97 (~b(elem!1, s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[4819, 15544, 15533, 15531])).
% 2.70/2.97 tff(15546,plain,
% 2.70/2.97 (r(elem!1, s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[560, 15545, 15143])).
% 2.70/2.97 tff(15547,plain,
% 2.70/2.97 (~r(z, s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[2393, 15546, 670, 15525])).
% 2.70/2.97 tff(15548,plain,
% 2.70/2.97 (b(z, s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[583, 15547])).
% 2.70/2.97 tff(15549,plain,
% 2.70/2.97 (~r(s(elem!1), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[678, 15546, 670, 2322])).
% 2.70/2.97 tff(15550,plain,
% 2.70/2.97 (b(s(elem!1), z)),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[507, 15549])).
% 2.70/2.97 tff(15551,plain,
% 2.70/2.97 (~r(s(z), s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[7651, 15546, 15166, 15525])).
% 2.70/2.97 tff(15552,plain,
% 2.70/2.97 (b(s(z), s(elem!1))),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[1244, 15551, 1229])).
% 2.70/2.97 tff(15553,plain,
% 2.70/2.97 ($false),
% 2.70/2.97 inference(unit_resolution,[status(thm)],[2383, 15552, 15550, 15527, 15548])).
% 2.70/2.97 tff(15554,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.97 tff(15555,plain,
% 2.70/2.98 (b(elem!1, z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15554, 7265, 112, 11546, 1])).
% 2.70/2.98 tff(15556,plain,
% 2.70/2.98 (~r(elem!1, s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[10960, 354, 15166, 7265])).
% 2.70/2.98 tff(15557,plain,
% 2.70/2.98 (b(elem!1, s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[720, 15556, 15402])).
% 2.70/2.98 tff(15558,plain,
% 2.70/2.98 (~r(s(elem!1), elem!1)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[5456, 15557, 1, 15555, 15172, 354, 323, 15168, 15143, 7265])).
% 2.70/2.98 tff(15559,plain,
% 2.70/2.98 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[3868, 15558, 2358])).
% 2.70/2.98 tff(15560,plain,
% 2.70/2.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[472, 15559, 15144])).
% 2.70/2.98 tff(15561,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15560, 2547])).
% 2.70/2.98 tff(15562,plain,
% 2.70/2.98 (~r(elem!1, z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[417, 323, 15157, 15166])).
% 2.70/2.98 tff(15563,plain,
% 2.70/2.98 (b(s(elem!1), s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[8704, 354, 15166, 71, 606, 15143, 15562])).
% 2.70/2.98 tff(15564,plain,
% 2.70/2.98 (~b(s(z), s(elem!1))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[4409, 15557, 15563, 15168])).
% 2.70/2.98 tff(15565,plain,
% 2.70/2.98 (r(s(z), s(elem!1))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[1244, 15564, 1229])).
% 2.70/2.98 tff(15566,plain,
% 2.70/2.98 (~r(s(elem!1), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[1235, 15565, 323, 354])).
% 2.70/2.98 tff(15567,plain,
% 2.70/2.98 (b(s(elem!1), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[507, 15566])).
% 2.70/2.98 tff(15568,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15567, 2398])).
% 2.70/2.98 tff(15569,plain,
% 2.70/2.98 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15570,plain,
% 2.70/2.98 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15571,plain,
% 2.70/2.98 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.98 inference(monotonicity,[status(thm)],[15570])).
% 2.70/2.98 tff(15572,plain,
% 2.70/2.98 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.98 inference(transitivity,[status(thm)],[15571, 15569])).
% 2.70/2.98 tff(15573,plain,
% 2.70/2.98 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 2.70/2.98 inference(quant_inst,[status(thm)],[])).
% 2.70/2.98 tff(15574,plain,
% 2.70/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15573, 15572])).
% 2.70/2.98 tff(15575,plain,
% 2.70/2.98 ($false),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15574, 333, 354, 11546, 224, 51])).
% 2.70/2.98 tff(15576,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.98 tff(15577,plain,
% 2.70/2.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15576, 354, 11546, 15157])).
% 2.70/2.98 tff(15578,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[249, 15577])).
% 2.70/2.98 tff(15579,plain,
% 2.70/2.98 (b(elem!1, s(s(s(z))))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15578, 15203])).
% 2.70/2.98 tff(15580,plain,
% 2.70/2.98 (~b(s(s(s(z))), s(elem!1))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[12903, 15579, 15555, 15168, 15567])).
% 2.70/2.98 tff(15581,plain,
% 2.70/2.98 (~b(z, s(elem!1))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[949, 15567, 15555, 15168])).
% 2.70/2.98 tff(15582,plain,
% 2.70/2.98 (r(z, s(elem!1))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[583, 15581])).
% 2.70/2.98 tff(15583,plain,
% 2.70/2.98 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.70/2.98 inference(monotonicity,[status(thm)],[112])).
% 2.70/2.98 tff(15584,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15555, 15583])).
% 2.70/2.98 tff(15585,plain,
% 2.70/2.98 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[429, 354, 15157, 15166])).
% 2.70/2.98 tff(15586,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[319, 15585])).
% 2.70/2.98 tff(15587,plain,
% 2.70/2.98 (~r(s(s(s(z))), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[7314, 353, 323, 354])).
% 2.70/2.98 tff(15588,plain,
% 2.70/2.98 (b(s(s(s(z))), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[396, 15587])).
% 2.70/2.98 tff(15589,plain,
% 2.70/2.98 (~b(z, s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[294, 15588, 286, 283])).
% 2.70/2.98 tff(15590,plain,
% 2.70/2.98 (r(z, s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[619, 15589])).
% 2.70/2.98 tff(15591,plain,
% 2.70/2.98 (~r(s(s(s(z))), elem!1)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[1519, 15590, 354, 353])).
% 2.70/2.98 tff(15592,plain,
% 2.70/2.98 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15487, 15591, 112])).
% 2.70/2.98 tff(15593,plain,
% 2.70/2.98 (b(s(elem!1), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[4807, 15590, 562, 15156, 3296])).
% 2.70/2.98 tff(15594,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15595,plain,
% 2.70/2.98 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15596,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.70/2.98 inference(monotonicity,[status(thm)],[15595])).
% 2.70/2.98 tff(15597,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.70/2.98 inference(transitivity,[status(thm)],[15596, 15594])).
% 2.70/2.98 tff(15598,plain,
% 2.70/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.70/2.98 inference(quant_inst,[status(thm)],[])).
% 2.70/2.98 tff(15599,plain,
% 2.70/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15598, 15597])).
% 2.70/2.98 tff(15600,plain,
% 2.70/2.98 ($false),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15599, 144, 491, 1794, 2254, 286, 450])).
% 2.70/2.98 tff(15601,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.98 tff(15602,plain,
% 2.70/2.98 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15601, 15593, 286, 491, 450])).
% 2.70/2.98 tff(15603,plain,
% 2.70/2.98 ($false),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[1137, 15602, 15592])).
% 2.70/2.98 tff(15604,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.98 tff(15605,plain,
% 2.70/2.98 (~r(s(z), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15604, 15567, 15584, 15560, 112, 15582, 15580, 354, 15578, 323])).
% 2.70/2.98 tff(15606,plain,
% 2.70/2.98 (b(s(z), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[172, 15605])).
% 2.70/2.98 tff(15607,plain,
% 2.70/2.98 (~b(s(s(s(z))), s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[846, 15606, 15586, 15578])).
% 2.70/2.98 tff(15608,plain,
% 2.70/2.98 (r(s(s(s(z))), s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[2794, 15607])).
% 2.70/2.98 tff(15609,plain,
% 2.70/2.98 (~r(s(s(s(z))), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[11212, 15608, 7265, 323])).
% 2.70/2.98 tff(15610,plain,
% 2.70/2.98 (b(s(s(s(z))), z)),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[396, 15609])).
% 2.70/2.98 tff(15611,plain,
% 2.70/2.98 (~b(z, s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[294, 15610, 15584, 15578])).
% 2.70/2.98 tff(15612,plain,
% 2.70/2.98 (r(z, s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[619, 15611])).
% 2.70/2.98 tff(15613,plain,
% 2.70/2.98 (b(s(elem!1), s(s(s(z))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[4807, 15612, 15582, 15156, 15580])).
% 2.70/2.98 tff(15614,plain,
% 2.70/2.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15613, 15151])).
% 2.70/2.98 tff(15615,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15616,plain,
% 2.70/2.98 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.98 inference(rewrite,[status(thm)],[])).
% 2.70/2.98 tff(15617,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.70/2.98 inference(monotonicity,[status(thm)],[15616])).
% 2.70/2.98 tff(15618,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.70/2.98 inference(transitivity,[status(thm)],[15617, 15615])).
% 2.70/2.98 tff(15619,plain,
% 2.70/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.98 inference(quant_inst,[status(thm)],[])).
% 2.70/2.98 tff(15620,plain,
% 2.70/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.70/2.98 inference(modus_ponens,[status(thm)],[15619, 15618])).
% 2.70/2.98 tff(15621,plain,
% 2.70/2.98 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15620, 144, 15610, 15578])).
% 2.70/2.98 tff(15622,plain,
% 2.70/2.98 ($false),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15621, 15614, 15568, 15561])).
% 2.70/2.98 tff(15623,plain,((~r(z, s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.70/2.98 tff(15624,plain,
% 2.70/2.98 (~r(z, s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[15623, 323, 112, 11546, 1, 606])).
% 2.70/2.98 tff(15625,plain,
% 2.70/2.98 (b(z, s(z))),
% 2.70/2.98 inference(unit_resolution,[status(thm)],[372, 15624])).
% 2.70/2.98 tff(15626,plain,
% 2.70/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15627,plain,
% 2.70/2.99 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15628,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(monotonicity,[status(thm)],[15627])).
% 2.70/2.99 tff(15629,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(transitivity,[status(thm)],[15628, 15626])).
% 2.70/2.99 tff(15630,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 2.70/2.99 inference(quant_inst,[status(thm)],[])).
% 2.70/2.99 tff(15631,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15630, 15629])).
% 2.70/2.99 tff(15632,plain,
% 2.70/2.99 ($false),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15631, 333, 323, 11546, 322, 51])).
% 2.70/2.99 tff(15633,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.99 tff(15634,plain,
% 2.70/2.99 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15633, 323, 11546, 15157])).
% 2.70/2.99 tff(15635,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[319, 15634])).
% 2.70/2.99 tff(15636,plain,
% 2.70/2.99 (b(elem!1, s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[735, 15635, 2358])).
% 2.70/2.99 tff(15637,plain,
% 2.70/2.99 (~r(s(elem!1), z)),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[7112, 15636, 323, 15625, 15143, 1, 7265])).
% 2.70/2.99 tff(15638,plain,
% 2.70/2.99 (b(s(elem!1), z)),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[507, 15637])).
% 2.70/2.99 tff(15639,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15638, 2398])).
% 2.70/2.99 tff(15640,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15641,plain,
% 2.70/2.99 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15642,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.70/2.99 inference(monotonicity,[status(thm)],[15641])).
% 2.70/2.99 tff(15643,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(transitivity,[status(thm)],[15642, 15640])).
% 2.70/2.99 tff(15644,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(quant_inst,[status(thm)],[])).
% 2.70/2.99 tff(15645,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15644, 15643])).
% 2.70/2.99 tff(15646,plain,
% 2.70/2.99 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15645, 144, 15625, 15635, 15584])).
% 2.70/2.99 tff(15647,plain,
% 2.70/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15646, 15639])).
% 2.70/2.99 tff(15648,plain,
% 2.70/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15647, 15163])).
% 2.70/2.99 tff(15649,plain,
% 2.70/2.99 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[542, 15648, 15161])).
% 2.70/2.99 tff(15650,plain,
% 2.70/2.99 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15649, 15159])).
% 2.70/2.99 tff(15651,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15652,plain,
% 2.70/2.99 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15653,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.70/2.99 inference(monotonicity,[status(thm)],[15652])).
% 2.70/2.99 tff(15654,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(transitivity,[status(thm)],[15653, 15651])).
% 2.70/2.99 tff(15655,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 2.70/2.99 inference(quant_inst,[status(thm)],[])).
% 2.70/2.99 tff(15656,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15655, 15654])).
% 2.70/2.99 tff(15657,plain,
% 2.70/2.99 ($false),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15656, 333, 323, 11546, 15157, 15650])).
% 2.70/2.99 tff(15658,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.70/2.99 tff(15659,plain,
% 2.70/2.99 (~r(s(z), z)),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15658, 606, 112, 1, 11546])).
% 2.70/2.99 tff(15660,plain,
% 2.70/2.99 (b(s(z), z)),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[348, 15659])).
% 2.70/2.99 tff(15661,plain,
% 2.70/2.99 (b(elem!1, z)),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15554, 670, 112, 11546, 1])).
% 2.70/2.99 tff(15662,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15661, 15583])).
% 2.70/2.99 tff(15663,plain,
% 2.70/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[7093, 490, 15662, 489])).
% 2.70/2.99 tff(15664,plain,
% 2.70/2.99 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[319, 15663])).
% 2.70/2.99 tff(15665,plain,
% 2.70/2.99 (~r(s(elem!1), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[1589, 354, 509, 409])).
% 2.70/2.99 tff(15666,plain,
% 2.70/2.99 (b(s(elem!1), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[486, 15665, 1])).
% 2.70/2.99 tff(15667,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15666, 2357])).
% 2.70/2.99 tff(15668,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.99 inference(symmetry,[status(thm)],[15162])).
% 2.70/2.99 tff(15669,plain,
% 2.70/2.99 (~r(elem!1, s(elem!1))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[10119, 354, 409, 670])).
% 2.70/2.99 tff(15670,plain,
% 2.70/2.99 (b(elem!1, s(elem!1))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[560, 15669, 15143])).
% 2.70/2.99 tff(15671,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[5657, 15670, 2358])).
% 2.70/2.99 tff(15672,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15671, 15668])).
% 2.70/2.99 tff(15673,plain,
% 2.70/2.99 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[429, 354, 15173, 409])).
% 2.70/2.99 tff(15674,plain,
% 2.70/2.99 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[319, 15673])).
% 2.70/2.99 tff(15675,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15676,plain,
% 2.70/2.99 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(rewrite,[status(thm)],[])).
% 2.70/2.99 tff(15677,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.70/2.99 inference(monotonicity,[status(thm)],[15676])).
% 2.70/2.99 tff(15678,plain,
% 2.70/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(transitivity,[status(thm)],[15677, 15675])).
% 2.70/2.99 tff(15679,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/2.99 inference(quant_inst,[status(thm)],[])).
% 2.70/2.99 tff(15680,plain,
% 2.70/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(modus_ponens,[status(thm)],[15679, 15678])).
% 2.70/2.99 tff(15681,plain,
% 2.70/2.99 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15680, 144, 489, 15674, 286])).
% 2.70/2.99 tff(15682,plain,
% 2.70/2.99 ($false),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15681, 15672, 15667])).
% 2.70/2.99 tff(15683,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.70/2.99 tff(15684,plain,
% 2.70/2.99 (~r(z, s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[15683, 509, 15662, 112, 1, 489, 15166, 670])).
% 2.70/2.99 tff(15685,plain,
% 2.70/2.99 (b(z, s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[372, 15684])).
% 2.70/2.99 tff(15686,plain,
% 2.70/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[7093, 15685, 15662, 489])).
% 2.70/2.99 tff(15687,plain,
% 2.70/2.99 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(unit_resolution,[status(thm)],[319, 15686])).
% 2.70/2.99 tff(15688,plain,
% 2.70/2.99 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/2.99 inference(monotonicity,[status(thm)],[112])).
% 2.70/2.99 tff(15689,plain,
% 2.70/2.99 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(elem!1, s(z))),
% 2.70/2.99 inference(symmetry,[status(thm)],[15688])).
% 2.70/3.01 tff(15690,plain,
% 2.70/3.01 (r(elem!1, s(z))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15687, 15689])).
% 2.70/3.01 tff(15691,plain,
% 2.70/3.01 (~r(s(elem!1), elem!1)),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[11139, 15690, 670, 509])).
% 2.70/3.01 tff(15692,plain,
% 2.70/3.01 (b(s(elem!1), elem!1)),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[448, 15691, 15142])).
% 2.70/3.01 tff(15693,plain,
% 2.70/3.01 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[3868, 15691, 2358])).
% 2.70/3.01 tff(15694,plain,
% 2.70/3.01 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[472, 15693, 15144])).
% 2.70/3.01 tff(15695,plain,
% 2.70/3.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15694, 2547])).
% 2.70/3.01 tff(15696,plain,
% 2.70/3.01 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[7093, 490, 286, 489])).
% 2.70/3.01 tff(15697,plain,
% 2.70/3.01 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[319, 15696])).
% 2.70/3.01 tff(15698,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15699,plain,
% 2.70/3.01 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15700,plain,
% 2.70/3.01 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(monotonicity,[status(thm)],[15699])).
% 2.70/3.01 tff(15701,plain,
% 2.70/3.01 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(transitivity,[status(thm)],[15700, 15698])).
% 2.70/3.01 tff(15702,plain,
% 2.70/3.01 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.70/3.01 inference(quant_inst,[status(thm)],[])).
% 2.70/3.01 tff(15703,plain,
% 2.70/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15702, 15701])).
% 2.70/3.01 tff(15704,plain,
% 2.70/3.01 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15703, 333, 11012, 11546, 15697])).
% 2.70/3.01 tff(15705,plain,
% 2.70/3.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[249, 15704])).
% 2.70/3.01 tff(15706,plain,
% 2.70/3.01 (~b(z, s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[294, 15705, 286, 285])).
% 2.70/3.01 tff(15707,plain,
% 2.70/3.01 (r(z, s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[619, 15706])).
% 2.70/3.01 tff(15708,plain,
% 2.70/3.01 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15418, 15707, 15386, 11012])).
% 2.70/3.01 tff(15709,plain,
% 2.70/3.01 (~r(s(elem!1), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15327, 15708, 112])).
% 2.70/3.01 tff(15710,plain,
% 2.70/3.01 (b(s(elem!1), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[965, 15709, 15156])).
% 2.70/3.01 tff(15711,plain,
% 2.70/3.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15710, 15151])).
% 2.70/3.01 tff(15712,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.70/3.01 tff(15713,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15714,plain,
% 2.70/3.01 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15715,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(monotonicity,[status(thm)],[15714])).
% 2.70/3.01 tff(15716,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(transitivity,[status(thm)],[15715, 15713])).
% 2.70/3.01 tff(15717,plain,
% 2.70/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 2.70/3.01 inference(quant_inst,[status(thm)],[])).
% 2.70/3.01 tff(15718,plain,
% 2.70/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15717, 15716])).
% 2.70/3.01 tff(15719,plain,
% 2.70/3.01 ($false),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15718, 333, 3193, 11546, 6107, 322])).
% 2.70/3.01 tff(15720,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.70/3.01 tff(15721,plain,
% 2.70/3.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15720, 11012, 11546, 15697])).
% 2.70/3.01 tff(15722,plain,
% 2.70/3.01 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[1137, 15721])).
% 2.70/3.01 tff(15723,plain,
% 2.70/3.01 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15317, 144, 15705, 15722, 15712])).
% 2.70/3.01 tff(15724,plain,
% 2.70/3.01 ($false),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15723, 15711])).
% 2.70/3.01 tff(15725,plain,((~b(s(s(s(z))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.70/3.01 tff(15726,plain,
% 2.70/3.01 (~b(s(s(s(z))), z)),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15725, 15695, 112, 15410, 15662, 11546, 489, 15685])).
% 2.70/3.01 tff(15727,plain,
% 2.70/3.01 (r(s(s(s(z))), z)),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[396, 15726])).
% 2.70/3.01 tff(15728,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(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(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15729,plain,
% 2.70/3.01 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(rewrite,[status(thm)],[])).
% 2.70/3.01 tff(15730,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.70/3.01 inference(monotonicity,[status(thm)],[15729])).
% 2.70/3.01 tff(15731,plain,
% 2.70/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(transitivity,[status(thm)],[15730, 15728])).
% 2.70/3.01 tff(15732,plain,
% 2.70/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.70/3.01 inference(quant_inst,[status(thm)],[])).
% 2.70/3.01 tff(15733,plain,
% 2.70/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15732, 15731])).
% 2.70/3.01 tff(15734,plain,
% 2.70/3.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15733, 333, 15727, 15173, 15410])).
% 2.70/3.01 tff(15735,plain,
% 2.70/3.01 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[4518, 44, 15734])).
% 2.70/3.01 tff(15736,plain,
% 2.70/3.01 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[15735, 15224])).
% 2.70/3.01 tff(15737,plain,
% 2.70/3.01 (b(s(s(s(z))), s(elem!1))),
% 2.70/3.01 inference(modus_ponens,[status(thm)],[15736, 15225])).
% 2.70/3.01 tff(15738,plain,
% 2.70/3.01 (~r(s(elem!1), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[5835, 15727, 670, 509])).
% 2.70/3.01 tff(15739,plain,
% 2.70/3.01 (b(s(elem!1), s(s(s(z))))),
% 2.70/3.01 inference(unit_resolution,[status(thm)],[965, 15738, 15156])).
% 2.80/3.01 tff(15740,plain,
% 2.80/3.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.01 inference(modus_ponens,[status(thm)],[15739, 15151])).
% 2.80/3.01 tff(15741,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 2.80/3.01 tff(15742,plain,
% 2.80/3.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[13763, 524, 51, 1699])).
% 2.80/3.01 tff(15743,plain,
% 2.80/3.01 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[1137, 15742])).
% 2.80/3.01 tff(15744,plain,
% 2.80/3.01 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 2.80/3.01 inference(monotonicity,[status(thm)],[2353])).
% 2.80/3.01 tff(15745,plain,
% 2.80/3.01 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.01 inference(symmetry,[status(thm)],[15744])).
% 2.80/3.01 tff(15746,plain,
% 2.80/3.01 (~r(z, s(elem!1))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[12046, 524, 51, 509])).
% 2.80/3.01 tff(15747,plain,
% 2.80/3.01 (b(z, s(elem!1))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[583, 15746])).
% 2.80/3.01 tff(15748,plain,
% 2.80/3.01 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.01 inference(modus_ponens,[status(thm)],[15747, 15745])).
% 2.80/3.01 tff(15749,plain,
% 2.80/3.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[15733, 333, 1699, 51, 15410])).
% 2.80/3.01 tff(15750,plain,
% 2.80/3.01 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[4518, 44, 15749])).
% 2.80/3.01 tff(15751,plain,
% 2.80/3.01 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.01 inference(unit_resolution,[status(thm)],[15750, 15224])).
% 2.80/3.01 tff(15752,plain,
% 2.80/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.01 inference(rewrite,[status(thm)],[])).
% 2.80/3.01 tff(15753,plain,
% 2.80/3.01 (((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.01 inference(rewrite,[status(thm)],[])).
% 2.80/3.01 tff(15754,plain,
% 2.80/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.01 inference(monotonicity,[status(thm)],[15753])).
% 2.80/3.01 tff(15755,plain,
% 2.80/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.01 inference(transitivity,[status(thm)],[15754, 15752])).
% 2.80/3.01 tff(15756,plain,
% 2.80/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.02 inference(quant_inst,[status(thm)],[])).
% 2.80/3.02 tff(15757,plain,
% 2.80/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.80/3.02 inference(modus_ponens,[status(thm)],[15756, 15755])).
% 2.80/3.02 tff(15758,plain,
% 2.80/3.02 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15757, 144, 15751, 15741])).
% 2.80/3.02 tff(15759,plain,
% 2.80/3.02 (~b(z, s(s(s(z))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15758, 15748])).
% 2.80/3.02 tff(15760,plain,
% 2.80/3.02 (r(z, s(s(s(z))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[619, 15759])).
% 2.80/3.02 tff(15761,plain,
% 2.80/3.02 ($false),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[11964, 333, 1699, 623, 224, 51])).
% 2.80/3.02 tff(15762,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.02 tff(15763,plain,
% 2.80/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15762, 15760, 1699, 51])).
% 2.80/3.02 tff(15764,plain,
% 2.80/3.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[249, 15763])).
% 2.80/3.02 tff(15765,plain,
% 2.80/3.02 ($false),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15317, 144, 15764, 15743, 15712, 15741])).
% 2.80/3.02 tff(15766,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.02 tff(15767,plain,
% 2.80/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15766, 15695, 15740, 15727, 15173, 112, 509])).
% 2.80/3.02 tff(15768,plain,
% 2.80/3.02 (~r(elem!1, s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[3851, 15767, 2358])).
% 2.80/3.02 tff(15769,plain,
% 2.80/3.02 (b(elem!1, s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[560, 15768, 15143])).
% 2.80/3.02 tff(15770,plain,
% 2.80/3.02 (~b(s(s(s(z))), elem!1)),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[4819, 15769, 15737, 15692])).
% 2.80/3.02 tff(15771,plain,
% 2.80/3.02 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[9194, 15770, 2358])).
% 2.80/3.02 tff(15772,plain,
% 2.80/3.02 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[1137, 15771])).
% 2.80/3.02 tff(15773,plain,
% 2.80/3.02 ($false),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[11054, 333, 15727, 15772, 15687, 15173])).
% 2.80/3.02 tff(15774,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.02 tff(15775,plain,
% 2.80/3.02 (~r(s(elem!1), z)),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15774, 670, 112, 11546, 489, 1])).
% 2.80/3.02 tff(15776,plain,
% 2.80/3.02 (b(s(elem!1), z)),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[507, 15775])).
% 2.80/3.02 tff(15777,plain,
% 2.80/3.02 (~b(s(elem!1), s(z))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[499, 490, 489, 15776])).
% 2.80/3.02 tff(15778,plain,
% 2.80/3.02 (r(s(elem!1), s(z))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[486, 15777, 1])).
% 2.80/3.02 tff(15779,plain,
% 2.80/3.02 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15239, 15778, 112])).
% 2.80/3.02 tff(15780,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.02 tff(15781,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(z))), introduced(assumption)).
% 2.80/3.02 tff(15782,plain,
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% 2.80/3.02 inference(rewrite,[status(thm)],[])).
% 2.80/3.02 tff(15783,plain,
% 2.80/3.02 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.02 inference(rewrite,[status(thm)],[])).
% 2.80/3.02 tff(15784,plain,
% 2.80/3.02 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.02 inference(monotonicity,[status(thm)],[15783])).
% 2.80/3.02 tff(15785,plain,
% 2.80/3.02 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.02 inference(transitivity,[status(thm)],[15784, 15782])).
% 2.80/3.02 tff(15786,plain,
% 2.80/3.02 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.02 inference(quant_inst,[status(thm)],[])).
% 2.80/3.02 tff(15787,plain,
% 2.80/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.02 inference(modus_ponens,[status(thm)],[15786, 15785])).
% 2.80/3.02 tff(15788,plain,
% 2.80/3.02 ($false),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15787, 333, 11546, 322, 15781, 15780])).
% 2.80/3.02 tff(15789,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.02 tff(15790,plain,
% 2.80/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15789, 15779, 15664, 11546])).
% 2.80/3.02 tff(15791,plain,
% 2.80/3.02 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.02 inference(modus_ponens,[status(thm)],[524, 15159])).
% 2.80/3.02 tff(15792,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.02 tff(15793,plain,
% 2.80/3.02 ($false),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15792, 15791])).
% 2.80/3.02 tff(15794,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.02 tff(15795,plain,
% 2.80/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[15794, 15790, 112])).
% 2.80/3.02 tff(15796,plain,
% 2.80/3.02 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[542, 15795, 15161])).
% 2.80/3.02 tff(15797,plain,
% 2.80/3.02 (~b(z, s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[12069, 15796, 15662, 15776])).
% 2.80/3.02 tff(15798,plain,
% 2.80/3.02 (r(z, s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[583, 15797])).
% 2.80/3.02 tff(15799,plain,
% 2.80/3.02 (~r(elem!1, s(elem!1))),
% 2.80/3.02 inference(unit_resolution,[status(thm)],[10119, 354, 15166, 670])).
% 2.80/3.03 tff(15800,plain,
% 2.80/3.03 (b(elem!1, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[560, 15799, 15143])).
% 2.80/3.03 tff(15801,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[5657, 15800, 2358])).
% 2.80/3.03 tff(15802,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15801, 15668])).
% 2.80/3.03 tff(15803,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[624, 15583])).
% 2.80/3.03 tff(15804,plain,
% 2.80/3.03 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15576, 354, 11546, 15173])).
% 2.80/3.03 tff(15805,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[249, 15804])).
% 2.80/3.03 tff(15806,plain,
% 2.80/3.03 (~b(z, s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[294, 15805, 15803, 285])).
% 2.80/3.03 tff(15807,plain,
% 2.80/3.03 (r(z, s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[619, 15806])).
% 2.80/3.03 tff(15808,plain,
% 2.80/3.03 (~b(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[949, 15800, 624, 491])).
% 2.80/3.03 tff(15809,plain,
% 2.80/3.03 (r(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[583, 15808])).
% 2.80/3.03 tff(15810,plain,
% 2.80/3.03 (b(elem!1, s(s(s(z))))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15805, 15203])).
% 2.80/3.03 tff(15811,plain,
% 2.80/3.03 (~b(s(s(s(z))), s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[12903, 15810, 624, 491, 15800])).
% 2.80/3.03 tff(15812,plain,
% 2.80/3.03 (b(s(elem!1), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[4807, 15811, 15809, 15156, 15807])).
% 2.80/3.03 tff(15813,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15812, 15151])).
% 2.80/3.03 tff(15814,plain,
% 2.80/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.03 inference(rewrite,[status(thm)],[])).
% 2.80/3.03 tff(15815,plain,
% 2.80/3.03 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.03 inference(rewrite,[status(thm)],[])).
% 2.80/3.03 tff(15816,plain,
% 2.80/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.03 inference(monotonicity,[status(thm)],[15815])).
% 2.80/3.03 tff(15817,plain,
% 2.80/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.03 inference(transitivity,[status(thm)],[15816, 15814])).
% 2.80/3.03 tff(15818,plain,
% 2.80/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.03 inference(quant_inst,[status(thm)],[])).
% 2.80/3.03 tff(15819,plain,
% 2.80/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15818, 15817])).
% 2.80/3.03 tff(15820,plain,
% 2.80/3.03 ($false),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15819, 144, 285, 15805, 15803, 15813, 15802])).
% 2.80/3.03 tff(15821,plain,((~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.03 tff(15822,plain,
% 2.80/3.03 (~r(z, s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15821, 285, 112, 15661, 15776, 11546, 670])).
% 2.80/3.03 tff(15823,plain,
% 2.80/3.03 (b(z, s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[372, 15822])).
% 2.80/3.03 tff(15824,plain,
% 2.80/3.03 (~b(s(s(s(z))), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[2273, 15823, 489, 285])).
% 2.80/3.03 tff(15825,plain,
% 2.80/3.03 (r(s(s(s(z))), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[2794, 15824])).
% 2.80/3.03 tff(15826,plain,
% 2.80/3.03 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[7093, 15823, 15662, 489])).
% 2.80/3.03 tff(15827,plain,
% 2.80/3.03 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[319, 15826])).
% 2.80/3.03 tff(15828,plain,
% 2.80/3.03 (~b(s(elem!1), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[499, 15823, 489, 15776])).
% 2.80/3.03 tff(15829,plain,
% 2.80/3.03 (r(s(elem!1), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[486, 15828, 1])).
% 2.80/3.03 tff(15830,plain,
% 2.80/3.03 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15239, 15829, 112])).
% 2.80/3.03 tff(15831,plain,
% 2.80/3.03 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15789, 15830, 15827, 11546])).
% 2.80/3.03 tff(15832,plain,
% 2.80/3.03 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15794, 15831, 112])).
% 2.80/3.03 tff(15833,plain,
% 2.80/3.03 (~r(elem!1, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[3851, 15832, 2358])).
% 2.80/3.03 tff(15834,plain,
% 2.80/3.03 (b(elem!1, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[560, 15833, 15143])).
% 2.80/3.03 tff(15835,plain,
% 2.80/3.03 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15720, 15825, 11546, 15827])).
% 2.80/3.03 tff(15836,plain,
% 2.80/3.03 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[1137, 15835])).
% 2.80/3.03 tff(15837,plain,
% 2.80/3.03 (b(s(s(s(z))), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[9194, 15836, 2358])).
% 2.80/3.03 tff(15838,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[542, 15832, 15161])).
% 2.80/3.03 tff(15839,plain,
% 2.80/3.03 (~b(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[12069, 15838, 15662, 15776])).
% 2.80/3.03 tff(15840,plain,
% 2.80/3.03 (r(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[583, 15839])).
% 2.80/3.03 tff(15841,plain,
% 2.80/3.03 (r(elem!1, s(z))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15827, 15689])).
% 2.80/3.03 tff(15842,plain,
% 2.80/3.03 (~r(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[1863, 15841, 670, 15840])).
% 2.80/3.03 tff(15843,plain,
% 2.80/3.03 (b(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[448, 15842, 15142])).
% 2.80/3.03 tff(15844,plain,
% 2.80/3.03 (~b(s(s(s(z))), s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[4819, 15843, 15837, 15834])).
% 2.80/3.03 tff(15845,plain,
% 2.80/3.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[3868, 15842, 2358])).
% 2.80/3.03 tff(15846,plain,
% 2.80/3.03 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[472, 15845, 15144])).
% 2.80/3.03 tff(15847,plain,
% 2.80/3.03 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15601, 15846, 15662, 15776, 15836])).
% 2.80/3.03 tff(15848,plain,
% 2.80/3.03 (~r(z, s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[4807, 15847, 15840, 15156, 15844])).
% 2.80/3.03 tff(15849,plain,
% 2.80/3.03 (b(z, s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[619, 15848])).
% 2.80/3.03 tff(15850,plain,
% 2.80/3.03 (~b(s(z), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[2156, 15849, 489, 285])).
% 2.80/3.03 tff(15851,plain,
% 2.80/3.03 (r(s(z), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[172, 15850])).
% 2.80/3.03 tff(15852,plain,
% 2.80/3.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[294, 15849, 15662, 285])).
% 2.80/3.03 tff(15853,plain,
% 2.80/3.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[249, 15852])).
% 2.80/3.03 tff(15854,plain,
% 2.80/3.03 ($false),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15519, 15853, 15851, 11546, 15825])).
% 2.80/3.03 tff(15855,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.03 tff(15856,plain,
% 2.80/3.03 (~b(s(s(s(z))), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15855, 489, 11546, 670, 112, 1])).
% 2.80/3.03 tff(15857,plain,
% 2.80/3.03 (r(s(s(s(z))), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[396, 15856])).
% 2.80/3.03 tff(15858,plain,
% 2.80/3.03 (r(elem!1, s(z))),
% 2.80/3.03 inference(modus_ponens,[status(thm)],[15664, 15689])).
% 2.80/3.03 tff(15859,plain,
% 2.80/3.03 (~r(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[1863, 15858, 670, 15798])).
% 2.80/3.03 tff(15860,plain,
% 2.80/3.03 (b(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[448, 15859, 15142])).
% 2.80/3.03 tff(15861,plain,
% 2.80/3.03 (~b(s(s(s(z))), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15249, 15860, 112, 15857, 15798, 670, 15778])).
% 2.80/3.03 tff(15862,plain,
% 2.80/3.03 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[9194, 15861, 2358])).
% 2.80/3.03 tff(15863,plain,
% 2.80/3.03 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[1137, 15862])).
% 2.80/3.03 tff(15864,plain,
% 2.80/3.03 ($false),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[11054, 333, 15857, 15863, 15664, 15173])).
% 2.80/3.03 tff(15865,plain,((~b(z, s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.03 tff(15866,plain,
% 2.80/3.03 (~b(z, s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15865, 7265, 112, 11546, 1, 15660])).
% 2.80/3.03 tff(15867,plain,
% 2.80/3.03 (r(z, s(z))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[372, 15866])).
% 2.80/3.03 tff(15868,plain,
% 2.80/3.03 (~r(s(elem!1), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15774, 7265, 112, 11546, 15660, 1])).
% 2.80/3.03 tff(15869,plain,
% 2.80/3.03 (b(s(elem!1), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[507, 15868])).
% 2.80/3.03 tff(15870,plain,
% 2.80/3.03 (~r(elem!1, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[10119, 15867, 15166, 7265])).
% 2.80/3.03 tff(15871,plain,
% 2.80/3.03 (b(elem!1, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[560, 15870, 15143])).
% 2.80/3.03 tff(15872,plain,
% 2.80/3.03 (~b(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[949, 15871, 15555, 15869])).
% 2.80/3.03 tff(15873,plain,
% 2.80/3.03 (r(z, s(elem!1))),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[583, 15872])).
% 2.80/3.03 tff(15874,plain,
% 2.80/3.03 (~r(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[6950, 15873, 2358, 1, 7265, 15143, 15867, 15157])).
% 2.80/3.03 tff(15875,plain,
% 2.80/3.03 (b(s(elem!1), elem!1)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[448, 15874, 15142])).
% 2.80/3.03 tff(15876,plain,
% 2.80/3.03 (~b(s(s(s(z))), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[15855, 15660, 11546, 7265, 112, 1])).
% 2.80/3.03 tff(15877,plain,
% 2.80/3.03 (r(s(s(s(z))), z)),
% 2.80/3.03 inference(unit_resolution,[status(thm)],[396, 15876])).
% 2.80/3.03 tff(15878,plain,
% 2.80/3.03 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15869, 2398])).
% 2.80/3.04 tff(15879,plain,
% 2.80/3.04 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[3868, 15874, 2358])).
% 2.80/3.04 tff(15880,plain,
% 2.80/3.04 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[472, 15879, 15144])).
% 2.80/3.04 tff(15881,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15880, 2547])).
% 2.80/3.04 tff(15882,plain,
% 2.80/3.04 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[429, 15867, 15157, 15166])).
% 2.80/3.04 tff(15883,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[319, 15882])).
% 2.80/3.04 tff(15884,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15885,plain,
% 2.80/3.04 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15886,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.04 inference(monotonicity,[status(thm)],[15885])).
% 2.80/3.04 tff(15887,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(transitivity,[status(thm)],[15886, 15884])).
% 2.80/3.04 tff(15888,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.04 inference(quant_inst,[status(thm)],[])).
% 2.80/3.04 tff(15889,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15888, 15887])).
% 2.80/3.04 tff(15890,plain,
% 2.80/3.04 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15889, 144, 15660, 15883, 15881])).
% 2.80/3.04 tff(15891,plain,
% 2.80/3.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15890, 15878])).
% 2.80/3.04 tff(15892,plain,
% 2.80/3.04 (~b(s(elem!1), s(z))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15891, 15150])).
% 2.80/3.04 tff(15893,plain,
% 2.80/3.04 (r(s(elem!1), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[486, 15892, 1])).
% 2.80/3.04 tff(15894,plain,
% 2.80/3.04 (~b(s(s(s(z))), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15249, 15893, 112, 15877, 15873, 7265, 15875])).
% 2.80/3.04 tff(15895,plain,
% 2.80/3.04 (r(elem!1, z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[8704, 15892, 15166, 71, 606, 15143, 15867])).
% 2.80/3.04 tff(15896,plain,
% 2.80/3.04 (~r(s(s(s(z))), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[2122, 15895, 15877, 15867])).
% 2.80/3.04 tff(15897,plain,
% 2.80/3.04 ($false),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[704, 15896, 15894, 15140])).
% 2.80/3.04 tff(15898,plain,(b(z, elem!1) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.04 tff(15899,plain,
% 2.80/3.04 (b(z, elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15898, 112, 1, 11546])).
% 2.80/3.04 tff(15900,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(monotonicity,[status(thm)],[2353])).
% 2.80/3.04 tff(15901,plain,
% 2.80/3.04 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(symmetry,[status(thm)],[15900])).
% 2.80/3.04 tff(15902,plain,
% 2.80/3.04 (~r(elem!1, z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1376, 354, 15166, 323])).
% 2.80/3.04 tff(15903,plain,
% 2.80/3.04 (b(elem!1, z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1380, 15902, 77])).
% 2.80/3.04 tff(15904,plain,
% 2.80/3.04 (~r(s(elem!1), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1392, 354, 15166, 15899, 77, 323, 15143])).
% 2.80/3.04 tff(15905,plain,
% 2.80/3.04 (b(s(elem!1), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[486, 15904, 1])).
% 2.80/3.04 tff(15906,plain,
% 2.80/3.04 (b(elem!1, s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[735, 304, 2358])).
% 2.80/3.04 tff(15907,plain,
% 2.80/3.04 (~b(s(s(s(z))), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[10565, 15903, 15899, 285])).
% 2.80/3.04 tff(15908,plain,
% 2.80/3.04 (r(s(s(s(z))), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[704, 15907, 15140])).
% 2.80/3.04 tff(15909,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15905, 2357])).
% 2.80/3.04 tff(15910,plain,
% 2.80/3.04 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[9194, 15907, 2358])).
% 2.80/3.04 tff(15911,plain,
% 2.80/3.04 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1137, 15910])).
% 2.80/3.04 tff(15912,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[3851, 563, 2358])).
% 2.80/3.04 tff(15913,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15794, 15912, 112])).
% 2.80/3.04 tff(15914,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(z))), introduced(assumption)).
% 2.80/3.04 tff(15915,plain,
% 2.80/3.04 (((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15916,plain,
% 2.80/3.04 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15917,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.04 inference(monotonicity,[status(thm)],[15916])).
% 2.80/3.04 tff(15918,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.04 inference(transitivity,[status(thm)],[15917, 15915])).
% 2.80/3.04 tff(15919,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))))),
% 2.80/3.04 inference(quant_inst,[status(thm)],[])).
% 2.80/3.04 tff(15920,plain,
% 2.80/3.04 ((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15919, 15918])).
% 2.80/3.04 tff(15921,plain,
% 2.80/3.04 (~r(s(z), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15920, 333, 11546, 6107, 15913])).
% 2.80/3.04 tff(15922,plain,
% 2.80/3.04 (b(s(z), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[172, 15921])).
% 2.80/3.04 tff(15923,plain,
% 2.80/3.04 (~r(s(s(s(z))), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[8710, 563, 15166, 707])).
% 2.80/3.04 tff(15924,plain,
% 2.80/3.04 (b(s(s(s(z))), s(z))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[2794, 15923])).
% 2.80/3.04 tff(15925,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15926,plain,
% 2.80/3.04 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15927,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.04 inference(monotonicity,[status(thm)],[15926])).
% 2.80/3.04 tff(15928,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(transitivity,[status(thm)],[15927, 15925])).
% 2.80/3.04 tff(15929,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.04 inference(quant_inst,[status(thm)],[])).
% 2.80/3.04 tff(15930,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15929, 15928])).
% 2.80/3.04 tff(15931,plain,
% 2.80/3.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15930, 144, 15924, 15922, 15914])).
% 2.80/3.04 tff(15932,plain,
% 2.80/3.04 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15931, 2355])).
% 2.80/3.04 tff(15933,plain,
% 2.80/3.04 (r(s(elem!1), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[965, 15932, 15156])).
% 2.80/3.04 tff(15934,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15327, 15933, 112])).
% 2.80/3.04 tff(15935,plain,
% 2.80/3.04 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[846, 15922, 304, 15924])).
% 2.80/3.04 tff(15936,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[249, 15935])).
% 2.80/3.04 tff(15937,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15938,plain,
% 2.80/3.04 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.04 inference(rewrite,[status(thm)],[])).
% 2.80/3.04 tff(15939,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.04 inference(monotonicity,[status(thm)],[15938])).
% 2.80/3.04 tff(15940,plain,
% 2.80/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.04 inference(transitivity,[status(thm)],[15939, 15937])).
% 2.80/3.04 tff(15941,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.04 inference(quant_inst,[status(thm)],[])).
% 2.80/3.04 tff(15942,plain,
% 2.80/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15941, 15940])).
% 2.80/3.04 tff(15943,plain,
% 2.80/3.04 ($false),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15942, 333, 15936, 6107, 15934, 15913])).
% 2.80/3.04 tff(15944,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.04 tff(15945,plain,
% 2.80/3.04 (~r(elem!1, s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15944, 15911, 112, 15909, 304, 11546, 15908])).
% 2.80/3.04 tff(15946,plain,
% 2.80/3.04 (b(elem!1, s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[560, 15945, 15143])).
% 2.80/3.04 tff(15947,plain,
% 2.80/3.04 (~b(s(z), s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[4409, 15946, 15906, 15905])).
% 2.80/3.04 tff(15948,plain,
% 2.80/3.04 (r(s(z), s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1244, 15947, 1229])).
% 2.80/3.04 tff(15949,plain,
% 2.80/3.04 (~r(s(elem!1), z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[1235, 15948, 323, 354])).
% 2.80/3.04 tff(15950,plain,
% 2.80/3.04 (b(s(elem!1), z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[507, 15949])).
% 2.80/3.04 tff(15951,plain,
% 2.80/3.04 (~b(s(elem!1), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[916, 15950, 15899, 15903])).
% 2.80/3.04 tff(15952,plain,
% 2.80/3.04 (r(s(elem!1), elem!1)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[448, 15951, 15142])).
% 2.80/3.04 tff(15953,plain,
% 2.80/3.04 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[2623, 15952, 112])).
% 2.80/3.04 tff(15954,plain,
% 2.80/3.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[15953, 15901])).
% 2.80/3.04 tff(15955,plain,
% 2.80/3.04 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15397, 15948, 112])).
% 2.80/3.04 tff(15956,plain,
% 2.80/3.04 (~b(z, s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[949, 15950, 15903, 15946])).
% 2.80/3.04 tff(15957,plain,
% 2.80/3.04 (r(z, s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[583, 15956])).
% 2.80/3.04 tff(15958,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[5657, 15946, 2358])).
% 2.80/3.04 tff(15959,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.04 inference(modus_ponens,[status(thm)],[546, 15668])).
% 2.80/3.04 tff(15960,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.04 tff(15961,plain,
% 2.80/3.04 ($false),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15960, 15959])).
% 2.80/3.04 tff(15962,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.04 tff(15963,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[15962, 15958, 112])).
% 2.80/3.04 tff(15964,plain,
% 2.80/3.04 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[2558, 15902, 2358])).
% 2.80/3.04 tff(15965,plain,
% 2.80/3.04 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[302, 15964])).
% 2.80/3.04 tff(15966,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.04 tff(15967,plain,
% 2.80/3.04 (~b(z, s(s(s(z))))),
% 2.80/3.04 inference(unit_resolution,[status(thm)],[294, 283, 285, 286])).
% 2.80/3.05 tff(15968,plain,
% 2.80/3.05 (r(z, s(s(s(z))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[619, 15967])).
% 2.80/3.05 tff(15969,plain,
% 2.80/3.05 (~r(s(elem!1), s(s(s(z))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[1929, 15968, 707, 562])).
% 2.80/3.05 tff(15970,plain,
% 2.80/3.05 (b(s(elem!1), s(s(s(z))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[965, 15969, 15156])).
% 2.80/3.05 tff(15971,plain,
% 2.80/3.05 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.05 inference(modus_ponens,[status(thm)],[15970, 15151])).
% 2.80/3.05 tff(15972,plain,
% 2.80/3.05 ($false),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15819, 144, 285, 283, 286, 15971, 15966])).
% 2.80/3.05 tff(15973,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.05 tff(15974,plain,
% 2.80/3.05 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15973, 15965, 285, 15963, 112, 15908, 15957])).
% 2.80/3.05 tff(15975,plain,
% 2.80/3.05 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[249, 15974])).
% 2.80/3.05 tff(15976,plain,
% 2.80/3.05 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(15977,plain,
% 2.80/3.05 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(15978,plain,
% 2.80/3.05 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.05 inference(monotonicity,[status(thm)],[15977])).
% 2.80/3.05 tff(15979,plain,
% 2.80/3.05 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(transitivity,[status(thm)],[15978, 15976])).
% 2.80/3.05 tff(15980,plain,
% 2.80/3.05 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(quant_inst,[status(thm)],[])).
% 2.80/3.05 tff(15981,plain,
% 2.80/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.05 inference(modus_ponens,[status(thm)],[15980, 15979])).
% 2.80/3.05 tff(15982,plain,
% 2.80/3.05 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15981, 333, 11546, 15975, 15955])).
% 2.80/3.05 tff(15983,plain,
% 2.80/3.05 ($false),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15982, 15954])).
% 2.80/3.05 tff(15984,plain,((~r(z, s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.05 tff(15985,plain,
% 2.80/3.05 (~r(z, s(z))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15984, 285, 11546, 112, 323, 304, 1])).
% 2.80/3.05 tff(15986,plain,
% 2.80/3.05 (b(z, s(z))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[372, 15985])).
% 2.80/3.05 tff(15987,plain,
% 2.80/3.05 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 2.80/3.05 inference(monotonicity,[status(thm)],[112])).
% 2.80/3.05 tff(15988,plain,
% 2.80/3.05 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.80/3.05 inference(modus_ponens,[status(thm)],[15899, 15987])).
% 2.80/3.05 tff(15989,plain,
% 2.80/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(15990,plain,
% 2.80/3.05 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(15991,plain,
% 2.80/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(monotonicity,[status(thm)],[15990])).
% 2.80/3.05 tff(15992,plain,
% 2.80/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.05 inference(transitivity,[status(thm)],[15991, 15989])).
% 2.80/3.05 tff(15993,plain,
% 2.80/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))),
% 2.80/3.05 inference(quant_inst,[status(thm)],[])).
% 2.80/3.05 tff(15994,plain,
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% 2.80/3.05 inference(modus_ponens,[status(thm)],[15993, 15992])).
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% 2.80/3.05 tff(15998,plain,
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[472, 15997, 15144])).
% 2.80/3.05 tff(15999,plain,
% 2.80/3.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.05 inference(modus_ponens,[status(thm)],[15998, 15901])).
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[2558, 321, 2358])).
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[3868, 15998, 2358])).
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% 2.80/3.05 (~r(s(elem!1), s(z))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[443, 16001, 15166, 16000])).
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[486, 16002, 1])).
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[1853, 16003, 490, 585])).
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% 2.80/3.05 inference(unit_resolution,[status(thm)],[1244, 16004, 1229])).
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% 2.80/3.05 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[15397, 16005, 112])).
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% 2.80/3.05 inference(monotonicity,[status(thm)],[16008])).
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% 2.80/3.05 inference(transitivity,[status(thm)],[16009, 16007])).
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% 2.80/3.05 inference(quant_inst,[status(thm)],[])).
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% 2.80/3.05 inference(modus_ponens,[status(thm)],[16011, 16010])).
% 2.80/3.05 tff(16013,plain,
% 2.80/3.05 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[16012, 333, 11546, 321, 16006])).
% 2.80/3.05 tff(16014,plain,
% 2.80/3.05 ($false),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[16013, 15999])).
% 2.80/3.05 tff(16015,plain,((~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.05 tff(16016,plain,
% 2.80/3.05 (~b(z, s(elem!1))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[16015, 321, 11546, 112, 490, 1, 304])).
% 2.80/3.05 tff(16017,plain,
% 2.80/3.05 (r(z, s(elem!1))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[583, 16016])).
% 2.80/3.05 tff(16018,plain,
% 2.80/3.05 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.05 inference(modus_ponens,[status(thm)],[16017, 15136])).
% 2.80/3.05 tff(16019,plain,
% 2.80/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(16020,plain,
% 2.80/3.05 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.05 inference(rewrite,[status(thm)],[])).
% 2.80/3.05 tff(16021,plain,
% 2.80/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.05 inference(monotonicity,[status(thm)],[16020])).
% 2.80/3.05 tff(16022,plain,
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% 2.80/3.05 inference(transitivity,[status(thm)],[16021, 16019])).
% 2.80/3.05 tff(16023,plain,
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% 2.80/3.05 inference(quant_inst,[status(thm)],[])).
% 2.80/3.05 tff(16024,plain,
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% 2.80/3.05 inference(modus_ponens,[status(thm)],[16023, 16022])).
% 2.80/3.05 tff(16025,plain,
% 2.80/3.05 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[16024, 333, 323, 11546, 321])).
% 2.80/3.05 tff(16026,plain,
% 2.80/3.05 ($false),
% 2.80/3.05 inference(unit_resolution,[status(thm)],[16025, 16018])).
% 2.80/3.05 tff(16027,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.06 tff(16028,plain,
% 2.80/3.06 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16027, 15986, 323, 11546, 112, 1, 304])).
% 2.80/3.06 tff(16029,plain,
% 2.80/3.06 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[302, 16028])).
% 2.80/3.06 tff(16030,plain,
% 2.80/3.06 (b(elem!1, z)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[787, 16029, 2358])).
% 2.80/3.06 tff(16031,plain,
% 2.80/3.06 (~b(s(s(s(z))), elem!1)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[10565, 16030, 15899, 285])).
% 2.80/3.06 tff(16032,plain,
% 2.80/3.06 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[9194, 16031, 2358])).
% 2.80/3.06 tff(16033,plain,
% 2.80/3.06 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[1137, 16032])).
% 2.80/3.06 tff(16034,plain,
% 2.80/3.06 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[9217, 144, 15986, 285, 304])).
% 2.80/3.06 tff(16035,plain,
% 2.80/3.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16034, 16029])).
% 2.80/3.06 tff(16036,plain,
% 2.80/3.06 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[249, 16035])).
% 2.80/3.06 tff(16037,plain,
% 2.80/3.06 (((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16038,plain,
% 2.80/3.06 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16039,plain,
% 2.80/3.06 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.06 inference(monotonicity,[status(thm)],[16038])).
% 2.80/3.06 tff(16040,plain,
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% 2.80/3.06 inference(transitivity,[status(thm)],[16039, 16037])).
% 2.80/3.06 tff(16041,plain,
% 2.80/3.06 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))))),
% 2.80/3.06 inference(quant_inst,[status(thm)],[])).
% 2.80/3.06 tff(16042,plain,
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% 2.80/3.06 inference(modus_ponens,[status(thm)],[16041, 16040])).
% 2.80/3.06 tff(16043,plain,
% 2.80/3.06 (~r(s(z), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16042, 333, 11546, 16036, 16033])).
% 2.80/3.06 tff(16044,plain,
% 2.80/3.06 (b(s(z), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[172, 16043])).
% 2.80/3.06 tff(16045,plain,
% 2.80/3.06 ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[11554, 244])).
% 2.80/3.06 tff(16046,plain,
% 2.80/3.06 (~r(s(s(s(z))), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16045, 16032, 11546, 16035])).
% 2.80/3.06 tff(16047,plain,
% 2.80/3.06 (b(s(s(s(z))), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[2794, 16046])).
% 2.80/3.06 tff(16048,plain,
% 2.80/3.06 (~b(z, s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[2025, 144, 15986, 16047, 16044])).
% 2.80/3.06 tff(16049,plain,
% 2.80/3.06 (r(z, s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[619, 16048])).
% 2.80/3.06 tff(16050,plain,
% 2.80/3.06 (r(s(s(s(z))), elem!1)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[704, 16031, 15140])).
% 2.80/3.06 tff(16051,plain,
% 2.80/3.06 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16052,plain,
% 2.80/3.06 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(quant_inst,[status(thm)],[])).
% 2.80/3.06 tff(16053,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16052, 16051])).
% 2.80/3.06 tff(16054,plain,
% 2.80/3.06 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16053, 333, 11546, 224])).
% 2.80/3.06 tff(16055,plain,
% 2.80/3.06 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16054, 15999])).
% 2.80/3.06 tff(16056,plain,
% 2.80/3.06 (~r(s(elem!1), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[15239, 16055, 112])).
% 2.80/3.06 tff(16057,plain,
% 2.80/3.06 (b(s(elem!1), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[486, 16056, 1])).
% 2.80/3.06 tff(16058,plain,
% 2.80/3.06 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[15981, 333, 11546, 224])).
% 2.80/3.06 tff(16059,plain,
% 2.80/3.06 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16058, 15999])).
% 2.80/3.06 tff(16060,plain,
% 2.80/3.06 (~r(s(z), s(elem!1))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[15397, 16059, 112])).
% 2.80/3.06 tff(16061,plain,
% 2.80/3.06 (b(s(z), s(elem!1))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[1244, 16060, 1229])).
% 2.80/3.06 tff(16062,plain,
% 2.80/3.06 ($false),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[1853, 16061, 16057, 490, 585])).
% 2.80/3.06 tff(16063,plain,((~b(z, s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.06 tff(16064,plain,
% 2.80/3.06 (~b(z, s(elem!1))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16063, 15986, 1, 112, 11546, 16036, 304])).
% 2.80/3.06 tff(16065,plain,
% 2.80/3.06 (r(z, s(elem!1))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[583, 16064])).
% 2.80/3.06 tff(16066,plain,
% 2.80/3.06 (~r(s(elem!1), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[1929, 16065, 16050, 16049])).
% 2.80/3.06 tff(16067,plain,
% 2.80/3.06 (b(s(elem!1), s(s(s(z))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[965, 16066, 15156])).
% 2.80/3.06 tff(16068,plain,
% 2.80/3.06 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16067, 15151])).
% 2.80/3.06 tff(16069,plain,
% 2.80/3.06 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16070,plain,
% 2.80/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.06 inference(monotonicity,[status(thm)],[16069])).
% 2.80/3.06 tff(16071,plain,
% 2.80/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(transitivity,[status(thm)],[16070, 15925])).
% 2.80/3.06 tff(16072,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.06 inference(quant_inst,[status(thm)],[])).
% 2.80/3.06 tff(16073,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16072, 16071])).
% 2.80/3.06 tff(16074,plain,
% 2.80/3.06 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16073, 144, 16047, 16044, 16068])).
% 2.80/3.06 tff(16075,plain,
% 2.80/3.06 (~b(s(elem!1), s(z))),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16074, 15150])).
% 2.80/3.06 tff(16076,plain,
% 2.80/3.06 (r(s(elem!1), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[486, 16075, 1])).
% 2.80/3.06 tff(16077,plain,
% 2.80/3.06 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[15239, 16076, 112])).
% 2.80/3.06 tff(16078,plain,
% 2.80/3.06 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16079,plain,
% 2.80/3.06 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(rewrite,[status(thm)],[])).
% 2.80/3.06 tff(16080,plain,
% 2.80/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.06 inference(monotonicity,[status(thm)],[16079])).
% 2.80/3.06 tff(16081,plain,
% 2.80/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(transitivity,[status(thm)],[16080, 16078])).
% 2.80/3.06 tff(16082,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.06 inference(quant_inst,[status(thm)],[])).
% 2.80/3.06 tff(16083,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16082, 16081])).
% 2.80/3.06 tff(16084,plain,
% 2.80/3.06 ($false),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16083, 333, 323, 623, 15386, 15781])).
% 2.80/3.06 tff(16085,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.06 tff(16086,plain,
% 2.80/3.06 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[16085, 16049, 323, 16077])).
% 2.80/3.06 tff(16087,plain,
% 2.80/3.06 (~r(s(elem!1), z)),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16086, 15149])).
% 2.80/3.06 tff(16088,plain,
% 2.80/3.06 (b(s(elem!1), z)),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[507, 16087])).
% 2.80/3.06 tff(16089,plain,
% 2.80/3.06 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.06 inference(modus_ponens,[status(thm)],[16088, 2398])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[916, 16088, 15899, 16030])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[448, 16090, 15142])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[560, 16092, 15143])).
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% 2.80/3.06 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[5657, 16093, 2358])).
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% 2.80/3.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.06 inference(unit_resolution,[status(thm)],[15962, 16094, 112])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[1376, 354, 409, 323])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[507, 16104])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[916, 16105, 251, 16101])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[448, 16106, 15142])).
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% 2.80/3.06 inference(modus_ponens,[status(thm)],[16103, 2357])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[7314, 354, 323, 1699])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[6555, 354, 323, 1699])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[249, 16119])).
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% 2.80/3.06 tff(16122,plain,
% 2.80/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
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% 2.80/3.06 inference(modus_ponens,[status(thm)],[16122, 16121])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[16123, 333, 1699, 16120, 16118, 16109])).
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% 2.80/3.06 tff(16126,plain,
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[16125, 16099, 112, 15899, 304, 323, 1, 15166])).
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% 2.80/3.06 inference(unit_resolution,[status(thm)],[302, 16128])).
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% 2.80/3.06 (((~![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(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
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% 2.80/3.07 inference(modus_ponens,[status(thm)],[16134, 16133])).
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% 2.80/3.07 (~r(s(elem!1), s(s(s(z))))),
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% 2.80/3.07 ($false),
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% 2.80/3.07 tff(16167,plain,((~r(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.07 tff(16168,plain,
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% 2.80/3.07 tff(16169,plain,
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% 2.80/3.07 inference(modus_ponens,[status(thm)],[585, 15745])).
% 2.80/3.07 tff(16171,assumption,(~b(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.07 tff(16172,plain,
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% 2.80/3.07 inference(unit_resolution,[status(thm)],[16171, 16170])).
% 2.80/3.07 tff(16173,plain,(b(z, s(s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.07 tff(16174,plain,
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% 2.80/3.07 tff(16177,plain,
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% 2.80/3.07 inference(unit_resolution,[status(thm)],[3868, 16176, 2358])).
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% 2.80/3.07 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.07 inference(modus_ponens,[status(thm)],[525, 15901])).
% 2.80/3.07 tff(16179,assumption,(~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.80/3.07 tff(16180,plain,
% 2.80/3.07 ($false),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[16179, 16178])).
% 2.80/3.07 tff(16181,plain,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.07 tff(16182,plain,
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% 2.80/3.07 tff(16183,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
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% 2.80/3.07 tff(16186,plain,
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% 2.80/3.07 tff(16187,plain,
% 2.80/3.07 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.07 inference(rewrite,[status(thm)],[])).
% 2.80/3.07 tff(16188,plain,
% 2.80/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.07 inference(monotonicity,[status(thm)],[16187])).
% 2.80/3.07 tff(16189,plain,
% 2.80/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.07 inference(transitivity,[status(thm)],[16188, 16186])).
% 2.80/3.07 tff(16190,plain,
% 2.80/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
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% 2.80/3.07 tff(16192,plain,
% 2.80/3.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[16191, 144, 304, 286, 16185, 16184])).
% 2.80/3.07 tff(16193,plain,
% 2.80/3.07 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[15962, 16192, 112])).
% 2.80/3.07 tff(16194,plain,
% 2.80/3.07 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[542, 16193, 15161])).
% 2.80/3.07 tff(16195,plain,
% 2.80/3.07 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
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% 2.80/3.07 tff(16196,plain,
% 2.80/3.07 (~b(s(z), s(elem!1))),
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% 2.80/3.07 tff(16197,plain,
% 2.80/3.07 (r(s(z), s(elem!1))),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[1244, 16196, 1237])).
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% 2.80/3.07 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
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% 2.80/3.07 tff(16199,plain,
% 2.80/3.07 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
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% 2.80/3.07 tff(16200,plain,
% 2.80/3.07 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.07 inference(rewrite,[status(thm)],[])).
% 2.80/3.07 tff(16201,plain,
% 2.80/3.07 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.07 inference(monotonicity,[status(thm)],[16200])).
% 2.80/3.07 tff(16202,plain,
% 2.80/3.07 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.07 inference(transitivity,[status(thm)],[16201, 16199])).
% 2.80/3.07 tff(16203,plain,
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% 2.80/3.07 tff(16204,plain,
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% 2.80/3.07 inference(modus_ponens,[status(thm)],[16203, 16202])).
% 2.80/3.07 tff(16205,plain,
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% 2.80/3.07 inference(unit_resolution,[status(thm)],[16204, 333, 11546, 16198, 16195, 16183])).
% 2.80/3.07 tff(16206,plain,((~b(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.07 tff(16207,plain,
% 2.80/3.07 (~b(s(elem!1), s(z))),
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% 2.80/3.07 tff(16208,plain,
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% 2.80/3.07 tff(16210,plain,
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% 2.80/3.07 inference(unit_resolution,[status(thm)],[15962, 16211, 112])).
% 2.80/3.07 tff(16213,plain,
% 2.80/3.07 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
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% 2.80/3.07 tff(16214,plain,
% 2.80/3.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
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% 2.80/3.07 tff(16215,plain,
% 2.80/3.07 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.07 inference(unit_resolution,[status(thm)],[15239, 16208, 112])).
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% 2.80/3.08 inference(unit_resolution,[status(thm)],[8030, 16274, 323, 562])).
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% 2.80/3.08 (b(s(s(s(z))), s(z))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[2794, 16275])).
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% 2.80/3.08 (~r(z, s(s(s(z))))),
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% 2.80/3.08 tff(16278,plain,
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% 2.80/3.08 inference(unit_resolution,[status(thm)],[619, 16277])).
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% 2.80/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
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% 2.80/3.08 tff(16280,plain,
% 2.80/3.08 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.08 inference(rewrite,[status(thm)],[])).
% 2.80/3.08 tff(16281,plain,
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% 2.80/3.08 inference(monotonicity,[status(thm)],[16280])).
% 2.80/3.08 tff(16282,plain,
% 2.80/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.08 inference(transitivity,[status(thm)],[16281, 16279])).
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% 2.80/3.08 inference(modus_ponens,[status(thm)],[16283, 16282])).
% 2.80/3.08 tff(16285,plain,
% 2.80/3.08 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[16284, 144, 16278, 16276, 16185, 16261])).
% 2.80/3.08 tff(16286,plain,
% 2.80/3.08 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16285, 2355])).
% 2.80/3.08 tff(16287,plain,
% 2.80/3.08 (r(s(elem!1), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[965, 16286, 15156])).
% 2.80/3.08 tff(16288,plain,
% 2.80/3.08 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15327, 16287, 112])).
% 2.80/3.08 tff(16289,plain,
% 2.80/3.08 ($false),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[16123, 333, 16274, 224, 16288, 16260])).
% 2.80/3.08 tff(16290,plain,((~b(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.08 tff(16291,plain,
% 2.80/3.08 (~b(s(elem!1), z)),
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% 2.80/3.08 tff(16292,plain,
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% 2.80/3.08 inference(unit_resolution,[status(thm)],[507, 16291])).
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% 2.80/3.08 (~r(s(s(s(z))), z)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[8561, 16292, 354, 323, 488, 15156])).
% 2.80/3.08 tff(16294,plain,
% 2.80/3.08 (b(s(s(s(z))), z)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[396, 16293])).
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% 2.80/3.08 (~(s(s(s(z))) = s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1934, 15156])).
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% 2.80/3.08 (~b(s(s(s(z))), elem!1)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[10565, 16294, 251, 16159])).
% 2.80/3.08 tff(16297,plain,
% 2.80/3.08 (r(s(s(s(z))), elem!1)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[704, 16296, 15140])).
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% 2.80/3.08 (~r(s(s(s(z))), s(z))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[8824, 16297, 323, 722])).
% 2.80/3.08 tff(16299,plain,
% 2.80/3.08 (b(s(s(s(z))), s(z))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[2794, 16298])).
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% 2.80/3.08 (~r(z, s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1960, 16299, 323, 488, 562, 16292, 1237, 16295])).
% 2.80/3.08 tff(16301,plain,
% 2.80/3.08 (b(z, s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[619, 16300])).
% 2.80/3.08 tff(16302,plain,
% 2.80/3.08 (~r(s(elem!1), elem!1)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[16270, 16297, 112, 323, 722, 354, 286, 16185])).
% 2.80/3.08 tff(16303,plain,
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% 2.80/3.08 inference(unit_resolution,[status(thm)],[448, 16302, 15142])).
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% 2.80/3.08 (~r(s(z), s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1235, 16292, 323, 354])).
% 2.80/3.08 tff(16305,plain,
% 2.80/3.08 (b(s(z), s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1244, 16304, 1237])).
% 2.80/3.08 tff(16306,plain,
% 2.80/3.08 (~r(s(z), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1550, 16297, 2358, 323, 722, 15141, 354, 286])).
% 2.80/3.08 tff(16307,plain,
% 2.80/3.08 (b(s(z), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[172, 16306])).
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% 2.80/3.08 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15930, 144, 16299, 16307, 16185])).
% 2.80/3.08 tff(16309,plain,
% 2.80/3.08 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16308, 2355])).
% 2.80/3.08 tff(16310,plain,
% 2.80/3.08 (r(s(elem!1), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[965, 16309, 15156])).
% 2.80/3.08 tff(16311,plain,
% 2.80/3.08 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15327, 16310, 112])).
% 2.80/3.08 tff(16312,plain,
% 2.80/3.08 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[9194, 16296, 2358])).
% 2.80/3.08 tff(16313,plain,
% 2.80/3.08 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1137, 16312])).
% 2.80/3.08 tff(16314,plain,
% 2.80/3.08 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15942, 333, 224, 16313, 16311])).
% 2.80/3.08 tff(16315,plain,
% 2.80/3.08 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15794, 16314, 112])).
% 2.80/3.08 tff(16316,plain,
% 2.80/3.08 (~r(elem!1, s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[3851, 16315, 2358])).
% 2.80/3.08 tff(16317,plain,
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% 2.80/3.08 inference(unit_resolution,[status(thm)],[560, 16316, 15143])).
% 2.80/3.08 tff(16318,plain,
% 2.80/3.08 (~b(s(s(elem!1)), s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1278, 16317, 722, 16305, 488, 15252, 16303, 409])).
% 2.80/3.08 tff(16319,plain,
% 2.80/3.08 (r(s(s(elem!1)), s(elem!1))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[1283, 16318, 15198])).
% 2.80/3.08 tff(16320,plain,
% 2.80/3.08 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16319, 15197])).
% 2.80/3.08 tff(16321,plain,
% 2.80/3.08 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[16155, 16292, 112])).
% 2.80/3.08 tff(16322,plain,
% 2.80/3.08 ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[15456, 333, 16321])).
% 2.80/3.08 tff(16323,plain,
% 2.80/3.08 (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[16322, 16320, 15219])).
% 2.80/3.08 tff(16324,plain,
% 2.80/3.08 (~r(s(s(elem!1)), z)),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16323, 15422])).
% 2.80/3.08 tff(16325,plain,
% 2.80/3.08 (b(s(s(elem!1)), z)),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[5509, 16324])).
% 2.80/3.08 tff(16326,plain,
% 2.80/3.08 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.80/3.08 inference(unit_resolution,[status(thm)],[5708, 16325, 16301, 16294])).
% 2.80/3.08 tff(16327,plain,
% 2.80/3.08 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16326, 15407])).
% 2.80/3.08 tff(16328,plain,
% 2.80/3.08 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.08 inference(modus_ponens,[status(thm)],[16305, 15288])).
% 2.80/3.08 tff(16329,plain,
% 2.80/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.08 inference(rewrite,[status(thm)],[])).
% 2.80/3.08 tff(16330,plain,
% 2.80/3.08 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.08 inference(rewrite,[status(thm)],[])).
% 2.80/3.08 tff(16331,plain,
% 2.80/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.80/3.08 inference(monotonicity,[status(thm)],[16330])).
% 2.80/3.08 tff(16332,plain,
% 2.80/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.08 inference(transitivity,[status(thm)],[16331, 16329])).
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% 2.80/3.09 inference(unit_resolution,[status(thm)],[4518, 44, 16335])).
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% 2.80/3.09 inference(unit_resolution,[status(thm)],[15275, 44, 16338])).
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% 2.80/3.09 inference(unit_resolution,[status(thm)],[16339, 16327, 15195])).
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% 2.80/3.09 inference(unit_resolution,[status(thm)],[619, 16349])).
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% 2.80/3.09 tff(16405,plain,
% 2.80/3.09 (~b(s(s(s(z))), elem!1)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[10565, 285, 251, 624])).
% 2.80/3.09 tff(16406,plain,
% 2.80/3.09 (r(s(s(s(z))), elem!1)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[704, 16405, 15140])).
% 2.80/3.09 tff(16407,plain,
% 2.80/3.09 (~r(s(elem!1), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[1694, 16406, 722, 435])).
% 2.80/3.09 tff(16408,plain,
% 2.80/3.09 (b(s(elem!1), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[965, 16407, 15156])).
% 2.80/3.09 tff(16409,plain,
% 2.80/3.09 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.09 inference(modus_ponens,[status(thm)],[16408, 15151])).
% 2.80/3.09 tff(16410,plain,
% 2.80/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.09 inference(rewrite,[status(thm)],[])).
% 2.80/3.09 tff(16411,plain,
% 2.80/3.09 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.09 inference(rewrite,[status(thm)],[])).
% 2.80/3.09 tff(16412,plain,
% 2.80/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.80/3.09 inference(monotonicity,[status(thm)],[16411])).
% 2.80/3.09 tff(16413,plain,
% 2.80/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.80/3.09 inference(transitivity,[status(thm)],[16412, 16410])).
% 2.80/3.09 tff(16414,plain,
% 2.80/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.09 inference(quant_inst,[status(thm)],[])).
% 2.80/3.09 tff(16415,plain,
% 2.80/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.80/3.09 inference(modus_ponens,[status(thm)],[16414, 16413])).
% 2.80/3.09 tff(16416,plain,
% 2.80/3.09 ($false),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16415, 144, 490, 285, 16409, 15914, 16404])).
% 2.80/3.09 tff(16417,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.09 tff(16418,plain,
% 2.80/3.09 (~b(s(s(s(z))), z)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16417, 16372, 16403, 16402, 112, 16251, 16401, 15899, 16254])).
% 2.80/3.09 tff(16419,plain,
% 2.80/3.09 ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16135, 333, 323, 1964])).
% 2.80/3.09 tff(16420,plain,
% 2.80/3.09 (~r(s(z), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16419, 15219])).
% 2.80/3.09 tff(16421,plain,
% 2.80/3.09 (b(s(z), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[172, 16420])).
% 2.80/3.09 tff(16422,plain,
% 2.80/3.09 (~r(z, s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[1990, 1963, 562, 488, 491, 56, 323])).
% 2.80/3.09 tff(16423,plain,
% 2.80/3.09 (b(z, s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[619, 16422])).
% 2.80/3.09 tff(16424,plain,
% 2.80/3.09 ($false),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[2025, 144, 490, 16423, 56, 16421])).
% 2.80/3.09 tff(16425,plain,(b(s(s(s(z))), z) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.09 tff(16426,plain,
% 2.80/3.09 (~b(s(s(s(z))), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16425, 16418, 16372, 323, 562, 112, 16256, 16399])).
% 2.80/3.09 tff(16427,plain,
% 2.80/3.09 (r(s(s(s(z))), z)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[396, 16418])).
% 2.80/3.09 tff(16428,plain,
% 2.80/3.09 (~r(s(s(s(z))), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[8030, 16427, 323, 562])).
% 2.80/3.09 tff(16429,plain,
% 2.80/3.09 ($false),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[2794, 16428, 16426])).
% 2.80/3.09 tff(16430,plain,((~r(z, s(elem!1))) | (~r(s(z), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.09 tff(16431,plain,
% 2.80/3.09 (~r(z, s(elem!1))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16430, 323, 112, 11546, 1])).
% 2.80/3.09 tff(16432,plain,
% 2.80/3.09 (b(z, s(elem!1))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[583, 16431])).
% 2.80/3.09 tff(16433,plain,
% 2.80/3.09 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[15789, 15240, 322, 11546])).
% 2.80/3.09 tff(16434,plain,
% 2.80/3.09 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[15794, 16433, 112])).
% 2.80/3.09 tff(16435,plain,
% 2.80/3.09 (r(elem!1, s(z))),
% 2.80/3.09 inference(modus_ponens,[status(thm)],[322, 15689])).
% 2.80/3.09 tff(16436,plain,
% 2.80/3.09 (~b(elem!1, z)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[1911, 434, 251, 323, 15142, 16435])).
% 2.80/3.09 tff(16437,plain,
% 2.80/3.09 (r(elem!1, z)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[653, 16436, 1368])).
% 2.80/3.09 tff(16438,plain,
% 2.80/3.09 (~r(s(elem!1), elem!1)),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[443, 16437, 15166, 434])).
% 2.80/3.09 tff(16439,plain,
% 2.80/3.09 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[3868, 16438, 2358])).
% 2.80/3.09 tff(16440,plain,
% 2.80/3.09 ($false),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[8386, 16439, 16434, 16361, 15161, 585])).
% 2.80/3.09 tff(16441,plain,((~r(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.09 tff(16442,plain,
% 2.80/3.09 (~r(s(elem!1), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16441, 16432, 112, 16250, 11546, 77, 15899, 323])).
% 2.80/3.09 tff(16443,plain,
% 2.80/3.09 (b(s(elem!1), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[486, 16442, 1])).
% 2.80/3.09 tff(16444,plain,
% 2.80/3.09 (~r(z, s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[642, 15175, 323, 322])).
% 2.80/3.09 tff(16445,plain,
% 2.80/3.09 (b(z, s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[619, 16444])).
% 2.80/3.09 tff(16446,plain,
% 2.80/3.09 (~r(z, s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[1376, 4414, 15166, 323])).
% 2.80/3.09 tff(16447,plain,
% 2.80/3.09 (b(z, s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[372, 16446])).
% 2.80/3.09 tff(16448,plain,
% 2.80/3.09 (~r(s(z), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16388, 6107, 11546, 322])).
% 2.80/3.09 tff(16449,plain,
% 2.80/3.09 (b(s(z), s(s(s(z))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[172, 16448])).
% 2.80/3.09 tff(16450,plain,
% 2.80/3.09 (~r(s(s(s(z))), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[15720, 6107, 11546, 322])).
% 2.80/3.09 tff(16451,plain,
% 2.80/3.09 (b(s(s(s(z))), s(z))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[2794, 16450])).
% 2.80/3.09 tff(16452,plain,
% 2.80/3.09 ($false),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[2176, 144, 490, 284, 16451, 16449])).
% 2.80/3.09 tff(16453,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.09 tff(16454,plain,
% 2.80/3.09 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[16453, 16447, 16445, 11546, 322])).
% 2.80/3.09 tff(16455,plain,
% 2.80/3.09 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.09 inference(unit_resolution,[status(thm)],[1137, 16454])).
% 2.80/3.10 tff(16456,assumption,(b(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.80/3.10 tff(16457,plain,
% 2.80/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.10 inference(rewrite,[status(thm)],[])).
% 2.80/3.10 tff(16458,plain,
% 2.80/3.10 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.10 inference(rewrite,[status(thm)],[])).
% 2.80/3.10 tff(16459,plain,
% 2.80/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.10 inference(monotonicity,[status(thm)],[16458])).
% 2.80/3.10 tff(16460,plain,
% 2.80/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.10 inference(transitivity,[status(thm)],[16459, 16457])).
% 2.80/3.10 tff(16461,plain,
% 2.80/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.10 inference(quant_inst,[status(thm)],[])).
% 2.80/3.10 tff(16462,plain,
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% 2.80/3.10 tff(16463,plain,
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% 2.80/3.10 tff(16468,plain,
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% 2.80/3.10 tff(16470,assumption,(~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 2.80/3.10 tff(16471,plain,
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% 2.80/3.10 tff(16473,plain,
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% 2.80/3.10 inference(quant_inst,[status(thm)],[])).
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% 2.80/3.10 inference(modus_ponens,[status(thm)],[16478, 16477])).
% 2.80/3.10 tff(16480,plain,
% 2.80/3.10 ($false),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16479, 333, 1699, 224, 15335, 15780])).
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% 2.80/3.10 tff(16482,plain,
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% 2.80/3.10 tff(16483,plain,
% 2.80/3.10 (b(s(s(s(z))), z)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[396, 16482])).
% 2.80/3.10 tff(16484,plain,
% 2.80/3.10 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 2.80/3.10 tff(16485,plain,
% 2.80/3.10 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.10 inference(modus_ponens,[status(thm)],[16484, 2547])).
% 2.80/3.10 tff(16486,plain,
% 2.80/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
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% 2.80/3.10 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
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% 2.80/3.10 tff(16488,plain,
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% 2.80/3.10 inference(monotonicity,[status(thm)],[16487])).
% 2.80/3.10 tff(16489,plain,
% 2.80/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.10 inference(transitivity,[status(thm)],[16488, 16486])).
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% 2.80/3.10 inference(quant_inst,[status(thm)],[])).
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% 2.80/3.10 inference(modus_ponens,[status(thm)],[16490, 16489])).
% 2.80/3.10 tff(16492,plain,
% 2.80/3.10 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
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% 2.80/3.10 tff(16493,plain,
% 2.80/3.10 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
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% 2.80/3.10 tff(16494,plain,
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% 2.80/3.10 inference(unit_resolution,[status(thm)],[4518, 44, 16493])).
% 2.80/3.10 tff(16495,plain,
% 2.80/3.10 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
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% 2.80/3.10 tff(16496,plain,
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% 2.80/3.10 tff(16497,plain,
% 2.80/3.10 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.10 inference(rewrite,[status(thm)],[])).
% 2.80/3.10 tff(16498,plain,
% 2.80/3.10 (((~![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(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.10 inference(monotonicity,[status(thm)],[16497])).
% 2.80/3.10 tff(16499,plain,
% 2.80/3.10 (((~![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(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.10 inference(transitivity,[status(thm)],[16498, 16496])).
% 2.80/3.10 tff(16500,plain,
% 2.80/3.10 ((~![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(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.80/3.10 inference(quant_inst,[status(thm)],[])).
% 2.80/3.10 tff(16501,plain,
% 2.80/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.80/3.10 inference(modus_ponens,[status(thm)],[16500, 16499])).
% 2.80/3.10 tff(16502,plain,
% 2.80/3.10 ($false),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16501, 333, 224, 16473, 16495, 16469])).
% 2.80/3.10 tff(16503,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.10 tff(16504,plain,
% 2.80/3.10 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16503, 16467, 112, 16455, 16465, 259, 585])).
% 2.80/3.10 tff(16505,plain,
% 2.80/3.10 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16181, 16504, 112])).
% 2.80/3.10 tff(16506,plain,
% 2.80/3.10 (~b(s(z), s(elem!1))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[1853, 16447, 585, 488])).
% 2.80/3.10 tff(16507,plain,
% 2.80/3.10 (r(s(z), s(elem!1))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[1244, 16506, 1237])).
% 2.80/3.10 tff(16508,plain,
% 2.80/3.10 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[15397, 16507, 112])).
% 2.80/3.10 tff(16509,plain,
% 2.80/3.10 ($false),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[15981, 333, 11546, 16467, 16508, 16505])).
% 2.80/3.10 tff(16510,plain,(b(elem!1, z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.80/3.10 tff(16511,plain,
% 2.80/3.10 (b(elem!1, z)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16510, 16432, 112, 15988, 11546, 16250, 1229, 16443, 323, 77])).
% 2.80/3.10 tff(16512,plain,
% 2.80/3.10 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.80/3.10 inference(modus_ponens,[status(thm)],[16443, 2357])).
% 2.80/3.10 tff(16513,plain,
% 2.80/3.10 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.80/3.10 inference(modus_ponens,[status(thm)],[16511, 15583])).
% 2.80/3.10 tff(16514,plain,
% 2.80/3.10 (r(s(s(s(z))), elem!1)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[15487, 6107, 112])).
% 2.80/3.10 tff(16515,plain,
% 2.80/3.10 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.80/3.10 inference(symmetry,[status(thm)],[15280])).
% 2.80/3.10 tff(16516,plain,
% 2.80/3.10 ((~b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.80/3.10 inference(monotonicity,[status(thm)],[15278])).
% 2.80/3.10 tff(16517,plain,
% 2.80/3.10 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.80/3.10 inference(monotonicity,[status(thm)],[15188, 2353])).
% 2.80/3.10 tff(16518,plain,
% 2.80/3.10 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.80/3.10 inference(symmetry,[status(thm)],[16517])).
% 2.80/3.10 tff(16519,plain,
% 2.80/3.10 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 2.80/3.10 inference(monotonicity,[status(thm)],[15196])).
% 2.80/3.10 tff(16520,plain,
% 2.80/3.10 (r(s(s(s(z))), elem!1)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[704, 55, 15140])).
% 2.80/3.10 tff(16521,plain,
% 2.80/3.10 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[9194, 55, 2358])).
% 2.80/3.10 tff(16522,plain,
% 2.80/3.10 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[1137, 16521])).
% 2.80/3.10 tff(16523,plain,
% 2.80/3.10 (~r(s(z), s(s(s(z))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16388, 16522, 11546, 322])).
% 2.80/3.10 tff(16524,plain,
% 2.80/3.10 (b(s(z), s(s(s(z))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[172, 16523])).
% 2.80/3.10 tff(16525,plain,
% 2.80/3.10 (~r(s(s(s(z))), s(z))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[8824, 16520, 323, 16435])).
% 2.80/3.10 tff(16526,plain,
% 2.80/3.10 (b(s(s(s(z))), s(z))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[2794, 16525])).
% 2.80/3.10 tff(16527,plain,
% 2.80/3.10 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[15930, 144, 16526, 16524, 15914])).
% 2.80/3.10 tff(16528,plain,
% 2.80/3.10 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.10 inference(modus_ponens,[status(thm)],[16527, 2355])).
% 2.80/3.10 tff(16529,plain,
% 2.80/3.10 (r(s(elem!1), s(s(s(z))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[965, 16528, 15156])).
% 2.80/3.10 tff(16530,plain,
% 2.80/3.10 (~r(s(elem!1), elem!1)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[1694, 16529, 16435, 16520])).
% 2.80/3.10 tff(16531,plain,
% 2.80/3.10 (b(s(elem!1), elem!1)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[448, 16530, 15142])).
% 2.80/3.10 tff(16532,plain,
% 2.80/3.10 (~b(s(elem!1), z)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[916, 16531, 251, 624])).
% 2.80/3.10 tff(16533,plain,
% 2.80/3.10 (r(s(elem!1), z)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[507, 16532])).
% 2.80/3.10 tff(16534,plain,
% 2.80/3.10 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[16155, 16533, 112])).
% 2.80/3.10 tff(16535,plain,
% 2.80/3.10 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.10 inference(unit_resolution,[status(thm)],[15327, 16529, 112])).
% 2.80/3.11 tff(16536,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16537,plain,
% 2.80/3.11 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16538,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.11 inference(monotonicity,[status(thm)],[16537])).
% 2.80/3.11 tff(16539,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(transitivity,[status(thm)],[16538, 16536])).
% 2.80/3.11 tff(16540,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.80/3.11 inference(quant_inst,[status(thm)],[])).
% 2.80/3.11 tff(16541,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.80/3.11 inference(modus_ponens,[status(thm)],[16540, 16539])).
% 2.80/3.11 tff(16542,plain,
% 2.80/3.11 ($false),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16541, 333, 623, 16522, 16535, 16534])).
% 2.80/3.11 tff(16543,plain,(b(s(s(s(z))), elem!1) | (~r(z, s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.80/3.11 tff(16544,plain,
% 2.80/3.11 (b(s(s(s(z))), elem!1)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16543, 623, 112, 251, 624, 16185, 11546, 322, 323])).
% 2.80/3.11 tff(16545,plain,
% 2.80/3.11 (~b(s(s(s(z))), z)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[10565, 16544, 251, 624])).
% 2.80/3.11 tff(16546,plain,
% 2.80/3.11 (r(s(s(s(z))), z)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[396, 16545])).
% 2.80/3.11 tff(16547,plain,
% 2.80/3.11 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16548,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.80/3.11 inference(monotonicity,[status(thm)],[16547])).
% 2.80/3.11 tff(16549,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.80/3.11 inference(transitivity,[status(thm)],[16548, 11992])).
% 2.80/3.11 tff(16550,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.80/3.11 inference(quant_inst,[status(thm)],[])).
% 2.80/3.11 tff(16551,plain,
% 2.80/3.11 ((~![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, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.80/3.11 inference(modus_ponens,[status(thm)],[16550, 16549])).
% 2.80/3.11 tff(16552,plain,
% 2.80/3.11 (~r(s(z), s(s(s(z))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16551, 333, 323, 16546, 623])).
% 2.80/3.11 tff(16553,plain,
% 2.80/3.11 (b(s(z), s(s(s(z))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[172, 16552])).
% 2.80/3.11 tff(16554,plain,
% 2.80/3.11 (((~![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, s(s(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16555,plain,
% 2.80/3.11 (((~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16556,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.80/3.11 inference(monotonicity,[status(thm)],[16555])).
% 2.80/3.11 tff(16557,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.80/3.11 inference(transitivity,[status(thm)],[16556, 16554])).
% 2.80/3.11 tff(16558,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.80/3.11 inference(quant_inst,[status(thm)],[])).
% 2.80/3.11 tff(16559,plain,
% 2.80/3.11 ((~![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, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.80/3.11 inference(modus_ponens,[status(thm)],[16558, 16557])).
% 2.80/3.11 tff(16560,plain,
% 2.80/3.11 (~r(s(s(s(z))), s(z))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16559, 333, 323, 16546, 623])).
% 2.80/3.11 tff(16561,plain,
% 2.80/3.11 (b(s(s(s(z))), s(z))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[2794, 16560])).
% 2.80/3.11 tff(16562,plain,
% 2.80/3.11 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[15930, 144, 16561, 16553, 16185])).
% 2.80/3.11 tff(16563,plain,
% 2.80/3.11 (~b(s(elem!1), s(s(s(z))))),
% 2.80/3.11 inference(modus_ponens,[status(thm)],[16562, 2355])).
% 2.80/3.11 tff(16564,plain,
% 2.80/3.11 (r(s(elem!1), s(s(s(z))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[965, 16563, 15156])).
% 2.80/3.11 tff(16565,plain,
% 2.80/3.11 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[15327, 16564, 112])).
% 2.80/3.11 tff(16566,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16567,plain,
% 2.80/3.11 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.80/3.11 tff(16568,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.80/3.11 inference(monotonicity,[status(thm)],[16567])).
% 2.80/3.11 tff(16569,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.80/3.11 inference(transitivity,[status(thm)],[16568, 16566])).
% 2.80/3.11 tff(16570,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.80/3.11 inference(quant_inst,[status(thm)],[])).
% 2.80/3.11 tff(16571,plain,
% 2.80/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.80/3.11 inference(modus_ponens,[status(thm)],[16570, 16569])).
% 2.80/3.11 tff(16572,plain,
% 2.80/3.11 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16571, 333, 16546, 623, 16565])).
% 2.80/3.11 tff(16573,plain,
% 2.80/3.11 (~r(s(elem!1), z)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16155, 16572, 112])).
% 2.80/3.11 tff(16574,plain,
% 2.80/3.11 (b(s(elem!1), z)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[507, 16573])).
% 2.80/3.11 tff(16575,plain,
% 2.80/3.11 (~b(s(elem!1), elem!1)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[916, 16574, 251, 624])).
% 2.80/3.11 tff(16576,plain,
% 2.80/3.11 (r(s(elem!1), elem!1)),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[448, 16575, 15142])).
% 2.80/3.11 tff(16577,plain,
% 2.80/3.11 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[2623, 16576, 112])).
% 2.80/3.11 tff(16578,plain,
% 2.80/3.11 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.80/3.11 inference(unit_resolution,[status(thm)],[16181, 16577, 112])).
% 2.80/3.11 tff(16579,plain,
% 2.80/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.80/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(16580,plain,
% 2.89/3.11 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(16581,plain,
% 2.89/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[16580])).
% 2.89/3.11 tff(16582,plain,
% 2.89/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(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(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.11 inference(transitivity,[status(thm)],[16581, 16579])).
% 2.89/3.11 tff(16583,plain,
% 2.89/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(16584,plain,
% 2.89/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[16583, 16582])).
% 2.89/3.11 tff(16585,plain,
% 2.89/3.11 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[16584, 333, 11546, 322, 16578])).
% 2.89/3.11 tff(16586,plain,
% 2.89/3.11 (~r(s(z), s(elem!1))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[15397, 16585, 112])).
% 2.89/3.11 tff(16587,plain,
% 2.89/3.11 (b(s(z), s(elem!1))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[1244, 16586, 1237])).
% 2.89/3.11 tff(16588,plain,
% 2.89/3.11 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[16587, 15288])).
% 2.89/3.11 tff(16589,plain,
% 2.89/3.11 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[16334, 144, 16561, 16185, 16588])).
% 2.89/3.11 tff(16590,plain,
% 2.89/3.11 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[4518, 44, 16589])).
% 2.89/3.11 tff(16591,plain,
% 2.89/3.11 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[16590, 15224])).
% 2.89/3.11 tff(16592,plain,
% 2.89/3.11 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[12069, 16574, 585, 15803])).
% 2.89/3.11 tff(16593,plain,
% 2.89/3.11 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[542, 16592, 15161])).
% 2.89/3.11 tff(16594,plain,
% 2.89/3.11 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[15794, 16593, 112])).
% 2.89/3.11 tff(16595,plain,
% 2.89/3.11 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[112])).
% 2.89/3.11 tff(16596,plain,
% 2.89/3.11 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[16544, 16595])).
% 2.89/3.11 tff(16597,plain,
% 2.89/3.11 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[16481, 16594, 16546, 16565])).
% 2.89/3.12 tff(16598,plain,
% 2.89/3.12 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[249, 16597])).
% 2.89/3.12 tff(16599,plain,
% 2.89/3.12 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[15188])).
% 2.89/3.12 tff(16600,plain,
% 2.89/3.12 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.89/3.12 inference(transitivity,[status(thm)],[16599, 13328])).
% 2.89/3.12 tff(16601,plain,
% 2.89/3.12 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(symmetry,[status(thm)],[16600])).
% 2.89/3.12 tff(16602,plain,
% 2.89/3.12 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16601])).
% 2.89/3.12 tff(16603,plain,
% 2.89/3.12 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[112])).
% 2.89/3.12 tff(16604,plain,
% 2.89/3.12 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16603])).
% 2.89/3.12 tff(16605,plain,
% 2.89/3.12 (~(elem!1 = s(s(elem!1)))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[5603, 15252])).
% 2.89/3.12 tff(16606,plain,
% 2.89/3.12 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16605, 16604])).
% 2.89/3.12 tff(16607,plain,
% 2.89/3.12 (~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16606, 16602])).
% 2.89/3.12 tff(16608,assumption,(r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.89/3.12 tff(16609,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16610,plain,
% 2.89/3.12 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16611,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16610])).
% 2.89/3.12 tff(16612,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(transitivity,[status(thm)],[16611, 16609])).
% 2.89/3.12 tff(16613,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(16614,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16613, 16612])).
% 2.89/3.12 tff(16615,plain,
% 2.89/3.12 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16614, 333, 15335, 15780])).
% 2.89/3.12 tff(16616,plain,
% 2.89/3.12 (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16615, 16608])).
% 2.89/3.12 tff(16617,plain,
% 2.89/3.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16618,plain,
% 2.89/3.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(16619,plain,
% 2.89/3.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16618, 16617])).
% 2.89/3.12 tff(16620,plain,
% 2.89/3.12 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16619, 44, 16616])).
% 2.89/3.12 tff(16621,plain,
% 2.89/3.12 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16620, 16607])).
% 2.89/3.12 tff(16622,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(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(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16623,plain,
% 2.89/3.12 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16624,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16623])).
% 2.89/3.12 tff(16625,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.12 inference(transitivity,[status(thm)],[16624, 16622])).
% 2.89/3.12 tff(16626,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(16627,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16626, 16625])).
% 2.89/3.12 tff(16628,plain,
% 2.89/3.12 ((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16627, 333, 15335, 15385])).
% 2.89/3.12 tff(16629,plain,
% 2.89/3.12 (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16628, 16608])).
% 2.89/3.12 tff(16630,plain,
% 2.89/3.12 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[15275, 44, 16629])).
% 2.89/3.12 tff(16631,plain,
% 2.89/3.12 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16630, 15195])).
% 2.89/3.12 tff(16632,plain,
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% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16633,plain,
% 2.89/3.12 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(16634,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16633])).
% 2.89/3.12 tff(16635,plain,
% 2.89/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.12 inference(transitivity,[status(thm)],[16634, 16632])).
% 2.89/3.12 tff(16636,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(16637,plain,
% 2.89/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[16636, 16635])).
% 2.89/3.12 tff(16638,plain,
% 2.89/3.12 ($false),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[16637, 144, 283, 2254, 16631, 16621])).
% 2.89/3.12 tff(16639,plain,((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.12 tff(16640,plain,
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% 2.89/3.12 inference(unit_resolution,[status(thm)],[16639, 16598, 16596, 112, 16565, 16594, 16591])).
% 2.89/3.12 tff(16641,plain,
% 2.89/3.12 (~r(s(s(elem!1)), s(elem!1))),
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% 2.89/3.12 tff(16642,plain,
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% 2.89/3.12 tff(16643,plain,
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% 2.89/3.12 tff(16644,plain,
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% 2.89/3.12 tff(16645,plain,
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% 2.89/3.12 tff(16646,plain,
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% 2.89/3.12 tff(16647,plain,
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% 2.89/3.12 inference(transitivity,[status(thm)],[16646, 16644])).
% 2.89/3.12 tff(16648,plain,
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% 2.89/3.12 tff(16649,plain,
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% 2.89/3.12 tff(16650,plain,
% 2.89/3.12 ((~b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z))))))))))),
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% 2.89/3.12 tff(16651,plain,
% 2.89/3.12 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
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% 2.89/3.12 tff(16652,plain,
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% 2.89/3.12 inference(modus_ponens,[status(thm)],[16651, 16516])).
% 2.89/3.12 tff(16653,plain,
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% 2.89/3.12 tff(16655,plain,
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% 2.89/3.12 tff(16656,plain,
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% 2.89/3.12 tff(16657,plain,
% 2.89/3.12 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(s(s(s(s(s(s(z))))))))), z))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[16656])).
% 2.89/3.12 tff(16658,plain,
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% 2.89/3.12 tff(16660,plain,
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% 2.89/3.13 tff(16661,plain,
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% 2.89/3.13 tff(16662,plain,
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% 2.89/3.13 tff(16663,plain,
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% 2.89/3.13 tff(16664,plain,
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% 2.89/3.13 inference(modus_ponens,[status(thm)],[16663, 16662])).
% 2.89/3.13 tff(16665,plain,
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% 2.89/3.13 tff(16666,plain,
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% 2.89/3.13 tff(16667,plain,
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% 2.89/3.13 inference(unit_resolution,[status(thm)],[372, 16666])).
% 2.89/3.13 tff(16668,plain,
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% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(16669,plain,
% 2.89/3.13 ((~![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(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))))),
% 2.89/3.13 inference(quant_inst,[status(thm)],[])).
% 2.89/3.13 tff(16670,plain,
% 2.89/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z)))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16669, 16668])).
% 2.89/3.13 tff(16671,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16670, 333, 16667, 323, 16665, 16654])).
% 2.89/3.13 tff(16672,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16673,plain,
% 2.89/3.13 (~r(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16672, 323, 112, 16432, 16443, 1229, 11546, 16250, 15899, 16511])).
% 2.89/3.13 tff(16674,plain,
% 2.89/3.13 (b(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[619, 16673])).
% 2.89/3.13 tff(16675,plain,
% 2.89/3.13 (~b(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16453, 6107, 16674, 11546, 16250])).
% 2.89/3.13 tff(16676,plain,
% 2.89/3.13 (r(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[372, 16675])).
% 2.89/3.13 tff(16677,plain,
% 2.89/3.13 (~r(s(elem!1), elem!1)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16270, 16676, 112, 323, 16251, 16514, 16513, 16512])).
% 2.89/3.13 tff(16678,plain,
% 2.89/3.13 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[3868, 16677, 2358])).
% 2.89/3.13 tff(16679,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[8386, 16678, 15988, 15161, 16432])).
% 2.89/3.13 tff(16680,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15794, 16679, 112])).
% 2.89/3.13 tff(16681,plain,
% 2.89/3.13 (~r(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16388, 6107, 11546, 16250])).
% 2.89/3.13 tff(16682,plain,
% 2.89/3.13 (b(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[172, 16681])).
% 2.89/3.13 tff(16683,plain,
% 2.89/3.13 (~r(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15720, 6107, 11546, 16250])).
% 2.89/3.13 tff(16684,plain,
% 2.89/3.13 (b(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2794, 16683])).
% 2.89/3.13 tff(16685,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15930, 144, 16684, 16682, 16512])).
% 2.89/3.13 tff(16686,plain,
% 2.89/3.13 (~b(s(elem!1), s(s(s(z))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16685, 2355])).
% 2.89/3.13 tff(16687,plain,
% 2.89/3.13 (r(s(elem!1), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[965, 16686, 15156])).
% 2.89/3.13 tff(16688,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15327, 16687, 112])).
% 2.89/3.13 tff(16689,plain,
% 2.89/3.13 (b(s(elem!1), elem!1)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[448, 16677, 15142])).
% 2.89/3.13 tff(16690,plain,
% 2.89/3.13 (~b(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[916, 16689, 15899, 16511])).
% 2.89/3.13 tff(16691,plain,
% 2.89/3.13 (r(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[507, 16690])).
% 2.89/3.13 tff(16692,plain,
% 2.89/3.13 (~r(s(s(s(z))), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[7383, 16691, 15172, 15143, 1, 1575, 16676, 323, 15156, 16684])).
% 2.89/3.13 tff(16693,plain,
% 2.89/3.13 (b(s(s(s(z))), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[396, 16692])).
% 2.89/3.13 tff(16694,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[294, 16693, 16674, 16513])).
% 2.89/3.13 tff(16695,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[249, 16694])).
% 2.89/3.13 tff(16696,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15942, 333, 16695, 6107, 16688, 16680])).
% 2.89/3.13 tff(16697,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(z, elem!1) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16698,plain,
% 2.89/3.13 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16697, 323, 1, 1575, 112, 11546])).
% 2.89/3.13 tff(16699,plain,
% 2.89/3.13 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[1137, 16698])).
% 2.89/3.13 tff(16700,plain,
% 2.89/3.13 (b(s(s(s(z))), elem!1)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[9194, 16699, 2358])).
% 2.89/3.13 tff(16701,plain,
% 2.89/3.13 (~b(s(s(s(z))), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[10565, 16700, 15899, 16511])).
% 2.89/3.13 tff(16702,plain,
% 2.89/3.13 (r(s(s(s(z))), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[396, 16701])).
% 2.89/3.13 tff(16703,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16228, 16699, 16674, 15988])).
% 2.89/3.13 tff(16704,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[249, 16703])).
% 2.89/3.13 tff(16705,plain,
% 2.89/3.13 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16173, 16432, 112])).
% 2.89/3.13 tff(16706,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16464, 16699, 15988, 16674, 16705])).
% 2.89/3.13 tff(16707,plain,
% 2.89/3.13 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16503, 16704, 112, 16699, 16706, 15988, 16432])).
% 2.89/3.13 tff(16708,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16181, 16707, 112])).
% 2.89/3.13 tff(16709,plain,
% 2.89/3.13 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15981, 333, 11546, 16704, 16708])).
% 2.89/3.13 tff(16710,plain,
% 2.89/3.13 (~r(s(z), s(elem!1))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15397, 16709, 112])).
% 2.89/3.13 tff(16711,plain,
% 2.89/3.13 (b(s(z), s(elem!1))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[1244, 16710, 1229])).
% 2.89/3.13 tff(16712,plain,
% 2.89/3.13 (~b(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[1853, 16711, 16432, 16443])).
% 2.89/3.13 tff(16713,plain,
% 2.89/3.13 (r(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[372, 16712])).
% 2.89/3.13 tff(16714,plain,
% 2.89/3.13 (~r(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[8561, 16713, 16702, 323, 16443, 15156])).
% 2.89/3.13 tff(16715,plain,
% 2.89/3.13 (b(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[507, 16714])).
% 2.89/3.13 tff(16716,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[12069, 16715, 16432, 16513])).
% 2.89/3.13 tff(16717,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[542, 16716, 15161])).
% 2.89/3.13 tff(16718,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15794, 16717, 112])).
% 2.89/3.13 tff(16719,plain,
% 2.89/3.13 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16481, 16718, 16704, 16702])).
% 2.89/3.13 tff(16720,plain,
% 2.89/3.13 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15327, 16719, 112])).
% 2.89/3.13 tff(16721,plain,
% 2.89/3.13 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[965, 16720, 15156])).
% 2.89/3.13 tff(16722,plain,
% 2.89/3.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16721, 15151])).
% 2.89/3.13 tff(16723,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16706, 16722])).
% 2.89/3.13 tff(16724,plain,((~r(s(z), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16725,plain,
% 2.89/3.13 (r(z, elem!1)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16724, 323, 11546, 1, 112])).
% 2.89/3.13 tff(16726,plain,
% 2.89/3.13 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2305, 16725, 2358])).
% 2.89/3.13 tff(16727,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15633, 16726, 16250, 11546, 323])).
% 2.89/3.13 tff(16728,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16729,plain,
% 2.89/3.13 (~r(s(z), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16728, 112, 1, 11546])).
% 2.89/3.13 tff(16730,plain,
% 2.89/3.13 (b(s(z), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[348, 16729])).
% 2.89/3.13 tff(16731,plain,
% 2.89/3.13 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[14521, 354, 15166, 321])).
% 2.89/3.13 tff(16732,plain,
% 2.89/3.13 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[319, 16731])).
% 2.89/3.13 tff(16733,plain,
% 2.89/3.13 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(monotonicity,[status(thm)],[112])).
% 2.89/3.13 tff(16734,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.89/3.13 inference(symmetry,[status(thm)],[16733])).
% 2.89/3.13 tff(16735,plain,
% 2.89/3.13 (~r(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[9952, 16514, 15166, 408])).
% 2.89/3.13 tff(16736,plain,
% 2.89/3.13 (b(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2794, 16735])).
% 2.89/3.13 tff(16737,plain,
% 2.89/3.13 (((~![X0: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(16738,plain,
% 2.89/3.13 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(16739,plain,
% 2.89/3.13 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.13 inference(monotonicity,[status(thm)],[16738])).
% 2.89/3.13 tff(16740,plain,
% 2.89/3.13 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(transitivity,[status(thm)],[16739, 16737])).
% 2.89/3.13 tff(16741,plain,
% 2.89/3.13 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))))),
% 2.89/3.13 inference(quant_inst,[status(thm)],[])).
% 2.89/3.13 tff(16742,plain,
% 2.89/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16741, 16740])).
% 2.89/3.13 tff(16743,plain,
% 2.89/3.13 (~r(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16742, 333, 11546, 6107, 321])).
% 2.89/3.13 tff(16744,plain,
% 2.89/3.13 (b(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[172, 16743])).
% 2.89/3.13 tff(16745,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[846, 16744, 304, 16736])).
% 2.89/3.13 tff(16746,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[249, 16745])).
% 2.89/3.13 tff(16747,plain,
% 2.89/3.13 (r(elem!1, s(s(s(z))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16746, 16734])).
% 2.89/3.13 tff(16748,plain,
% 2.89/3.13 (~b(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2156, 16744, 489, 285])).
% 2.89/3.13 tff(16749,plain,
% 2.89/3.13 (r(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[619, 16748])).
% 2.89/3.13 tff(16750,plain,
% 2.89/3.13 (~r(elem!1, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[7510, 16749, 408, 16514])).
% 2.89/3.13 tff(16751,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16750, 16747])).
% 2.89/3.13 tff(16752,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16753,plain,
% 2.89/3.13 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16752, 16732, 408, 489, 285, 112, 11546, 321])).
% 2.89/3.13 tff(16754,plain,
% 2.89/3.13 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[1137, 16753])).
% 2.89/3.13 tff(16755,plain,
% 2.89/3.13 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2801, 144, 489, 285, 16732])).
% 2.89/3.13 tff(16756,plain,
% 2.89/3.13 (~b(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16755, 16754])).
% 2.89/3.13 tff(16757,plain,
% 2.89/3.13 (r(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2794, 16756])).
% 2.89/3.13 tff(16758,plain,
% 2.89/3.13 (((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(16759,plain,
% 2.89/3.13 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(16760,plain,
% 2.89/3.13 (((~![X0: $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(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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.13 inference(monotonicity,[status(thm)],[16759])).
% 2.89/3.13 tff(16761,plain,
% 2.89/3.13 (((~![X0: $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(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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.13 inference(transitivity,[status(thm)],[16760, 16758])).
% 2.89/3.13 tff(16762,plain,
% 2.89/3.13 ((~![X0: $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(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.89/3.13 inference(quant_inst,[status(thm)],[])).
% 2.89/3.13 tff(16763,plain,
% 2.89/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[16762, 16761])).
% 2.89/3.13 tff(16764,plain,
% 2.89/3.13 (~r(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16763, 333, 354, 16757, 11546])).
% 2.89/3.13 tff(16765,plain,
% 2.89/3.13 (b(z, s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[619, 16764])).
% 2.89/3.13 tff(16766,plain,
% 2.89/3.13 (~b(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2156, 16765, 489, 285])).
% 2.89/3.13 tff(16767,plain,
% 2.89/3.13 (r(s(z), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[172, 16766])).
% 2.89/3.13 tff(16768,plain,
% 2.89/3.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16228, 16765, 16754, 259])).
% 2.89/3.13 tff(16769,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[249, 16768])).
% 2.89/3.13 tff(16770,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15519, 16769, 16767, 11546, 16757])).
% 2.89/3.13 tff(16771,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.13 tff(16772,plain,
% 2.89/3.13 (~r(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16771, 285, 15988, 489, 11546, 408, 112, 321])).
% 2.89/3.13 tff(16773,plain,
% 2.89/3.13 (b(z, s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[372, 16772])).
% 2.89/3.13 tff(16774,plain,
% 2.89/3.13 (~b(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2273, 16773, 489, 285])).
% 2.89/3.13 tff(16775,plain,
% 2.89/3.13 (r(s(s(s(z))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[2794, 16774])).
% 2.89/3.13 tff(16776,plain,
% 2.89/3.13 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15418, 15335, 3193, 623])).
% 2.89/3.13 tff(16777,plain,
% 2.89/3.13 (~r(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[16155, 16776, 112])).
% 2.89/3.13 tff(16778,plain,
% 2.89/3.13 (b(s(elem!1), z)),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[507, 16777])).
% 2.89/3.13 tff(16779,plain,
% 2.89/3.13 (~b(s(elem!1), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[499, 16778, 489, 490])).
% 2.89/3.13 tff(16780,plain,
% 2.89/3.13 (r(s(elem!1), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[486, 16779, 1])).
% 2.89/3.13 tff(16781,plain,
% 2.89/3.13 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15239, 16780, 112])).
% 2.89/3.13 tff(16782,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[15506, 333, 3193, 11546, 15335, 16781])).
% 2.89/3.13 tff(16783,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16784,plain,
% 2.89/3.14 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16783, 623, 11546, 112, 1, 489, 16773, 16775])).
% 2.89/3.14 tff(16785,plain,
% 2.89/3.14 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15327, 16784, 112])).
% 2.89/3.14 tff(16786,plain,
% 2.89/3.14 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[965, 16785, 15156])).
% 2.89/3.14 tff(16787,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[1794, 16471])).
% 2.89/3.14 tff(16788,plain,((~b(s(elem!1), s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16789,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16788, 16786, 112])).
% 2.89/3.14 tff(16790,plain,
% 2.89/3.14 (~r(s(elem!1), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[10865, 435, 408, 623])).
% 2.89/3.14 tff(16791,plain,
% 2.89/3.14 (b(s(elem!1), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[507, 16790])).
% 2.89/3.14 tff(16792,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[499, 16791, 15214, 489, 490])).
% 2.89/3.14 tff(16793,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16794,plain,
% 2.89/3.14 (~r(s(elem!1), elem!1)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16793, 623, 16773, 1, 408, 489, 15166])).
% 2.89/3.14 tff(16795,plain,
% 2.89/3.14 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[3868, 16794, 2358])).
% 2.89/3.14 tff(16796,plain,
% 2.89/3.14 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[472, 16795, 15144])).
% 2.89/3.14 tff(16797,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(modus_ponens,[status(thm)],[16796, 2547])).
% 2.89/3.14 tff(16798,plain,
% 2.89/3.14 (~r(s(s(s(z))), elem!1)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[9952, 16775, 15166, 408])).
% 2.89/3.14 tff(16799,plain,
% 2.89/3.14 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15487, 16798, 112])).
% 2.89/3.14 tff(16800,plain,
% 2.89/3.14 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[1137, 16799])).
% 2.89/3.14 tff(16801,plain,
% 2.89/3.14 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~b(s(elem!1), z))),
% 2.89/3.14 inference(monotonicity,[status(thm)],[2397])).
% 2.89/3.14 tff(16802,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16803,plain,
% 2.89/3.14 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16804,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.89/3.14 inference(monotonicity,[status(thm)],[16803])).
% 2.89/3.14 tff(16805,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.14 inference(transitivity,[status(thm)],[16804, 16802])).
% 2.89/3.14 tff(16806,plain,
% 2.89/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.14 inference(quant_inst,[status(thm)],[])).
% 2.89/3.14 tff(16807,plain,
% 2.89/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.89/3.14 inference(modus_ponens,[status(thm)],[16806, 16805])).
% 2.89/3.14 tff(16808,plain,
% 2.89/3.14 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16807, 144, 285, 15988, 16797, 16789])).
% 2.89/3.14 tff(16809,plain,
% 2.89/3.14 (~b(s(elem!1), z)),
% 2.89/3.14 inference(modus_ponens,[status(thm)],[16808, 16801])).
% 2.89/3.14 tff(16810,plain,
% 2.89/3.14 (r(s(elem!1), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[507, 16809])).
% 2.89/3.14 tff(16811,plain,
% 2.89/3.14 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16155, 16810, 112])).
% 2.89/3.14 tff(16812,plain,
% 2.89/3.14 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), 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(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16813,plain,
% 2.89/3.14 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16814,plain,
% 2.89/3.14 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))))),
% 2.89/3.14 inference(monotonicity,[status(thm)],[16813])).
% 2.89/3.14 tff(16815,plain,
% 2.89/3.14 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.89/3.14 inference(transitivity,[status(thm)],[16814, 16812])).
% 2.89/3.14 tff(16816,plain,
% 2.89/3.14 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(quant_inst,[status(thm)],[])).
% 2.89/3.14 tff(16817,plain,
% 2.89/3.14 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 2.89/3.14 inference(modus_ponens,[status(thm)],[16816, 16815])).
% 2.89/3.14 tff(16818,plain,
% 2.89/3.14 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16817, 333, 623, 321, 16811])).
% 2.89/3.14 tff(16819,plain,
% 2.89/3.14 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15794, 16818, 112])).
% 2.89/3.14 tff(16820,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[542, 16819, 15161])).
% 2.89/3.14 tff(16821,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15962, 16820, 112])).
% 2.89/3.14 tff(16822,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16823,plain,
% 2.89/3.14 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16824,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.14 inference(monotonicity,[status(thm)],[16823])).
% 2.89/3.14 tff(16825,plain,
% 2.89/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(transitivity,[status(thm)],[16824, 16822])).
% 2.89/3.14 tff(16826,plain,
% 2.89/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.14 inference(quant_inst,[status(thm)],[])).
% 2.89/3.14 tff(16827,plain,
% 2.89/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.14 inference(modus_ponens,[status(thm)],[16826, 16825])).
% 2.89/3.14 tff(16828,plain,
% 2.89/3.14 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16827, 144, 16800, 16797, 16821])).
% 2.89/3.14 tff(16829,plain,
% 2.89/3.14 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[4518, 44, 16828])).
% 2.89/3.14 tff(16830,plain,
% 2.89/3.14 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16829, 15224])).
% 2.89/3.14 tff(16831,plain,
% 2.89/3.14 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15394, 16830, 16811, 16775])).
% 2.89/3.14 tff(16832,plain,
% 2.89/3.14 (~r(s(z), s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15397, 16831, 112])).
% 2.89/3.14 tff(16833,plain,
% 2.89/3.14 (b(s(z), s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[1244, 16832, 1229])).
% 2.89/3.14 tff(16834,plain,
% 2.89/3.14 (~b(s(z), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[2631, 16833, 489, 285, 16786])).
% 2.89/3.14 tff(16835,plain,
% 2.89/3.14 (r(s(z), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[172, 16834])).
% 2.89/3.14 tff(16836,plain,
% 2.89/3.14 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15519, 16835, 11546, 16775])).
% 2.89/3.14 tff(16837,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[249, 16836])).
% 2.89/3.14 tff(16838,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15317, 144, 16837, 16800, 16797, 16789])).
% 2.89/3.14 tff(16839,plain,((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16840,plain,
% 2.89/3.14 (~r(z, s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16839, 285, 489, 11546, 112, 321, 1, 408])).
% 2.89/3.14 tff(16841,plain,
% 2.89/3.14 (b(z, s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[619, 16840])).
% 2.89/3.14 tff(16842,plain,
% 2.89/3.14 (~b(s(z), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[2156, 16841, 489, 285])).
% 2.89/3.14 tff(16843,plain,
% 2.89/3.14 (r(s(z), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[172, 16842])).
% 2.89/3.14 tff(16844,plain,
% 2.89/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16228, 16841, 16800, 15988])).
% 2.89/3.14 tff(16845,plain,
% 2.89/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[249, 16844])).
% 2.89/3.14 tff(16846,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15519, 16845, 16843, 11546, 16775])).
% 2.89/3.14 tff(16847,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16848,plain,
% 2.89/3.14 (~b(s(s(s(z))), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16847, 321, 489, 112, 11546, 1, 408])).
% 2.89/3.14 tff(16849,plain,
% 2.89/3.14 (r(s(s(s(z))), z)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[396, 16848])).
% 2.89/3.14 tff(16850,plain,
% 2.89/3.14 (~r(s(s(s(z))), elem!1)),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[2122, 354, 408, 1699])).
% 2.89/3.14 tff(16851,plain,
% 2.89/3.14 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[15487, 16850, 112])).
% 2.89/3.14 tff(16852,plain,
% 2.89/3.14 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[1137, 16851])).
% 2.89/3.14 tff(16853,plain,
% 2.89/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16228, 16852, 284, 259])).
% 2.89/3.14 tff(16854,plain,
% 2.89/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[249, 16853])).
% 2.89/3.14 tff(16855,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[12304, 333, 354, 1699, 16854, 321])).
% 2.89/3.14 tff(16856,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16857,plain,
% 2.89/3.14 (~r(z, s(z))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16856, 284, 321, 1699, 15988, 112, 408])).
% 2.89/3.14 tff(16858,plain,
% 2.89/3.14 (b(z, s(z))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[372, 16857])).
% 2.89/3.14 tff(16859,plain,
% 2.89/3.14 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16453, 6107, 284, 11546, 490])).
% 2.89/3.14 tff(16860,plain,
% 2.89/3.14 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[319, 16859])).
% 2.89/3.14 tff(16861,plain,
% 2.89/3.14 (~r(z, s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[10450, 6107, 321, 1699])).
% 2.89/3.14 tff(16862,plain,
% 2.89/3.14 (b(z, s(elem!1))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[583, 16861])).
% 2.89/3.14 tff(16863,plain,
% 2.89/3.14 ($false),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16015, 16862, 16860, 11546, 112, 321, 1, 490])).
% 2.89/3.14 tff(16864,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.14 tff(16865,plain,
% 2.89/3.14 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16864, 16858, 112, 321, 1, 11546, 1699, 284])).
% 2.89/3.14 tff(16866,plain,
% 2.89/3.14 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[1137, 16865])).
% 2.89/3.14 tff(16867,plain,
% 2.89/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[16228, 16866, 284, 15988])).
% 2.89/3.14 tff(16868,plain,
% 2.89/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.14 inference(unit_resolution,[status(thm)],[249, 16867])).
% 2.89/3.14 tff(16869,plain,
% 2.89/3.14 (((~![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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16870,plain,
% 2.89/3.14 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.14 inference(rewrite,[status(thm)],[])).
% 2.89/3.14 tff(16871,plain,
% 2.89/3.14 (((~![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(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.14 inference(monotonicity,[status(thm)],[16870])).
% 2.89/3.14 tff(16872,plain,
% 2.89/3.14 (((~![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(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.15 inference(transitivity,[status(thm)],[16871, 16869])).
% 2.89/3.15 tff(16873,plain,
% 2.89/3.15 ((~![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(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.89/3.15 inference(quant_inst,[status(thm)],[])).
% 2.89/3.15 tff(16874,plain,
% 2.89/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16873, 16872])).
% 2.89/3.15 tff(16875,plain,
% 2.89/3.15 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16874, 333, 1699, 224, 321])).
% 2.89/3.15 tff(16876,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16875, 15219])).
% 2.89/3.15 tff(16877,plain,((~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.15 tff(16878,plain,
% 2.89/3.15 (~r(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16877, 16868, 1699, 112, 321])).
% 2.89/3.15 tff(16879,plain,
% 2.89/3.15 (b(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[583, 16878])).
% 2.89/3.15 tff(16880,plain,
% 2.89/3.15 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16173, 16879, 112])).
% 2.89/3.15 tff(16881,plain,
% 2.89/3.15 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16464, 16880, 15988, 16866, 284])).
% 2.89/3.15 tff(16882,plain,
% 2.89/3.15 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16503, 16881, 112, 16866, 16868, 15988, 16879])).
% 2.89/3.15 tff(16883,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16181, 16882, 112])).
% 2.89/3.15 tff(16884,plain,
% 2.89/3.15 (r(s(elem!1), elem!1)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[3868, 16882, 2358])).
% 2.89/3.15 tff(16885,plain,
% 2.89/3.15 (~r(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[443, 16884, 15166, 408])).
% 2.89/3.15 tff(16886,plain,
% 2.89/3.15 (b(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[486, 16885, 1])).
% 2.89/3.15 tff(16887,plain,
% 2.89/3.15 (~b(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1853, 16886, 16858, 16879])).
% 2.89/3.15 tff(16888,plain,
% 2.89/3.15 (r(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1244, 16887, 1229])).
% 2.89/3.15 tff(16889,plain,
% 2.89/3.15 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15397, 16888, 112])).
% 2.89/3.15 tff(16890,plain,
% 2.89/3.15 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16015, 16879, 11546, 112, 321, 1, 16858])).
% 2.89/3.15 tff(16891,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[319, 16890])).
% 2.89/3.15 tff(16892,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16584, 333, 11546, 16891, 16889, 16883])).
% 2.89/3.15 tff(16893,plain,((~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.15 tff(16894,plain,
% 2.89/3.15 (~b(z, s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16893, 408, 112, 1, 11546, 321, 16849])).
% 2.89/3.15 tff(16895,plain,
% 2.89/3.15 (r(z, s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[619, 16894])).
% 2.89/3.15 tff(16896,plain,
% 2.89/3.15 (b(elem!1, s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[735, 16732, 2358])).
% 2.89/3.15 tff(16897,plain,
% 2.89/3.15 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 2.89/3.15 inference(symmetry,[status(thm)],[2548])).
% 2.89/3.15 tff(16898,plain,
% 2.89/3.15 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 2.89/3.15 inference(transitivity,[status(thm)],[2546, 16897])).
% 2.89/3.15 tff(16899,plain,
% 2.89/3.15 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), elem!1))),
% 2.89/3.15 inference(monotonicity,[status(thm)],[16898])).
% 2.89/3.15 tff(16900,assumption,(~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.89/3.15 tff(16901,plain,
% 2.89/3.15 (~b(s(elem!1), elem!1)),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16900, 16899])).
% 2.89/3.15 tff(16902,plain,
% 2.89/3.15 (r(s(elem!1), elem!1)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[448, 16901, 15142])).
% 2.89/3.15 tff(16903,plain,
% 2.89/3.15 (~r(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[10865, 16902, 408, 16895])).
% 2.89/3.15 tff(16904,plain,
% 2.89/3.15 (b(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[507, 16903])).
% 2.89/3.15 tff(16905,plain,
% 2.89/3.15 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(monotonicity,[status(thm)],[2546])).
% 2.89/3.15 tff(16906,plain,
% 2.89/3.15 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16900, 16905])).
% 2.89/3.15 tff(16907,plain,
% 2.89/3.15 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[472, 16906, 15144])).
% 2.89/3.15 tff(16908,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16181, 16907, 112])).
% 2.89/3.15 tff(16909,plain,
% 2.89/3.15 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16012, 333, 11546, 321, 16908])).
% 2.89/3.15 tff(16910,plain,
% 2.89/3.15 (~r(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15397, 16909, 112])).
% 2.89/3.15 tff(16911,plain,
% 2.89/3.15 (b(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1244, 16910, 1229])).
% 2.89/3.15 tff(16912,plain,
% 2.89/3.15 (~b(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[2383, 16911, 489, 16904])).
% 2.89/3.15 tff(16913,plain,
% 2.89/3.15 (r(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[583, 16912])).
% 2.89/3.15 tff(16914,plain,
% 2.89/3.15 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16913, 15136])).
% 2.89/3.15 tff(16915,plain,
% 2.89/3.15 (~r(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[443, 16902, 15166, 408])).
% 2.89/3.15 tff(16916,plain,
% 2.89/3.15 (b(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[486, 16915, 1])).
% 2.89/3.15 tff(16917,plain,
% 2.89/3.15 (~b(elem!1, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[4409, 16911, 305, 16916])).
% 2.89/3.15 tff(16918,plain,
% 2.89/3.15 (r(elem!1, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[560, 16917, 15143])).
% 2.89/3.15 tff(16919,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[3851, 16918, 2358])).
% 2.89/3.15 tff(16920,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15794, 16919, 112])).
% 2.89/3.15 tff(16921,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(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(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.15 inference(rewrite,[status(thm)],[])).
% 2.89/3.15 tff(16922,plain,
% 2.89/3.15 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.15 inference(rewrite,[status(thm)],[])).
% 2.89/3.15 tff(16923,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.15 inference(monotonicity,[status(thm)],[16922])).
% 2.89/3.15 tff(16924,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.15 inference(transitivity,[status(thm)],[16923, 16921])).
% 2.89/3.15 tff(16925,plain,
% 2.89/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.89/3.15 inference(quant_inst,[status(thm)],[])).
% 2.89/3.15 tff(16926,plain,
% 2.89/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16925, 16924])).
% 2.89/3.15 tff(16927,plain,
% 2.89/3.15 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16926, 333, 321, 16920, 16908])).
% 2.89/3.15 tff(16928,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16927, 16914])).
% 2.89/3.15 tff(16929,plain,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.15 tff(16930,plain,
% 2.89/3.15 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16929, 16896, 321, 112, 489, 11546, 1, 408])).
% 2.89/3.15 tff(16931,plain,
% 2.89/3.15 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[9440, 333, 16849, 16895, 321])).
% 2.89/3.15 tff(16932,plain,
% 2.89/3.15 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1137, 16931])).
% 2.89/3.15 tff(16933,plain,
% 2.89/3.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[9433, 333, 16849, 16895, 321])).
% 2.89/3.15 tff(16934,plain,
% 2.89/3.15 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[249, 16933])).
% 2.89/3.15 tff(16935,plain,
% 2.89/3.15 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15317, 144, 16934, 16932, 16930])).
% 2.89/3.15 tff(16936,plain,
% 2.89/3.15 (~b(s(elem!1), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16788, 16935, 112])).
% 2.89/3.15 tff(16937,plain,
% 2.89/3.15 (r(s(elem!1), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[965, 16936, 15156])).
% 2.89/3.15 tff(16938,plain,
% 2.89/3.15 (~r(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1972, 16937, 16849, 16895])).
% 2.89/3.15 tff(16939,plain,
% 2.89/3.15 (b(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[583, 16938])).
% 2.89/3.15 tff(16940,plain,
% 2.89/3.15 (b(s(elem!1), elem!1)),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16930, 16898])).
% 2.89/3.15 tff(16941,plain,
% 2.89/3.15 (~b(elem!1, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1642, 16939, 15899, 16940])).
% 2.89/3.15 tff(16942,plain,
% 2.89/3.15 (r(elem!1, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[560, 16941, 15143])).
% 2.89/3.15 tff(16943,plain,
% 2.89/3.15 (~r(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1620, 16942, 408, 354])).
% 2.89/3.15 tff(16944,plain,
% 2.89/3.15 (b(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[507, 16943])).
% 2.89/3.15 tff(16945,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15327, 1686, 112])).
% 2.89/3.15 tff(16946,plain,
% 2.89/3.15 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16571, 333, 16849, 16895, 16945])).
% 2.89/3.15 tff(16947,plain,
% 2.89/3.15 (~r(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16155, 16946, 112])).
% 2.89/3.15 tff(16948,plain,
% 2.89/3.15 (b(s(elem!1), z)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[507, 16947])).
% 2.89/3.15 tff(16949,plain,
% 2.89/3.15 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16948, 2398])).
% 2.89/3.15 tff(16950,plain,
% 2.89/3.15 (~r(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1972, 1686, 16849, 16895])).
% 2.89/3.15 tff(16951,plain,
% 2.89/3.15 (b(z, s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[583, 16950])).
% 2.89/3.15 tff(16952,plain,
% 2.89/3.15 (~b(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[2383, 16948, 489, 16951])).
% 2.89/3.15 tff(16953,plain,
% 2.89/3.15 (b(s(s(s(z))), elem!1)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[9194, 16932, 2358])).
% 2.89/3.15 tff(16954,plain,
% 2.89/3.15 (~b(s(elem!1), elem!1)),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15346, 434, 353, 112, 1, 15335, 4367, 409, 1239])).
% 2.89/3.15 tff(16955,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[448, 16954, 444, 15142])).
% 2.89/3.15 tff(16956,plain,((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | b(s(z), s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.15 tff(16957,plain,
% 2.89/3.15 (~r(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16956, 16945, 112, 1, 353, 16953, 15166, 16952, 408])).
% 2.89/3.15 tff(16958,plain,
% 2.89/3.15 (b(s(elem!1), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[486, 16957, 1])).
% 2.89/3.15 tff(16959,plain,
% 2.89/3.15 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16958, 2357])).
% 2.89/3.15 tff(16960,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.15 inference(rewrite,[status(thm)],[])).
% 2.89/3.15 tff(16961,plain,
% 2.89/3.15 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.15 inference(rewrite,[status(thm)],[])).
% 2.89/3.15 tff(16962,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.89/3.15 inference(monotonicity,[status(thm)],[16961])).
% 2.89/3.15 tff(16963,plain,
% 2.89/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.15 inference(transitivity,[status(thm)],[16962, 16960])).
% 2.89/3.15 tff(16964,plain,
% 2.89/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 2.89/3.15 inference(quant_inst,[status(thm)],[])).
% 2.89/3.15 tff(16965,plain,
% 2.89/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16964, 16963])).
% 2.89/3.15 tff(16966,plain,
% 2.89/3.15 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16965, 144, 304, 15988, 16959, 16949])).
% 2.89/3.15 tff(16967,plain,
% 2.89/3.15 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(modus_ponens,[status(thm)],[16966, 16905])).
% 2.89/3.15 tff(16968,plain,
% 2.89/3.15 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[472, 16967, 15144])).
% 2.89/3.15 tff(16969,plain,
% 2.89/3.15 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16181, 16968, 112])).
% 2.89/3.15 tff(16970,plain,
% 2.89/3.15 (r(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1244, 16952, 1229])).
% 2.89/3.15 tff(16971,plain,
% 2.89/3.15 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[15397, 16970, 112])).
% 2.89/3.15 tff(16972,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16012, 333, 11546, 321, 16971, 16969])).
% 2.89/3.15 tff(16973,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.15 tff(16974,plain,
% 2.89/3.15 (~r(s(z), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[16973, 16937, 321, 112, 16732, 1, 11546, 408, 489])).
% 2.89/3.15 tff(16975,plain,
% 2.89/3.15 (b(s(z), s(s(s(z))))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[172, 16974])).
% 2.89/3.15 tff(16976,plain,
% 2.89/3.15 (~b(s(s(s(z))), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[846, 16975, 16934, 16732])).
% 2.89/3.15 tff(16977,plain,
% 2.89/3.15 (r(s(s(s(z))), s(z))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[2794, 16976])).
% 2.89/3.15 tff(16978,plain,
% 2.89/3.15 (~r(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[6565, 16977, 16849, 354])).
% 2.89/3.15 tff(16979,plain,
% 2.89/3.15 (b(s(z), s(elem!1))),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[1244, 16978, 1229])).
% 2.89/3.15 tff(16980,plain,
% 2.89/3.15 ($false),
% 2.89/3.15 inference(unit_resolution,[status(thm)],[2383, 16979, 16944, 489, 16939])).
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% 2.89/3.17 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
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% 2.89/3.17 inference(monotonicity,[status(thm)],[17119])).
% 2.89/3.17 tff(17121,plain,
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% 2.89/3.17 inference(transitivity,[status(thm)],[17120, 17118])).
% 2.89/3.17 tff(17122,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.17 inference(quant_inst,[status(thm)],[])).
% 2.89/3.17 tff(17123,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17122, 17121])).
% 2.89/3.17 tff(17124,plain,
% 2.89/3.17 (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17123, 144, 286, 259, 17117])).
% 2.89/3.17 tff(17125,plain,
% 2.89/3.17 (r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[16664, 44, 16661, 17124])).
% 2.89/3.17 tff(17126,assumption,(r(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.89/3.17 tff(17127,plain,
% 2.89/3.17 (((~![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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17128,plain,
% 2.89/3.17 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17129,plain,
% 2.89/3.17 (((~![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(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))))),
% 2.89/3.17 inference(monotonicity,[status(thm)],[17128])).
% 2.89/3.17 tff(17130,plain,
% 2.89/3.17 (((~![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(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.17 inference(transitivity,[status(thm)],[17129, 17127])).
% 2.89/3.17 tff(17131,plain,
% 2.89/3.17 ((~![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(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.17 inference(quant_inst,[status(thm)],[])).
% 2.89/3.17 tff(17132,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17131, 17130])).
% 2.89/3.17 tff(17133,plain,
% 2.89/3.17 ($false),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17132, 333, 1699, 17126, 17111, 17125])).
% 2.89/3.17 tff(17134,plain,((~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.17 tff(17135,plain,
% 2.89/3.17 (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17134, 17107, 1699, 286, 259, 112, 17110])).
% 2.89/3.17 tff(17136,plain,
% 2.89/3.17 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[15275, 44, 17135])).
% 2.89/3.17 tff(17137,plain,
% 2.89/3.17 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17136, 15195])).
% 2.89/3.17 tff(17138,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.89/3.17 tff(17139,plain,
% 2.89/3.17 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))),
% 2.89/3.17 inference(symmetry,[status(thm)],[17138])).
% 2.89/3.17 tff(17140,plain,
% 2.89/3.17 (s(elem!1) = s(s(s(z)))),
% 2.89/3.17 inference(transitivity,[status(thm)],[2352, 17139])).
% 2.89/3.17 tff(17141,plain,
% 2.89/3.17 ($false),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[15156, 17140])).
% 2.89/3.17 tff(17142,plain,((~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.17 tff(17143,plain,
% 2.89/3.17 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17142, 112])).
% 2.89/3.17 tff(17144,plain,
% 2.89/3.17 (((~![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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(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(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17145,plain,
% 2.89/3.17 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17146,plain,
% 2.89/3.17 (((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(monotonicity,[status(thm)],[17145])).
% 2.89/3.17 tff(17147,plain,
% 2.89/3.17 (((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(transitivity,[status(thm)],[17146, 17144])).
% 2.89/3.17 tff(17148,plain,
% 2.89/3.17 ((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(quant_inst,[status(thm)],[])).
% 2.89/3.17 tff(17149,plain,
% 2.89/3.17 ((~![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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17148, 17147])).
% 2.89/3.17 tff(17150,plain,
% 2.89/3.17 ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17149, 333, 1699, 15386])).
% 2.89/3.17 tff(17151,plain,
% 2.89/3.17 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17150, 17107])).
% 2.89/3.17 tff(17152,plain,
% 2.89/3.17 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[4518, 44, 17151, 17143])).
% 2.89/3.17 tff(17153,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17154,plain,
% 2.89/3.17 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17155,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(monotonicity,[status(thm)],[17154])).
% 2.89/3.17 tff(17156,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(transitivity,[status(thm)],[17155, 17153])).
% 2.89/3.17 tff(17157,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.89/3.17 inference(quant_inst,[status(thm)],[])).
% 2.89/3.17 tff(17158,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17157, 17156])).
% 2.89/3.17 tff(17159,plain,
% 2.89/3.17 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17158, 144, 15741, 17152, 17137])).
% 2.89/3.17 tff(17160,plain,
% 2.89/3.17 (~b(s(s(elem!1)), s(elem!1))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17159, 17108])).
% 2.89/3.17 tff(17161,plain,
% 2.89/3.17 (r(s(s(elem!1)), s(elem!1))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[1283, 17160, 15198])).
% 2.89/3.17 tff(17162,plain,
% 2.89/3.17 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17161, 15197])).
% 2.89/3.17 tff(17163,plain,
% 2.89/3.17 (((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17164,plain,
% 2.89/3.17 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17165,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.89/3.17 inference(monotonicity,[status(thm)],[17164])).
% 2.89/3.17 tff(17166,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(transitivity,[status(thm)],[17165, 17163])).
% 2.89/3.17 tff(17167,plain,
% 2.89/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(quant_inst,[status(thm)],[])).
% 2.89/3.17 tff(17168,plain,
% 2.89/3.17 ((~![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(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.17 inference(modus_ponens,[status(thm)],[17167, 17166])).
% 2.89/3.17 tff(17169,plain,
% 2.89/3.17 (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.17 inference(unit_resolution,[status(thm)],[17168, 333, 15386, 17162, 17107])).
% 2.89/3.17 tff(17170,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17171,plain,
% 2.89/3.17 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.17 inference(rewrite,[status(thm)],[])).
% 2.89/3.17 tff(17172,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.89/3.17 inference(monotonicity,[status(thm)],[17171])).
% 2.89/3.17 tff(17173,plain,
% 2.89/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.18 inference(transitivity,[status(thm)],[17172, 17170])).
% 2.89/3.18 tff(17174,plain,
% 2.89/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.18 inference(quant_inst,[status(thm)],[])).
% 2.89/3.18 tff(17175,plain,
% 2.89/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17174, 17173])).
% 2.89/3.18 tff(17176,plain,
% 2.89/3.18 (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17175, 144, 284, 2254, 259, 17137])).
% 2.89/3.18 tff(17177,plain,
% 2.89/3.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(s(z)))))))))) | b(z, s(s(s(s(s(s(s(s(s(z)))))))))) | r(z, s(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(s(z)))))))))) | b(z, s(s(s(s(s(s(s(s(s(z)))))))))) | r(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17178,plain,
% 2.89/3.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(s(z)))))))))) | b(z, s(s(s(s(s(s(s(s(s(z)))))))))) | r(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.18 inference(quant_inst,[status(thm)],[])).
% 2.89/3.18 tff(17179,plain,
% 2.89/3.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(s(s(z)))))))))) | b(z, s(s(s(s(s(s(s(s(s(z)))))))))) | r(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17178, 17177])).
% 2.89/3.18 tff(17180,plain,
% 2.89/3.18 ((z = s(s(s(s(s(s(s(s(s(z)))))))))) | r(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17179, 44, 17176])).
% 2.89/3.18 tff(17181,plain,
% 2.89/3.18 ($false),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17180, 17169, 17103])).
% 2.89/3.18 tff(17182,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.18 tff(17183,plain,
% 2.89/3.18 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
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% 2.89/3.18 tff(17184,plain,
% 2.89/3.18 (~b(s(elem!1), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16788, 17183, 112])).
% 2.89/3.18 tff(17185,plain,
% 2.89/3.18 (r(s(elem!1), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[965, 17184, 15156])).
% 2.89/3.18 tff(17186,plain,
% 2.89/3.18 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
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% 2.89/3.18 tff(17187,plain,
% 2.89/3.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16481, 17186, 17074, 17072])).
% 2.89/3.18 tff(17188,plain,
% 2.89/3.18 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[15794, 17187, 112])).
% 2.89/3.18 tff(17189,plain,
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% 2.89/3.18 inference(unit_resolution,[status(thm)],[17084, 17186, 17074, 17072])).
% 2.89/3.18 tff(17190,plain,
% 2.89/3.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16181, 17189, 112])).
% 2.89/3.18 tff(17191,plain,
% 2.89/3.18 (~b(z, s(elem!1))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[8386, 17190, 15988, 15161, 17188])).
% 2.89/3.18 tff(17192,plain,
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% 2.89/3.18 inference(unit_resolution,[status(thm)],[583, 17191])).
% 2.89/3.18 tff(17193,plain,
% 2.89/3.18 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17192, 15136])).
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% 2.89/3.18 (((~![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))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17195,plain,
% 2.89/3.18 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17196,plain,
% 2.89/3.18 (((~![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(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.89/3.18 inference(monotonicity,[status(thm)],[17195])).
% 2.89/3.18 tff(17197,plain,
% 2.89/3.18 (((~![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(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(transitivity,[status(thm)],[17196, 17194])).
% 2.89/3.18 tff(17198,plain,
% 2.89/3.18 ((~![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(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(quant_inst,[status(thm)],[])).
% 2.89/3.18 tff(17199,plain,
% 2.89/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17198, 17197])).
% 2.89/3.18 tff(17200,plain,
% 2.89/3.18 ($false),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17199, 333, 17072, 17186, 17099, 17193])).
% 2.89/3.18 tff(17201,plain,((~b(z, s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.18 tff(17202,plain,
% 2.89/3.18 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17201, 284, 112, 1, 11546])).
% 2.89/3.18 tff(17203,plain,
% 2.89/3.18 (~r(z, elem!1)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[15774, 509, 112, 11546, 16730, 1])).
% 2.89/3.18 tff(17204,plain,
% 2.89/3.18 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[1137, 11541])).
% 2.89/3.18 tff(17205,plain,
% 2.89/3.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[249, 11544])).
% 2.89/3.18 tff(17206,plain,
% 2.89/3.18 (~r(s(z), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16042, 333, 11546, 17205, 17204])).
% 2.89/3.18 tff(17207,plain,
% 2.89/3.18 (b(s(z), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[172, 17206])).
% 2.89/3.18 tff(17208,plain,
% 2.89/3.18 (~r(s(s(s(z))), s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16045, 11541, 11546, 11544])).
% 2.89/3.18 tff(17209,plain,
% 2.89/3.18 (b(s(s(s(z))), s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[2794, 17208])).
% 2.89/3.18 tff(17210,plain,
% 2.89/3.18 (~b(z, s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[2176, 144, 284, 17209, 17207])).
% 2.89/3.18 tff(17211,plain,
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% 2.89/3.18 inference(unit_resolution,[status(thm)],[372, 17210])).
% 2.89/3.18 tff(17212,plain,
% 2.89/3.18 (~r(s(z), z)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16724, 1575, 11546, 1, 112])).
% 2.89/3.18 tff(17213,plain,
% 2.89/3.18 (b(s(z), z)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[348, 17212])).
% 2.89/3.18 tff(17214,plain,
% 2.89/3.18 (b(elem!1, z)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17013, 489, 112, 1, 11546])).
% 2.89/3.18 tff(17215,plain,
% 2.89/3.18 (~b(s(elem!1), elem!1)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[916, 491, 15899, 17214])).
% 2.89/3.18 tff(17216,plain,
% 2.89/3.18 (r(s(elem!1), elem!1)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[448, 17215, 15142])).
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% 2.89/3.18 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[2623, 17216, 112])).
% 2.89/3.18 tff(17218,plain,
% 2.89/3.18 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16181, 17217, 112])).
% 2.89/3.18 tff(17219,plain,
% 2.89/3.18 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16053, 333, 11546, 224, 17218])).
% 2.89/3.18 tff(17220,plain,
% 2.89/3.18 (~r(s(elem!1), s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[15239, 17219, 112])).
% 2.89/3.18 tff(17221,plain,
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% 2.89/3.18 inference(unit_resolution,[status(thm)],[486, 17220, 1])).
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% 2.89/3.18 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17221, 2357])).
% 2.89/3.18 tff(17223,plain,
% 2.89/3.18 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17224,plain,
% 2.89/3.18 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.18 inference(quant_inst,[status(thm)],[])).
% 2.89/3.18 tff(17225,plain,
% 2.89/3.18 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17224, 17223])).
% 2.89/3.18 tff(17226,plain,
% 2.89/3.18 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17225, 333, 224, 6107, 17218])).
% 2.89/3.18 tff(17227,plain,
% 2.89/3.18 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[15327, 17226, 112])).
% 2.89/3.18 tff(17228,plain,
% 2.89/3.18 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[965, 17227, 15156])).
% 2.89/3.18 tff(17229,plain,
% 2.89/3.18 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16788, 17228, 112])).
% 2.89/3.18 tff(17230,plain,
% 2.89/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17231,plain,
% 2.89/3.18 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.18 inference(rewrite,[status(thm)],[])).
% 2.89/3.18 tff(17232,plain,
% 2.89/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.89/3.18 inference(monotonicity,[status(thm)],[17231])).
% 2.89/3.18 tff(17233,plain,
% 2.89/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.89/3.18 inference(transitivity,[status(thm)],[17232, 17230])).
% 2.89/3.18 tff(17234,plain,
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% 2.89/3.18 inference(quant_inst,[status(thm)],[])).
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% 2.89/3.18 inference(modus_ponens,[status(thm)],[17234, 17233])).
% 2.89/3.18 tff(17236,plain,
% 2.89/3.18 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17235, 144, 489, 56, 16261])).
% 2.89/3.18 tff(17237,plain,
% 2.89/3.18 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17236, 17229])).
% 2.89/3.18 tff(17238,plain,
% 2.89/3.18 ($false),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[17237, 17222])).
% 2.89/3.18 tff(17239,plain,((~b(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.18 tff(17240,plain,
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% 2.89/3.18 inference(unit_resolution,[status(thm)],[17239, 17209, 17213, 112, 1, 17205, 17204, 11546])).
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% 2.89/3.18 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.18 inference(modus_ponens,[status(thm)],[17242, 2357])).
% 2.89/3.18 tff(17244,plain,
% 2.89/3.18 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
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% 2.89/3.18 tff(17245,plain,
% 2.89/3.18 (~b(s(elem!1), s(s(s(z))))),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16788, 17244, 112])).
% 2.89/3.18 tff(17246,plain,
% 2.89/3.18 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.18 inference(unit_resolution,[status(thm)],[16155, 17241, 112])).
% 2.89/3.18 tff(17247,plain,
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% 2.89/3.19 inference(unit_resolution,[status(thm)],[17013, 17213, 112, 1, 11546])).
% 2.89/3.19 tff(17248,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17247, 15583])).
% 2.89/3.19 tff(17249,plain,
% 2.89/3.19 (~b(s(s(s(z))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17025, 284, 2358, 17248, 11546, 15899, 17247, 17213])).
% 2.89/3.19 tff(17250,plain,
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% 2.89/3.19 inference(unit_resolution,[status(thm)],[396, 17249])).
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% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17252,plain,
% 2.89/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.89/3.19 inference(quant_inst,[status(thm)],[])).
% 2.89/3.19 tff(17253,plain,
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% 2.89/3.19 inference(modus_ponens,[status(thm)],[17252, 17251])).
% 2.89/3.19 tff(17254,plain,
% 2.89/3.19 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17253, 333, 17211, 17250, 17246])).
% 2.89/3.19 tff(17255,plain,
% 2.89/3.19 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15327, 17254, 112])).
% 2.89/3.19 tff(17256,plain,
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% 2.89/3.19 inference(unit_resolution,[status(thm)],[965, 17255, 17245, 15156])).
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% 2.89/3.19 tff(17258,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17257, 284, 17203, 1, 11546, 17202, 112])).
% 2.89/3.19 tff(17259,plain,
% 2.89/3.19 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[1137, 17202])).
% 2.89/3.19 tff(17260,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17261,plain,
% 2.89/3.19 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17262,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.89/3.19 inference(monotonicity,[status(thm)],[17261])).
% 2.89/3.19 tff(17263,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.89/3.19 inference(transitivity,[status(thm)],[17262, 17260])).
% 2.89/3.19 tff(17264,plain,
% 2.89/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.89/3.19 inference(quant_inst,[status(thm)],[])).
% 2.89/3.19 tff(17265,plain,
% 2.89/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17264, 17263])).
% 2.89/3.19 tff(17266,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17265, 144, 17039, 284, 283, 17052])).
% 2.89/3.19 tff(17267,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[319, 17266])).
% 2.89/3.19 tff(17268,plain,
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% 2.89/3.19 inference(unit_resolution,[status(thm)],[16453, 17267, 6107, 11546, 284])).
% 2.89/3.19 tff(17269,plain,
% 2.89/3.19 (r(z, s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[372, 17268])).
% 2.89/3.19 tff(17270,plain,
% 2.89/3.19 (b(s(elem!1), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[1653, 17269, 15172, 17040, 15143, 1, 509])).
% 2.89/3.19 tff(17271,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17270, 2357])).
% 2.89/3.19 tff(17272,plain,
% 2.89/3.19 (~b(s(s(s(z))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17025, 284, 2358, 17052, 11546, 15899, 17051, 17039])).
% 2.89/3.19 tff(17273,plain,
% 2.89/3.19 (r(s(s(s(z))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[396, 17272])).
% 2.89/3.19 tff(17274,plain,
% 2.89/3.19 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17253, 333, 17269, 17273, 17028])).
% 2.89/3.19 tff(17275,plain,
% 2.89/3.19 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15327, 17274, 112])).
% 2.89/3.19 tff(17276,plain,
% 2.89/3.19 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[965, 17275, 15156])).
% 2.89/3.19 tff(17277,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16788, 17276, 112])).
% 2.89/3.19 tff(17278,plain,
% 2.89/3.19 (~r(s(z), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16388, 17267, 11546, 6107])).
% 2.89/3.19 tff(17279,plain,
% 2.89/3.19 (b(s(z), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[172, 17278])).
% 2.89/3.19 tff(17280,plain,
% 2.89/3.19 (~r(s(s(s(z))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15720, 17267, 11546, 6107])).
% 2.89/3.19 tff(17281,plain,
% 2.89/3.19 (b(s(s(s(z))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[2794, 17280])).
% 2.89/3.19 tff(17282,plain,
% 2.89/3.19 ($false),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16073, 144, 17281, 17279, 17277, 17271])).
% 2.89/3.19 tff(17283,plain,((~b(z, s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.19 tff(17284,plain,
% 2.89/3.19 (~b(z, s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17283, 6107, 1, 509, 11546, 112, 283])).
% 2.89/3.19 tff(17285,plain,
% 2.89/3.19 (r(z, s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[619, 17284])).
% 2.89/3.19 tff(17286,plain,
% 2.89/3.19 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17044, 17285, 6107, 17028])).
% 2.89/3.19 tff(17287,plain,
% 2.89/3.19 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15327, 17286, 112])).
% 2.89/3.19 tff(17288,plain,
% 2.89/3.19 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[965, 17287, 15156])).
% 2.89/3.19 tff(17289,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16788, 17288, 112])).
% 2.89/3.19 tff(17290,plain,
% 2.89/3.19 (~r(z, s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17065, 6107, 11546, 112, 17285, 1, 509])).
% 2.89/3.19 tff(17291,plain,
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% 2.89/3.19 inference(unit_resolution,[status(thm)],[372, 17290])).
% 2.89/3.19 tff(17292,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
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% 2.89/3.19 tff(17293,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[319, 17292])).
% 2.89/3.19 tff(17294,plain,
% 2.89/3.19 (~r(s(z), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16388, 17293, 11546, 6107])).
% 2.89/3.19 tff(17295,plain,
% 2.89/3.19 (b(s(z), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[172, 17294])).
% 2.89/3.19 tff(17296,plain,
% 2.89/3.19 (~r(s(s(s(z))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15720, 17293, 11546, 6107])).
% 2.89/3.19 tff(17297,plain,
% 2.89/3.19 (b(s(s(s(z))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[2794, 17296])).
% 2.89/3.19 tff(17298,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16073, 144, 17297, 17295, 17289])).
% 2.89/3.19 tff(17299,plain,
% 2.89/3.19 (~b(s(elem!1), s(z))),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17298, 15150])).
% 2.89/3.19 tff(17300,plain,
% 2.89/3.19 (~b(s(s(s(z))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[2273, 17297, 17039, 17291])).
% 2.89/3.19 tff(17301,plain,
% 2.89/3.19 (r(s(s(s(z))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[396, 17300])).
% 2.89/3.19 tff(17302,plain,
% 2.89/3.19 (((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17303,plain,
% 2.89/3.19 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17304,plain,
% 2.89/3.19 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.19 inference(monotonicity,[status(thm)],[17303])).
% 2.89/3.19 tff(17305,plain,
% 2.89/3.19 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(transitivity,[status(thm)],[17304, 17302])).
% 2.89/3.19 tff(17306,plain,
% 2.89/3.19 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(quant_inst,[status(thm)],[])).
% 2.89/3.19 tff(17307,plain,
% 2.89/3.19 ((~![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(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17306, 17305])).
% 2.89/3.19 tff(17308,plain,
% 2.89/3.19 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17307, 333, 17301, 17285, 17028])).
% 2.89/3.19 tff(17309,plain,
% 2.89/3.19 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[4518, 44, 17308, 17143])).
% 2.89/3.19 tff(17310,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17311,plain,
% 2.89/3.19 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(rewrite,[status(thm)],[])).
% 2.89/3.19 tff(17312,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.89/3.19 inference(monotonicity,[status(thm)],[17311])).
% 2.89/3.19 tff(17313,plain,
% 2.89/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.89/3.19 inference(transitivity,[status(thm)],[17312, 17310])).
% 2.89/3.19 tff(17314,plain,
% 2.89/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.89/3.19 inference(quant_inst,[status(thm)],[])).
% 2.89/3.19 tff(17315,plain,
% 2.89/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.89/3.19 inference(modus_ponens,[status(thm)],[17314, 17313])).
% 2.89/3.19 tff(17316,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17315, 144, 283, 17289, 17309])).
% 2.89/3.19 tff(17317,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15962, 17316, 112])).
% 2.89/3.19 tff(17318,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[542, 17317, 15161])).
% 2.89/3.19 tff(17319,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15794, 17318, 112])).
% 2.89/3.19 tff(17320,plain,
% 2.89/3.19 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15789, 17319, 17293, 11546])).
% 2.89/3.19 tff(17321,plain,
% 2.89/3.19 (~r(s(elem!1), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15239, 17320, 112])).
% 2.89/3.19 tff(17322,plain,
% 2.89/3.19 (b(s(elem!1), s(z))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[486, 17321, 1])).
% 2.89/3.19 tff(17323,plain,
% 2.89/3.19 ($false),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17322, 17299])).
% 2.89/3.19 tff(17324,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.19 tff(17325,plain,
% 2.89/3.19 ($false),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17324, 17259, 17258, 1, 11546, 509, 112])).
% 2.89/3.19 tff(17326,plain,((~b(z, s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.19 tff(17327,plain,
% 2.89/3.19 (~b(z, s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17326, 17016, 11546, 1, 112])).
% 2.89/3.19 tff(17328,plain,
% 2.89/3.19 (r(z, s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[619, 17327])).
% 2.89/3.19 tff(17329,plain,
% 2.89/3.19 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16571, 333, 1699, 623, 16945])).
% 2.89/3.19 tff(17330,plain,
% 2.89/3.19 (~r(s(elem!1), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16155, 17329, 112])).
% 2.89/3.19 tff(17331,plain,
% 2.89/3.19 (b(s(elem!1), z)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[507, 17330])).
% 2.89/3.19 tff(17332,plain,
% 2.89/3.19 (~b(s(elem!1), elem!1)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[916, 17331, 251, 624])).
% 2.89/3.19 tff(17333,plain,
% 2.89/3.19 (r(s(elem!1), elem!1)),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[448, 17332, 15142])).
% 2.89/3.19 tff(17334,plain,
% 2.89/3.19 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[2623, 17333, 112])).
% 2.89/3.19 tff(17335,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16181, 17334, 112])).
% 2.89/3.19 tff(17336,plain,
% 2.89/3.19 (~r(z, s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[1972, 1686, 623, 1699])).
% 2.89/3.19 tff(17337,plain,
% 2.89/3.19 (b(z, s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[583, 17336])).
% 2.89/3.19 tff(17338,plain,
% 2.89/3.19 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[12069, 17331, 15803, 17337])).
% 2.89/3.19 tff(17339,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[542, 17338, 15161])).
% 2.89/3.19 tff(17340,plain,
% 2.89/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15794, 17339, 112])).
% 2.89/3.19 tff(17341,plain,
% 2.89/3.19 (~b(s(z), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[2383, 17331, 489, 17337])).
% 2.89/3.19 tff(17342,plain,
% 2.89/3.19 (r(s(z), s(elem!1))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[1244, 17341, 1237])).
% 2.89/3.19 tff(17343,plain,
% 2.89/3.19 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[15397, 17342, 112])).
% 2.89/3.19 tff(17344,plain,
% 2.89/3.19 ($false),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[16204, 333, 11546, 17343, 17340, 17335])).
% 2.89/3.19 tff(17345,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.19 tff(17346,plain,
% 2.89/3.19 (~r(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[17345, 17328, 112, 1229, 16730, 15899, 17014, 11546, 17069])).
% 2.89/3.19 tff(17347,plain,
% 2.89/3.19 (b(s(elem!1), s(s(s(z))))),
% 2.89/3.19 inference(unit_resolution,[status(thm)],[965, 17346, 15156])).
% 2.89/3.19 tff(17348,plain,
% 2.89/3.19 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[16788, 17347, 112])).
% 2.97/3.20 tff(17349,plain,
% 2.97/3.20 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[8386, 15145, 16361, 15161, 585])).
% 2.97/3.20 tff(17350,plain,
% 2.97/3.20 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[15794, 17349, 112])).
% 2.97/3.20 tff(17351,plain,
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% 2.97/3.20 inference(unit_resolution,[status(thm)],[916, 15495, 251, 624])).
% 2.97/3.20 tff(17352,plain,
% 2.97/3.20 (r(s(elem!1), z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[507, 17351])).
% 2.97/3.20 tff(17353,plain,
% 2.97/3.20 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[16155, 17352, 112])).
% 2.97/3.20 tff(17354,plain,
% 2.97/3.20 (((~![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(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(17355,plain,
% 2.97/3.20 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(17356,plain,
% 2.97/3.20 (((~![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(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[17355])).
% 2.97/3.20 tff(17357,plain,
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% 2.97/3.20 inference(unit_resolution,[status(thm)],[17374, 17373])).
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% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(17379,plain,
% 2.97/3.20 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
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% 2.97/3.20 tff(17385,plain,
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% 2.97/3.20 inference(monotonicity,[status(thm)],[17389])).
% 2.97/3.20 tff(17391,plain,
% 2.97/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.20 inference(transitivity,[status(thm)],[17390, 17153])).
% 2.97/3.20 tff(17392,plain,
% 2.97/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.20 inference(quant_inst,[status(thm)],[])).
% 2.97/3.20 tff(17393,plain,
% 2.97/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(modus_ponens,[status(thm)],[17392, 17391])).
% 2.97/3.20 tff(17394,plain,
% 2.97/3.20 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[17393, 144, 15741, 17388, 17377])).
% 2.97/3.20 tff(17395,plain,
% 2.97/3.20 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[15275, 44, 17394])).
% 2.97/3.20 tff(17396,plain,
% 2.97/3.20 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[17395, 15195])).
% 2.97/3.20 tff(17397,plain,
% 2.97/3.20 (((~![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(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(17398,plain,
% 2.97/3.20 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17399,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(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(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[17398])).
% 2.97/3.21 tff(17400,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(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(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17399, 17397])).
% 2.97/3.21 tff(17401,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.21 inference(quant_inst,[status(thm)],[])).
% 2.97/3.21 tff(17402,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17401, 17400])).
% 2.97/3.21 tff(17403,plain,
% 2.97/3.21 ($false),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17402, 333, 1699, 623, 17396, 17386])).
% 2.97/3.21 tff(17404,plain,(r(s(elem!1), elem!1) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.21 tff(17405,plain,
% 2.97/3.21 (~b(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17404, 17348, 1727, 112, 17328, 15899, 17014, 17069])).
% 2.97/3.21 tff(17406,plain,
% 2.97/3.21 (r(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[583, 17405])).
% 2.97/3.21 tff(17407,plain,
% 2.97/3.21 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17406, 15136])).
% 2.97/3.21 tff(17408,assumption,(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))), introduced(assumption)).
% 2.97/3.21 tff(17409,plain,
% 2.97/3.21 (s(s(s(z))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(symmetry,[status(thm)],[17408])).
% 2.97/3.21 tff(17410,plain,
% 2.97/3.21 (s(s(s(z))) = s(s(elem!1))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17409, 15188])).
% 2.97/3.21 tff(17411,plain,
% 2.97/3.21 ($false),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15194, 17410])).
% 2.97/3.21 tff(17412,plain,((~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.21 tff(17413,plain,
% 2.97/3.21 (~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17412, 112])).
% 2.97/3.21 tff(17414,plain,
% 2.97/3.21 (~b(z, s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17201, 2254, 112, 1, 11546])).
% 2.97/3.21 tff(17415,plain,
% 2.97/3.21 (r(z, s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[619, 17414])).
% 2.97/3.21 tff(17416,plain,
% 2.97/3.21 (~r(s(elem!1), s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17345, 17072, 112, 1229, 16730, 15899, 17014, 11546, 17415])).
% 2.97/3.21 tff(17417,plain,
% 2.97/3.21 (b(s(elem!1), s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[965, 17416, 15156])).
% 2.97/3.21 tff(17418,plain,
% 2.97/3.21 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16788, 17417, 112])).
% 2.97/3.21 tff(17419,plain,
% 2.97/3.21 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17420,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[17419])).
% 2.97/3.21 tff(17421,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17420, 15312])).
% 2.97/3.21 tff(17422,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.97/3.21 inference(quant_inst,[status(thm)],[])).
% 2.97/3.21 tff(17423,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17422, 17421])).
% 2.97/3.21 tff(17424,plain,
% 2.97/3.21 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17423, 144, 283, 2254, 17418])).
% 2.97/3.21 tff(17425,plain,
% 2.97/3.21 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17424, 16905])).
% 2.97/3.21 tff(17426,plain,
% 2.97/3.21 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[472, 17425, 15144])).
% 2.97/3.21 tff(17427,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16181, 17426, 112])).
% 2.97/3.21 tff(17428,plain,
% 2.97/3.21 (~b(s(elem!1), elem!1)),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17424, 16899])).
% 2.97/3.21 tff(17429,plain,
% 2.97/3.21 (r(s(elem!1), elem!1)),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[448, 17428, 15142])).
% 2.97/3.21 tff(17430,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16181, 525, 112])).
% 2.97/3.21 tff(17431,plain,
% 2.97/3.21 (~b(z, s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[7093, 304, 16730, 17017])).
% 2.97/3.21 tff(17432,plain,
% 2.97/3.21 (r(z, s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[372, 17431])).
% 2.97/3.21 tff(17433,plain,
% 2.97/3.21 (~r(elem!1, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[1390, 434, 15166, 435])).
% 2.97/3.21 tff(17434,plain,
% 2.97/3.21 (b(elem!1, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[560, 17433, 15143])).
% 2.97/3.21 tff(17435,plain,
% 2.97/3.21 (~b(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[949, 17434, 624, 491])).
% 2.97/3.21 tff(17436,plain,
% 2.97/3.21 (r(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[583, 17435])).
% 2.97/3.21 tff(17437,plain,
% 2.97/3.21 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17436, 15136])).
% 2.97/3.21 tff(17438,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(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(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17439,plain,
% 2.97/3.21 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17440,plain,
% 2.97/3.21 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[17439])).
% 2.97/3.21 tff(17441,plain,
% 2.97/3.21 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17440, 17438])).
% 2.97/3.21 tff(17442,plain,
% 2.97/3.21 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.21 inference(quant_inst,[status(thm)],[])).
% 2.97/3.21 tff(17443,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17442, 17441])).
% 2.97/3.21 tff(17444,plain,
% 2.97/3.21 ($false),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17443, 333, 354, 11546, 15240, 17437])).
% 2.97/3.21 tff(17445,plain,((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.21 tff(17446,plain,
% 2.97/3.21 (~r(s(elem!1), s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17445, 17432, 11546, 112, 17014, 491, 435])).
% 2.97/3.21 tff(17447,plain,
% 2.97/3.21 (b(s(elem!1), s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[486, 17446, 1])).
% 2.97/3.21 tff(17448,plain,
% 2.97/3.21 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17447, 2357])).
% 2.97/3.21 tff(17449,plain,
% 2.97/3.21 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15680, 144, 16730, 304, 17017, 17448])).
% 2.97/3.21 tff(17450,plain,
% 2.97/3.21 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15962, 17449, 112])).
% 2.97/3.21 tff(17451,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[542, 17450, 15161])).
% 2.97/3.21 tff(17452,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15794, 17451, 112])).
% 2.97/3.21 tff(17453,plain,
% 2.97/3.21 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16204, 333, 11546, 17452, 17430])).
% 2.97/3.21 tff(17454,plain,
% 2.97/3.21 (~r(s(z), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15397, 17453, 112])).
% 2.97/3.21 tff(17455,plain,
% 2.97/3.21 (b(s(z), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[1244, 17454, 1229])).
% 2.97/3.21 tff(17456,plain,
% 2.97/3.21 (~b(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[2383, 17455, 16730, 491])).
% 2.97/3.21 tff(17457,plain,
% 2.97/3.21 (r(z, s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[583, 17456])).
% 2.97/3.21 tff(17458,plain,
% 2.97/3.21 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[112])).
% 2.97/3.21 tff(17459,plain,
% 2.97/3.21 (~b(elem!1, s(s(elem!1)))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[5640, 2737, 435, 562, 624])).
% 2.97/3.21 tff(17460,plain,
% 2.97/3.21 (r(elem!1, s(s(elem!1)))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[2522, 17459, 16605])).
% 2.97/3.21 tff(17461,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17460, 17458])).
% 2.97/3.21 tff(17462,plain,
% 2.97/3.21 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[3662, 2737, 525, 524])).
% 2.97/3.21 tff(17463,plain,
% 2.97/3.21 ($false),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17462, 17461])).
% 2.97/3.21 tff(17464,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.21 tff(17465,plain,
% 2.97/3.21 (~r(s(s(elem!1)), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17464, 17451, 525, 112, 435, 17457, 17014])).
% 2.97/3.21 tff(17466,plain,
% 2.97/3.21 (b(s(s(elem!1)), s(elem!1))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[1283, 17465, 15198])).
% 2.97/3.21 tff(17467,plain,
% 2.97/3.21 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17466, 16518])).
% 2.97/3.21 tff(17468,plain,
% 2.97/3.21 ((s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[15293, 44, 17453])).
% 2.97/3.21 tff(17469,plain,
% 2.97/3.21 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17468, 15286])).
% 2.97/3.21 tff(17470,plain,
% 2.97/3.21 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16649, 144, 17448, 17469, 17467])).
% 2.97/3.21 tff(17471,plain,
% 2.97/3.21 (~b(s(s(elem!1)), s(z))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17470, 16516])).
% 2.97/3.21 tff(17472,plain,
% 2.97/3.21 (r(s(s(elem!1)), s(z))),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[4983, 17471])).
% 2.97/3.21 tff(17473,plain,
% 2.97/3.21 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17472, 16515])).
% 2.97/3.21 tff(17474,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17475,plain,
% 2.97/3.21 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17476,plain,
% 2.97/3.21 (((~![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(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[17475])).
% 2.97/3.21 tff(17477,plain,
% 2.97/3.21 (((~![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(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17476, 17474])).
% 2.97/3.21 tff(17478,plain,
% 2.97/3.21 ((~![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(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.21 inference(quant_inst,[status(thm)],[])).
% 2.97/3.21 tff(17479,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17478, 17477])).
% 2.97/3.21 tff(17480,plain,
% 2.97/3.21 (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[17479, 333, 17432, 11546, 17473])).
% 2.97/3.21 tff(17481,plain,
% 2.97/3.21 (b(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.97/3.21 inference(unit_resolution,[status(thm)],[16664, 44, 16661, 17480])).
% 2.97/3.21 tff(17482,plain,
% 2.97/3.21 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.21 inference(rewrite,[status(thm)],[])).
% 2.97/3.21 tff(17483,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.21 inference(monotonicity,[status(thm)],[17482])).
% 2.97/3.21 tff(17484,plain,
% 2.97/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.21 inference(transitivity,[status(thm)],[17483, 17118])).
% 2.97/3.21 tff(17485,plain,
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% 2.97/3.21 inference(quant_inst,[status(thm)],[])).
% 2.97/3.21 tff(17486,plain,
% 2.97/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.21 inference(modus_ponens,[status(thm)],[17485, 17484])).
% 2.97/3.22 tff(17487,plain,
% 2.97/3.22 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17486, 144, 17017, 15988, 17481])).
% 2.97/3.22 tff(17488,plain,
% 2.97/3.22 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[16619, 44, 17487])).
% 2.97/3.22 tff(17489,plain,
% 2.97/3.22 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17488, 16607])).
% 2.97/3.22 tff(17490,plain,
% 2.97/3.22 (((~![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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), 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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17491,plain,
% 2.97/3.22 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17492,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[17491])).
% 2.97/3.22 tff(17493,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(transitivity,[status(thm)],[17492, 17490])).
% 2.97/3.22 tff(17494,plain,
% 2.97/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))))),
% 2.97/3.22 inference(quant_inst,[status(thm)],[])).
% 2.97/3.22 tff(17495,plain,
% 2.97/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17494, 17493])).
% 2.97/3.22 tff(17496,plain,
% 2.97/3.22 ($false),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17495, 333, 11546, 17452, 17473, 17489])).
% 2.97/3.22 tff(17497,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.22 tff(17498,plain,
% 2.97/3.22 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17497, 491, 112, 525, 435, 1, 11546])).
% 2.97/3.22 tff(17499,plain,
% 2.97/3.22 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[319, 17498])).
% 2.97/3.22 tff(17500,plain,
% 2.97/3.22 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[16584, 333, 11546, 17499, 17430])).
% 2.97/3.22 tff(17501,plain,
% 2.97/3.22 ((s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[15293, 44, 17500])).
% 2.97/3.22 tff(17502,plain,
% 2.97/3.22 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17501, 15286])).
% 2.97/3.22 tff(17503,plain,
% 2.97/3.22 (~b(s(z), elem!1)),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[1602, 17014, 15899, 16730])).
% 2.97/3.22 tff(17504,plain,
% 2.97/3.22 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[112])).
% 2.97/3.22 tff(17505,plain,
% 2.97/3.22 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 2.97/3.22 inference(symmetry,[status(thm)],[17504])).
% 2.97/3.22 tff(17506,plain,
% 2.97/3.22 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(elem!1, s(z)))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[17505])).
% 2.97/3.22 tff(17507,plain,
% 2.97/3.22 (~b(elem!1, s(z))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17498, 17506])).
% 2.97/3.22 tff(17508,plain,
% 2.97/3.22 (~r(s(z), s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[7675, 17507, 15172, 17503, 435])).
% 2.97/3.22 tff(17509,plain,
% 2.97/3.22 (b(s(z), s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[1244, 17508, 1229])).
% 2.97/3.22 tff(17510,plain,
% 2.97/3.22 (~b(z, s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[2383, 17509, 16730, 491])).
% 2.97/3.22 tff(17511,plain,
% 2.97/3.22 (r(z, s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[583, 17510])).
% 2.97/3.22 tff(17512,plain,
% 2.97/3.22 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17511, 15136])).
% 2.97/3.22 tff(17513,plain,
% 2.97/3.22 (b(s(z), s(s(s(s(s(s(s(s(s(z)))))))))) <=> b(s(z), s(s(elem!1)))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[15188])).
% 2.97/3.22 tff(17514,plain,
% 2.97/3.22 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(symmetry,[status(thm)],[17513])).
% 2.97/3.22 tff(17515,plain,
% 2.97/3.22 (b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[5486, 17514])).
% 2.97/3.22 tff(17516,assumption,(b(s(z), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.97/3.22 tff(17517,assumption,(b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.97/3.22 tff(17518,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17519,plain,
% 2.97/3.22 (((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17520,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[17519])).
% 2.97/3.22 tff(17521,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(transitivity,[status(thm)],[17520, 17518])).
% 2.97/3.22 tff(17522,plain,
% 2.97/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(quant_inst,[status(thm)],[])).
% 2.97/3.22 tff(17523,plain,
% 2.97/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17522, 17521])).
% 2.97/3.22 tff(17524,plain,
% 2.97/3.22 ((~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17523, 144, 489, 16404, 17516])).
% 2.97/3.22 tff(17525,plain,
% 2.97/3.22 ($false),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17524, 17515, 17517])).
% 2.97/3.22 tff(17526,plain,((~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.22 tff(17527,plain,
% 2.97/3.22 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17526, 5486, 16404, 17516, 489, 112])).
% 2.97/3.22 tff(17528,plain,
% 2.97/3.22 (~b(s(s(elem!1)), s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17376, 17527, 112])).
% 2.97/3.22 tff(17529,plain,
% 2.97/3.22 (r(s(s(elem!1)), s(elem!1))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[1283, 17528, 15198])).
% 2.97/3.22 tff(17530,plain,
% 2.97/3.22 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17529, 15197])).
% 2.97/3.22 tff(17531,plain,
% 2.97/3.22 (((~![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(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17532,plain,
% 2.97/3.22 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17533,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(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(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.97/3.22 inference(monotonicity,[status(thm)],[17532])).
% 2.97/3.22 tff(17534,plain,
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% 2.97/3.22 inference(transitivity,[status(thm)],[17533, 17531])).
% 2.97/3.22 tff(17535,plain,
% 2.97/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.22 inference(quant_inst,[status(thm)],[])).
% 2.97/3.22 tff(17536,plain,
% 2.97/3.22 ((~![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(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.22 inference(modus_ponens,[status(thm)],[17535, 17534])).
% 2.97/3.22 tff(17537,plain,
% 2.97/3.22 (~r(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17536, 333, 16183, 17530, 17126])).
% 2.97/3.22 tff(17538,plain,
% 2.97/3.22 ((z = s(s(s(s(s(s(s(s(s(z)))))))))) | b(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17179, 44, 17537])).
% 2.97/3.22 tff(17539,plain,
% 2.97/3.22 (b(z, s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.22 inference(unit_resolution,[status(thm)],[17538, 17103])).
% 2.97/3.22 tff(17540,plain,
% 2.97/3.22 (((~![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(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17541,plain,
% 2.97/3.22 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))) <=> ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.22 inference(rewrite,[status(thm)],[])).
% 2.97/3.22 tff(17542,plain,
% 2.97/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))))),
% 2.97/3.23 inference(monotonicity,[status(thm)],[17541])).
% 2.97/3.23 tff(17543,plain,
% 2.97/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.23 inference(transitivity,[status(thm)],[17542, 17540])).
% 2.97/3.23 tff(17544,plain,
% 2.97/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.23 inference(quant_inst,[status(thm)],[])).
% 2.97/3.23 tff(17545,plain,
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% 2.97/3.23 inference(modus_ponens,[status(thm)],[17544, 17543])).
% 2.97/3.23 tff(17546,plain,
% 2.97/3.23 (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[17545, 333, 16183, 17530, 17126])).
% 2.97/3.23 tff(17547,plain,
% 2.97/3.23 (b(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[16664, 44, 16661, 17546])).
% 2.97/3.23 tff(17548,plain,
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% 2.97/3.23 inference(rewrite,[status(thm)],[])).
% 2.97/3.23 tff(17549,plain,
% 2.97/3.23 (((~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.23 inference(rewrite,[status(thm)],[])).
% 2.97/3.23 tff(17550,plain,
% 2.97/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(s(z))))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 2.97/3.23 inference(monotonicity,[status(thm)],[17549])).
% 2.97/3.23 tff(17551,plain,
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% 2.97/3.23 inference(transitivity,[status(thm)],[17550, 17548])).
% 2.97/3.23 tff(17552,plain,
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% 2.97/3.23 inference(quant_inst,[status(thm)],[])).
% 2.97/3.23 tff(17553,plain,
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% 2.97/3.23 inference(modus_ponens,[status(thm)],[17552, 17551])).
% 2.97/3.23 tff(17554,plain,
% 2.97/3.23 ($false),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[17553, 144, 489, 17547, 17539, 17515])).
% 2.97/3.23 tff(17555,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.23 tff(17556,plain,
% 2.97/3.23 (~b(s(z), s(s(elem!1)))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[17555, 17512, 112, 17430, 16730, 16261, 17502])).
% 2.97/3.23 tff(17557,plain,
% 2.97/3.23 (r(s(z), s(s(elem!1)))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[5484, 17556])).
% 2.97/3.23 tff(17558,plain,
% 2.97/3.23 (r(s(z), s(s(s(s(s(s(s(s(s(z)))))))))) <=> r(s(z), s(s(elem!1)))),
% 2.97/3.23 inference(monotonicity,[status(thm)],[15188])).
% 2.97/3.23 tff(17559,plain,
% 2.97/3.23 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.23 inference(symmetry,[status(thm)],[17558])).
% 2.97/3.23 tff(17560,plain,
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% 2.97/3.23 tff(17561,plain,
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% 2.97/3.23 tff(17562,plain,
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% 2.97/3.23 tff(17612,plain,
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% 2.97/3.23 inference(unit_resolution,[status(thm)],[5657, 17606, 2358])).
% 2.97/3.23 tff(17613,plain,
% 2.97/3.23 (r(elem!1, s(elem!1))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[560, 17612, 15143])).
% 2.97/3.23 tff(17614,plain,
% 2.97/3.23 (~r(s(elem!1), s(z))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[1390, 17613, 15166, 17429])).
% 2.97/3.23 tff(17615,plain,
% 2.97/3.23 (b(s(elem!1), s(z))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[486, 17614, 1])).
% 2.97/3.23 tff(17616,plain,
% 2.97/3.23 (~r(s(z), s(elem!1))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[15397, 17609, 112])).
% 2.97/3.23 tff(17617,plain,
% 2.97/3.23 (b(s(z), s(elem!1))),
% 2.97/3.23 inference(unit_resolution,[status(thm)],[1244, 17616, 1229])).
% 2.97/3.23 tff(17618,plain,
% 2.97/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.23 inference(rewrite,[status(thm)],[])).
% 2.97/3.23 tff(17619,plain,
% 2.97/3.23 (((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.23 inference(rewrite,[status(thm)],[])).
% 2.97/3.23 tff(17620,plain,
% 2.97/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.23 inference(monotonicity,[status(thm)],[17619])).
% 2.97/3.23 tff(17621,plain,
% 2.97/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.23 inference(transitivity,[status(thm)],[17620, 17618])).
% 2.97/3.23 tff(17622,plain,
% 2.97/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(quant_inst,[status(thm)],[])).
% 2.97/3.24 tff(17623,plain,
% 2.97/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17622, 17621])).
% 2.97/3.24 tff(17624,plain,
% 2.97/3.24 (~b(s(z), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17623, 144, 17418, 17604, 17611])).
% 2.97/3.24 tff(17625,plain,
% 2.97/3.24 (r(s(z), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[172, 17624])).
% 2.97/3.24 tff(17626,plain,
% 2.97/3.24 (~r(z, s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[11983, 333, 17072, 17415, 17625])).
% 2.97/3.24 tff(17627,plain,
% 2.97/3.24 (b(z, s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[372, 17626])).
% 2.97/3.24 tff(17628,plain,
% 2.97/3.24 (~b(z, s(elem!1))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[1853, 17627, 17617, 17615])).
% 2.97/3.24 tff(17629,plain,
% 2.97/3.24 (r(z, s(elem!1))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[583, 17628])).
% 2.97/3.24 tff(17630,plain,
% 2.97/3.24 (~r(s(s(elem!1)), s(elem!1))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17464, 17629, 17426, 112, 17429, 17607, 17014])).
% 2.97/3.24 tff(17631,plain,
% 2.97/3.24 (b(s(s(elem!1)), s(elem!1))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[1283, 17630, 15198])).
% 2.97/3.24 tff(17632,plain,
% 2.97/3.24 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17376, 17631, 112])).
% 2.97/3.24 tff(17633,plain,
% 2.97/3.24 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17615, 2357])).
% 2.97/3.24 tff(17634,plain,
% 2.97/3.24 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[16649, 144, 17633, 17632, 17611])).
% 2.97/3.24 tff(17635,plain,
% 2.97/3.24 (~b(s(s(elem!1)), s(z))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17634, 16516])).
% 2.97/3.24 tff(17636,plain,
% 2.97/3.24 (r(s(s(elem!1)), s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[4983, 17635])).
% 2.97/3.24 tff(17637,plain,
% 2.97/3.24 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17636, 16515])).
% 2.97/3.24 tff(17638,plain,
% 2.97/3.24 (~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17393, 144, 17418, 17604, 17632])).
% 2.97/3.24 tff(17639,plain,
% 2.97/3.24 ((s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[15275, 44, 17638])).
% 2.97/3.24 tff(17640,plain,
% 2.97/3.24 (r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17639, 15195])).
% 2.97/3.24 tff(17641,plain,
% 2.97/3.24 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(rewrite,[status(thm)],[])).
% 2.97/3.24 tff(17642,plain,
% 2.97/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.24 inference(monotonicity,[status(thm)],[17641])).
% 2.97/3.24 tff(17643,plain,
% 2.97/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(transitivity,[status(thm)],[17642, 16329])).
% 2.97/3.24 tff(17644,plain,
% 2.97/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(quant_inst,[status(thm)],[])).
% 2.97/3.24 tff(17645,plain,
% 2.97/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17644, 17643])).
% 2.97/3.24 tff(17646,plain,
% 2.97/3.24 (~b(s(s(s(z))), s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17645, 144, 17633, 17604, 17611])).
% 2.97/3.24 tff(17647,plain,
% 2.97/3.24 (r(s(s(s(z))), s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[2794, 17646])).
% 2.97/3.24 tff(17648,plain,
% 2.97/3.24 (((~![X0: $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(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(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(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.97/3.24 inference(rewrite,[status(thm)],[])).
% 2.97/3.24 tff(17649,plain,
% 2.97/3.24 ((~![X0: $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(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))))),
% 2.97/3.24 inference(quant_inst,[status(thm)],[])).
% 2.97/3.24 tff(17650,plain,
% 2.97/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17649, 17648])).
% 2.97/3.24 tff(17651,plain,
% 2.97/3.24 ($false),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17650, 333, 17647, 17625, 17640, 17637])).
% 2.97/3.24 tff(17652,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.24 tff(17653,plain,
% 2.97/3.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17652, 2254, 1, 11546, 112])).
% 2.97/3.24 tff(17654,plain,
% 2.97/3.24 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[249, 17653])).
% 2.97/3.24 tff(17655,plain,
% 2.97/3.24 (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17134, 17654, 17126, 17017, 15988, 112, 1699])).
% 2.97/3.24 tff(17656,assumption,(~b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))), introduced(assumption)).
% 2.97/3.24 tff(17657,assumption,(~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z))))), introduced(assumption)).
% 2.97/3.24 tff(17658,assumption,(~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))), introduced(assumption)).
% 2.97/3.24 tff(17659,plain,
% 2.97/3.24 ($false),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[15275, 44, 17658, 17657, 17656])).
% 2.97/3.24 tff(17660,plain,(b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z)))) | (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.24 tff(17661,plain,
% 2.97/3.24 (b(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(z))))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[17660, 17655, 17413])).
% 2.97/3.24 tff(17662,plain,
% 2.97/3.24 (~b(s(elem!1), z)),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[916, 451, 15899, 17014])).
% 2.97/3.24 tff(17663,plain,
% 2.97/3.24 (r(s(elem!1), z)),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[507, 17662])).
% 2.97/3.24 tff(17664,plain,
% 2.97/3.24 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[16155, 17663, 112])).
% 2.97/3.24 tff(17665,plain,
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% 2.97/3.24 tff(17694,assumption,(b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
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% 2.97/3.24 tff(17697,plain,
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% 2.97/3.24 tff(17702,plain,
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% 2.97/3.24 inference(unit_resolution,[status(thm)],[372, 17701])).
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% 2.97/3.24 tff(17708,plain,
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% 2.97/3.24 inference(unit_resolution,[status(thm)],[2794, 17707])).
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% 2.97/3.24 tff(17710,plain,
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% 2.97/3.24 inference(modus_ponens,[status(thm)],[17709, 15150])).
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% 2.97/3.24 inference(unit_resolution,[status(thm)],[486, 17710, 1])).
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% 2.97/3.24 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[15239, 17711, 112])).
% 2.97/3.24 tff(17713,plain,
% 2.97/3.24 (((~![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(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(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(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.24 inference(rewrite,[status(thm)],[])).
% 2.97/3.24 tff(17714,plain,
% 2.97/3.24 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))) <=> ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.24 inference(rewrite,[status(thm)],[])).
% 2.97/3.24 tff(17715,plain,
% 2.97/3.24 (((~![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(s(s(s(s(z)))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))))),
% 2.97/3.24 inference(monotonicity,[status(thm)],[17714])).
% 2.97/3.24 tff(17716,plain,
% 2.97/3.24 (((~![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(s(s(s(s(z)))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(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(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.24 inference(transitivity,[status(thm)],[17715, 17713])).
% 2.97/3.24 tff(17717,plain,
% 2.97/3.24 ((~![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(s(s(s(s(z)))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)))),
% 2.97/3.24 inference(quant_inst,[status(thm)],[])).
% 2.97/3.24 tff(17718,plain,
% 2.97/3.24 ((~![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(s(s(s(s(s(s(s(z))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(s(z))))))))), z))),
% 2.97/3.24 inference(modus_ponens,[status(thm)],[17717, 17716])).
% 2.97/3.24 tff(17719,plain,
% 2.97/3.24 (~r(s(s(s(s(s(s(s(s(s(z))))))))), z)),
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% 2.97/3.24 tff(17720,plain,
% 2.97/3.24 (b(s(s(s(s(s(s(s(s(s(z))))))))), z)),
% 2.97/3.24 inference(unit_resolution,[status(thm)],[16664, 44, 16661, 17719])).
% 2.97/3.24 tff(17721,plain,
% 2.97/3.24 ((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(z), s(elem!1)))),
% 2.97/3.24 inference(monotonicity,[status(thm)],[15287])).
% 2.97/3.24 tff(17722,plain,
% 2.97/3.24 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(rewrite,[status(thm)],[])).
% 2.97/3.24 tff(17723,plain,
% 2.97/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.97/3.24 inference(monotonicity,[status(thm)],[17722])).
% 2.97/3.24 tff(17724,plain,
% 2.97/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.24 inference(transitivity,[status(thm)],[17723, 17618])).
% 2.97/3.24 tff(17725,plain,
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% 2.97/3.25 inference(modus_ponens,[status(thm)],[17725, 17724])).
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% 2.97/3.25 inference(unit_resolution,[status(thm)],[15397, 17729, 112])).
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% 2.97/3.25 ($false),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[279, 17798, 17797])).
% 2.97/3.25 tff(17800,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.25 tff(17801,plain,
% 2.97/3.25 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[17800, 4367, 114, 624, 3, 251])).
% 2.97/3.25 tff(17802,plain,
% 2.97/3.25 (((~![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(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17803,plain,
% 2.97/3.25 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17804,plain,
% 2.97/3.25 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.25 inference(monotonicity,[status(thm)],[17803])).
% 2.97/3.25 tff(17805,plain,
% 2.97/3.25 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(transitivity,[status(thm)],[17804, 17802])).
% 2.97/3.25 tff(17806,plain,
% 2.97/3.25 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 2.97/3.25 inference(quant_inst,[status(thm)],[])).
% 2.97/3.25 tff(17807,plain,
% 2.97/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.25 inference(modus_ponens,[status(thm)],[17806, 17805])).
% 2.97/3.25 tff(17808,plain,
% 2.97/3.25 ($false),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[17807, 333, 3193, 11546, 2484, 6107])).
% 2.97/3.25 tff(17809,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.25 tff(17810,plain,
% 2.97/3.25 (~r(s(s(s(z))), s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[17809, 6107, 11546, 2484])).
% 2.97/3.25 tff(17811,plain,
% 2.97/3.25 (b(s(s(s(z))), s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[2794, 17810])).
% 2.97/3.25 tff(17812,plain,
% 2.97/3.25 (((~![X0: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17813,plain,
% 2.97/3.25 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17814,plain,
% 2.97/3.25 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.25 inference(monotonicity,[status(thm)],[17813])).
% 2.97/3.25 tff(17815,plain,
% 2.97/3.25 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.25 inference(transitivity,[status(thm)],[17814, 17812])).
% 2.97/3.25 tff(17816,plain,
% 2.97/3.25 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))))),
% 2.97/3.25 inference(quant_inst,[status(thm)],[])).
% 2.97/3.25 tff(17817,plain,
% 2.97/3.25 ((~![X0: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.25 inference(modus_ponens,[status(thm)],[17816, 17815])).
% 2.97/3.25 tff(17818,plain,
% 2.97/3.25 (~r(s(z), s(s(s(z))))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[17817, 333, 11546, 2484, 6107])).
% 2.97/3.25 tff(17819,plain,
% 2.97/3.25 (b(s(z), s(s(s(z))))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[172, 17818])).
% 2.97/3.25 tff(17820,plain,
% 2.97/3.25 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[846, 17819, 283, 17811])).
% 2.97/3.25 tff(17821,plain,
% 2.97/3.25 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[319, 17820])).
% 2.97/3.25 tff(17822,plain,
% 2.97/3.25 (~r(elem!1, s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[12830, 17821, 624, 706, 251, 2484])).
% 2.97/3.25 tff(17823,plain,
% 2.97/3.25 (b(elem!1, s(z))),
% 2.97/3.25 inference(unit_resolution,[status(thm)],[720, 17822, 713])).
% 2.97/3.25 tff(17824,plain,
% 2.97/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17825,plain,
% 2.97/3.25 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.97/3.25 inference(rewrite,[status(thm)],[])).
% 2.97/3.25 tff(17826,plain,
% 2.97/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 2.97/3.25 inference(monotonicity,[status(thm)],[17825])).
% 2.97/3.25 tff(17827,plain,
% 2.97/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.97/3.25 inference(transitivity,[status(thm)],[17826, 17824])).
% 2.97/3.25 tff(17828,plain,
% 2.97/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.97/3.26 inference(quant_inst,[status(thm)],[])).
% 2.97/3.26 tff(17829,plain,
% 2.97/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 2.97/3.26 inference(modus_ponens,[status(thm)],[17828, 17827])).
% 2.97/3.26 tff(17830,plain,
% 2.97/3.26 (~b(elem!1, s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17829, 144, 17823, 17811, 17819])).
% 2.97/3.26 tff(17831,plain,
% 2.97/3.26 (r(elem!1, s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1538, 17830, 1524])).
% 2.97/3.26 tff(17832,plain,
% 2.97/3.26 (~b(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[4375, 17823, 4367, 17811])).
% 2.97/3.26 tff(17833,plain,
% 2.97/3.26 (r(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[406, 17832, 706])).
% 2.97/3.26 tff(17834,plain,
% 2.97/3.26 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(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(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17835,plain,
% 2.97/3.26 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17836,plain,
% 2.97/3.26 (((~![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(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.97/3.26 inference(monotonicity,[status(thm)],[17835])).
% 2.97/3.26 tff(17837,plain,
% 2.97/3.26 (((~![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(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.97/3.26 inference(transitivity,[status(thm)],[17836, 17834])).
% 2.97/3.26 tff(17838,plain,
% 2.97/3.26 ((~![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(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.26 inference(quant_inst,[status(thm)],[])).
% 2.97/3.26 tff(17839,plain,
% 2.97/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.97/3.26 inference(modus_ponens,[status(thm)],[17838, 17837])).
% 2.97/3.26 tff(17840,plain,
% 2.97/3.26 ($false),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17839, 333, 17833, 17831, 2484, 17821])).
% 2.97/3.26 tff(17841,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(z)))) | (s(z) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.26 tff(17842,plain,
% 2.97/3.26 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17841, 17801, 1524, 17796, 4367, 624, 251, 283, 11546])).
% 2.97/3.26 tff(17843,plain,
% 2.97/3.26 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1137, 17842])).
% 2.97/3.26 tff(17844,plain,
% 2.97/3.26 (~b(elem!1, s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[8765, 144, 132, 283, 17843])).
% 2.97/3.26 tff(17845,plain,
% 2.97/3.26 (r(elem!1, s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1538, 17844, 1524])).
% 2.97/3.26 tff(17846,plain,
% 2.97/3.26 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17847,plain,
% 2.97/3.26 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17848,plain,
% 2.97/3.26 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.26 inference(monotonicity,[status(thm)],[17847])).
% 2.97/3.26 tff(17849,plain,
% 2.97/3.26 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(transitivity,[status(thm)],[17848, 17846])).
% 2.97/3.26 tff(17850,plain,
% 2.97/3.26 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(quant_inst,[status(thm)],[])).
% 2.97/3.26 tff(17851,plain,
% 2.97/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.26 inference(modus_ponens,[status(thm)],[17850, 17849])).
% 2.97/3.26 tff(17852,plain,
% 2.97/3.26 ($false),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17851, 333, 409, 1525, 11546, 2484])).
% 2.97/3.26 tff(17853,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.26 tff(17854,plain,
% 2.97/3.26 (~r(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17853, 17845, 11546, 17801])).
% 2.97/3.26 tff(17855,plain,
% 2.97/3.26 (b(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[406, 17854, 17796])).
% 2.97/3.26 tff(17856,plain,
% 2.97/3.26 (~b(s(z), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1602, 17855, 624, 251])).
% 2.97/3.26 tff(17857,plain,
% 2.97/3.26 (r(s(z), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[348, 17856])).
% 2.97/3.26 tff(17858,plain,
% 2.97/3.26 (~r(s(s(s(z))), s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[16559, 333, 17857, 12853, 623])).
% 2.97/3.26 tff(17859,plain,
% 2.97/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17860,plain,
% 2.97/3.26 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17861,plain,
% 2.97/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.26 inference(monotonicity,[status(thm)],[17860])).
% 2.97/3.26 tff(17862,plain,
% 2.97/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(transitivity,[status(thm)],[17861, 17859])).
% 2.97/3.26 tff(17863,plain,
% 2.97/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.97/3.26 inference(quant_inst,[status(thm)],[])).
% 2.97/3.26 tff(17864,plain,
% 2.97/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.26 inference(modus_ponens,[status(thm)],[17863, 17862])).
% 2.97/3.26 tff(17865,plain,
% 2.97/3.26 (~b(s(s(s(z))), s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17864, 144, 17855, 132, 17843, 4367])).
% 2.97/3.26 tff(17866,plain,
% 2.97/3.26 ($false),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[2794, 17865, 17858])).
% 2.97/3.26 tff(17867,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.26 tff(17868,plain,
% 2.97/3.26 (~b(s(s(s(z))), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17867, 17795, 623, 624, 13636, 15126, 12398, 17789, 17787, 3])).
% 2.97/3.26 tff(17869,plain,
% 2.97/3.26 (r(s(s(s(z))), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[704, 17868, 698])).
% 2.97/3.26 tff(17870,plain,
% 2.97/3.26 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[880, 17788, 624, 13636])).
% 2.97/3.26 tff(17871,plain,
% 2.97/3.26 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[302, 17870])).
% 2.97/3.26 tff(17872,plain,
% 2.97/3.26 (((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17873,plain,
% 2.97/3.26 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(rewrite,[status(thm)],[])).
% 2.97/3.26 tff(17874,plain,
% 2.97/3.26 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.26 inference(monotonicity,[status(thm)],[17873])).
% 2.97/3.26 tff(17875,plain,
% 2.97/3.26 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.26 inference(transitivity,[status(thm)],[17874, 17872])).
% 2.97/3.26 tff(17876,plain,
% 2.97/3.26 ((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 2.97/3.26 inference(quant_inst,[status(thm)],[])).
% 2.97/3.26 tff(17877,plain,
% 2.97/3.26 ((~![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(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.26 inference(modus_ponens,[status(thm)],[17876, 17875])).
% 2.97/3.26 tff(17878,plain,
% 2.97/3.26 (~r(s(z), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[17877, 333, 15126, 17871, 17794])).
% 2.97/3.26 tff(17879,plain,
% 2.97/3.26 (b(s(z), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[348, 17878])).
% 2.97/3.26 tff(17880,plain,
% 2.97/3.26 (~b(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1602, 17879, 624, 13636])).
% 2.97/3.26 tff(17881,plain,
% 2.97/3.26 (r(s(z), elem!1)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[406, 17880, 15133])).
% 2.97/3.26 tff(17882,plain,
% 2.97/3.26 (~r(z, s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[15183, 17794, 15126, 17871])).
% 2.97/3.26 tff(17883,plain,
% 2.97/3.26 (b(z, s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[372, 17882])).
% 2.97/3.26 tff(17884,plain,
% 2.97/3.26 (~b(elem!1, s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[387, 144, 624, 17883, 17879])).
% 2.97/3.26 tff(17885,plain,
% 2.97/3.26 (r(elem!1, s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[720, 17884, 15134])).
% 2.97/3.26 tff(17886,plain,
% 2.97/3.26 (~r(s(s(s(z))), s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[9910, 17885, 17881, 17869])).
% 2.97/3.26 tff(17887,plain,
% 2.97/3.26 (b(s(s(s(z))), s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[2794, 17886])).
% 2.97/3.26 tff(17888,plain,
% 2.97/3.26 (~b(s(s(s(z))), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[2273, 17887, 17879, 17883])).
% 2.97/3.26 tff(17889,plain,
% 2.97/3.26 (r(s(s(s(z))), z)),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[396, 17888])).
% 2.97/3.26 tff(17890,plain,
% 2.97/3.26 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[11754, 17889, 17794, 17871])).
% 2.97/3.26 tff(17891,plain,
% 2.97/3.26 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[1137, 17890])).
% 2.97/3.26 tff(17892,plain,
% 2.97/3.26 (~b(elem!1, s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[8765, 144, 17789, 17795, 17891])).
% 2.97/3.26 tff(17893,plain,
% 2.97/3.26 (~r(s(z), s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[12402, 17892, 17868, 698, 17885])).
% 2.97/3.26 tff(17894,plain,
% 2.97/3.26 (b(s(z), s(s(s(z))))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[172, 17893])).
% 2.97/3.26 tff(17895,plain,
% 2.97/3.26 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.26 inference(unit_resolution,[status(thm)],[846, 17894, 17795, 17887])).
% 2.97/3.27 tff(17896,plain,
% 2.97/3.27 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[319, 17895])).
% 2.97/3.27 tff(17897,plain,
% 2.97/3.27 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17898,plain,
% 2.97/3.27 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17899,plain,
% 2.97/3.27 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17898])).
% 2.97/3.27 tff(17900,plain,
% 2.97/3.27 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.97/3.27 inference(transitivity,[status(thm)],[17899, 17897])).
% 2.97/3.27 tff(17901,plain,
% 2.97/3.27 ((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.97/3.27 inference(quant_inst,[status(thm)],[])).
% 2.97/3.27 tff(17902,plain,
% 2.97/3.27 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17901, 17900])).
% 2.97/3.27 tff(17903,plain,
% 2.97/3.27 (~r(s(s(z)), z)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17902, 333, 2671, 322, 51])).
% 2.97/3.27 tff(17904,plain,
% 2.97/3.27 (b(s(s(z)), z)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1462, 44, 164, 17903])).
% 2.97/3.27 tff(17905,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17906,plain,
% 2.97/3.27 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17907,plain,
% 2.97/3.27 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17906])).
% 2.97/3.27 tff(17908,plain,
% 2.97/3.27 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.27 inference(transitivity,[status(thm)],[17907, 17905])).
% 2.97/3.27 tff(17909,plain,
% 2.97/3.27 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 2.97/3.27 inference(quant_inst,[status(thm)],[])).
% 2.97/3.27 tff(17910,plain,
% 2.97/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17909, 17908])).
% 2.97/3.27 tff(17911,plain,
% 2.97/3.27 (~r(s(s(z)), s(z))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17910, 333, 2671, 11546, 322])).
% 2.97/3.27 tff(17912,plain,
% 2.97/3.27 (b(s(s(z)), s(z))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1429, 44, 17911, 1416])).
% 2.97/3.27 tff(17913,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17914,plain,
% 2.97/3.27 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17915,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17914])).
% 2.97/3.27 tff(17916,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.97/3.27 inference(transitivity,[status(thm)],[17915, 17913])).
% 2.97/3.27 tff(17917,plain,
% 2.97/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), z)) | (~b(s(s(z)), s(z))))),
% 2.97/3.27 inference(quant_inst,[status(thm)],[])).
% 2.97/3.27 tff(17918,plain,
% 2.97/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17917, 17916])).
% 2.97/3.27 tff(17919,plain,
% 2.97/3.27 ($false),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17918, 144, 490, 489, 17912, 17904])).
% 2.97/3.27 tff(17920,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.27 tff(17921,plain,
% 2.97/3.27 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17920, 17883, 17879, 17896, 17794, 15126])).
% 2.97/3.27 tff(17922,plain,
% 2.97/3.27 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1451, 17921])).
% 2.97/3.27 tff(17923,plain,
% 2.97/3.27 (~b(s(s(z)), elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[11650, 144, 17922, 17788, 17789])).
% 2.97/3.27 tff(17924,plain,
% 2.97/3.27 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[7952, 17922, 17890, 7926])).
% 2.97/3.27 tff(17925,plain,
% 2.97/3.27 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1473, 44, 17924, 217])).
% 2.97/3.27 tff(17926,plain,
% 2.97/3.27 (r(elem!1, s(s(s(z))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1538, 17892, 12398])).
% 2.97/3.27 tff(17927,plain,
% 2.97/3.27 (((~![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))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, 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))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17928,plain,
% 2.97/3.27 (((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17929,plain,
% 2.97/3.27 (((~![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))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17928])).
% 2.97/3.27 tff(17930,plain,
% 2.97/3.27 (((~![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))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.27 inference(transitivity,[status(thm)],[17929, 17927])).
% 2.97/3.27 tff(17931,plain,
% 2.97/3.27 ((~![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))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.97/3.27 inference(quant_inst,[status(thm)],[])).
% 2.97/3.27 tff(17932,plain,
% 2.97/3.27 ((~![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))), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17931, 17930])).
% 2.97/3.27 tff(17933,plain,
% 2.97/3.27 (~r(s(s(z)), elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17932, 333, 17926, 17889, 17925])).
% 2.97/3.27 tff(17934,plain,
% 2.97/3.27 (s(s(z)) = elem!1),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[7970, 17933, 17923])).
% 2.97/3.27 tff(17935,plain,
% 2.97/3.27 (s(elem!1) = s(s(s(z)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[11670, 17934])).
% 2.97/3.27 tff(17936,plain,
% 2.97/3.27 (s(s(s(z))) = s(elem!1)),
% 2.97/3.27 inference(symmetry,[status(thm)],[17935])).
% 2.97/3.27 tff(17937,plain,
% 2.97/3.27 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17936])).
% 2.97/3.27 tff(17938,plain,
% 2.97/3.27 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17937])).
% 2.97/3.27 tff(17939,plain,
% 2.97/3.27 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17935])).
% 2.97/3.27 tff(17940,plain,
% 2.97/3.27 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17939])).
% 2.97/3.27 tff(17941,plain,
% 2.97/3.27 (~b(s(elem!1), z)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[6057, 17935, 17888])).
% 2.97/3.27 tff(17942,plain,
% 2.97/3.27 (~(elem!1 = s(elem!1))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[12198, 17941, 624])).
% 2.97/3.27 tff(17943,plain,
% 2.97/3.27 (~(s(s(elem!1)) = s(elem!1))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1196, 17942])).
% 2.97/3.27 tff(17944,plain,
% 2.97/3.27 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[11084, 17935])).
% 2.97/3.27 tff(17945,plain,
% 2.97/3.27 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17935])).
% 2.97/3.27 tff(17946,plain,
% 2.97/3.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17945])).
% 2.97/3.27 tff(17947,plain,
% 2.97/3.27 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17946])).
% 2.97/3.27 tff(17948,plain,
% 2.97/3.27 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17890, 17947])).
% 2.97/3.27 tff(17949,plain,
% 2.97/3.27 (~b(s(elem!1), elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[8316, 982, 55])).
% 2.97/3.27 tff(17950,plain,
% 2.97/3.27 (s(elem!1) = elem!1),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[448, 17949, 1727])).
% 2.97/3.27 tff(17951,plain,
% 2.97/3.27 (elem!1 = s(elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[906, 17950])).
% 2.97/3.27 tff(17952,plain,
% 2.97/3.27 (s(s(s(elem!1))) = elem!1),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[2482, 17951])).
% 2.97/3.27 tff(17953,plain,
% 2.97/3.27 ($false),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[2584, 17952, 17951, 3060])).
% 2.97/3.27 tff(17954,plain,((~(s(elem!1) = s(s(s(z))))) | r(s(elem!1), elem!1) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.27 tff(17955,plain,
% 2.97/3.27 (r(s(elem!1), elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17954, 17935, 17868, 1])).
% 2.97/3.27 tff(17956,plain,
% 2.97/3.27 (~r(s(elem!1), s(s(s(z))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[1694, 17955, 17869, 17885])).
% 2.97/3.27 tff(17957,plain,
% 2.97/3.27 (s(s(s(z))) = s(elem!1)),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17935, 998])).
% 2.97/3.27 tff(17958,plain,
% 2.97/3.27 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[11095, 17957, 1])).
% 2.97/3.27 tff(17959,plain,
% 2.97/3.27 (~(elem!1 = s(s(elem!1)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[5603, 17958])).
% 2.97/3.27 tff(17960,plain,
% 2.97/3.27 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.97/3.27 inference(commutativity,[status(thm)],[])).
% 2.97/3.27 tff(17961,plain,
% 2.97/3.27 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17960])).
% 2.97/3.27 tff(17962,plain,
% 2.97/3.27 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17961])).
% 2.97/3.27 tff(17963,plain,
% 2.97/3.27 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[517, 408, 435, 509])).
% 2.97/3.27 tff(17964,plain,
% 2.97/3.27 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[278, 17963, 274])).
% 2.97/3.27 tff(17965,plain,
% 2.97/3.27 (((~![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(s(elem!1)))) | (~r(elem!1, 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), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17966,plain,
% 2.97/3.27 (((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.97/3.27 inference(rewrite,[status(thm)],[])).
% 2.97/3.27 tff(17967,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17966])).
% 2.97/3.27 tff(17968,plain,
% 2.97/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.97/3.27 inference(transitivity,[status(thm)],[17967, 17965])).
% 2.97/3.27 tff(17969,plain,
% 2.97/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.97/3.27 inference(quant_inst,[status(thm)],[])).
% 2.97/3.27 tff(17970,plain,
% 2.97/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17969, 17968])).
% 2.97/3.27 tff(17971,plain,
% 2.97/3.27 ($false),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17970, 333, 435, 408, 509, 4223])).
% 2.97/3.27 tff(17972,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.27 tff(17973,plain,
% 2.97/3.27 (~r(z, s(s(elem!1)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17972, 408, 435, 509])).
% 2.97/3.27 tff(17974,plain,
% 2.97/3.27 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[5631, 44, 17973])).
% 2.97/3.27 tff(17975,plain,
% 2.97/3.27 (b(z, s(s(elem!1)))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[17974, 5621])).
% 2.97/3.27 tff(17976,plain,
% 2.97/3.27 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[8401, 10641, 1249, 17975, 17964])).
% 2.97/3.27 tff(17977,plain,
% 2.97/3.27 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[472, 17976, 466])).
% 2.97/3.27 tff(17978,plain,
% 2.97/3.27 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17977])).
% 2.97/3.27 tff(17979,plain,
% 2.97/3.27 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17978])).
% 2.97/3.27 tff(17980,plain,
% 2.97/3.27 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17979])).
% 2.97/3.27 tff(17981,plain,
% 2.97/3.27 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17980])).
% 2.97/3.27 tff(17982,plain,
% 2.97/3.27 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17977])).
% 2.97/3.27 tff(17983,plain,
% 2.97/3.27 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[1249, 17982])).
% 2.97/3.27 tff(17984,plain,
% 2.97/3.27 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17983, 17981])).
% 2.97/3.27 tff(17985,plain,
% 2.97/3.27 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(s(elem!1)))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17979])).
% 2.97/3.27 tff(17986,plain,
% 2.97/3.27 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17985])).
% 2.97/3.27 tff(17987,plain,
% 2.97/3.27 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[17975, 17986])).
% 2.97/3.27 tff(17988,plain,
% 2.97/3.27 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17977])).
% 2.97/3.27 tff(17989,plain,
% 2.97/3.27 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.97/3.27 inference(monotonicity,[status(thm)],[17988])).
% 2.97/3.27 tff(17990,plain,
% 2.97/3.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.27 inference(modus_ponens,[status(thm)],[959, 17989])).
% 2.97/3.27 tff(17991,plain,
% 2.97/3.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.27 inference(unit_resolution,[status(thm)],[249, 17990])).
% 2.97/3.27 tff(17992,plain,
% 2.97/3.27 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), elem!1)),
% 2.97/3.27 inference(monotonicity,[status(thm)],[6165])).
% 2.97/3.27 tff(17993,plain,
% 2.97/3.27 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.97/3.27 inference(symmetry,[status(thm)],[17992])).
% 2.97/3.27 tff(17994,plain,
% 2.97/3.27 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[707, 17993])).
% 2.97/3.28 tff(17995,plain,
% 2.97/3.28 (r(s(s(s(s(s(s(z)))))), z) <=> r(elem!1, z)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[6165])).
% 2.97/3.28 tff(17996,plain,
% 2.97/3.28 (r(elem!1, z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 2.97/3.28 inference(symmetry,[status(thm)],[17995])).
% 2.97/3.28 tff(17997,plain,
% 2.97/3.28 (r(s(s(s(s(s(s(z)))))), z)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[408, 17996])).
% 2.97/3.28 tff(17998,plain,
% 2.97/3.28 (((~![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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(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(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(17999,plain,
% 2.97/3.28 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(18000,plain,
% 2.97/3.28 (((~![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(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[17999])).
% 2.97/3.28 tff(18001,plain,
% 2.97/3.28 (((~![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(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18000, 17998])).
% 2.97/3.28 tff(18002,plain,
% 2.97/3.28 ((~![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(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.97/3.28 inference(quant_inst,[status(thm)],[])).
% 2.97/3.28 tff(18003,plain,
% 2.97/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18002, 18001])).
% 2.97/3.28 tff(18004,plain,
% 2.97/3.28 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18003, 333, 1699, 623])).
% 2.97/3.28 tff(18005,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18004, 17997, 17994])).
% 2.97/3.28 tff(18006,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.28 tff(18007,plain,
% 2.97/3.28 (~r(z, s(s(s(z))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18006, 408, 1699, 17977, 707])).
% 2.97/3.28 tff(18008,plain,
% 2.97/3.28 (b(z, s(s(s(z))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[619, 18007])).
% 2.97/3.28 tff(18009,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(18010,plain,
% 2.97/3.28 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(18011,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18010])).
% 2.97/3.28 tff(18012,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18011, 18009])).
% 2.97/3.28 tff(18013,plain,
% 2.97/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.28 inference(quant_inst,[status(thm)],[])).
% 2.97/3.28 tff(18014,plain,
% 2.97/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18013, 18012])).
% 2.97/3.28 tff(18015,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18014, 144, 18008, 17991, 17964, 17987, 17984])).
% 2.97/3.28 tff(18016,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.28 tff(18017,plain,
% 2.97/3.28 (~r(elem!1, z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18016, 466, 707, 959, 1249, 1699, 435, 12191])).
% 2.97/3.28 tff(18018,plain,
% 2.97/3.28 (b(elem!1, z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[1380, 77, 18017])).
% 2.97/3.28 tff(18019,plain,
% 2.97/3.28 (z = elem!1),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[8683, 8677])).
% 2.97/3.28 tff(18020,plain,
% 2.97/3.28 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18019])).
% 2.97/3.28 tff(18021,plain,
% 2.97/3.28 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.28 inference(symmetry,[status(thm)],[18020])).
% 2.97/3.28 tff(18022,plain,
% 2.97/3.28 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18021])).
% 2.97/3.28 tff(18023,plain,
% 2.97/3.28 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[8677])).
% 2.97/3.28 tff(18024,plain,
% 2.97/3.28 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18019])).
% 2.97/3.28 tff(18025,plain,
% 2.97/3.28 (b(elem!1, s(z)) <=> b(z, s(z))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18024])).
% 2.97/3.28 tff(18026,plain,
% 2.97/3.28 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[8677])).
% 2.97/3.28 tff(18027,plain,
% 2.97/3.28 (b(elem!1, s(z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[547, 18026])).
% 2.97/3.28 tff(18028,plain,
% 2.97/3.28 (b(z, s(z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18027, 18025])).
% 2.97/3.28 tff(18029,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[9362, 18028])).
% 2.97/3.28 tff(18030,plain,((~(s(elem!1) = s(z))) | b(z, s(z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.28 tff(18031,plain,
% 2.97/3.28 (~b(elem!1, s(elem!1))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18030, 8677, 9362])).
% 2.97/3.28 tff(18032,plain,
% 2.97/3.28 (r(elem!1, s(elem!1))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[560, 18031, 13418])).
% 2.97/3.28 tff(18033,plain,
% 2.97/3.28 (r(elem!1, s(z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18032, 18023])).
% 2.97/3.28 tff(18034,plain,
% 2.97/3.28 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[8677])).
% 2.97/3.28 tff(18035,plain,
% 2.97/3.28 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.97/3.28 inference(symmetry,[status(thm)],[18034])).
% 2.97/3.28 tff(18036,plain,
% 2.97/3.28 ((~r(s(z), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18035])).
% 2.97/3.28 tff(18037,plain,
% 2.97/3.28 (~r(s(elem!1), elem!1)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[2310, 18036])).
% 2.97/3.28 tff(18038,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[435, 18037])).
% 2.97/3.28 tff(18039,plain,((~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.28 tff(18040,plain,
% 2.97/3.28 (r(s(z), elem!1)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18039, 8677, 435])).
% 2.97/3.28 tff(18041,plain,
% 2.97/3.28 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[12170, 333, 18040, 18033, 322])).
% 2.97/3.28 tff(18042,plain,
% 2.97/3.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18041, 18022])).
% 2.97/3.28 tff(18043,plain,
% 2.97/3.28 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18019])).
% 2.97/3.28 tff(18044,plain,
% 2.97/3.28 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 2.97/3.28 inference(symmetry,[status(thm)],[18043])).
% 2.97/3.28 tff(18045,plain,
% 2.97/3.28 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18044])).
% 2.97/3.28 tff(18046,plain,
% 2.97/3.28 (~b(elem!1, z)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[5882, 18045])).
% 2.97/3.28 tff(18047,plain,
% 2.97/3.28 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[2899, 297, 12191])).
% 2.97/3.28 tff(18048,plain,
% 2.97/3.28 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[930, 18047])).
% 2.97/3.28 tff(18049,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[472, 18048, 466])).
% 2.97/3.28 tff(18050,plain,
% 2.97/3.28 (z = elem!1),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[76, 72])).
% 2.97/3.28 tff(18051,plain,
% 2.97/3.28 (s(elem!1) = s(z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[70, 18050])).
% 2.97/3.28 tff(18052,plain,
% 2.97/3.28 (~(s(s(elem!1)) = s(elem!1))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[1196, 13418])).
% 2.97/3.28 tff(18053,plain,
% 2.97/3.28 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[4281, 18052])).
% 2.97/3.28 tff(18054,plain,
% 2.97/3.28 (s(elem!1) = s(z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[70, 66])).
% 2.97/3.28 tff(18055,plain,
% 2.97/3.28 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18054])).
% 2.97/3.28 tff(18056,plain,
% 2.97/3.28 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.97/3.28 inference(symmetry,[status(thm)],[18055])).
% 2.97/3.28 tff(18057,plain,
% 2.97/3.28 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[66])).
% 2.97/3.28 tff(18058,plain,
% 2.97/3.28 (b(s(z), elem!1)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[489, 18057])).
% 2.97/3.28 tff(18059,plain,
% 2.97/3.28 (b(s(elem!1), elem!1)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18058, 18056])).
% 2.97/3.28 tff(18060,plain,
% 2.97/3.28 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.97/3.28 inference(monotonicity,[status(thm)],[66])).
% 2.97/3.28 tff(18061,plain,
% 2.97/3.28 ((~b(s(elem!1), z)) <=> (~b(s(elem!1), elem!1))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18060])).
% 2.97/3.28 tff(18062,plain,
% 2.97/3.28 (~b(s(elem!1), elem!1)),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[502, 18061])).
% 2.97/3.28 tff(18063,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18062, 18059])).
% 2.97/3.28 tff(18064,plain,((~(z = elem!1)) | (~b(s(z), z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.28 tff(18065,plain,
% 2.97/3.28 (~b(s(z), z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18064, 18050, 502])).
% 2.97/3.28 tff(18066,plain,
% 2.97/3.28 (r(s(z), z)),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[348, 18065])).
% 2.97/3.28 tff(18067,plain,
% 2.97/3.28 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18068,plain,
% 2.97/3.28 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18067, 3061])).
% 2.97/3.28 tff(18069,plain,
% 2.97/3.28 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18068])).
% 2.97/3.28 tff(18070,plain,
% 2.97/3.28 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18069])).
% 2.97/3.28 tff(18071,plain,
% 2.97/3.28 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[1096, 18070])).
% 2.97/3.28 tff(18072,plain,
% 2.97/3.28 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18073,plain,
% 2.97/3.28 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18072])).
% 2.97/3.28 tff(18074,plain,
% 2.97/3.28 (s(s(elem!1)) = s(s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18075,plain,
% 2.97/3.28 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18074])).
% 2.97/3.28 tff(18076,plain,
% 2.97/3.28 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18075])).
% 2.97/3.28 tff(18077,plain,
% 2.97/3.28 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18076])).
% 2.97/3.28 tff(18078,plain,
% 2.97/3.28 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18077, 18073])).
% 2.97/3.28 tff(18079,plain,
% 2.97/3.28 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18078])).
% 2.97/3.28 tff(18080,plain,
% 2.97/3.28 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18081,plain,
% 2.97/3.28 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18080])).
% 2.97/3.28 tff(18082,plain,
% 2.97/3.28 (~r(s(z), s(s(s(z))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[959, 18081])).
% 2.97/3.28 tff(18083,plain,
% 2.97/3.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18082, 18079])).
% 2.97/3.28 tff(18084,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[1067, 18083, 18071])).
% 2.97/3.28 tff(18085,plain,
% 2.97/3.28 (s(s(z)) = s(s(elem!1))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18074])).
% 2.97/3.28 tff(18086,plain,
% 2.97/3.28 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18085])).
% 2.97/3.28 tff(18087,plain,
% 2.97/3.28 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18086])).
% 2.97/3.28 tff(18088,plain,
% 2.97/3.28 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18089,plain,
% 2.97/3.28 (b(s(s(elem!1)), s(z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[1249, 18088])).
% 2.97/3.28 tff(18090,plain,
% 2.97/3.28 (b(s(s(z)), s(z))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18089, 18087])).
% 2.97/3.28 tff(18091,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18092,plain,
% 2.97/3.28 ((s(elem!1) = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18093,plain,
% 2.97/3.28 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18092, 157])).
% 2.97/3.28 tff(18094,plain,
% 2.97/3.28 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(s(s(z))))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18093])).
% 2.97/3.28 tff(18095,plain,
% 2.97/3.28 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18094])).
% 2.97/3.28 tff(18096,plain,
% 2.97/3.28 (~(s(elem!1) = s(s(s(z))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[166, 18095])).
% 2.97/3.28 tff(18097,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(z))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[965, 18096, 959])).
% 2.97/3.28 tff(18098,plain,
% 2.97/3.28 (b(s(z), s(s(s(z))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18097, 18091])).
% 2.97/3.28 tff(18099,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18051])).
% 2.97/3.28 tff(18100,plain,
% 2.97/3.28 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[450, 18099])).
% 2.97/3.28 tff(18101,plain,
% 2.97/3.28 (s(s(elem!1)) = s(s(z))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[8677])).
% 2.97/3.28 tff(18102,plain,
% 2.97/3.28 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18101])).
% 2.97/3.28 tff(18103,plain,
% 2.97/3.28 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18102])).
% 2.97/3.28 tff(18104,plain,
% 2.97/3.28 (s(z) = s(elem!1)),
% 2.97/3.28 inference(symmetry,[status(thm)],[8677])).
% 2.97/3.28 tff(18105,plain,
% 2.97/3.28 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18104, 18103])).
% 2.97/3.28 tff(18106,plain,
% 2.97/3.28 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.97/3.28 inference(symmetry,[status(thm)],[18105])).
% 2.97/3.28 tff(18107,plain,
% 2.97/3.28 (b(s(z), s(s(s(z))))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[10356, 18106])).
% 2.97/3.28 tff(18108,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(18109,plain,
% 2.97/3.28 (((~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(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(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))))),
% 2.97/3.28 inference(rewrite,[status(thm)],[])).
% 2.97/3.28 tff(18110,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.97/3.28 inference(monotonicity,[status(thm)],[18109])).
% 2.97/3.28 tff(18111,plain,
% 2.97/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.97/3.28 inference(transitivity,[status(thm)],[18110, 18108])).
% 2.97/3.28 tff(18112,plain,
% 2.97/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.97/3.28 inference(quant_inst,[status(thm)],[])).
% 2.97/3.28 tff(18113,plain,
% 2.97/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.97/3.28 inference(modus_ponens,[status(thm)],[18112, 18111])).
% 2.97/3.28 tff(18114,plain,
% 2.97/3.28 (~b(s(z), s(s(s(z))))),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18113, 144, 56, 7943, 1417])).
% 2.97/3.28 tff(18115,plain,
% 2.97/3.28 ($false),
% 2.97/3.28 inference(unit_resolution,[status(thm)],[18114, 18107])).
% 2.97/3.28 tff(18116,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18117,plain,
% 2.97/3.29 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18116, 16140, 8677, 1417, 10356])).
% 2.97/3.29 tff(18118,plain,
% 2.97/3.29 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18101, 18102])).
% 2.97/3.29 tff(18119,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.97/3.29 tff(18120,plain,
% 2.97/3.29 (b(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18119, 18118])).
% 2.97/3.29 tff(18121,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[7933, 18120])).
% 2.97/3.29 tff(18122,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(z)), s(s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18123,plain,
% 2.97/3.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18122, 18117, 8677])).
% 2.97/3.29 tff(18124,plain,
% 2.97/3.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[4311, 18123, 4620])).
% 2.97/3.29 tff(18125,plain,
% 2.97/3.29 (s(s(z)) = s(s(elem!1))),
% 2.97/3.29 inference(symmetry,[status(thm)],[18101])).
% 2.97/3.29 tff(18126,plain,
% 2.97/3.29 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18125, 18103])).
% 2.97/3.29 tff(18127,plain,
% 2.97/3.29 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(symmetry,[status(thm)],[18126])).
% 2.97/3.29 tff(18128,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.97/3.29 tff(18129,plain,
% 2.97/3.29 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18128, 18127])).
% 2.97/3.29 tff(18130,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.97/3.29 tff(18131,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18130, 18129])).
% 2.97/3.29 tff(18132,plain,(r(s(s(z)), s(s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18133,plain,
% 2.97/3.29 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18132, 18124, 8677])).
% 2.97/3.29 tff(18134,plain,
% 2.97/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[6352, 18133, 1699, 1417, 123, 16140, 838])).
% 2.97/3.29 tff(18135,plain,
% 2.97/3.29 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[319, 18134])).
% 2.97/3.29 tff(18136,plain,
% 2.97/3.29 (r(z, s(elem!1)) <=> r(z, s(z))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[8677])).
% 2.97/3.29 tff(18137,plain,
% 2.97/3.29 (r(z, s(z))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[562, 18136])).
% 2.97/3.29 tff(18138,plain,
% 2.97/3.29 (((~![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(z))), 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(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18139,plain,
% 2.97/3.29 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18140,plain,
% 2.97/3.29 (((~![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(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(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18139])).
% 2.97/3.29 tff(18141,plain,
% 2.97/3.29 (((~![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(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(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.97/3.29 inference(transitivity,[status(thm)],[18140, 18138])).
% 2.97/3.29 tff(18142,plain,
% 2.97/3.29 ((~![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(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.29 inference(quant_inst,[status(thm)],[])).
% 2.97/3.29 tff(18143,plain,
% 2.97/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18142, 18141])).
% 2.97/3.29 tff(18144,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18143, 333, 354, 1699, 6330, 9615])).
% 2.97/3.29 tff(18145,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18146,plain,
% 2.97/3.29 (~r(s(s(z)), z)),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18145, 18137, 1699, 18133])).
% 2.97/3.29 tff(18147,plain,
% 2.97/3.29 (b(s(s(z)), z)),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[1462, 44, 164, 18146])).
% 2.97/3.29 tff(18148,plain,
% 2.97/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18149,plain,
% 2.97/3.29 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18150,plain,
% 2.97/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18149])).
% 2.97/3.29 tff(18151,plain,
% 2.97/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.29 inference(transitivity,[status(thm)],[18150, 18148])).
% 2.97/3.29 tff(18152,plain,
% 2.97/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))),
% 2.97/3.29 inference(quant_inst,[status(thm)],[])).
% 2.97/3.29 tff(18153,plain,
% 2.97/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18152, 18151])).
% 2.97/3.29 tff(18154,plain,
% 2.97/3.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18153, 144, 1417, 123, 286, 18147])).
% 2.97/3.29 tff(18155,plain,
% 2.97/3.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[1451, 18154])).
% 2.97/3.29 tff(18156,plain,
% 2.97/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18157,plain,
% 2.97/3.29 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18158,plain,
% 2.97/3.29 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18157])).
% 2.97/3.29 tff(18159,plain,
% 2.97/3.29 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.29 inference(transitivity,[status(thm)],[18158, 18156])).
% 2.97/3.29 tff(18160,plain,
% 2.97/3.29 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.29 inference(quant_inst,[status(thm)],[])).
% 2.97/3.29 tff(18161,plain,
% 2.97/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18160, 18159])).
% 2.97/3.29 tff(18162,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18161, 333, 2671, 6107, 322, 6330])).
% 2.97/3.29 tff(18163,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18164,plain,
% 2.97/3.29 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18163, 18155, 18135, 18133])).
% 2.97/3.29 tff(18165,plain,
% 2.97/3.29 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[1137, 18164])).
% 2.97/3.29 tff(18166,plain,
% 2.97/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[2262, 18165, 123, 838])).
% 2.97/3.29 tff(18167,plain,
% 2.97/3.29 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[249, 18166])).
% 2.97/3.29 tff(18168,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[6350, 333, 1699, 18155, 18167, 18133])).
% 2.97/3.29 tff(18169,plain,((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(elem!1) = s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18170,plain,
% 2.97/3.29 (~r(z, s(elem!1))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18169, 18100, 1699, 18098, 18090, 286, 18051, 18053, 18084, 18066])).
% 2.97/3.29 tff(18171,plain,
% 2.97/3.29 (b(z, s(elem!1))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[583, 18170])).
% 2.97/3.29 tff(18172,plain,
% 2.97/3.29 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[72])).
% 2.97/3.29 tff(18173,plain,
% 2.97/3.29 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.97/3.29 inference(symmetry,[status(thm)],[18172])).
% 2.97/3.29 tff(18174,plain,
% 2.97/3.29 (b(elem!1, s(elem!1))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[585, 18173])).
% 2.97/3.29 tff(18175,plain,
% 2.97/3.29 ($false),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[5775, 18174])).
% 2.97/3.29 tff(18176,plain,((~(elem!1 = z)) | b(elem!1, s(elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.29 tff(18177,plain,
% 2.97/3.29 (b(elem!1, s(elem!1))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18176, 18171, 72])).
% 2.97/3.29 tff(18178,plain,
% 2.97/3.29 (b(z, s(z))),
% 2.97/3.29 inference(unit_resolution,[status(thm)],[18030, 18177, 18051])).
% 2.97/3.29 tff(18179,plain,
% 2.97/3.29 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18085])).
% 2.97/3.29 tff(18180,plain,
% 2.97/3.29 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.97/3.29 inference(symmetry,[status(thm)],[18179])).
% 2.97/3.29 tff(18181,plain,
% 2.97/3.29 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[72])).
% 2.97/3.29 tff(18182,plain,
% 2.97/3.29 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[72])).
% 2.97/3.29 tff(18183,plain,
% 2.97/3.29 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.29 inference(symmetry,[status(thm)],[18182])).
% 2.97/3.29 tff(18184,plain,
% 2.97/3.29 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18085])).
% 2.97/3.29 tff(18185,plain,
% 2.97/3.29 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.29 inference(transitivity,[status(thm)],[18184, 18183])).
% 2.97/3.29 tff(18186,plain,
% 2.97/3.29 ((~r(z, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18185])).
% 2.97/3.29 tff(18187,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 2.97/3.29 tff(18188,plain,
% 2.97/3.29 (((~![X0: $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))), z)) | (~r(s(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(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18189,plain,
% 2.97/3.29 (((~r(z, 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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))))),
% 2.97/3.29 inference(rewrite,[status(thm)],[])).
% 2.97/3.29 tff(18190,plain,
% 2.97/3.29 (((~![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(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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z))))))),
% 2.97/3.29 inference(monotonicity,[status(thm)],[18189])).
% 2.97/3.29 tff(18191,plain,
% 2.97/3.29 (((~![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(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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))))),
% 2.97/3.29 inference(transitivity,[status(thm)],[18190, 18188])).
% 2.97/3.29 tff(18192,plain,
% 2.97/3.29 ((~![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(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.97/3.29 inference(quant_inst,[status(thm)],[])).
% 2.97/3.29 tff(18193,plain,
% 2.97/3.29 ((~![X0: $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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z))))),
% 2.97/3.29 inference(modus_ponens,[status(thm)],[18192, 18191])).
% 3.07/3.30 tff(18194,plain,
% 3.07/3.30 (~r(s(s(s(z))), s(z))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18193, 333, 323, 1699, 18187])).
% 3.07/3.30 tff(18195,plain,
% 3.07/3.30 (b(s(s(s(z))), s(z))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[2794, 18194])).
% 3.07/3.30 tff(18196,plain,
% 3.07/3.30 (~b(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18116, 18195, 8677, 1417, 10356])).
% 3.07/3.30 tff(18197,plain,
% 3.07/3.30 (((~![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))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18198,plain,
% 3.07/3.30 (((~r(z, 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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18199,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 3.07/3.30 inference(monotonicity,[status(thm)],[18198])).
% 3.07/3.30 tff(18200,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(transitivity,[status(thm)],[18199, 18197])).
% 3.07/3.30 tff(18201,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.07/3.30 inference(quant_inst,[status(thm)],[])).
% 3.07/3.30 tff(18202,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18201, 18200])).
% 3.07/3.30 tff(18203,plain,
% 3.07/3.30 (~r(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18202, 333, 1699, 9615, 18187])).
% 3.07/3.30 tff(18204,plain,
% 3.07/3.30 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18132, 18203, 8677])).
% 3.07/3.30 tff(18205,plain,
% 3.07/3.30 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[4311, 18204, 4620])).
% 3.07/3.30 tff(18206,plain,
% 3.07/3.30 ($false),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18122, 18205, 18196, 8677])).
% 3.07/3.30 tff(18207,plain,((~r(z, s(s(z)))) | (~(s(elem!1) = s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.30 tff(18208,plain,
% 3.07/3.30 (~r(z, s(s(z)))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18207, 9615, 18053, 1417, 10356, 1699, 18051, 323])).
% 3.07/3.30 tff(18209,plain,
% 3.07/3.30 (~r(elem!1, s(s(elem!1)))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18208, 18186])).
% 3.07/3.30 tff(18210,plain,
% 3.07/3.30 (b(elem!1, s(s(elem!1)))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[2522, 18209, 1221])).
% 3.07/3.30 tff(18211,plain,
% 3.07/3.30 (b(z, s(s(elem!1)))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18210, 18181])).
% 3.07/3.30 tff(18212,plain,
% 3.07/3.30 (b(z, s(s(z)))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18211, 18180])).
% 3.07/3.30 tff(18213,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 3.07/3.30 tff(18214,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18215,plain,
% 3.07/3.30 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(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(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18216,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.30 inference(monotonicity,[status(thm)],[18215])).
% 3.07/3.30 tff(18217,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.30 inference(transitivity,[status(thm)],[18216, 18214])).
% 3.07/3.30 tff(18218,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 3.07/3.30 inference(quant_inst,[status(thm)],[])).
% 3.07/3.30 tff(18219,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18218, 18217])).
% 3.07/3.30 tff(18220,plain,
% 3.07/3.30 ($false),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18219, 144, 490, 1417, 123, 259, 18213])).
% 3.07/3.30 tff(18221,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.30 tff(18222,plain,
% 3.07/3.30 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18221, 18212, 1417, 123, 490])).
% 3.07/3.30 tff(18223,plain,
% 3.07/3.30 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[278, 18222, 274])).
% 3.07/3.30 tff(18224,plain,
% 3.07/3.30 (~r(s(s(s(z))), s(z))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[12583, 333, 323, 1699, 18223])).
% 3.07/3.30 tff(18225,plain,
% 3.07/3.30 (b(s(s(s(z))), s(z))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[2794, 18224])).
% 3.07/3.30 tff(18226,plain,
% 3.07/3.30 (~b(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18116, 18225, 18051, 1417, 10356])).
% 3.07/3.30 tff(18227,plain,
% 3.07/3.30 (((~![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))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18228,plain,
% 3.07/3.30 (((~r(z, s(s(s(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18229,plain,
% 3.07/3.30 (((~![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(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 3.07/3.30 inference(monotonicity,[status(thm)],[18228])).
% 3.07/3.30 tff(18230,plain,
% 3.07/3.30 (((~![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(s(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(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 3.07/3.30 inference(transitivity,[status(thm)],[18229, 18227])).
% 3.07/3.30 tff(18231,plain,
% 3.07/3.30 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.07/3.30 inference(quant_inst,[status(thm)],[])).
% 3.07/3.30 tff(18232,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18231, 18230])).
% 3.07/3.30 tff(18233,plain,
% 3.07/3.30 (~r(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18232, 333, 1699, 18223, 9615])).
% 3.07/3.30 tff(18234,plain,
% 3.07/3.30 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18132, 18233, 18051])).
% 3.07/3.30 tff(18235,plain,
% 3.07/3.30 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[4311, 18234, 18053])).
% 3.07/3.30 tff(18236,plain,
% 3.07/3.30 ($false),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18122, 18235, 18226, 18051])).
% 3.07/3.30 tff(18237,plain,((~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~(elem!1 = z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.30 tff(18238,plain,
% 3.07/3.30 (~r(s(s(z)), z)),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18237, 18090, 18084, 1699, 18066, 18100, 18178, 72, 1221])).
% 3.07/3.30 tff(18239,plain,
% 3.07/3.30 (b(s(s(z)), z)),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[1462, 44, 164, 18238])).
% 3.07/3.30 tff(18240,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 3.07/3.30 tff(18241,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18242,plain,
% 3.07/3.30 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18243,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 3.07/3.30 inference(monotonicity,[status(thm)],[18242])).
% 3.07/3.30 tff(18244,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 3.07/3.30 inference(transitivity,[status(thm)],[18243, 18241])).
% 3.07/3.30 tff(18245,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 3.07/3.30 inference(quant_inst,[status(thm)],[])).
% 3.07/3.30 tff(18246,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 3.07/3.30 inference(modus_ponens,[status(thm)],[18245, 18244])).
% 3.07/3.30 tff(18247,plain,
% 3.07/3.30 ($false),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18246, 144, 490, 7943, 1417, 838, 18240])).
% 3.07/3.30 tff(18248,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.30 tff(18249,plain,
% 3.07/3.30 (~b(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18248, 18178, 18090, 18098, 18239])).
% 3.07/3.30 tff(18250,plain,
% 3.07/3.30 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18122, 18249, 18051])).
% 3.07/3.30 tff(18251,plain,
% 3.07/3.30 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[4311, 18250, 18053])).
% 3.07/3.30 tff(18252,plain,
% 3.07/3.30 (r(s(s(z)), s(s(s(z))))),
% 3.07/3.30 inference(unit_resolution,[status(thm)],[18132, 18251, 18051])).
% 3.07/3.30 tff(18253,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18254,plain,
% 3.07/3.30 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.30 inference(rewrite,[status(thm)],[])).
% 3.07/3.30 tff(18255,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.07/3.30 inference(monotonicity,[status(thm)],[18254])).
% 3.07/3.30 tff(18256,plain,
% 3.07/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.30 inference(transitivity,[status(thm)],[18255, 18253])).
% 3.07/3.30 tff(18257,plain,
% 3.07/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.31 inference(quant_inst,[status(thm)],[])).
% 3.07/3.31 tff(18258,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18257, 18256])).
% 3.07/3.31 tff(18259,plain,
% 3.07/3.31 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18258, 144, 18178, 18090, 286])).
% 3.07/3.31 tff(18260,plain,
% 3.07/3.31 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18259, 18239])).
% 3.07/3.31 tff(18261,plain,
% 3.07/3.31 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1451, 18260])).
% 3.07/3.31 tff(18262,plain,
% 3.07/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[7412, 18261, 1699, 18252])).
% 3.07/3.31 tff(18263,plain,
% 3.07/3.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[249, 18262])).
% 3.07/3.31 tff(18264,plain,
% 3.07/3.31 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[2262, 18263, 18100, 18098])).
% 3.07/3.31 tff(18265,plain,
% 3.07/3.31 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1137, 18264])).
% 3.07/3.31 tff(18266,plain,
% 3.07/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18163, 18265, 18261, 18252])).
% 3.07/3.31 tff(18267,plain,
% 3.07/3.31 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[319, 18266])).
% 3.07/3.31 tff(18268,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18269,plain,
% 3.07/3.31 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18270,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18269])).
% 3.07/3.31 tff(18271,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.31 inference(transitivity,[status(thm)],[18270, 18268])).
% 3.07/3.31 tff(18272,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.31 inference(quant_inst,[status(thm)],[])).
% 3.07/3.31 tff(18273,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18272, 18271])).
% 3.07/3.31 tff(18274,plain,
% 3.07/3.31 ($false),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18273, 144, 18178, 18098, 18263, 18267, 286])).
% 3.07/3.31 tff(18275,plain,((~(elem!1 = z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.31 tff(18276,plain,
% 3.07/3.31 (~(elem!1 = z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18275, 2097, 1699, 1221, 959, 18049, 1249, 502])).
% 3.07/3.31 tff(18277,plain,
% 3.07/3.31 (r(elem!1, z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1380, 18276, 377])).
% 3.07/3.31 tff(18278,plain,
% 3.07/3.31 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[517, 18277, 435, 12191])).
% 3.07/3.31 tff(18279,plain,
% 3.07/3.31 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[278, 18278, 274])).
% 3.07/3.31 tff(18280,plain,
% 3.07/3.31 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[14780, 18047, 435, 466, 12191, 377, 2097])).
% 3.07/3.31 tff(18281,plain,
% 3.07/3.31 (~r(z, s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[9017, 18277, 435, 12191])).
% 3.07/3.31 tff(18282,plain,
% 3.07/3.31 (b(z, s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[583, 18281])).
% 3.07/3.31 tff(18283,plain,
% 3.07/3.31 ((elem!1 = z) <=> (z = elem!1)),
% 3.07/3.31 inference(commutativity,[status(thm)],[])).
% 3.07/3.31 tff(18284,plain,
% 3.07/3.31 ((z = elem!1) <=> (elem!1 = z)),
% 3.07/3.31 inference(symmetry,[status(thm)],[18283])).
% 3.07/3.31 tff(18285,plain,
% 3.07/3.31 (elem!1 = z),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[66, 18284])).
% 3.07/3.31 tff(18286,plain,
% 3.07/3.31 ($false),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1368, 18285])).
% 3.07/3.31 tff(18287,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.31 tff(18288,plain,
% 3.07/3.31 (~(z = elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18287, 18276])).
% 3.07/3.31 tff(18289,plain,
% 3.07/3.31 (b(z, elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[658, 18288, 1575])).
% 3.07/3.31 tff(18290,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18291,plain,
% 3.07/3.31 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18292,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18291])).
% 3.07/3.31 tff(18293,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.31 inference(transitivity,[status(thm)],[18292, 18290])).
% 3.07/3.31 tff(18294,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))))),
% 3.07/3.31 inference(quant_inst,[status(thm)],[])).
% 3.07/3.31 tff(18295,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18294, 18293])).
% 3.07/3.31 tff(18296,plain,
% 3.07/3.31 ($false),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18295, 144, 18289, 18282, 18280, 18049, 18279])).
% 3.07/3.31 tff(18297,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~r(s(elem!1), elem!1)) | r(z, elem!1) | b(elem!1, z) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.31 tff(18298,plain,
% 3.07/3.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18297, 18046, 1575, 435, 1699, 1221, 959, 1249, 502, 466])).
% 3.07/3.31 tff(18299,plain,
% 3.07/3.31 ($false),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18298, 18042])).
% 3.07/3.31 tff(18300,plain,((~(s(elem!1) = s(z))) | r(z, elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.31 tff(18301,plain,
% 3.07/3.31 (~(s(elem!1) = s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18300, 9362, 435, 1699, 1221, 959, 1249, 502, 466, 322, 1575])).
% 3.07/3.31 tff(18302,plain,
% 3.07/3.31 (b(elem!1, z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1380, 77, 1378])).
% 3.07/3.31 tff(18303,plain,
% 3.07/3.31 (b(s(elem!1), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1653, 1, 706, 1575, 902, 509, 354])).
% 3.07/3.31 tff(18304,plain,
% 3.07/3.31 (~b(s(z), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[2219, 123, 259, 354, 322, 706, 624, 251])).
% 3.07/3.31 tff(18305,plain,
% 3.07/3.31 (r(s(z), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[348, 18304])).
% 3.07/3.31 tff(18306,plain,
% 3.07/3.31 (~r(s(s(s(z))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[6555, 18305, 1699, 354])).
% 3.07/3.31 tff(18307,plain,
% 3.07/3.31 (b(s(s(s(z))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[2794, 18306])).
% 3.07/3.31 tff(18308,plain,
% 3.07/3.31 (s(elem!1) = s(s(s(z)))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1716, 18307, 1699, 509, 354, 488, 18305])).
% 3.07/3.31 tff(18309,plain,
% 3.07/3.31 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18308])).
% 3.07/3.31 tff(18310,plain,
% 3.07/3.31 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.07/3.31 inference(symmetry,[status(thm)],[18309])).
% 3.07/3.31 tff(18311,plain,
% 3.07/3.31 (s(s(z)) = elem!1),
% 3.07/3.31 inference(transitivity,[status(thm)],[87, 18310, 850])).
% 3.07/3.31 tff(18312,plain,
% 3.07/3.31 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18311])).
% 3.07/3.31 tff(18313,plain,
% 3.07/3.31 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.07/3.31 inference(symmetry,[status(thm)],[18312])).
% 3.07/3.31 tff(18314,plain,
% 3.07/3.31 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18308])).
% 3.07/3.31 tff(18315,plain,
% 3.07/3.31 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 3.07/3.31 inference(transitivity,[status(thm)],[18314, 18313])).
% 3.07/3.31 tff(18316,plain,
% 3.07/3.31 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[990, 18308, 1])).
% 3.07/3.31 tff(18317,plain,
% 3.07/3.31 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[12459, 18316])).
% 3.07/3.31 tff(18318,plain,
% 3.07/3.31 (s(s(s(z))) = s(elem!1)),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18308, 998])).
% 3.07/3.31 tff(18319,plain,
% 3.07/3.31 (~(s(s(s(elem!1))) = elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1010, 18318])).
% 3.07/3.31 tff(18320,plain,
% 3.07/3.31 (~r(s(elem!1), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[12497, 3127, 488, 323, 435, 1012, 251, 624, 354, 714, 547, 1237])).
% 3.07/3.31 tff(18321,plain,
% 3.07/3.31 (b(s(elem!1), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[507, 18320])).
% 3.07/3.31 tff(18322,plain,
% 3.07/3.31 (~b(z, s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[949, 18321, 547, 624])).
% 3.07/3.31 tff(18323,plain,
% 3.07/3.31 (r(z, s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[583, 18322])).
% 3.07/3.31 tff(18324,plain,
% 3.07/3.31 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[3254, 3127])).
% 3.07/3.31 tff(18325,plain,
% 3.07/3.31 (~r(s(s(s(elem!1))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1088, 18324, 435, 18321, 624, 1012, 251, 354, 323])).
% 3.07/3.31 tff(18326,plain,
% 3.07/3.31 (b(s(s(s(elem!1))), s(z))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1101, 18325])).
% 3.07/3.31 tff(18327,plain,
% 3.07/3.31 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[4692, 3584, 488, 1262])).
% 3.07/3.31 tff(18328,plain,
% 3.07/3.31 (r(s(s(s(elem!1))), s(elem!1))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[4697, 18327, 3127])).
% 3.07/3.31 tff(18329,plain,
% 3.07/3.31 (~r(z, s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[13102, 18328, 435, 562])).
% 3.07/3.31 tff(18330,plain,
% 3.07/3.31 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1031, 44, 18329])).
% 3.07/3.31 tff(18331,plain,
% 3.07/3.31 (b(z, s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18330, 1023])).
% 3.07/3.31 tff(18332,plain,
% 3.07/3.31 (((~![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(s(s(elem!1))), z)) | (~r(s(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(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18333,plain,
% 3.07/3.31 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18334,plain,
% 3.07/3.31 (((~![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(s(s(elem!1))), 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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18333])).
% 3.07/3.31 tff(18335,plain,
% 3.07/3.31 (((~![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(s(s(elem!1))), 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(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.07/3.31 inference(transitivity,[status(thm)],[18334, 18332])).
% 3.07/3.31 tff(18336,plain,
% 3.07/3.31 ((~![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(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 3.07/3.31 inference(quant_inst,[status(thm)],[])).
% 3.07/3.31 tff(18337,plain,
% 3.07/3.31 ((~![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(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18336, 18335])).
% 3.07/3.31 tff(18338,plain,
% 3.07/3.31 (~r(s(s(s(elem!1))), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18337, 333, 435, 562, 18328])).
% 3.07/3.31 tff(18339,plain,
% 3.07/3.31 (b(s(s(s(elem!1))), z)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 18338])).
% 3.07/3.31 tff(18340,plain,
% 3.07/3.31 (~b(elem!1, s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1050, 144, 624, 18339, 18331])).
% 3.07/3.31 tff(18341,plain,
% 3.07/3.31 (r(elem!1, s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1054, 44, 18340, 1017])).
% 3.07/3.31 tff(18342,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18343,plain,
% 3.07/3.31 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(18344,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 3.07/3.31 inference(monotonicity,[status(thm)],[18343])).
% 3.07/3.31 tff(18345,plain,
% 3.07/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 3.07/3.31 inference(transitivity,[status(thm)],[18344, 18342])).
% 3.07/3.31 tff(18346,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 3.07/3.31 inference(quant_inst,[status(thm)],[])).
% 3.07/3.31 tff(18347,plain,
% 3.07/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 3.07/3.31 inference(modus_ponens,[status(thm)],[18346, 18345])).
% 3.07/3.31 tff(18348,plain,
% 3.07/3.31 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[18347, 144, 491, 3584, 488, 18331])).
% 3.07/3.31 tff(18349,plain,
% 3.07/3.31 (r(s(elem!1), s(s(s(elem!1))))),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1067, 18348, 18324])).
% 3.07/3.31 tff(18350,plain,
% 3.07/3.31 (~b(s(s(s(elem!1))), elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1074, 144, 251, 624, 18339])).
% 3.07/3.31 tff(18351,plain,
% 3.07/3.31 (r(s(s(s(elem!1))), elem!1)),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1079, 18350, 1012])).
% 3.07/3.31 tff(18352,plain,
% 3.07/3.31 ($false),
% 3.07/3.31 inference(unit_resolution,[status(thm)],[1086, 333, 435, 18351, 18349, 18341])).
% 3.07/3.31 tff(18353,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~r(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.32 tff(18354,plain,
% 3.07/3.32 (~b(s(z), s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18353, 18326, 624, 18321, 488, 1012, 251, 18323, 3127, 435])).
% 3.07/3.32 tff(18355,plain,
% 3.07/3.32 (r(s(z), s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1244, 18354, 1237])).
% 3.07/3.32 tff(18356,plain,
% 3.07/3.32 ($false),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[4476, 333, 435, 323, 18323, 18355])).
% 3.07/3.32 tff(18357,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.32 tff(18358,plain,
% 3.07/3.32 (~b(elem!1, s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18357, 18319, 435, 354, 1229, 624, 488, 251, 18305, 18317, 713])).
% 3.07/3.32 tff(18359,plain,
% 3.07/3.32 (r(elem!1, s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[560, 18358, 902])).
% 3.07/3.32 tff(18360,plain,
% 3.07/3.32 (r(s(s(z)), s(s(s(z))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18359, 18315])).
% 3.07/3.32 tff(18361,plain,
% 3.07/3.32 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18308])).
% 3.07/3.32 tff(18362,plain,
% 3.07/3.32 (~r(s(z), s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1235, 18305, 509, 354])).
% 3.07/3.32 tff(18363,plain,
% 3.07/3.32 (b(s(z), s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1244, 18362, 1229])).
% 3.07/3.32 tff(18364,plain,
% 3.07/3.32 (b(s(z), s(s(s(z))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18363, 18361])).
% 3.07/3.32 tff(18365,plain,
% 3.07/3.32 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18308])).
% 3.07/3.32 tff(18366,plain,
% 3.07/3.32 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18365])).
% 3.07/3.32 tff(18367,plain,
% 3.07/3.32 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[466, 18366])).
% 3.07/3.32 tff(18368,plain,
% 3.07/3.32 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1137, 18367])).
% 3.07/3.32 tff(18369,plain,
% 3.07/3.32 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[2262, 18368, 123, 18364])).
% 3.07/3.32 tff(18370,plain,
% 3.07/3.32 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[249, 18369])).
% 3.07/3.32 tff(18371,plain,
% 3.07/3.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[6350, 333, 1699, 18370, 18360])).
% 3.07/3.32 tff(18372,plain,
% 3.07/3.32 (elem!1 = s(s(z))),
% 3.07/3.32 inference(transitivity,[status(thm)],[1193, 18309, 86])).
% 3.07/3.32 tff(18373,plain,
% 3.07/3.32 (b(elem!1, z) <=> b(s(s(z)), z)),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18372])).
% 3.07/3.32 tff(18374,plain,
% 3.07/3.32 (b(s(s(z)), z)),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[624, 18373])).
% 3.07/3.32 tff(18375,plain,
% 3.07/3.32 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1497, 333, 354, 18305, 322])).
% 3.07/3.32 tff(18376,plain,
% 3.07/3.32 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[302, 18375])).
% 3.07/3.32 tff(18377,plain,
% 3.07/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18378,plain,
% 3.07/3.32 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18379,plain,
% 3.07/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18378])).
% 3.07/3.32 tff(18380,plain,
% 3.07/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.32 inference(transitivity,[status(thm)],[18379, 18377])).
% 3.07/3.32 tff(18381,plain,
% 3.07/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))),
% 3.07/3.32 inference(quant_inst,[status(thm)],[])).
% 3.07/3.32 tff(18382,plain,
% 3.07/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18381, 18380])).
% 3.07/3.32 tff(18383,plain,
% 3.07/3.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18382, 144, 18376, 259, 18374])).
% 3.07/3.32 tff(18384,plain,
% 3.07/3.32 ($false),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1451, 18383, 18371])).
% 3.07/3.32 tff(18385,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.32 tff(18386,plain,
% 3.07/3.32 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18385, 18302, 1699, 902, 435, 354, 259, 18303, 1594, 322, 466, 1, 509, 706])).
% 3.07/3.32 tff(18387,plain,
% 3.07/3.32 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[49, 18386])).
% 3.07/3.32 tff(18388,plain,
% 3.07/3.32 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[2623, 466, 435])).
% 3.07/3.32 tff(18389,plain,
% 3.07/3.32 (((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18390,plain,
% 3.07/3.32 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18391,plain,
% 3.07/3.32 (((~![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(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18390])).
% 3.07/3.32 tff(18392,plain,
% 3.07/3.32 (((~![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(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(transitivity,[status(thm)],[18391, 18389])).
% 3.07/3.32 tff(18393,plain,
% 3.07/3.32 ((~![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(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.07/3.32 inference(quant_inst,[status(thm)],[])).
% 3.07/3.32 tff(18394,plain,
% 3.07/3.32 ((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18393, 18392])).
% 3.07/3.32 tff(18395,plain,
% 3.07/3.32 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18394, 333, 354, 18387, 322])).
% 3.07/3.32 tff(18396,plain,
% 3.07/3.32 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[302, 18395])).
% 3.07/3.32 tff(18397,plain,
% 3.07/3.32 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[6809, 144, 18302, 18396, 259])).
% 3.07/3.32 tff(18398,plain,
% 3.07/3.32 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[121, 18397, 18388])).
% 3.07/3.32 tff(18399,plain,
% 3.07/3.32 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18400,plain,
% 3.07/3.32 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18401,plain,
% 3.07/3.32 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18400])).
% 3.07/3.32 tff(18402,plain,
% 3.07/3.32 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.32 inference(transitivity,[status(thm)],[18401, 18399])).
% 3.07/3.32 tff(18403,plain,
% 3.07/3.32 ((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))),
% 3.07/3.32 inference(quant_inst,[status(thm)],[])).
% 3.07/3.32 tff(18404,plain,
% 3.07/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18403, 18402])).
% 3.07/3.32 tff(18405,plain,
% 3.07/3.32 ($false),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18404, 333, 409, 11546, 2323, 322])).
% 3.07/3.32 tff(18406,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.32 tff(18407,plain,
% 3.07/3.32 (~r(s(z), elem!1)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18406, 18398, 322, 18387])).
% 3.07/3.32 tff(18408,plain,
% 3.07/3.32 (b(s(z), elem!1)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[406, 18407, 706])).
% 3.07/3.32 tff(18409,plain,
% 3.07/3.32 (~b(s(z), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1602, 18408, 18302, 1594])).
% 3.07/3.32 tff(18410,plain,
% 3.07/3.32 (r(s(z), z)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[348, 18409])).
% 3.07/3.32 tff(18411,plain,
% 3.07/3.32 (~r(s(s(s(z))), s(z))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[6555, 18410, 1699, 354])).
% 3.07/3.32 tff(18412,plain,
% 3.07/3.32 (b(s(s(s(z))), s(z))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[2794, 18411])).
% 3.07/3.32 tff(18413,plain,
% 3.07/3.32 (s(elem!1) = s(s(s(z)))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1716, 18412, 1699, 509, 354, 18303, 18410])).
% 3.07/3.32 tff(18414,plain,
% 3.07/3.32 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18413])).
% 3.07/3.32 tff(18415,plain,
% 3.07/3.32 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18414])).
% 3.07/3.32 tff(18416,plain,
% 3.07/3.32 ((s(s(s(s(z)))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18415])).
% 3.07/3.32 tff(18417,plain,
% 3.07/3.32 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18416])).
% 3.07/3.32 tff(18418,plain,
% 3.07/3.32 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18417])).
% 3.07/3.32 tff(18419,plain,
% 3.07/3.32 (~(s(s(s(s(z)))) = s(z))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[107, 18418])).
% 3.07/3.32 tff(18420,plain,
% 3.07/3.32 (s(s(s(z))) = s(elem!1)),
% 3.07/3.32 inference(symmetry,[status(thm)],[18413])).
% 3.07/3.32 tff(18421,plain,
% 3.07/3.32 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18420])).
% 3.07/3.32 tff(18422,plain,
% 3.07/3.32 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18421])).
% 3.07/3.32 tff(18423,plain,
% 3.07/3.32 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18414])).
% 3.07/3.32 tff(18424,plain,
% 3.07/3.32 (b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[1249, 18423])).
% 3.07/3.32 tff(18425,plain,
% 3.07/3.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18424, 18422])).
% 3.07/3.32 tff(18426,plain,
% 3.07/3.32 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18413])).
% 3.07/3.32 tff(18427,plain,
% 3.07/3.32 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[2899, 18395, 509])).
% 3.07/3.32 tff(18428,plain,
% 3.07/3.32 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[930, 18427])).
% 3.07/3.32 tff(18429,plain,
% 3.07/3.32 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[472, 18428, 466])).
% 3.07/3.32 tff(18430,plain,
% 3.07/3.32 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18429, 18426])).
% 3.07/3.32 tff(18431,plain,
% 3.07/3.32 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18413])).
% 3.07/3.32 tff(18432,plain,
% 3.07/3.32 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18431])).
% 3.07/3.32 tff(18433,plain,
% 3.07/3.32 (s(s(z)) = elem!1),
% 3.07/3.32 inference(transitivity,[status(thm)],[87, 18432, 850])).
% 3.07/3.32 tff(18434,plain,
% 3.07/3.32 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18433])).
% 3.07/3.32 tff(18435,plain,
% 3.07/3.32 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18434])).
% 3.07/3.32 tff(18436,plain,
% 3.07/3.32 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18388, 2425])).
% 3.07/3.32 tff(18437,plain,
% 3.07/3.32 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[880, 18396, 18302, 1594])).
% 3.07/3.32 tff(18438,plain,
% 3.07/3.32 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[130, 18437, 18436])).
% 3.07/3.32 tff(18439,plain,
% 3.07/3.32 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18438, 18435])).
% 3.07/3.32 tff(18440,plain,
% 3.07/3.32 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18433])).
% 3.07/3.32 tff(18441,plain,
% 3.07/3.32 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18440])).
% 3.07/3.32 tff(18442,plain,
% 3.07/3.32 (r(s(s(s(z))), s(s(z)))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[707, 18441])).
% 3.07/3.32 tff(18443,plain,
% 3.07/3.32 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18433])).
% 3.07/3.32 tff(18444,plain,
% 3.07/3.32 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.07/3.32 inference(symmetry,[status(thm)],[18443])).
% 3.07/3.32 tff(18445,plain,
% 3.07/3.32 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 3.07/3.32 inference(monotonicity,[status(thm)],[18413])).
% 3.07/3.32 tff(18446,plain,
% 3.07/3.32 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 3.07/3.32 inference(transitivity,[status(thm)],[18445, 18444])).
% 3.07/3.32 tff(18447,plain,
% 3.07/3.32 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[990, 18413, 1])).
% 3.07/3.32 tff(18448,plain,
% 3.07/3.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[12459, 18447])).
% 3.07/3.32 tff(18449,plain,
% 3.07/3.32 (s(s(s(z))) = s(elem!1)),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18413, 998])).
% 3.07/3.32 tff(18450,plain,
% 3.07/3.32 (~(s(s(s(elem!1))) = elem!1)),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[1010, 18449])).
% 3.07/3.32 tff(18451,plain,
% 3.07/3.32 (~b(elem!1, s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18357, 18450, 435, 354, 1229, 18302, 18303, 1594, 18410, 18448, 713])).
% 3.07/3.32 tff(18452,plain,
% 3.07/3.32 (r(elem!1, s(elem!1))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[560, 18451, 902])).
% 3.07/3.32 tff(18453,plain,
% 3.07/3.32 (r(s(s(z)), s(s(s(z))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18452, 18446])).
% 3.07/3.32 tff(18454,plain,
% 3.07/3.32 (((~![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(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.07/3.32 inference(rewrite,[status(thm)],[])).
% 3.07/3.32 tff(18455,plain,
% 3.07/3.32 ((~![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(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.07/3.32 inference(quant_inst,[status(thm)],[])).
% 3.07/3.32 tff(18456,plain,
% 3.07/3.32 ((~![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(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.07/3.32 inference(modus_ponens,[status(thm)],[18455, 18454])).
% 3.07/3.32 tff(18457,plain,
% 3.07/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[18456, 333, 18453, 18442, 18439])).
% 3.07/3.32 tff(18458,plain,
% 3.07/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.32 inference(unit_resolution,[status(thm)],[249, 18457])).
% 3.07/3.32 tff(18459,plain,
% 3.07/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18460,plain,
% 3.07/3.33 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18461,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18460])).
% 3.07/3.33 tff(18462,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.33 inference(transitivity,[status(thm)],[18461, 18459])).
% 3.07/3.33 tff(18463,plain,
% 3.07/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.33 inference(quant_inst,[status(thm)],[])).
% 3.07/3.33 tff(18464,plain,
% 3.07/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18463, 18462])).
% 3.07/3.33 tff(18465,plain,
% 3.07/3.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18464, 144, 18458, 18430, 18425])).
% 3.07/3.33 tff(18466,plain,
% 3.07/3.33 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18414])).
% 3.07/3.33 tff(18467,plain,
% 3.07/3.33 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(transitivity,[status(thm)],[18466, 12720])).
% 3.07/3.33 tff(18468,plain,
% 3.07/3.33 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18467])).
% 3.07/3.33 tff(18469,plain,
% 3.07/3.33 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[2725, 18468])).
% 3.07/3.33 tff(18470,plain,
% 3.07/3.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[3556, 44, 18469, 18465])).
% 3.07/3.33 tff(18471,plain,
% 3.07/3.33 (((~![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(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18472,plain,
% 3.07/3.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18473,plain,
% 3.07/3.33 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18472])).
% 3.07/3.33 tff(18474,plain,
% 3.07/3.33 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(transitivity,[status(thm)],[18473, 18471])).
% 3.07/3.33 tff(18475,plain,
% 3.07/3.33 ((~![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(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.07/3.33 inference(quant_inst,[status(thm)],[])).
% 3.07/3.33 tff(18476,plain,
% 3.07/3.33 ((~![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(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18475, 18474])).
% 3.07/3.33 tff(18477,plain,
% 3.07/3.33 (~r(s(s(s(s(z)))), s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18476, 333, 18387, 18439, 18470])).
% 3.07/3.33 tff(18478,plain,
% 3.07/3.33 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18413])).
% 3.07/3.33 tff(18479,plain,
% 3.07/3.33 (~r(s(z), s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1235, 18410, 509, 354])).
% 3.07/3.33 tff(18480,plain,
% 3.07/3.33 (b(s(z), s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1244, 18479, 1229])).
% 3.07/3.33 tff(18481,plain,
% 3.07/3.33 (b(s(z), s(s(s(z))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18480, 18478])).
% 3.07/3.33 tff(18482,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18483,plain,
% 3.07/3.33 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(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))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18484,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18483])).
% 3.07/3.33 tff(18485,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))))),
% 3.07/3.33 inference(transitivity,[status(thm)],[18484, 18482])).
% 3.07/3.33 tff(18486,plain,
% 3.07/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.33 inference(quant_inst,[status(thm)],[])).
% 3.07/3.33 tff(18487,plain,
% 3.07/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18486, 18485])).
% 3.07/3.33 tff(18488,plain,
% 3.07/3.33 (~b(s(s(s(s(z)))), s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18487, 144, 18412, 18481, 18425])).
% 3.07/3.33 tff(18489,plain,
% 3.07/3.33 (((~![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)))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18490,plain,
% 3.07/3.33 ((~![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)))),
% 3.07/3.33 inference(quant_inst,[status(thm)],[])).
% 3.07/3.33 tff(18491,plain,
% 3.07/3.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18490, 18489])).
% 3.07/3.33 tff(18492,plain,
% 3.07/3.33 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18491, 44, 18488])).
% 3.07/3.33 tff(18493,plain,
% 3.07/3.33 ($false),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18492, 18477, 18419])).
% 3.07/3.33 tff(18494,plain,((s(elem!1) = s(z)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.33 tff(18495,plain,
% 3.07/3.33 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18494, 18301, 13418, 435, 9363, 2725, 1249, 1699, 12191, 706, 322, 707, 466, 18017, 1575])).
% 3.07/3.33 tff(18496,plain,
% 3.07/3.33 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[278, 18495, 274])).
% 3.07/3.33 tff(18497,plain,
% 3.07/3.33 (~(z = elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[70, 18301])).
% 3.07/3.33 tff(18498,plain,
% 3.07/3.33 (b(z, elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[658, 18497, 1575])).
% 3.07/3.33 tff(18499,plain,
% 3.07/3.33 (~(elem!1 = z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[76, 18497])).
% 3.07/3.33 tff(18500,plain,
% 3.07/3.33 (b(elem!1, z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1380, 18499, 18017])).
% 3.07/3.33 tff(18501,plain,
% 3.07/3.33 (~r(s(z), elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[429, 18496, 322, 9363])).
% 3.07/3.33 tff(18502,plain,
% 3.07/3.33 (b(s(z), elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[406, 18501, 706])).
% 3.07/3.33 tff(18503,plain,
% 3.07/3.33 (~b(s(z), z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1602, 18502, 18500, 18498])).
% 3.07/3.33 tff(18504,plain,
% 3.07/3.33 (r(s(z), z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[348, 18503])).
% 3.07/3.33 tff(18505,plain,
% 3.07/3.33 ($false),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[12139, 333, 9363, 18504, 322, 18496])).
% 3.07/3.33 tff(18506,plain,(b(z, s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | r(z, elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.33 tff(18507,plain,
% 3.07/3.33 (b(z, s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18506, 322, 706, 1575, 435, 2725, 1249, 1699, 707, 466, 1221, 959, 502])).
% 3.07/3.33 tff(18508,plain,
% 3.07/3.33 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[880, 2097, 18018, 1594])).
% 3.07/3.33 tff(18509,plain,
% 3.07/3.33 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[130, 18508, 18436])).
% 3.07/3.33 tff(18510,plain,
% 3.07/3.33 (((~![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(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18511,plain,
% 3.07/3.33 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18512,plain,
% 3.07/3.33 (((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18511])).
% 3.07/3.33 tff(18513,plain,
% 3.07/3.33 (((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(elem!1), 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(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.33 inference(transitivity,[status(thm)],[18512, 18510])).
% 3.07/3.33 tff(18514,plain,
% 3.07/3.33 ((~![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(z))))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 3.07/3.33 inference(quant_inst,[status(thm)],[])).
% 3.07/3.33 tff(18515,plain,
% 3.07/3.33 ((~![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(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18514, 18513])).
% 3.07/3.33 tff(18516,plain,
% 3.07/3.33 (~r(s(elem!1), s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[18515, 333, 323, 12191, 51])).
% 3.07/3.33 tff(18517,plain,
% 3.07/3.33 (b(s(elem!1), s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[486, 18516, 1])).
% 3.07/3.33 tff(18518,plain,
% 3.07/3.33 (~r(s(z), s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[12415, 333, 323, 12191, 51])).
% 3.07/3.33 tff(18519,plain,
% 3.07/3.33 (b(s(z), s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1244, 18518, 1229])).
% 3.07/3.33 tff(18520,plain,
% 3.07/3.33 (~b(z, s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1853, 18517, 490, 18519])).
% 3.07/3.33 tff(18521,plain,
% 3.07/3.33 (r(z, s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[583, 18520])).
% 3.07/3.33 tff(18522,plain,
% 3.07/3.33 (s(elem!1) = s(s(s(z)))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[8142, 18521, 12191, 1699, 18517, 323])).
% 3.07/3.33 tff(18523,plain,
% 3.07/3.33 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18522])).
% 3.07/3.33 tff(18524,plain,
% 3.07/3.33 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18523])).
% 3.07/3.33 tff(18525,plain,
% 3.07/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[2655, 18521, 435, 51])).
% 3.07/3.33 tff(18526,plain,
% 3.07/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18525, 18524])).
% 3.07/3.33 tff(18527,plain,
% 3.07/3.33 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18522])).
% 3.07/3.33 tff(18528,plain,
% 3.07/3.33 (b(s(z), s(s(s(z))))),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18519, 18527])).
% 3.07/3.33 tff(18529,plain,
% 3.07/3.33 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(elem!1, s(z))),
% 3.07/3.33 inference(symmetry,[status(thm)],[14208])).
% 3.07/3.33 tff(18530,plain,
% 3.07/3.33 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(elem!1, s(z)))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18529])).
% 3.07/3.33 tff(18531,plain,
% 3.07/3.33 (b(s(s(s(s(s(s(z)))))), z) <=> b(elem!1, z)),
% 3.07/3.33 inference(monotonicity,[status(thm)],[6165])).
% 3.07/3.33 tff(18532,plain,
% 3.07/3.33 (b(elem!1, z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 3.07/3.33 inference(symmetry,[status(thm)],[18531])).
% 3.07/3.33 tff(18533,plain,
% 3.07/3.33 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 3.07/3.33 inference(monotonicity,[status(thm)],[6165])).
% 3.07/3.33 tff(18534,plain,
% 3.07/3.33 ((s(s(s(s(s(s(z)))))) = z) <=> (z = elem!1)),
% 3.07/3.33 inference(transitivity,[status(thm)],[18533, 18283])).
% 3.07/3.33 tff(18535,plain,
% 3.07/3.33 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 3.07/3.33 inference(transitivity,[status(thm)],[18534, 18284])).
% 3.07/3.33 tff(18536,plain,
% 3.07/3.33 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(elem!1 = z))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18535])).
% 3.07/3.33 tff(18537,plain,
% 3.07/3.33 (~(elem!1 = z)),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[31, 18536])).
% 3.07/3.33 tff(18538,plain,
% 3.07/3.33 (b(elem!1, z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[1380, 18537, 1378])).
% 3.07/3.33 tff(18539,plain,
% 3.07/3.33 (b(s(s(s(s(s(s(z)))))), z)),
% 3.07/3.33 inference(modus_ponens,[status(thm)],[18538, 18532])).
% 3.07/3.33 tff(18540,plain,
% 3.07/3.33 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[2899, 3326, 509])).
% 3.07/3.33 tff(18541,plain,
% 3.07/3.33 (~r(s(z), z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[17877, 333, 11546, 18540, 51])).
% 3.07/3.33 tff(18542,plain,
% 3.07/3.33 (b(s(z), z)),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[348, 18541])).
% 3.07/3.33 tff(18543,plain,
% 3.07/3.33 (~r(z, s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[15181, 333, 11546, 18540, 51])).
% 3.07/3.33 tff(18544,plain,
% 3.07/3.33 (b(z, s(z))),
% 3.07/3.33 inference(unit_resolution,[status(thm)],[372, 18543])).
% 3.07/3.33 tff(18545,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18546,plain,
% 3.07/3.33 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.07/3.33 inference(rewrite,[status(thm)],[])).
% 3.07/3.33 tff(18547,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 3.07/3.33 inference(monotonicity,[status(thm)],[18546])).
% 3.07/3.33 tff(18548,plain,
% 3.07/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.07/3.34 inference(transitivity,[status(thm)],[18547, 18545])).
% 3.07/3.34 tff(18549,plain,
% 3.07/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 3.07/3.34 inference(quant_inst,[status(thm)],[])).
% 3.07/3.34 tff(18550,plain,
% 3.07/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[18549, 18548])).
% 3.07/3.34 tff(18551,plain,
% 3.07/3.34 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18550, 144, 18544, 18542])).
% 3.07/3.34 tff(18552,plain,
% 3.07/3.34 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18551, 18539])).
% 3.07/3.34 tff(18553,plain,
% 3.07/3.34 (~b(elem!1, s(z))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[18552, 18530])).
% 3.07/3.34 tff(18554,plain,
% 3.07/3.34 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[927])).
% 3.07/3.34 tff(18555,plain,
% 3.07/3.34 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(elem!1))),
% 3.07/3.34 inference(symmetry,[status(thm)],[18554])).
% 3.07/3.34 tff(18556,plain,
% 3.07/3.34 (r(s(z), s(elem!1))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[11546, 18555])).
% 3.07/3.34 tff(18557,plain,
% 3.07/3.34 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = elem!1))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[18534])).
% 3.07/3.34 tff(18558,plain,
% 3.07/3.34 (~(z = elem!1)),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[31, 18557])).
% 3.07/3.34 tff(18559,plain,
% 3.07/3.34 (b(z, elem!1)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[658, 18558, 1575])).
% 3.07/3.34 tff(18560,plain,
% 3.07/3.34 (~b(s(z), elem!1)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[1602, 18542, 18538, 18559])).
% 3.07/3.34 tff(18561,plain,
% 3.07/3.34 (b(elem!1, s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[7675, 18560, 706, 435, 18556])).
% 3.07/3.34 tff(18562,plain,
% 3.07/3.34 ($false),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18561, 18553])).
% 3.07/3.34 tff(18563,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | r(elem!1, z) | r(z, elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.34 tff(18564,plain,
% 3.07/3.34 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18563, 11546, 435, 1378, 1575, 706, 51, 12191])).
% 3.07/3.34 tff(18565,plain,
% 3.07/3.34 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[472, 18564, 466])).
% 3.07/3.34 tff(18566,plain,
% 3.07/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[2655, 562, 435, 51])).
% 3.07/3.34 tff(18567,plain,
% 3.07/3.34 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[13329])).
% 3.07/3.34 tff(18568,plain,
% 3.07/3.34 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[2725, 18567])).
% 3.07/3.34 tff(18569,plain,
% 3.07/3.34 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[2948, 18047])).
% 3.07/3.34 tff(18570,plain,
% 3.07/3.34 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[13344, 144, 1249, 18569, 450])).
% 3.07/3.34 tff(18571,plain,
% 3.07/3.34 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[7819, 44, 18570])).
% 3.07/3.34 tff(18572,plain,
% 3.07/3.34 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18571, 18568])).
% 3.07/3.34 tff(18573,plain,
% 3.07/3.34 (~(elem!1 = z)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18275, 2097, 1699, 1221, 959, 450, 1249, 502])).
% 3.07/3.34 tff(18574,plain,
% 3.07/3.34 (~(z = elem!1)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18287, 18573])).
% 3.07/3.34 tff(18575,plain,
% 3.07/3.34 (~(s(elem!1) = s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[8683, 18574])).
% 3.07/3.34 tff(18576,plain,
% 3.07/3.34 (((~![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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18577,plain,
% 3.07/3.34 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18578,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[18577])).
% 3.07/3.34 tff(18579,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.07/3.34 inference(transitivity,[status(thm)],[18578, 18576])).
% 3.07/3.34 tff(18580,plain,
% 3.07/3.34 ((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 3.07/3.34 inference(quant_inst,[status(thm)],[])).
% 3.07/3.34 tff(18581,plain,
% 3.07/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[18580, 18579])).
% 3.07/3.34 tff(18582,plain,
% 3.07/3.34 ($false),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18581, 333, 354, 3654, 11546, 51])).
% 3.07/3.34 tff(18583,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.34 tff(18584,plain,
% 3.07/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18583, 354, 11546, 51])).
% 3.07/3.34 tff(18585,plain,
% 3.07/3.34 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[2758, 18584, 2725])).
% 3.07/3.34 tff(18586,plain,
% 3.07/3.34 (b(s(elem!1), s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[1653, 354, 706, 1575, 902, 509, 1])).
% 3.07/3.34 tff(18587,plain,
% 3.07/3.34 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[5667, 18586, 1249, 18585, 546])).
% 3.07/3.34 tff(18588,plain,
% 3.07/3.34 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[319, 18587])).
% 3.07/3.34 tff(18589,plain,
% 3.07/3.34 (((~![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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18590,plain,
% 3.07/3.34 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18591,plain,
% 3.07/3.34 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[18590])).
% 3.07/3.34 tff(18592,plain,
% 3.07/3.34 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(transitivity,[status(thm)],[18591, 18589])).
% 3.07/3.34 tff(18593,plain,
% 3.07/3.34 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(quant_inst,[status(thm)],[])).
% 3.07/3.34 tff(18594,plain,
% 3.07/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[18593, 18592])).
% 3.07/3.34 tff(18595,plain,
% 3.07/3.34 ($false),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18594, 333, 354, 11546, 18588, 51])).
% 3.07/3.34 tff(18596,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(z) = elem!1) | r(z, elem!1) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.34 tff(18597,plain,
% 3.07/3.34 (~r(z, s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18596, 18569, 51, 1249, 11546, 2725, 706, 1575, 13418, 12191, 18575])).
% 3.07/3.34 tff(18598,plain,
% 3.07/3.34 (b(z, s(z))),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[372, 18597])).
% 3.07/3.34 tff(18599,plain,
% 3.07/3.34 (((~![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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18600,plain,
% 3.07/3.34 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18601,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[18600])).
% 3.07/3.34 tff(18602,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(transitivity,[status(thm)],[18601, 18599])).
% 3.07/3.34 tff(18603,plain,
% 3.07/3.34 ((~![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(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)))),
% 3.07/3.34 inference(quant_inst,[status(thm)],[])).
% 3.07/3.34 tff(18604,plain,
% 3.07/3.34 ((~![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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.34 inference(modus_ponens,[status(thm)],[18603, 18602])).
% 3.07/3.34 tff(18605,plain,
% 3.07/3.34 (~r(s(s(elem!1)), z)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[18604, 333, 322, 51, 8162])).
% 3.07/3.34 tff(18606,plain,
% 3.07/3.34 (b(s(s(elem!1)), z)),
% 3.07/3.34 inference(unit_resolution,[status(thm)],[5041, 44, 1094, 18605])).
% 3.07/3.34 tff(18607,plain,
% 3.07/3.34 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18608,plain,
% 3.07/3.34 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(rewrite,[status(thm)],[])).
% 3.07/3.34 tff(18609,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.34 inference(monotonicity,[status(thm)],[18608])).
% 3.07/3.34 tff(18610,plain,
% 3.07/3.34 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.34 inference(transitivity,[status(thm)],[18609, 18607])).
% 3.07/3.34 tff(18611,plain,
% 3.07/3.34 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(z))))),
% 3.07/3.34 inference(quant_inst,[status(thm)],[])).
% 3.07/3.34 tff(18612,plain,
% 3.07/3.34 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18611, 18610])).
% 3.07/3.35 tff(18613,plain,
% 3.07/3.35 (~r(s(s(elem!1)), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18612, 333, 11546, 322, 8162])).
% 3.07/3.35 tff(18614,plain,
% 3.07/3.35 (b(s(s(elem!1)), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[4983, 18613])).
% 3.07/3.35 tff(18615,plain,
% 3.07/3.35 (~r(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[15631, 333, 11546, 322, 51])).
% 3.07/3.35 tff(18616,plain,
% 3.07/3.35 (b(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[348, 18615])).
% 3.07/3.35 tff(18617,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18618,plain,
% 3.07/3.35 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18619,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18618])).
% 3.07/3.35 tff(18620,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 3.07/3.35 inference(transitivity,[status(thm)],[18619, 18617])).
% 3.07/3.35 tff(18621,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 3.07/3.35 inference(quant_inst,[status(thm)],[])).
% 3.07/3.35 tff(18622,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18621, 18620])).
% 3.07/3.35 tff(18623,plain,
% 3.07/3.35 ($false),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18622, 144, 490, 18616, 18614, 18606])).
% 3.07/3.35 tff(18624,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.35 tff(18625,plain,
% 3.07/3.35 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18624, 18598, 51, 18572, 11546])).
% 3.07/3.35 tff(18626,plain,
% 3.07/3.35 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[319, 18625])).
% 3.07/3.35 tff(18627,plain,
% 3.07/3.35 (~b(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[7093, 18598, 18626, 2097])).
% 3.07/3.35 tff(18628,plain,
% 3.07/3.35 (r(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[348, 18627])).
% 3.07/3.35 tff(18629,plain,
% 3.07/3.35 (~r(s(elem!1), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1909, 333, 18628, 12191, 562])).
% 3.07/3.35 tff(18630,plain,
% 3.07/3.35 (b(s(elem!1), s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[486, 18629, 18575])).
% 3.07/3.35 tff(18631,plain,
% 3.07/3.35 (s(elem!1) = s(s(s(z)))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[8142, 18630, 12191, 1699, 18628, 562])).
% 3.07/3.35 tff(18632,plain,
% 3.07/3.35 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18631])).
% 3.07/3.35 tff(18633,plain,
% 3.07/3.35 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.07/3.35 inference(symmetry,[status(thm)],[18632])).
% 3.07/3.35 tff(18634,plain,
% 3.07/3.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18633])).
% 3.07/3.35 tff(18635,plain,
% 3.07/3.35 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.07/3.35 inference(symmetry,[status(thm)],[18634])).
% 3.07/3.35 tff(18636,plain,
% 3.07/3.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[5667, 18630, 1249, 18626, 18569])).
% 3.07/3.35 tff(18637,plain,
% 3.07/3.35 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[2758, 18636, 2725])).
% 3.07/3.35 tff(18638,plain,
% 3.07/3.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18637, 18635])).
% 3.07/3.35 tff(18639,plain,
% 3.07/3.35 (((~![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(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18640,plain,
% 3.07/3.35 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18641,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18640])).
% 3.07/3.35 tff(18642,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.07/3.35 inference(transitivity,[status(thm)],[18641, 18639])).
% 3.07/3.35 tff(18643,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 3.07/3.35 inference(quant_inst,[status(thm)],[])).
% 3.07/3.35 tff(18644,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18643, 18642])).
% 3.07/3.35 tff(18645,plain,
% 3.07/3.35 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18644, 333, 18628, 11546, 51])).
% 3.07/3.35 tff(18646,plain,
% 3.07/3.35 ($false),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18645, 18638])).
% 3.07/3.35 tff(18647,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = elem!1) | r(z, elem!1) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.35 tff(18648,plain,
% 3.07/3.35 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18647, 11546, 51, 2725, 1699, 562, 1249, 706, 1575, 18565, 18566, 1221, 959, 502])).
% 3.07/3.35 tff(18649,plain,
% 3.07/3.35 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[6626, 333, 562, 1699, 18648])).
% 3.07/3.35 tff(18650,plain,
% 3.07/3.35 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1137, 18649])).
% 3.07/3.35 tff(18651,plain,
% 3.07/3.35 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[6618, 333, 562, 1699, 18648])).
% 3.07/3.35 tff(18652,plain,
% 3.07/3.35 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[249, 18651])).
% 3.07/3.35 tff(18653,plain,
% 3.07/3.35 (~b(s(elem!1), s(s(s(z))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[9088, 144, 18652, 18650, 18565])).
% 3.07/3.35 tff(18654,plain,
% 3.07/3.35 (s(elem!1) = s(s(s(z)))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[965, 18653, 959])).
% 3.07/3.35 tff(18655,plain,
% 3.07/3.35 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18654])).
% 3.07/3.35 tff(18656,plain,
% 3.07/3.35 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18655])).
% 3.07/3.35 tff(18657,plain,
% 3.07/3.35 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 3.07/3.35 inference(symmetry,[status(thm)],[18656])).
% 3.07/3.35 tff(18658,plain,
% 3.07/3.35 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(elem!1))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18657])).
% 3.07/3.35 tff(18659,plain,
% 3.07/3.35 (s(s(s(z))) = s(elem!1)),
% 3.07/3.35 inference(symmetry,[status(thm)],[18654])).
% 3.07/3.35 tff(18660,plain,
% 3.07/3.35 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18659])).
% 3.07/3.35 tff(18661,plain,
% 3.07/3.35 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.35 inference(symmetry,[status(thm)],[18660])).
% 3.07/3.35 tff(18662,plain,
% 3.07/3.35 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18655])).
% 3.07/3.35 tff(18663,plain,
% 3.07/3.35 (b(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[1249, 18662])).
% 3.07/3.35 tff(18664,plain,
% 3.07/3.35 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18663, 18661])).
% 3.07/3.35 tff(18665,plain,
% 3.07/3.35 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18464, 144, 18652, 18650])).
% 3.07/3.35 tff(18666,plain,
% 3.07/3.35 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18665, 18664])).
% 3.07/3.35 tff(18667,plain,
% 3.07/3.35 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18655])).
% 3.07/3.35 tff(18668,plain,
% 3.07/3.35 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(transitivity,[status(thm)],[18667, 12720])).
% 3.07/3.35 tff(18669,plain,
% 3.07/3.35 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18668])).
% 3.07/3.35 tff(18670,plain,
% 3.07/3.35 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[2725, 18669])).
% 3.07/3.35 tff(18671,plain,
% 3.07/3.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[3556, 44, 18670, 18666])).
% 3.07/3.35 tff(18672,plain,
% 3.07/3.35 (~r(z, s(s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[4250, 333, 18648, 51, 18671])).
% 3.07/3.35 tff(18673,plain,
% 3.07/3.35 (b(z, s(s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[4259, 18672, 4255])).
% 3.07/3.35 tff(18674,plain,
% 3.07/3.35 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18654])).
% 3.07/3.35 tff(18675,plain,
% 3.07/3.35 (~r(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[17877, 333, 11546, 18648, 51])).
% 3.07/3.35 tff(18676,plain,
% 3.07/3.35 (b(s(z), z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[348, 18675])).
% 3.07/3.35 tff(18677,plain,
% 3.07/3.35 (~(z = elem!1)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18064, 18676, 502])).
% 3.07/3.35 tff(18678,plain,
% 3.07/3.35 (~(s(elem!1) = s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[8683, 18677])).
% 3.07/3.35 tff(18679,plain,
% 3.07/3.35 (~(s(z) = s(elem!1))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1228, 18678])).
% 3.07/3.35 tff(18680,plain,
% 3.07/3.35 (b(z, elem!1)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[658, 18677, 1575])).
% 3.07/3.35 tff(18681,plain,
% 3.07/3.35 (~(elem!1 = z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[76, 18677])).
% 3.07/3.35 tff(18682,plain,
% 3.07/3.35 (b(elem!1, z)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1380, 18681, 1378])).
% 3.07/3.35 tff(18683,plain,
% 3.07/3.35 (~b(s(z), elem!1)),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1602, 18682, 18676, 18680])).
% 3.07/3.35 tff(18684,plain,
% 3.07/3.35 (~r(z, s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[15183, 18648, 11546, 51])).
% 3.07/3.35 tff(18685,plain,
% 3.07/3.35 (b(z, s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[372, 18684])).
% 3.07/3.35 tff(18686,plain,
% 3.07/3.35 (~b(elem!1, s(z))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[387, 144, 18682, 18685, 18676])).
% 3.07/3.35 tff(18687,plain,
% 3.07/3.35 (~r(s(z), s(elem!1))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[7675, 18686, 706, 435, 18683])).
% 3.07/3.35 tff(18688,plain,
% 3.07/3.35 (b(s(z), s(elem!1))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[1244, 18687, 18679])).
% 3.07/3.35 tff(18689,plain,
% 3.07/3.35 (b(s(z), s(s(s(z))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18688, 18674])).
% 3.07/3.35 tff(18690,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18691,plain,
% 3.07/3.35 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), 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(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18692,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18691])).
% 3.07/3.35 tff(18693,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.07/3.35 inference(transitivity,[status(thm)],[18692, 18690])).
% 3.07/3.35 tff(18694,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 3.07/3.35 inference(quant_inst,[status(thm)],[])).
% 3.07/3.35 tff(18695,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18694, 18693])).
% 3.07/3.35 tff(18696,plain,
% 3.07/3.35 (~b(s(z), s(s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18695, 144, 18676, 18689, 18673, 18664])).
% 3.07/3.35 tff(18697,plain,
% 3.07/3.35 (~b(s(z), s(s(elem!1)))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18696, 18658])).
% 3.07/3.35 tff(18698,plain,
% 3.07/3.35 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18655])).
% 3.07/3.35 tff(18699,plain,
% 3.07/3.35 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 3.07/3.35 inference(symmetry,[status(thm)],[18698])).
% 3.07/3.35 tff(18700,plain,
% 3.07/3.35 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(s(elem!1))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18699])).
% 3.07/3.35 tff(18701,plain,
% 3.07/3.35 (((~![X0: $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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18702,plain,
% 3.07/3.35 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(18703,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[18702])).
% 3.07/3.35 tff(18704,plain,
% 3.07/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.35 inference(transitivity,[status(thm)],[18703, 18701])).
% 3.07/3.35 tff(18705,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.07/3.35 inference(quant_inst,[status(thm)],[])).
% 3.07/3.35 tff(18706,plain,
% 3.07/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18705, 18704])).
% 3.07/3.35 tff(18707,plain,
% 3.07/3.35 (~r(s(z), s(s(s(s(z)))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18706, 333, 11546, 18648, 18671])).
% 3.07/3.35 tff(18708,plain,
% 3.07/3.35 (~r(s(z), s(s(elem!1)))),
% 3.07/3.35 inference(modus_ponens,[status(thm)],[18707, 18700])).
% 3.07/3.35 tff(18709,plain,
% 3.07/3.35 (b(s(z), s(s(elem!1)))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[5484, 18708])).
% 3.07/3.35 tff(18710,plain,
% 3.07/3.35 ($false),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18709, 18697])).
% 3.07/3.35 tff(18711,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(z)))) | r(elem!1, z) | r(z, elem!1) | b(s(elem!1), z) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.35 tff(18712,plain,
% 3.07/3.35 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.35 inference(unit_resolution,[status(thm)],[18711, 18521, 2725, 1249, 706, 435, 959, 1378, 1575, 502, 51, 1699, 1221, 466])).
% 3.07/3.36 tff(18713,plain,
% 3.07/3.36 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[49, 18712])).
% 3.07/3.36 tff(18714,plain,
% 3.07/3.36 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18522])).
% 3.07/3.36 tff(18715,plain,
% 3.07/3.36 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[450, 18714])).
% 3.07/3.36 tff(18716,plain,
% 3.07/3.36 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[2262, 18715, 18713, 18528])).
% 3.07/3.36 tff(18717,plain,
% 3.07/3.36 ($false),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[249, 18716, 18526])).
% 3.07/3.36 tff(18718,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = elem!1) | r(s(elem!1), s(s(s(z)))) | r(elem!1, z) | r(z, elem!1) | b(s(elem!1), z) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.36 tff(18719,plain,
% 3.07/3.36 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18718, 323, 435, 1699, 5465, 2725, 1249, 706, 959, 18017, 1575, 502, 1221, 466, 18507, 1])).
% 3.07/3.36 tff(18720,plain,
% 3.07/3.36 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[278, 18719, 274])).
% 3.07/3.36 tff(18721,plain,
% 3.07/3.36 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[6809, 144, 18018, 286, 18720])).
% 3.07/3.36 tff(18722,plain,
% 3.07/3.36 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[121, 18721, 18388])).
% 3.07/3.36 tff(18723,plain,
% 3.07/3.36 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[880, 286, 18018, 1594])).
% 3.07/3.36 tff(18724,plain,
% 3.07/3.36 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[130, 18723, 18436])).
% 3.07/3.36 tff(18725,plain,
% 3.07/3.36 (((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18726,plain,
% 3.07/3.36 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18727,plain,
% 3.07/3.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18726])).
% 3.07/3.36 tff(18728,plain,
% 3.07/3.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(transitivity,[status(thm)],[18727, 18725])).
% 3.07/3.36 tff(18729,plain,
% 3.07/3.36 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(quant_inst,[status(thm)],[])).
% 3.07/3.36 tff(18730,plain,
% 3.07/3.36 ((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18729, 18728])).
% 3.07/3.36 tff(18731,plain,
% 3.07/3.36 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18730, 333, 707, 18724, 18722])).
% 3.07/3.36 tff(18732,plain,
% 3.07/3.36 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1137, 18731])).
% 3.07/3.36 tff(18733,plain,
% 3.07/3.36 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18734,plain,
% 3.07/3.36 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18735,plain,
% 3.07/3.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18734])).
% 3.07/3.36 tff(18736,plain,
% 3.07/3.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(transitivity,[status(thm)],[18735, 18733])).
% 3.07/3.36 tff(18737,plain,
% 3.07/3.36 ((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.07/3.36 inference(quant_inst,[status(thm)],[])).
% 3.07/3.36 tff(18738,plain,
% 3.07/3.36 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18737, 18736])).
% 3.07/3.36 tff(18739,plain,
% 3.07/3.36 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18738, 333, 707, 18724, 18722])).
% 3.07/3.36 tff(18740,plain,
% 3.07/3.36 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[249, 18739])).
% 3.07/3.36 tff(18741,plain,
% 3.07/3.36 (~b(s(elem!1), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[9088, 144, 18740, 18732, 5465])).
% 3.07/3.36 tff(18742,plain,
% 3.07/3.36 (s(elem!1) = s(s(s(z)))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[965, 18741, 959])).
% 3.07/3.36 tff(18743,plain,
% 3.07/3.36 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18742])).
% 3.07/3.36 tff(18744,plain,
% 3.07/3.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.07/3.36 inference(symmetry,[status(thm)],[18743])).
% 3.07/3.36 tff(18745,plain,
% 3.07/3.36 (s(s(z)) = elem!1),
% 3.07/3.36 inference(transitivity,[status(thm)],[87, 18744, 850])).
% 3.07/3.36 tff(18746,plain,
% 3.07/3.36 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18745])).
% 3.07/3.36 tff(18747,plain,
% 3.07/3.36 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 3.07/3.36 inference(symmetry,[status(thm)],[18746])).
% 3.07/3.36 tff(18748,plain,
% 3.07/3.36 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18742])).
% 3.07/3.36 tff(18749,plain,
% 3.07/3.36 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[15009, 333, 435, 18724, 18722])).
% 3.07/3.36 tff(18750,plain,
% 3.07/3.36 (~b(z, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[8386, 18749, 18720, 466, 537])).
% 3.07/3.36 tff(18751,plain,
% 3.07/3.36 (r(z, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[583, 18750])).
% 3.07/3.36 tff(18752,plain,
% 3.07/3.36 (~r(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1938, 333, 323, 12191, 18751])).
% 3.07/3.36 tff(18753,plain,
% 3.07/3.36 (b(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1244, 18752, 1229])).
% 3.07/3.36 tff(18754,plain,
% 3.07/3.36 (b(s(z), s(s(s(z))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18753, 18748])).
% 3.07/3.36 tff(18755,plain,
% 3.07/3.36 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[2262, 18754, 18740, 18732])).
% 3.07/3.36 tff(18756,plain,
% 3.07/3.36 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[49, 18755])).
% 3.07/3.36 tff(18757,plain,
% 3.07/3.36 (~r(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18406, 18756, 322, 18722])).
% 3.07/3.36 tff(18758,plain,
% 3.07/3.36 (b(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[406, 18757, 706])).
% 3.07/3.36 tff(18759,plain,
% 3.07/3.36 (~b(elem!1, s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[7079, 18758, 18507, 1594])).
% 3.07/3.36 tff(18760,plain,
% 3.07/3.36 (r(elem!1, s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[720, 18759, 713])).
% 3.07/3.36 tff(18761,plain,
% 3.07/3.36 (r(s(s(z)), s(z))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18760, 18747])).
% 3.07/3.36 tff(18762,plain,
% 3.07/3.36 (elem!1 = s(s(z))),
% 3.07/3.36 inference(transitivity,[status(thm)],[1193, 18743, 86])).
% 3.07/3.36 tff(18763,plain,
% 3.07/3.36 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18762])).
% 3.07/3.36 tff(18764,plain,
% 3.07/3.36 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18722, 18763])).
% 3.07/3.36 tff(18765,plain,
% 3.07/3.36 (~r(s(s(z)), s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[17910, 333, 18764, 18756, 322])).
% 3.07/3.36 tff(18766,plain,
% 3.07/3.36 ($false),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18765, 18761])).
% 3.07/3.36 tff(18767,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | r(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | r(z, elem!1) | b(s(elem!1), z) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.36 tff(18768,plain,
% 3.07/3.36 (~r(s(z), z)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18767, 18047, 706, 959, 466, 322, 707, 435, 2097, 1699, 2725, 1249, 1575, 502, 1221, 1])).
% 3.07/3.36 tff(18769,plain,
% 3.07/3.36 (b(s(z), z)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[348, 18768])).
% 3.07/3.36 tff(18770,plain,
% 3.07/3.36 (~b(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1602, 18769, 18018, 1594])).
% 3.07/3.36 tff(18771,plain,
% 3.07/3.36 (r(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[406, 18770, 706])).
% 3.07/3.36 tff(18772,plain,
% 3.07/3.36 (~b(elem!1, s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[387, 144, 18018, 18507, 18769])).
% 3.07/3.36 tff(18773,plain,
% 3.07/3.36 (~r(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[7675, 18772, 706, 435, 18770])).
% 3.07/3.36 tff(18774,plain,
% 3.07/3.36 (b(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1244, 18773, 1229])).
% 3.07/3.36 tff(18775,plain,
% 3.07/3.36 ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[3220, 144, 18769, 2097, 18049])).
% 3.07/3.36 tff(18776,plain,
% 3.07/3.36 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18775, 18774])).
% 3.07/3.36 tff(18777,plain,
% 3.07/3.36 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[49, 18776])).
% 3.07/3.36 tff(18778,plain,
% 3.07/3.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18406, 18777, 322, 18771])).
% 3.07/3.36 tff(18779,plain,
% 3.07/3.36 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[121, 18778, 18388])).
% 3.07/3.36 tff(18780,plain,
% 3.07/3.36 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[2710, 144, 18018, 2097, 18049])).
% 3.07/3.36 tff(18781,plain,
% 3.07/3.36 (~b(elem!1, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18780, 18779])).
% 3.07/3.36 tff(18782,plain,
% 3.07/3.36 (r(elem!1, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[560, 18781, 13418])).
% 3.07/3.36 tff(18783,plain,
% 3.07/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18784,plain,
% 3.07/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.07/3.36 inference(quant_inst,[status(thm)],[])).
% 3.07/3.36 tff(18785,plain,
% 3.07/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18784, 18783])).
% 3.07/3.36 tff(18786,plain,
% 3.07/3.36 ($false),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18785, 333, 18782, 18771, 18509, 322])).
% 3.07/3.36 tff(18787,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | r(z, elem!1) | b(s(elem!1), z) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.36 tff(18788,plain,
% 3.07/3.36 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18787, 1, 706, 435, 959, 466, 707, 1699, 2725, 1249, 1575, 502, 1221, 322])).
% 3.07/3.36 tff(18789,plain,
% 3.07/3.36 (~b(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1602, 489, 18018, 1594])).
% 3.07/3.36 tff(18790,plain,
% 3.07/3.36 (~b(elem!1, s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[387, 144, 18018, 18507, 489])).
% 3.07/3.36 tff(18791,plain,
% 3.07/3.36 (~r(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[7675, 18790, 706, 435, 18789])).
% 3.07/3.36 tff(18792,plain,
% 3.07/3.36 (b(s(z), s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1244, 18791, 1229])).
% 3.07/3.36 tff(18793,plain,
% 3.07/3.36 (r(elem!1, s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[720, 18790, 713])).
% 3.07/3.36 tff(18794,plain,
% 3.07/3.36 (r(s(z), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[406, 18789, 706])).
% 3.07/3.36 tff(18795,plain,
% 3.07/3.36 (~r(s(elem!1), s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[7864, 333, 435, 18794, 18793])).
% 3.07/3.36 tff(18796,plain,
% 3.07/3.36 (b(s(elem!1), s(z))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[486, 18795, 1])).
% 3.07/3.36 tff(18797,plain,
% 3.07/3.36 (~b(z, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1853, 18796, 18507, 18792])).
% 3.07/3.36 tff(18798,plain,
% 3.07/3.36 (r(z, s(elem!1))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[583, 18797])).
% 3.07/3.36 tff(18799,plain,
% 3.07/3.36 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[6626, 333, 18798, 1699, 18788])).
% 3.07/3.36 tff(18800,plain,
% 3.07/3.36 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[1137, 18799])).
% 3.07/3.36 tff(18801,plain,
% 3.07/3.36 (~r(s(z), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[835, 333, 18794, 18793, 707])).
% 3.07/3.36 tff(18802,plain,
% 3.07/3.36 (b(s(z), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[170, 44, 167, 18801])).
% 3.07/3.36 tff(18803,plain,
% 3.07/3.36 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[6618, 333, 18798, 1699, 18788])).
% 3.07/3.36 tff(18804,plain,
% 3.07/3.36 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[249, 18803])).
% 3.07/3.36 tff(18805,plain,
% 3.07/3.36 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[2262, 18804, 18802, 18800])).
% 3.07/3.36 tff(18806,plain,
% 3.07/3.36 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(elem!1, 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18807,plain,
% 3.07/3.36 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(18808,plain,
% 3.07/3.36 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[18807])).
% 3.07/3.36 tff(18809,plain,
% 3.07/3.36 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(transitivity,[status(thm)],[18808, 18806])).
% 3.07/3.36 tff(18810,plain,
% 3.07/3.36 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.36 inference(quant_inst,[status(thm)],[])).
% 3.07/3.36 tff(18811,plain,
% 3.07/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.36 inference(modus_ponens,[status(thm)],[18810, 18809])).
% 3.07/3.36 tff(18812,plain,
% 3.07/3.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[18811, 333, 18794, 18793, 322])).
% 3.07/3.36 tff(18813,plain,
% 3.07/3.36 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[121, 18812, 18388])).
% 3.07/3.36 tff(18814,plain,
% 3.07/3.36 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[12170, 333, 18794, 18793, 322])).
% 3.07/3.36 tff(18815,plain,
% 3.07/3.36 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[130, 18814, 18436])).
% 3.07/3.36 tff(18816,plain,
% 3.07/3.36 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[265, 144, 1594, 18815, 18813])).
% 3.07/3.36 tff(18817,plain,
% 3.07/3.36 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.36 inference(unit_resolution,[status(thm)],[278, 18816, 274])).
% 3.07/3.36 tff(18818,plain,
% 3.07/3.36 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18711, 18817, 2725, 1249, 706, 435, 959, 18017, 1575, 502, 18798, 1699, 1221, 466])).
% 3.07/3.37 tff(18819,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[49, 18818, 18805])).
% 3.07/3.37 tff(18820,plain,((~b(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(z)))) | r(z, elem!1) | b(s(elem!1), z) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18821,plain,
% 3.07/3.37 (~b(s(z), z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18820, 1, 1249, 706, 435, 959, 1575, 502, 1699, 1221, 466, 2725, 707, 322])).
% 3.07/3.37 tff(18822,plain,
% 3.07/3.37 (r(s(z), z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[348, 18821])).
% 3.07/3.37 tff(18823,plain,
% 3.07/3.37 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[341, 18822, 322, 18788])).
% 3.07/3.37 tff(18824,plain,
% 3.07/3.37 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[278, 18823, 274])).
% 3.07/3.37 tff(18825,plain,
% 3.07/3.37 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[820, 18822, 322, 713, 18507, 1594, 18824, 18436])).
% 3.07/3.37 tff(18826,plain,
% 3.07/3.37 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[49, 18825])).
% 3.07/3.37 tff(18827,plain,
% 3.07/3.37 (~r(s(z), elem!1)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18406, 2323, 322, 11546])).
% 3.07/3.37 tff(18828,plain,
% 3.07/3.37 (b(s(z), elem!1)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[406, 18827, 706])).
% 3.07/3.37 tff(18829,plain,
% 3.07/3.37 (~b(elem!1, s(z))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[7079, 18828, 490, 251])).
% 3.07/3.37 tff(18830,plain,
% 3.07/3.37 (r(elem!1, s(z))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[720, 18829, 713])).
% 3.07/3.37 tff(18831,plain,
% 3.07/3.37 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18832,plain,
% 3.07/3.37 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18833,plain,
% 3.07/3.37 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18832])).
% 3.07/3.37 tff(18834,plain,
% 3.07/3.37 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(transitivity,[status(thm)],[18833, 18831])).
% 3.07/3.37 tff(18835,plain,
% 3.07/3.37 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 3.07/3.37 inference(quant_inst,[status(thm)],[])).
% 3.07/3.37 tff(18836,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18835, 18834])).
% 3.07/3.37 tff(18837,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18836, 333, 18830, 11546, 2323, 322])).
% 3.07/3.37 tff(18838,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18839,plain,
% 3.07/3.37 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18838, 18826, 322, 18507, 1594, 706])).
% 3.07/3.37 tff(18840,plain,
% 3.07/3.37 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[121, 18839, 18388])).
% 3.07/3.37 tff(18841,plain,
% 3.07/3.37 (~b(s(z), elem!1)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[14578, 1594, 18507, 18840, 18824])).
% 3.07/3.37 tff(18842,plain,
% 3.07/3.37 (r(s(z), elem!1)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[406, 18841, 706])).
% 3.07/3.37 tff(18843,plain,
% 3.07/3.37 (~r(z, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[8274, 18822, 322, 18788])).
% 3.07/3.37 tff(18844,plain,
% 3.07/3.37 (b(z, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[583, 18843])).
% 3.07/3.37 tff(18845,plain,
% 3.07/3.37 (~r(z, s(s(s(z))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[642, 18822, 322, 18788])).
% 3.07/3.37 tff(18846,plain,
% 3.07/3.37 (b(z, s(s(s(z))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[619, 18845])).
% 3.07/3.37 tff(18847,plain,
% 3.07/3.37 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[6165])).
% 3.07/3.37 tff(18848,plain,
% 3.07/3.37 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(symmetry,[status(thm)],[18847])).
% 3.07/3.37 tff(18849,plain,
% 3.07/3.37 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[132, 18848])).
% 3.07/3.37 tff(18850,plain,
% 3.07/3.37 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, elem!1)),
% 3.07/3.37 inference(monotonicity,[status(thm)],[6165])).
% 3.07/3.37 tff(18851,plain,
% 3.07/3.37 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(z)))))))),
% 3.07/3.37 inference(symmetry,[status(thm)],[18850])).
% 3.07/3.37 tff(18852,plain,
% 3.07/3.37 (b(z, s(s(s(s(s(s(z)))))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[251, 18851])).
% 3.07/3.37 tff(18853,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18854,plain,
% 3.07/3.37 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18855,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18854])).
% 3.07/3.37 tff(18856,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.37 inference(transitivity,[status(thm)],[18855, 18853])).
% 3.07/3.37 tff(18857,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 3.07/3.37 inference(quant_inst,[status(thm)],[])).
% 3.07/3.37 tff(18858,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18857, 18856])).
% 3.07/3.37 tff(18859,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18858, 144, 284, 5992, 259, 18852, 18849])).
% 3.07/3.37 tff(18860,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18861,plain,
% 3.07/3.37 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18860, 18846, 18824, 18840, 1594, 959])).
% 3.07/3.37 tff(18862,plain,
% 3.07/3.37 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[472, 18861, 466])).
% 3.07/3.37 tff(18863,plain,
% 3.07/3.37 (~b(s(elem!1), s(z))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[1853, 585, 490, 1262])).
% 3.07/3.37 tff(18864,plain,
% 3.07/3.37 (r(s(elem!1), s(z))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[486, 18863, 1])).
% 3.07/3.37 tff(18865,plain,
% 3.07/3.37 (~r(elem!1, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[1390, 18864, 435, 409])).
% 3.07/3.37 tff(18866,plain,
% 3.07/3.37 (b(elem!1, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[560, 18865, 902])).
% 3.07/3.37 tff(18867,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[5287, 144, 18866, 624, 585, 132, 450])).
% 3.07/3.37 tff(18868,plain,((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18869,plain,
% 3.07/3.37 (~b(s(z), s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18868, 18862, 18840, 18844, 13418, 435, 18842, 1, 18507, 18018])).
% 3.07/3.37 tff(18870,plain,
% 3.07/3.37 (r(s(z), s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[1244, 18869, 1229])).
% 3.07/3.37 tff(18871,plain,
% 3.07/3.37 (~b(elem!1, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[5287, 144, 18018, 18844, 18840, 18862])).
% 3.07/3.37 tff(18872,plain,
% 3.07/3.37 (r(elem!1, s(elem!1))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[560, 18871, 13418])).
% 3.07/3.37 tff(18873,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18874,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 3.07/3.37 inference(quant_inst,[status(thm)],[])).
% 3.07/3.37 tff(18875,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18874, 18873])).
% 3.07/3.37 tff(18876,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18875, 333, 18872, 435, 18842, 18870])).
% 3.07/3.37 tff(18877,plain,((s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(z)))) | (s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | r(z, elem!1) | b(s(elem!1), z) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18878,plain,
% 3.07/3.37 (s(elem!1) = s(z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18877, 322, 466, 959, 706, 435, 1249, 1575, 502, 1699, 1221, 2725, 707])).
% 3.07/3.37 tff(18879,plain,
% 3.07/3.37 (z = elem!1),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[8683, 18878])).
% 3.07/3.37 tff(18880,plain,
% 3.07/3.37 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18879])).
% 3.07/3.37 tff(18881,plain,
% 3.07/3.37 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18880])).
% 3.07/3.37 tff(18882,plain,
% 3.07/3.37 (~(s(s(z)) = elem!1)),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[164, 18881])).
% 3.07/3.37 tff(18883,plain,
% 3.07/3.37 (~(elem!1 = s(s(z)))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18882, 17962])).
% 3.07/3.37 tff(18884,plain,
% 3.07/3.37 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18878])).
% 3.07/3.37 tff(18885,plain,
% 3.07/3.37 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18884])).
% 3.07/3.37 tff(18886,plain,
% 3.07/3.37 (~r(s(z), s(s(s(z))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[959, 18885])).
% 3.07/3.37 tff(18887,plain,
% 3.07/3.37 (b(s(z), s(s(s(z))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[170, 44, 167, 18886])).
% 3.07/3.37 tff(18888,plain,
% 3.07/3.37 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18125])).
% 3.07/3.37 tff(18889,plain,
% 3.07/3.37 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 3.07/3.37 inference(symmetry,[status(thm)],[18888])).
% 3.07/3.37 tff(18890,plain,
% 3.07/3.37 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[8677])).
% 3.07/3.37 tff(18891,plain,
% 3.07/3.37 (b(s(s(elem!1)), s(z))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[1249, 18890])).
% 3.07/3.37 tff(18892,plain,
% 3.07/3.37 (b(s(s(z)), s(z))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18891, 18889])).
% 3.07/3.37 tff(18893,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 3.07/3.37 tff(18894,plain,
% 3.07/3.37 ($false),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18893, 18892])).
% 3.07/3.37 tff(18895,plain,((~(s(elem!1) = s(z))) | b(s(s(z)), s(z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.37 tff(18896,plain,
% 3.07/3.37 (b(s(s(z)), s(z))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18895, 18878, 1249])).
% 3.07/3.37 tff(18897,plain,
% 3.07/3.37 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18879])).
% 3.07/3.37 tff(18898,plain,
% 3.07/3.37 (b(elem!1, s(z))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18507, 18897])).
% 3.07/3.37 tff(18899,plain,
% 3.07/3.37 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18879])).
% 3.07/3.37 tff(18900,plain,
% 3.07/3.37 (~b(s(z), z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18064, 18879, 502])).
% 3.07/3.37 tff(18901,plain,
% 3.07/3.37 (r(s(z), z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[348, 18900])).
% 3.07/3.37 tff(18902,plain,
% 3.07/3.37 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18879])).
% 3.07/3.37 tff(18903,plain,
% 3.07/3.37 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 3.07/3.37 inference(symmetry,[status(thm)],[18902])).
% 3.07/3.37 tff(18904,plain,
% 3.07/3.37 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18903])).
% 3.07/3.37 tff(18905,plain,
% 3.07/3.37 (~b(elem!1, z)),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[5882, 18904])).
% 3.07/3.37 tff(18906,plain,
% 3.07/3.37 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18297, 18905, 1575, 435, 1699, 1221, 959, 1249, 502, 466])).
% 3.07/3.37 tff(18907,plain,
% 3.07/3.37 (~r(z, s(s(s(z))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[642, 18906, 322, 18901])).
% 3.07/3.37 tff(18908,plain,
% 3.07/3.37 (b(z, s(s(s(z))))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[619, 18907])).
% 3.07/3.37 tff(18909,plain,
% 3.07/3.37 (b(elem!1, s(s(s(z))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18908, 18899])).
% 3.07/3.37 tff(18910,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18911,plain,
% 3.07/3.37 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18912,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))))),
% 3.07/3.37 inference(monotonicity,[status(thm)],[18911])).
% 3.07/3.37 tff(18913,plain,
% 3.07/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 3.07/3.37 inference(transitivity,[status(thm)],[18912, 18910])).
% 3.07/3.37 tff(18914,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 3.07/3.37 inference(quant_inst,[status(thm)],[])).
% 3.07/3.37 tff(18915,plain,
% 3.07/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18914, 18913])).
% 3.07/3.37 tff(18916,plain,
% 3.07/3.37 (~b(elem!1, s(s(z)))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18915, 144, 18909, 18898, 18896, 18887])).
% 3.07/3.37 tff(18917,plain,
% 3.07/3.37 (((~![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))))),
% 3.07/3.37 inference(rewrite,[status(thm)],[])).
% 3.07/3.37 tff(18918,plain,
% 3.07/3.37 ((~![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))))),
% 3.07/3.37 inference(quant_inst,[status(thm)],[])).
% 3.07/3.37 tff(18919,plain,
% 3.07/3.37 ((~![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)))),
% 3.07/3.37 inference(modus_ponens,[status(thm)],[18918, 18917])).
% 3.07/3.37 tff(18920,plain,
% 3.07/3.37 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18919, 44, 18916])).
% 3.07/3.37 tff(18921,plain,
% 3.07/3.37 (r(elem!1, s(s(z)))),
% 3.07/3.37 inference(unit_resolution,[status(thm)],[18920, 18883])).
% 3.07/3.38 tff(18922,plain,
% 3.07/3.38 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.38 inference(monotonicity,[status(thm)],[18879])).
% 3.07/3.38 tff(18923,plain,
% 3.07/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18906, 18922])).
% 3.07/3.38 tff(18924,plain,
% 3.07/3.38 (r(s(z), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18039, 18878, 435])).
% 3.07/3.38 tff(18925,plain,
% 3.07/3.38 (((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18926,plain,
% 3.07/3.38 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18927,plain,
% 3.07/3.38 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[18926])).
% 3.07/3.38 tff(18928,plain,
% 3.07/3.38 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.07/3.38 inference(transitivity,[status(thm)],[18927, 18925])).
% 3.07/3.38 tff(18929,plain,
% 3.07/3.38 ((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.07/3.38 inference(quant_inst,[status(thm)],[])).
% 3.07/3.38 tff(18930,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18929, 18928])).
% 3.07/3.38 tff(18931,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18930, 333, 18924, 18923, 322, 18921])).
% 3.07/3.38 tff(18932,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18933,plain,
% 3.07/3.38 (~b(s(s(elem!1)), s(elem!1))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18932, 17959, 17955, 1575, 17941, 15133, 17896, 17956, 17889, 17948, 17944, 17869])).
% 3.07/3.38 tff(18934,plain,
% 3.07/3.38 (r(s(s(elem!1)), s(elem!1))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[1283, 18933, 17943])).
% 3.07/3.38 tff(18935,plain,
% 3.07/3.38 (r(s(s(s(s(z)))), s(elem!1))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18934, 17940])).
% 3.07/3.38 tff(18936,plain,
% 3.07/3.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18935, 17938])).
% 3.07/3.38 tff(18937,plain,
% 3.07/3.38 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[17939])).
% 3.07/3.38 tff(18938,plain,
% 3.07/3.38 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[17935])).
% 3.07/3.38 tff(18939,plain,
% 3.07/3.38 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 3.07/3.38 inference(symmetry,[status(thm)],[18938])).
% 3.07/3.38 tff(18940,plain,
% 3.07/3.38 (r(z, s(elem!1))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[623, 18939])).
% 3.07/3.38 tff(18941,plain,
% 3.07/3.38 (~b(elem!1, s(s(elem!1)))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[5640, 18934, 17955, 18940, 624])).
% 3.07/3.38 tff(18942,plain,
% 3.07/3.38 (r(elem!1, s(s(elem!1)))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[2522, 18941, 17959])).
% 3.07/3.38 tff(18943,plain,
% 3.07/3.38 (r(elem!1, s(s(s(s(z)))))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18942, 18937])).
% 3.07/3.38 tff(18944,plain,
% 3.07/3.38 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18945,plain,
% 3.07/3.38 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18946,plain,
% 3.07/3.38 (((~![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(elem!1, 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(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[18945])).
% 3.07/3.38 tff(18947,plain,
% 3.07/3.38 (((~![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(elem!1, 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(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.07/3.38 inference(transitivity,[status(thm)],[18946, 18944])).
% 3.07/3.38 tff(18948,plain,
% 3.07/3.38 ((~![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(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.07/3.38 inference(quant_inst,[status(thm)],[])).
% 3.07/3.38 tff(18949,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18948, 18947])).
% 3.07/3.38 tff(18950,plain,
% 3.07/3.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18949, 333, 17926, 17889, 18943])).
% 3.07/3.38 tff(18951,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18950, 18936])).
% 3.07/3.38 tff(18952,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(elem!1, z)) | r(z, elem!1) | (s(elem!1) = s(z)) | (~r(z, s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18953,plain,
% 3.07/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18952, 7926, 1575, 1, 623, 624, 698, 3])).
% 3.07/3.38 tff(18954,plain,
% 3.07/3.38 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18955,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[18954])).
% 3.07/3.38 tff(18956,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.38 inference(transitivity,[status(thm)],[18955, 8760])).
% 3.07/3.38 tff(18957,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))))),
% 3.07/3.38 inference(quant_inst,[status(thm)],[])).
% 3.07/3.38 tff(18958,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18957, 18956])).
% 3.07/3.38 tff(18959,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18958, 144, 2082, 132, 283, 2254])).
% 3.07/3.38 tff(18960,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18961,plain,
% 3.07/3.38 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18960, 2082, 132, 283])).
% 3.07/3.38 tff(18962,plain,
% 3.07/3.38 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[1137, 18961])).
% 3.07/3.38 tff(18963,plain,
% 3.07/3.38 (~r(s(s(s(z))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[17809, 18962, 11546, 2484])).
% 3.07/3.38 tff(18964,plain,
% 3.07/3.38 (b(s(s(s(z))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[2794, 18963])).
% 3.07/3.38 tff(18965,plain,
% 3.07/3.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[846, 838, 283, 56])).
% 3.07/3.38 tff(18966,plain,
% 3.07/3.38 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[319, 18965])).
% 3.07/3.38 tff(18967,plain,
% 3.07/3.38 (~r(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[12830, 18966, 624, 706, 251, 2484])).
% 3.07/3.38 tff(18968,plain,
% 3.07/3.38 (b(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[720, 18967, 713])).
% 3.07/3.38 tff(18969,plain,
% 3.07/3.38 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(18970,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[18969])).
% 3.07/3.38 tff(18971,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 3.07/3.38 inference(transitivity,[status(thm)],[18970, 17824])).
% 3.07/3.38 tff(18972,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 3.07/3.38 inference(quant_inst,[status(thm)],[])).
% 3.07/3.38 tff(18973,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 3.07/3.38 inference(modus_ponens,[status(thm)],[18972, 18971])).
% 3.07/3.38 tff(18974,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18973, 144, 2082, 18968, 56, 838])).
% 3.07/3.38 tff(18975,plain,((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18976,plain,
% 3.07/3.38 (~b(s(z), s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18975, 18964, 2082, 624, 706, 251, 2484, 283])).
% 3.07/3.38 tff(18977,plain,
% 3.07/3.38 (r(s(z), s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[172, 18976])).
% 3.07/3.38 tff(18978,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[17817, 333, 18977, 11546, 2484, 18962])).
% 3.07/3.38 tff(18979,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (s(z) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18980,plain,
% 3.07/3.38 (~b(elem!1, s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18979, 18953, 15126, 624, 15133, 13636, 17795, 17789])).
% 3.07/3.38 tff(18981,plain,
% 3.07/3.38 (r(elem!1, s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[1538, 18980, 12398])).
% 3.07/3.38 tff(18982,plain,
% 3.07/3.38 (~r(s(z), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[17853, 18981, 15126, 18953])).
% 3.07/3.38 tff(18983,plain,
% 3.07/3.38 (b(s(z), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[406, 18982, 15133])).
% 3.07/3.38 tff(18984,plain,
% 3.07/3.38 (~b(s(z), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[1602, 18983, 624, 13636])).
% 3.07/3.38 tff(18985,plain,
% 3.07/3.38 (r(s(z), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[348, 18984])).
% 3.07/3.38 tff(18986,plain,
% 3.07/3.38 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[15633, 322, 11546, 323])).
% 3.07/3.38 tff(18987,plain,
% 3.07/3.38 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[279, 18986])).
% 3.07/3.38 tff(18988,plain,
% 3.07/3.38 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[642, 322, 623, 323])).
% 3.07/3.38 tff(18989,plain,
% 3.07/3.38 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[302, 18988])).
% 3.07/3.38 tff(18990,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[14405, 18989, 18987, 132, 624])).
% 3.07/3.38 tff(18991,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(18992,plain,
% 3.07/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18991, 18985, 624, 623, 17789, 15126])).
% 3.07/3.38 tff(18993,plain,
% 3.07/3.38 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[319, 18992])).
% 3.07/3.38 tff(18994,plain,
% 3.07/3.38 (~r(z, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[1519, 353, 623, 8303])).
% 3.07/3.38 tff(18995,plain,
% 3.07/3.38 (b(z, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[372, 18994])).
% 3.07/3.38 tff(18996,plain,
% 3.07/3.38 (~r(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[12402, 353, 55, 698, 12397])).
% 3.07/3.38 tff(18997,plain,
% 3.07/3.38 (b(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[720, 18996, 714])).
% 3.07/3.38 tff(18998,plain,
% 3.07/3.38 ($false),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[7079, 18997, 18995, 251, 134])).
% 3.07/3.38 tff(18999,plain,((~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | b(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1) | b(elem!1, s(s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.38 tff(19000,plain,
% 3.07/3.38 (~r(s(z), s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[18999, 18983, 13636, 15134, 17868, 698, 18980, 623])).
% 3.07/3.38 tff(19001,plain,
% 3.07/3.38 (b(s(z), s(s(s(z))))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[172, 19000])).
% 3.07/3.38 tff(19002,plain,
% 3.07/3.38 (~b(s(s(s(z))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[846, 19001, 17795, 18993])).
% 3.07/3.38 tff(19003,plain,
% 3.07/3.38 (r(s(s(s(z))), s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[2794, 19002])).
% 3.07/3.38 tff(19004,plain,
% 3.07/3.38 (~r(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[8824, 19003, 17869, 18985])).
% 3.07/3.38 tff(19005,plain,
% 3.07/3.38 (b(elem!1, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[720, 19004, 15134])).
% 3.07/3.38 tff(19006,plain,
% 3.07/3.38 (~b(z, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[7079, 19005, 13636, 18983])).
% 3.07/3.38 tff(19007,plain,
% 3.07/3.38 (r(z, s(z))),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[372, 19006])).
% 3.07/3.38 tff(19008,plain,
% 3.07/3.38 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[15183, 51, 354, 11546])).
% 3.07/3.38 tff(19009,plain,
% 3.07/3.38 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[302, 19008])).
% 3.07/3.38 tff(19010,plain,
% 3.07/3.38 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[880, 19009, 624, 251])).
% 3.07/3.38 tff(19011,plain,
% 3.07/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.38 inference(unit_resolution,[status(thm)],[130, 19010, 114])).
% 3.07/3.38 tff(19012,plain,
% 3.07/3.38 (((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(19013,plain,
% 3.07/3.38 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.38 inference(rewrite,[status(thm)],[])).
% 3.07/3.38 tff(19014,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.38 inference(monotonicity,[status(thm)],[19013])).
% 3.07/3.38 tff(19015,plain,
% 3.07/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.38 inference(transitivity,[status(thm)],[19014, 19012])).
% 3.07/3.38 tff(19016,plain,
% 3.07/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 3.07/3.39 inference(quant_inst,[status(thm)],[])).
% 3.07/3.39 tff(19017,plain,
% 3.07/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[19016, 19015])).
% 3.07/3.39 tff(19018,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19017, 333, 354, 11546, 19011, 51])).
% 3.07/3.39 tff(19019,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19020,plain,
% 3.07/3.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19019, 19007, 15126, 17787, 624, 13636])).
% 3.07/3.39 tff(19021,plain,
% 3.07/3.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[279, 19020])).
% 3.07/3.39 tff(19022,plain,
% 3.07/3.39 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[14405, 19021, 17789, 624])).
% 3.07/3.39 tff(19023,plain,
% 3.07/3.39 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[302, 19022])).
% 3.07/3.39 tff(19024,plain,
% 3.07/3.39 (((~![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(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19025,plain,
% 3.07/3.39 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19026,plain,
% 3.07/3.39 (((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), 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(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[19025])).
% 3.07/3.39 tff(19027,plain,
% 3.07/3.39 (((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), 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(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(transitivity,[status(thm)],[19026, 19024])).
% 3.07/3.39 tff(19028,plain,
% 3.07/3.39 ((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(quant_inst,[status(thm)],[])).
% 3.07/3.39 tff(19029,plain,
% 3.07/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[19028, 19027])).
% 3.07/3.39 tff(19030,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19029, 333, 19007, 18985, 15126, 19023])).
% 3.07/3.39 tff(19031,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | r(z, elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19032,plain,
% 3.07/3.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19031, 17792, 624, 12930, 1575, 1, 3])).
% 3.07/3.39 tff(19033,plain,
% 3.07/3.39 (~(elem!1 = s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[712, 17796])).
% 3.07/3.39 tff(19034,plain,
% 3.07/3.39 (~b(s(s(s(z))), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[17800, 54, 114, 624, 3, 251])).
% 3.07/3.39 tff(19035,plain,
% 3.07/3.39 (r(s(s(s(z))), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[704, 19034, 698])).
% 3.07/3.39 tff(19036,plain,
% 3.07/3.39 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[279, 17797])).
% 3.07/3.39 tff(19037,plain,
% 3.07/3.39 (~r(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19019, 19036, 11546, 114, 624, 251])).
% 3.07/3.39 tff(19038,plain,
% 3.07/3.39 (b(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[372, 19037])).
% 3.07/3.39 tff(19039,plain,
% 3.07/3.39 (~r(s(s(s(z))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[15762, 19036, 623, 224])).
% 3.07/3.39 tff(19040,plain,
% 3.07/3.39 (b(s(s(s(z))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[396, 19039])).
% 3.07/3.39 tff(19041,plain,
% 3.07/3.39 (((~![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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19042,plain,
% 3.07/3.39 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19043,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[19042])).
% 3.07/3.39 tff(19044,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(transitivity,[status(thm)],[19043, 19041])).
% 3.07/3.39 tff(19045,plain,
% 3.07/3.39 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 3.07/3.39 inference(quant_inst,[status(thm)],[])).
% 3.07/3.39 tff(19046,plain,
% 3.07/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[19045, 19044])).
% 3.07/3.39 tff(19047,plain,
% 3.07/3.39 (~r(s(z), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19046, 333, 11546, 224, 19036])).
% 3.07/3.39 tff(19048,plain,
% 3.07/3.39 (b(s(z), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[348, 19047])).
% 3.07/3.39 tff(19049,plain,
% 3.07/3.39 (~b(s(s(s(z))), s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[2273, 19048, 19040, 19038])).
% 3.07/3.39 tff(19050,plain,
% 3.07/3.39 (r(s(s(s(z))), s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[2794, 19049])).
% 3.07/3.39 tff(19051,plain,
% 3.07/3.39 (~b(s(z), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[1602, 19048, 624, 251])).
% 3.07/3.39 tff(19052,plain,
% 3.07/3.39 (r(s(z), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[406, 19051, 17796])).
% 3.07/3.39 tff(19053,plain,
% 3.07/3.39 (~r(elem!1, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[9910, 19052, 19050, 19035])).
% 3.07/3.39 tff(19054,plain,
% 3.07/3.39 (b(elem!1, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[720, 19053, 19033])).
% 3.07/3.39 tff(19055,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[387, 144, 624, 19038, 19048, 19054])).
% 3.07/3.39 tff(19056,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19057,plain,
% 3.07/3.39 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19056, 13636, 624, 15126, 19032, 12930, 17787, 17792, 3])).
% 3.07/3.39 tff(19058,plain,
% 3.07/3.39 (((~![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(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19059,plain,
% 3.07/3.39 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19060,plain,
% 3.07/3.39 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[19059])).
% 3.07/3.39 tff(19061,plain,
% 3.07/3.39 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(transitivity,[status(thm)],[19060, 19058])).
% 3.07/3.39 tff(19062,plain,
% 3.07/3.39 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(quant_inst,[status(thm)],[])).
% 3.07/3.39 tff(19063,plain,
% 3.07/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[19062, 19061])).
% 3.07/3.39 tff(19064,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19063, 333, 323, 623, 11546, 321])).
% 3.07/3.39 tff(19065,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19066,plain,
% 3.07/3.39 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19065, 323, 623, 11546])).
% 3.07/3.39 tff(19067,plain,
% 3.07/3.39 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[302, 19066])).
% 3.07/3.39 tff(19068,plain,
% 3.07/3.39 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[14405, 19067, 132, 624])).
% 3.07/3.39 tff(19069,plain,
% 3.07/3.39 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[279, 19068])).
% 3.07/3.39 tff(19070,plain,
% 3.07/3.39 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19071,plain,
% 3.07/3.39 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19072,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[19071])).
% 3.07/3.39 tff(19073,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(transitivity,[status(thm)],[19072, 19070])).
% 3.07/3.39 tff(19074,plain,
% 3.07/3.39 ((~![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(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 3.07/3.39 inference(quant_inst,[status(thm)],[])).
% 3.07/3.39 tff(19075,plain,
% 3.07/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[19074, 19073])).
% 3.07/3.39 tff(19076,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19075, 333, 323, 11546, 2484, 19069])).
% 3.07/3.39 tff(19077,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19078,plain,
% 3.07/3.39 (~r(s(z), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19077, 19057, 15126, 17789, 624, 12930])).
% 3.07/3.39 tff(19079,plain,
% 3.07/3.39 (b(s(z), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[348, 19078])).
% 3.07/3.39 tff(19080,plain,
% 3.07/3.39 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[14405, 259, 132, 624])).
% 3.07/3.39 tff(19081,plain,
% 3.07/3.39 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[302, 19080])).
% 3.07/3.39 tff(19082,plain,
% 3.07/3.39 (~b(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[14578, 259, 132, 251, 134])).
% 3.07/3.39 tff(19083,plain,
% 3.07/3.39 (r(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[372, 19082])).
% 3.07/3.39 tff(19084,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19029, 333, 19083, 12351, 11546, 19081])).
% 3.07/3.39 tff(19085,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19086,plain,
% 3.07/3.39 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19085, 134, 132, 251, 11546, 624])).
% 3.07/3.39 tff(19087,plain,
% 3.07/3.39 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[279, 19086])).
% 3.07/3.39 tff(19088,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19075, 333, 12351, 11546, 2484, 19087])).
% 3.07/3.39 tff(19089,plain,((~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19090,plain,
% 3.07/3.39 (~b(s(z), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19089, 2484, 11546, 132, 251, 624])).
% 3.07/3.39 tff(19091,plain,
% 3.07/3.39 (r(s(z), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[406, 19090, 706])).
% 3.07/3.39 tff(19092,plain,
% 3.07/3.39 (~r(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19019, 51, 11546, 114, 624, 251])).
% 3.07/3.39 tff(19093,plain,
% 3.07/3.39 (b(z, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[372, 19092])).
% 3.07/3.39 tff(19094,plain,
% 3.07/3.39 (~r(s(s(s(z))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[15762, 51, 623, 224])).
% 3.07/3.39 tff(19095,plain,
% 3.07/3.39 (b(s(s(s(z))), z)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[396, 19094])).
% 3.07/3.39 tff(19096,plain,
% 3.07/3.39 (~b(s(s(s(z))), s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[2273, 19095, 489, 19093])).
% 3.07/3.39 tff(19097,plain,
% 3.07/3.39 (r(s(s(s(z))), s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[2794, 19096])).
% 3.07/3.39 tff(19098,plain,
% 3.07/3.39 (~r(elem!1, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[9910, 19097, 409, 707])).
% 3.07/3.39 tff(19099,plain,
% 3.07/3.39 (b(elem!1, s(z))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[720, 19098, 714])).
% 3.07/3.39 tff(19100,plain,
% 3.07/3.39 ($false),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[387, 144, 624, 19093, 489, 19099])).
% 3.07/3.39 tff(19101,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (elem!1 = s(z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.07/3.39 tff(19102,plain,
% 3.07/3.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[19101, 489, 624, 713, 19091, 707, 623, 224, 11546, 4416, 251])).
% 3.07/3.39 tff(19103,plain,
% 3.07/3.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[279, 19102])).
% 3.07/3.39 tff(19104,plain,
% 3.07/3.39 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.07/3.39 inference(modus_ponens,[status(thm)],[3396, 2425])).
% 3.07/3.39 tff(19105,plain,
% 3.07/3.39 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[6809, 144, 624, 286, 259])).
% 3.07/3.39 tff(19106,plain,
% 3.07/3.39 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[121, 19105, 3396])).
% 3.07/3.39 tff(19107,plain,
% 3.07/3.39 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[880, 286, 624, 251])).
% 3.07/3.39 tff(19108,plain,
% 3.07/3.39 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.07/3.39 inference(unit_resolution,[status(thm)],[130, 19107, 19104])).
% 3.07/3.39 tff(19109,plain,
% 3.07/3.39 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19110,plain,
% 3.07/3.39 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.07/3.39 inference(rewrite,[status(thm)],[])).
% 3.07/3.39 tff(19111,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[19110])).
% 3.07/3.39 tff(19112,plain,
% 3.07/3.39 (((~![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(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(transitivity,[status(thm)],[19111, 19109])).
% 3.16/3.40 tff(19113,plain,
% 3.16/3.40 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))),
% 3.16/3.40 inference(quant_inst,[status(thm)],[])).
% 3.16/3.40 tff(19114,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(modus_ponens,[status(thm)],[19113, 19112])).
% 3.16/3.40 tff(19115,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19114, 333, 409, 11546, 19108, 19106])).
% 3.16/3.40 tff(19116,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19117,plain,
% 3.16/3.40 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19116, 2206, 11546, 3396, 624, 259, 251])).
% 3.16/3.40 tff(19118,plain,
% 3.16/3.40 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[302, 19117])).
% 3.16/3.40 tff(19119,plain,
% 3.16/3.40 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19120,plain,
% 3.16/3.40 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19121,plain,
% 3.16/3.40 (((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.40 inference(monotonicity,[status(thm)],[19120])).
% 3.16/3.40 tff(19122,plain,
% 3.16/3.40 (((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(transitivity,[status(thm)],[19121, 19119])).
% 3.16/3.40 tff(19123,plain,
% 3.16/3.40 ((~![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(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))),
% 3.16/3.40 inference(quant_inst,[status(thm)],[])).
% 3.16/3.40 tff(19124,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(modus_ponens,[status(thm)],[19123, 19122])).
% 3.16/3.40 tff(19125,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19124, 333, 409, 11546, 2323, 321])).
% 3.16/3.40 tff(19126,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19127,plain,
% 3.16/3.40 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19126, 2206, 11546, 19118])).
% 3.16/3.40 tff(19128,plain,
% 3.16/3.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[121, 19127, 3396])).
% 3.16/3.40 tff(19129,plain,
% 3.16/3.40 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[267, 19128, 251, 259])).
% 3.16/3.40 tff(19130,plain,
% 3.16/3.40 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[130, 19129, 19104])).
% 3.16/3.40 tff(19131,plain,
% 3.16/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19132,plain,
% 3.16/3.40 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19133,plain,
% 3.16/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.40 inference(monotonicity,[status(thm)],[19132])).
% 3.16/3.40 tff(19134,plain,
% 3.16/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(transitivity,[status(thm)],[19133, 19131])).
% 3.16/3.40 tff(19135,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(quant_inst,[status(thm)],[])).
% 3.16/3.40 tff(19136,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(modus_ponens,[status(thm)],[19135, 19134])).
% 3.16/3.40 tff(19137,plain,
% 3.16/3.40 ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19136, 144, 624, 489, 304])).
% 3.16/3.40 tff(19138,plain,
% 3.16/3.40 (~b(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19137, 19128])).
% 3.16/3.40 tff(19139,plain,
% 3.16/3.40 (r(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[720, 19138, 713])).
% 3.16/3.40 tff(19140,plain,
% 3.16/3.40 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19141,plain,
% 3.16/3.40 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19142,plain,
% 3.16/3.40 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.40 inference(monotonicity,[status(thm)],[19141])).
% 3.16/3.40 tff(19143,plain,
% 3.16/3.40 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(transitivity,[status(thm)],[19142, 19140])).
% 3.16/3.40 tff(19144,plain,
% 3.16/3.40 ((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(quant_inst,[status(thm)],[])).
% 3.16/3.40 tff(19145,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(modus_ponens,[status(thm)],[19144, 19143])).
% 3.16/3.40 tff(19146,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19145, 333, 2206, 19139, 11546, 19130])).
% 3.16/3.40 tff(19147,plain,((~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19148,plain,
% 3.16/3.40 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19147, 19103, 11546, 3396, 624, 251, 489, 706])).
% 3.16/3.40 tff(19149,plain,
% 3.16/3.40 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[319, 19148])).
% 3.16/3.40 tff(19150,plain,
% 3.16/3.40 (~r(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[12830, 19149, 624, 706, 251, 2484])).
% 3.16/3.40 tff(19151,plain,
% 3.16/3.40 (b(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[720, 19150, 713])).
% 3.16/3.40 tff(19152,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[13823, 144, 624, 489, 19151, 132, 19103])).
% 3.16/3.40 tff(19153,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19154,plain,
% 3.16/3.40 (~r(s(s(s(z))), elem!1)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19153, 19079, 17789, 15133, 13636, 19057, 15126, 17786, 624, 12930, 19032])).
% 3.16/3.40 tff(19155,plain,
% 3.16/3.40 (b(s(s(s(z))), elem!1)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[704, 19154, 17792])).
% 3.16/3.40 tff(19156,plain,
% 3.16/3.40 (~b(s(s(s(z))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[10565, 19155, 624, 13636])).
% 3.16/3.40 tff(19157,plain,
% 3.16/3.40 (r(s(s(s(z))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[396, 19156])).
% 3.16/3.40 tff(19158,plain,
% 3.16/3.40 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[15762, 19157, 12930, 19032])).
% 3.16/3.40 tff(19159,plain,
% 3.16/3.40 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[279, 19158])).
% 3.16/3.40 tff(19160,plain,
% 3.16/3.40 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[14405, 19159, 17789, 624])).
% 3.16/3.40 tff(19161,plain,
% 3.16/3.40 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[302, 19160])).
% 3.16/3.40 tff(19162,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[9433, 333, 19157, 12930, 19032, 19161])).
% 3.16/3.40 tff(19163,plain,(r(z, elem!1) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19164,plain,
% 3.16/3.40 (r(z, elem!1)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19163, 4833, 3, 1, 255])).
% 3.16/3.40 tff(19165,plain,
% 3.16/3.40 (~r(s(z), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19077, 2484, 11546, 132, 624, 623])).
% 3.16/3.40 tff(19166,plain,
% 3.16/3.40 (b(s(z), z)),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[348, 19165])).
% 3.16/3.40 tff(19167,plain,
% 3.16/3.40 (((~![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, s(z))) | (~r(z, elem!1)) | (~r(s(z), 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(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19168,plain,
% 3.16/3.40 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(rewrite,[status(thm)],[])).
% 3.16/3.40 tff(19169,plain,
% 3.16/3.40 (((~![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(s(s(s(s(s(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(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.40 inference(monotonicity,[status(thm)],[19168])).
% 3.16/3.40 tff(19170,plain,
% 3.16/3.40 (((~![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(s(s(s(s(s(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(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.40 inference(transitivity,[status(thm)],[19169, 19167])).
% 3.16/3.40 tff(19171,plain,
% 3.16/3.40 ((~![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(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 3.16/3.40 inference(quant_inst,[status(thm)],[])).
% 3.16/3.40 tff(19172,plain,
% 3.16/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.40 inference(modus_ponens,[status(thm)],[19171, 19170])).
% 3.16/3.40 tff(19173,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19172, 333, 670, 354, 722, 11546])).
% 3.16/3.40 tff(19174,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.40 tff(19175,plain,
% 3.16/3.40 (~r(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[19174, 354, 670, 11546])).
% 3.16/3.40 tff(19176,plain,
% 3.16/3.40 (b(elem!1, s(z))),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[720, 19175, 714])).
% 3.16/3.40 tff(19177,plain,
% 3.16/3.40 ($false),
% 3.16/3.40 inference(unit_resolution,[status(thm)],[13823, 144, 624, 489, 305, 132, 259])).
% 3.16/3.41 tff(19178,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19179,plain,
% 3.16/3.41 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19178, 19176, 489, 624, 132])).
% 3.16/3.41 tff(19180,plain,
% 3.16/3.41 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[279, 19179])).
% 3.16/3.41 tff(19181,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19017, 333, 354, 11546, 2484, 19180])).
% 3.16/3.41 tff(19182,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19183,plain,
% 3.16/3.41 (~r(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19182, 2484, 11546, 19166, 624, 132, 714, 670])).
% 3.16/3.41 tff(19184,plain,
% 3.16/3.41 (b(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[372, 19183])).
% 3.16/3.41 tff(19185,plain,
% 3.16/3.41 (~b(elem!1, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[387, 144, 624, 19184, 19166])).
% 3.16/3.41 tff(19186,plain,
% 3.16/3.41 (r(elem!1, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[720, 19185, 714])).
% 3.16/3.41 tff(19187,plain,
% 3.16/3.41 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[12162, 333, 670, 19186, 2484])).
% 3.16/3.41 tff(19188,plain,
% 3.16/3.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[302, 19187])).
% 3.16/3.41 tff(19189,plain,
% 3.16/3.41 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19190,plain,
% 3.16/3.41 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19191,plain,
% 3.16/3.41 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19190])).
% 3.16/3.41 tff(19192,plain,
% 3.16/3.41 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(transitivity,[status(thm)],[19191, 19189])).
% 3.16/3.41 tff(19193,plain,
% 3.16/3.41 ((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(quant_inst,[status(thm)],[])).
% 3.16/3.41 tff(19194,plain,
% 3.16/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[19193, 19192])).
% 3.16/3.41 tff(19195,plain,
% 3.16/3.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19194, 333, 670, 19186, 2484])).
% 3.16/3.41 tff(19196,plain,
% 3.16/3.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[279, 19195])).
% 3.16/3.41 tff(19197,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[14405, 19196, 19188, 132, 624])).
% 3.16/3.41 tff(19198,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19199,plain,
% 3.16/3.41 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19198, 4833, 17789, 19164, 15134, 15126, 12930])).
% 3.16/3.41 tff(19200,plain,
% 3.16/3.41 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[130, 19199, 17787])).
% 3.16/3.41 tff(19201,plain,
% 3.16/3.41 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[14405, 259, 17789, 624])).
% 3.16/3.41 tff(19202,plain,
% 3.16/3.41 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[302, 19201])).
% 3.16/3.41 tff(19203,plain,
% 3.16/3.41 (~r(s(z), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19065, 19202, 623, 15126])).
% 3.16/3.41 tff(19204,plain,
% 3.16/3.41 (b(s(z), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[348, 19203])).
% 3.16/3.41 tff(19205,plain,
% 3.16/3.41 (~b(elem!1, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[13823, 144, 624, 19204, 17789, 259])).
% 3.16/3.41 tff(19206,plain,
% 3.16/3.41 (r(elem!1, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[720, 19205, 15134])).
% 3.16/3.41 tff(19207,plain,
% 3.16/3.41 (~(s(s(z)) = s(elem!1))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[855, 15133])).
% 3.16/3.41 tff(19208,plain,
% 3.16/3.41 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[862, 19207])).
% 3.16/3.41 tff(19209,plain,
% 3.16/3.41 (~r(s(s(s(z))), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[2227, 19206, 623, 670])).
% 3.16/3.41 tff(19210,plain,
% 3.16/3.41 (~r(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19174, 19206, 670, 15126])).
% 3.16/3.41 tff(19211,plain,
% 3.16/3.41 (b(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[372, 19210])).
% 3.16/3.41 tff(19212,plain,
% 3.16/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19213,plain,
% 3.16/3.41 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19214,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19213])).
% 3.16/3.41 tff(19215,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(transitivity,[status(thm)],[19214, 19212])).
% 3.16/3.41 tff(19216,plain,
% 3.16/3.41 ((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 3.16/3.41 inference(quant_inst,[status(thm)],[])).
% 3.16/3.41 tff(19217,plain,
% 3.16/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[19216, 19215])).
% 3.16/3.41 tff(19218,plain,
% 3.16/3.41 (~r(s(s(s(z))), s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19217, 333, 11546, 6107, 321])).
% 3.16/3.41 tff(19219,plain,
% 3.16/3.41 (b(s(s(s(z))), s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[2794, 19218])).
% 3.16/3.41 tff(19220,plain,
% 3.16/3.41 (~b(s(s(s(z))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[2273, 19219, 489, 490])).
% 3.16/3.41 tff(19221,plain,
% 3.16/3.41 (r(s(s(s(z))), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[396, 19220])).
% 3.16/3.41 tff(19222,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[10189, 333, 670, 19221, 6107, 321])).
% 3.16/3.41 tff(19223,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19224,plain,
% 3.16/3.41 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19223, 19202, 670, 19204, 19211, 15126])).
% 3.16/3.41 tff(19225,plain,
% 3.16/3.41 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[1137, 19224])).
% 3.16/3.41 tff(19226,plain,
% 3.16/3.41 (~b(s(s(s(z))), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[10110, 19225, 17787, 3, 54])).
% 3.16/3.41 tff(19227,plain,
% 3.16/3.41 (s(s(s(z))) = elem!1),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[704, 19226, 19209])).
% 3.16/3.41 tff(19228,plain,
% 3.16/3.41 (~(s(s(elem!1)) = elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[7595, 19227, 19208])).
% 3.16/3.41 tff(19229,plain,
% 3.16/3.41 (~(elem!1 = s(s(elem!1)))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[5603, 19228])).
% 3.16/3.41 tff(19230,plain,
% 3.16/3.41 (~(s(elem!1) = elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[5813, 19229])).
% 3.16/3.41 tff(19231,plain,
% 3.16/3.41 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19227])).
% 3.16/3.41 tff(19232,plain,
% 3.16/3.41 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.16/3.41 inference(symmetry,[status(thm)],[19231])).
% 3.16/3.41 tff(19233,plain,
% 3.16/3.41 (~r(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[13826, 350, 706, 670, 708])).
% 3.16/3.41 tff(19234,plain,
% 3.16/3.41 (b(z, s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[372, 19233])).
% 3.16/3.41 tff(19235,plain,
% 3.16/3.41 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 3.16/3.41 inference(monotonicity,[status(thm)],[78])).
% 3.16/3.41 tff(19236,plain,
% 3.16/3.41 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 3.16/3.41 inference(symmetry,[status(thm)],[19235])).
% 3.16/3.41 tff(19237,plain,
% 3.16/3.41 (r(s(z), s(s(s(z))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[2169, 19236])).
% 3.16/3.41 tff(19238,plain,
% 3.16/3.41 (~r(s(elem!1), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[7731, 19237, 670, 1, 489, 721, 19234])).
% 3.16/3.41 tff(19239,plain,
% 3.16/3.41 (b(s(elem!1), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[448, 19238, 14076])).
% 3.16/3.41 tff(19240,plain,
% 3.16/3.41 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[462, 19239, 133, 132])).
% 3.16/3.41 tff(19241,plain,
% 3.16/3.41 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[472, 19240, 14872])).
% 3.16/3.41 tff(19242,plain,
% 3.16/3.41 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19243,plain,
% 3.16/3.41 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19244,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19243])).
% 3.16/3.41 tff(19245,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(transitivity,[status(thm)],[19244, 19242])).
% 3.16/3.41 tff(19246,plain,
% 3.16/3.41 ((~![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(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))))),
% 3.16/3.41 inference(quant_inst,[status(thm)],[])).
% 3.16/3.41 tff(19247,plain,
% 3.16/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[19246, 19245])).
% 3.16/3.41 tff(19248,plain,
% 3.16/3.41 (~r(s(elem!1), s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19247, 333, 11546, 321, 19241])).
% 3.16/3.41 tff(19249,plain,
% 3.16/3.41 (b(s(elem!1), s(z))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[486, 19248, 1])).
% 3.16/3.41 tff(19250,plain,
% 3.16/3.41 (~b(s(elem!1), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[499, 19249, 489, 19234])).
% 3.16/3.41 tff(19251,plain,
% 3.16/3.41 (r(s(elem!1), z)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[507, 19250])).
% 3.16/3.41 tff(19252,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[3508, 333, 670, 19251, 321, 19241])).
% 3.16/3.41 tff(19253,plain,(b(s(z), elem!1) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(z))) = elem!1)) | (s(z) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19254,plain,
% 3.16/3.41 (b(s(z), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19253, 19227, 19202, 19204, 1, 15126, 17788, 17789, 670, 15133, 19205])).
% 3.16/3.41 tff(19255,plain,
% 3.16/3.41 (b(s(z), s(s(s(z))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[19254, 19232])).
% 3.16/3.41 tff(19256,plain,
% 3.16/3.41 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19227])).
% 3.16/3.41 tff(19257,plain,
% 3.16/3.41 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 3.16/3.41 inference(symmetry,[status(thm)],[19256])).
% 3.16/3.41 tff(19258,plain,
% 3.16/3.41 (b(s(s(s(z))), z)),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[624, 19257])).
% 3.16/3.41 tff(19259,plain,
% 3.16/3.41 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[462, 451, 133, 132])).
% 3.16/3.41 tff(19260,plain,
% 3.16/3.41 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[472, 19259, 14872])).
% 3.16/3.41 tff(19261,plain,
% 3.16/3.41 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 3.16/3.41 inference(monotonicity,[status(thm)],[78])).
% 3.16/3.41 tff(19262,plain,
% 3.16/3.41 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.16/3.41 inference(symmetry,[status(thm)],[19261])).
% 3.16/3.41 tff(19263,plain,
% 3.16/3.41 (b(s(elem!1), s(s(s(z))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[451, 19262])).
% 3.16/3.41 tff(19264,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[901, 19263])).
% 3.16/3.41 tff(19265,plain,((~(s(s(s(z))) = elem!1)) | b(s(elem!1), s(s(s(z)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19266,plain,
% 3.16/3.41 (b(s(elem!1), s(s(s(z))))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19265, 451, 78])).
% 3.16/3.41 tff(19267,plain,
% 3.16/3.41 (~b(s(z), s(elem!1))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[2631, 19266, 285, 489, 838])).
% 3.16/3.41 tff(19268,plain,
% 3.16/3.41 (r(s(z), s(elem!1))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[1244, 19267, 1237])).
% 3.16/3.41 tff(19269,plain,
% 3.16/3.41 (((~![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(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19270,plain,
% 3.16/3.41 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(rewrite,[status(thm)],[])).
% 3.16/3.41 tff(19271,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.41 inference(monotonicity,[status(thm)],[19270])).
% 3.16/3.41 tff(19272,plain,
% 3.16/3.41 (((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.41 inference(transitivity,[status(thm)],[19271, 19269])).
% 3.16/3.41 tff(19273,plain,
% 3.16/3.41 ((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 3.16/3.41 inference(quant_inst,[status(thm)],[])).
% 3.16/3.41 tff(19274,plain,
% 3.16/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.41 inference(modus_ponens,[status(thm)],[19273, 19272])).
% 3.16/3.41 tff(19275,plain,
% 3.16/3.41 ($false),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19274, 333, 19268, 11546, 321, 19260])).
% 3.16/3.41 tff(19276,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.41 tff(19277,plain,
% 3.16/3.41 (~b(s(elem!1), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[19276, 19202, 15126, 1229, 19258, 19204, 19255, 19227, 17788, 17789])).
% 3.16/3.41 tff(19278,plain,
% 3.16/3.41 (r(s(elem!1), elem!1)),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[448, 19277, 19230])).
% 3.16/3.41 tff(19279,plain,
% 3.16/3.41 (~r(z, s(elem!1))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[1863, 19278, 670, 19206])).
% 3.16/3.41 tff(19280,plain,
% 3.16/3.41 (b(z, s(elem!1))),
% 3.16/3.41 inference(unit_resolution,[status(thm)],[583, 19279])).
% 3.16/3.42 tff(19281,plain,
% 3.16/3.42 (~r(s(elem!1), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[11139, 19278, 670, 19206])).
% 3.16/3.42 tff(19282,plain,
% 3.16/3.42 (b(s(elem!1), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[507, 19281])).
% 3.16/3.42 tff(19283,plain,
% 3.16/3.42 (~b(s(z), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[2383, 19282, 19204, 19280])).
% 3.16/3.42 tff(19284,plain,
% 3.16/3.42 (r(s(z), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1244, 19283, 1229])).
% 3.16/3.42 tff(19285,plain,
% 3.16/3.42 (~b(s(elem!1), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[499, 19282, 19204, 19211])).
% 3.16/3.42 tff(19286,plain,
% 3.16/3.42 (r(s(elem!1), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[486, 19285, 1])).
% 3.16/3.42 tff(19287,plain,
% 3.16/3.42 (~(elem!1 = s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1569, 19230])).
% 3.16/3.42 tff(19288,plain,
% 3.16/3.42 (~b(elem!1, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[8787, 19282, 17789, 624, 259])).
% 3.16/3.42 tff(19289,plain,
% 3.16/3.42 (r(elem!1, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[560, 19288, 19287])).
% 3.16/3.42 tff(19290,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[7799, 19289, 19286, 19206, 19284])).
% 3.16/3.42 tff(19291,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~r(z, elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19292,plain,
% 3.16/3.42 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19291, 54, 4833, 670, 3, 1, 623])).
% 3.16/3.42 tff(19293,plain,
% 3.16/3.42 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[279, 19292])).
% 3.16/3.42 tff(19294,plain,
% 3.16/3.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19065, 323, 623, 15126])).
% 3.16/3.42 tff(19295,plain,
% 3.16/3.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[302, 19294])).
% 3.16/3.42 tff(19296,plain,
% 3.16/3.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[18991, 323, 4833, 623, 17789, 15126])).
% 3.16/3.42 tff(19297,plain,
% 3.16/3.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[319, 19296])).
% 3.16/3.42 tff(19298,plain,
% 3.16/3.42 (~b(s(z), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[3988, 19295, 4833, 17788, 19297])).
% 3.16/3.42 tff(19299,plain,
% 3.16/3.42 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[15576, 354, 15126, 19293])).
% 3.16/3.42 tff(19300,plain,
% 3.16/3.42 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[249, 19299])).
% 3.16/3.42 tff(19301,plain,
% 3.16/3.42 (~r(s(s(s(z))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[11212, 1699, 670, 323])).
% 3.16/3.42 tff(19302,plain,
% 3.16/3.42 (b(s(s(s(z))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[2794, 19301])).
% 3.16/3.42 tff(19303,plain,
% 3.16/3.42 (~r(s(z), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[7314, 1699, 323, 354])).
% 3.16/3.42 tff(19304,plain,
% 3.16/3.42 (b(s(z), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[172, 19303])).
% 3.16/3.42 tff(19305,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[846, 19304, 19302, 304, 283])).
% 3.16/3.42 tff(19306,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19307,plain,
% 3.16/3.42 (~r(s(s(s(z))), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19306, 19300, 19297, 323, 354, 670])).
% 3.16/3.42 tff(19308,plain,
% 3.16/3.42 (b(s(s(s(z))), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[396, 19307])).
% 3.16/3.42 tff(19309,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19310,plain,
% 3.16/3.42 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(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(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19311,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.42 inference(monotonicity,[status(thm)],[19310])).
% 3.16/3.42 tff(19312,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(transitivity,[status(thm)],[19311, 19309])).
% 3.16/3.42 tff(19313,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(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(s(s(z))))))))))),
% 3.16/3.42 inference(quant_inst,[status(thm)],[])).
% 3.16/3.42 tff(19314,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.42 inference(modus_ponens,[status(thm)],[19313, 19312])).
% 3.16/3.42 tff(19315,plain,
% 3.16/3.42 (~b(elem!1, s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19314, 144, 4833, 19308, 17789, 19300])).
% 3.16/3.42 tff(19316,plain,
% 3.16/3.42 (r(elem!1, s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1538, 12398, 12397])).
% 3.16/3.42 tff(19317,plain,
% 3.16/3.42 (~r(s(s(s(z))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[3201, 19316, 623, 670])).
% 3.16/3.42 tff(19318,plain,
% 3.16/3.42 (b(s(s(s(z))), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[2794, 19317])).
% 3.16/3.42 tff(19319,plain,
% 3.16/3.42 (~b(s(z), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[846, 19318, 304, 283])).
% 3.16/3.42 tff(19320,plain,
% 3.16/3.42 (r(s(z), s(s(s(z))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[172, 19319])).
% 3.16/3.42 tff(19321,plain,
% 3.16/3.42 (~r(s(s(s(z))), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1519, 19320, 623, 354])).
% 3.16/3.42 tff(19322,plain,
% 3.16/3.42 (b(s(s(s(z))), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[704, 19321, 698])).
% 3.16/3.42 tff(19323,plain,
% 3.16/3.42 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[10110, 19322, 114, 3, 54])).
% 3.16/3.42 tff(19324,plain,
% 3.16/3.42 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1137, 19323])).
% 3.16/3.42 tff(19325,plain,
% 3.16/3.42 (((~![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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), 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(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19326,plain,
% 3.16/3.42 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19327,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.42 inference(monotonicity,[status(thm)],[19326])).
% 3.16/3.42 tff(19328,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~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(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(transitivity,[status(thm)],[19327, 19325])).
% 3.16/3.42 tff(19329,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 3.16/3.42 inference(quant_inst,[status(thm)],[])).
% 3.16/3.42 tff(19330,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.42 inference(modus_ponens,[status(thm)],[19329, 19328])).
% 3.16/3.42 tff(19331,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19330, 333, 670, 19316, 623, 19324])).
% 3.16/3.42 tff(19332,plain,((s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19333,plain,
% 3.16/3.42 (s(s(s(z))) = elem!1),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19332, 354, 623, 17787, 3, 54, 670, 19297, 19300, 19315])).
% 3.16/3.42 tff(19334,plain,
% 3.16/3.42 (~(s(s(elem!1)) = elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[7595, 19333, 19208])).
% 3.16/3.42 tff(19335,plain,
% 3.16/3.42 (~(elem!1 = s(s(elem!1)))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[5603, 19334])).
% 3.16/3.42 tff(19336,plain,
% 3.16/3.42 (~(s(elem!1) = elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[5813, 19335])).
% 3.16/3.42 tff(19337,plain,
% 3.16/3.42 (~(elem!1 = s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1569, 19336])).
% 3.16/3.42 tff(19338,plain,
% 3.16/3.42 (r(s(z), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[406, 19298, 15133])).
% 3.16/3.42 tff(19339,plain,
% 3.16/3.42 (~r(elem!1, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[10119, 354, 670, 19338])).
% 3.16/3.42 tff(19340,plain,
% 3.16/3.42 (b(elem!1, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[560, 19337, 19339])).
% 3.16/3.42 tff(19341,plain,
% 3.16/3.42 (~r(s(elem!1), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[5456, 19340, 1, 4833, 670, 323, 15133, 305, 354, 19337])).
% 3.16/3.42 tff(19342,plain,
% 3.16/3.42 (b(s(elem!1), elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[448, 19341, 19336])).
% 3.16/3.42 tff(19343,plain,
% 3.16/3.42 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[3500, 19342, 4833, 19295, 17788])).
% 3.16/3.42 tff(19344,plain,
% 3.16/3.42 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[12214, 19333])).
% 3.16/3.42 tff(19345,plain,
% 3.16/3.42 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[462, 19342, 17788, 17789])).
% 3.16/3.42 tff(19346,plain,
% 3.16/3.42 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[472, 19345, 19344])).
% 3.16/3.42 tff(19347,plain,
% 3.16/3.42 (b(s(elem!1), s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[8704, 19337, 1378, 71, 606, 19338, 354])).
% 3.16/3.42 tff(19348,plain,
% 3.16/3.42 (~b(s(z), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[4409, 19340, 305, 19347])).
% 3.16/3.42 tff(19349,plain,
% 3.16/3.42 (r(s(z), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1244, 19348, 1229])).
% 3.16/3.42 tff(19350,plain,
% 3.16/3.42 (~r(s(elem!1), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[1235, 19349, 323, 354])).
% 3.16/3.42 tff(19351,plain,
% 3.16/3.42 (b(s(elem!1), z)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[507, 19350])).
% 3.16/3.42 tff(19352,plain,
% 3.16/3.42 (~b(z, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[949, 19351, 4833, 19340])).
% 3.16/3.42 tff(19353,plain,
% 3.16/3.42 (r(z, s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[583, 19352])).
% 3.16/3.42 tff(19354,plain,
% 3.16/3.42 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[3607, 19353, 19293, 19346])).
% 3.16/3.42 tff(19355,plain,
% 3.16/3.42 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[542, 19354, 19343])).
% 3.16/3.42 tff(19356,plain,
% 3.16/3.42 (~(s(s(s(elem!1))) = elem!1)),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[12928, 19355])).
% 3.16/3.42 tff(19357,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[13839, 19356, 19355, 19333])).
% 3.16/3.42 tff(19358,plain,((~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | r(elem!1, z) | b(z, elem!1) | (~r(z, s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19359,plain,
% 3.16/3.42 (~r(z, s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19358, 305, 1, 670, 323, 1378, 606, 623, 3, 54])).
% 3.16/3.42 tff(19360,plain,
% 3.16/3.42 (b(z, s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[372, 19359])).
% 3.16/3.42 tff(19361,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19362,plain,
% 3.16/3.42 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19363,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.16/3.42 inference(monotonicity,[status(thm)],[19362])).
% 3.16/3.42 tff(19364,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(transitivity,[status(thm)],[19363, 19361])).
% 3.16/3.42 tff(19365,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.42 inference(quant_inst,[status(thm)],[])).
% 3.16/3.42 tff(19366,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.42 inference(modus_ponens,[status(thm)],[19365, 19364])).
% 3.16/3.42 tff(19367,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19366, 144, 4833, 19360, 305, 17789, 19295])).
% 3.16/3.42 tff(19368,plain,((~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(s(z), z)) | r(elem!1, z) | b(z, elem!1) | (~r(z, s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19369,plain,
% 3.16/3.42 (~b(elem!1, s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19368, 323, 670, 1, 1378, 606, 623, 3, 54])).
% 3.16/3.42 tff(19370,plain,
% 3.16/3.42 (~r(z, s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[13826, 19369, 15133, 670, 19298])).
% 3.16/3.42 tff(19371,plain,
% 3.16/3.42 (b(z, s(z))),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[372, 19370])).
% 3.16/3.42 tff(19372,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19373,plain,
% 3.16/3.42 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(rewrite,[status(thm)],[])).
% 3.16/3.42 tff(19374,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.16/3.42 inference(monotonicity,[status(thm)],[19373])).
% 3.16/3.42 tff(19375,plain,
% 3.16/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.42 inference(transitivity,[status(thm)],[19374, 19372])).
% 3.16/3.42 tff(19376,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.16/3.42 inference(quant_inst,[status(thm)],[])).
% 3.16/3.42 tff(19377,plain,
% 3.16/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.42 inference(modus_ponens,[status(thm)],[19376, 19375])).
% 3.16/3.42 tff(19378,plain,
% 3.16/3.42 ($false),
% 3.16/3.42 inference(unit_resolution,[status(thm)],[19377, 144, 4833, 19371, 17788, 19297, 19295])).
% 3.16/3.42 tff(19379,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | r(elem!1, z) | b(z, elem!1) | (~r(z, s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.42 tff(19380,plain,
% 3.16/3.43 (~r(s(z), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19379, 54, 1, 1378, 606, 623, 3, 670])).
% 3.16/3.43 tff(19381,plain,
% 3.16/3.43 (b(s(z), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[348, 19380])).
% 3.16/3.43 tff(19382,plain,
% 3.16/3.43 (~b(elem!1, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[387, 144, 624, 490, 489])).
% 3.16/3.43 tff(19383,plain,
% 3.16/3.43 (r(elem!1, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[720, 19382, 15134])).
% 3.16/3.43 tff(19384,plain,
% 3.16/3.43 (~r(s(s(s(z))), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[2227, 19383, 623, 670])).
% 3.16/3.43 tff(19385,plain,
% 3.16/3.43 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19291, 54, 624, 670, 3, 1, 623])).
% 3.16/3.43 tff(19386,plain,
% 3.16/3.43 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[279, 19385])).
% 3.16/3.43 tff(19387,plain,
% 3.16/3.43 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[7093, 286, 489, 490])).
% 3.16/3.43 tff(19388,plain,
% 3.16/3.43 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[319, 19387])).
% 3.16/3.43 tff(19389,plain,
% 3.16/3.43 (~b(s(s(s(z))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[2273, 16451, 489, 490])).
% 3.16/3.43 tff(19390,plain,
% 3.16/3.43 (r(s(s(s(z))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[396, 19389])).
% 3.16/3.43 tff(19391,plain,
% 3.16/3.43 ($false),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[11054, 333, 19390, 6107, 322, 51])).
% 3.16/3.43 tff(19392,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.43 tff(19393,plain,
% 3.16/3.43 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19392, 19388, 51, 489, 490, 11546])).
% 3.16/3.43 tff(19394,plain,
% 3.16/3.43 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1137, 19393])).
% 3.16/3.43 tff(19395,plain,
% 3.16/3.43 (~b(s(s(s(z))), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[10110, 19394, 114, 3, 54])).
% 3.16/3.43 tff(19396,plain,
% 3.16/3.43 (s(s(s(z))) = elem!1),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[704, 19395, 699])).
% 3.16/3.43 tff(19397,plain,
% 3.16/3.43 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19396])).
% 3.16/3.43 tff(19398,plain,
% 3.16/3.43 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.16/3.43 inference(symmetry,[status(thm)],[19397])).
% 3.16/3.43 tff(19399,plain,
% 3.16/3.43 (~(s(s(z)) = elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[14611, 19396, 17796])).
% 3.16/3.43 tff(19400,plain,
% 3.16/3.43 (~(elem!1 = s(s(z)))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19399, 17962])).
% 3.16/3.43 tff(19401,plain,
% 3.16/3.43 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[17920, 19388, 51, 489, 490, 11546])).
% 3.16/3.43 tff(19402,plain,
% 3.16/3.43 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1451, 19401])).
% 3.16/3.43 tff(19403,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19404,plain,
% 3.16/3.43 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19405,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19404])).
% 3.16/3.43 tff(19406,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(transitivity,[status(thm)],[19405, 19403])).
% 3.16/3.43 tff(19407,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))),
% 3.16/3.43 inference(quant_inst,[status(thm)],[])).
% 3.16/3.43 tff(19408,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19407, 19406])).
% 3.16/3.43 tff(19409,plain,
% 3.16/3.43 (~b(elem!1, s(s(z)))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19408, 144, 624, 19402, 132, 286])).
% 3.16/3.43 tff(19410,plain,
% 3.16/3.43 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[18919, 44, 19409])).
% 3.16/3.43 tff(19411,plain,
% 3.16/3.43 (r(elem!1, s(s(z)))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19410, 19400])).
% 3.16/3.43 tff(19412,plain,
% 3.16/3.43 (r(s(s(s(z))), s(s(z)))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19411, 19398])).
% 3.16/3.43 tff(19413,plain,
% 3.16/3.43 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19396])).
% 3.16/3.43 tff(19414,plain,
% 3.16/3.43 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 3.16/3.43 inference(symmetry,[status(thm)],[19413])).
% 3.16/3.43 tff(19415,plain,
% 3.16/3.43 (r(elem!1, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[720, 19382, 19033])).
% 3.16/3.43 tff(19416,plain,
% 3.16/3.43 (r(s(s(s(z))), s(z))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19415, 19414])).
% 3.16/3.43 tff(19417,plain,
% 3.16/3.43 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[130, 54, 114])).
% 3.16/3.43 tff(19418,plain,
% 3.16/3.43 (~b(s(s(z)), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[11650, 144, 19402, 19417, 132])).
% 3.16/3.43 tff(19419,plain,
% 3.16/3.43 (r(s(s(z)), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[7970, 19399, 19418])).
% 3.16/3.43 tff(19420,plain,
% 3.16/3.43 (((~![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(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(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19421,plain,
% 3.16/3.43 ((~![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(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 3.16/3.43 inference(quant_inst,[status(thm)],[])).
% 3.16/3.43 tff(19422,plain,
% 3.16/3.43 ((~![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(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19421, 19420])).
% 3.16/3.43 tff(19423,plain,
% 3.16/3.43 (~r(s(s(z)), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19422, 333, 670, 19415, 19419])).
% 3.16/3.43 tff(19424,plain,
% 3.16/3.43 (b(s(s(z)), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1462, 44, 164, 19423])).
% 3.16/3.43 tff(19425,plain,
% 3.16/3.43 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19426,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19425])).
% 3.16/3.43 tff(19427,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 3.16/3.43 inference(transitivity,[status(thm)],[19426, 17913])).
% 3.16/3.43 tff(19428,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)), s(z))) | (~b(s(s(z)), z)))),
% 3.16/3.43 inference(quant_inst,[status(thm)],[])).
% 3.16/3.43 tff(19429,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19428, 19427])).
% 3.16/3.43 tff(19430,plain,
% 3.16/3.43 (~b(s(s(z)), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19429, 144, 490, 489, 19424])).
% 3.16/3.43 tff(19431,plain,
% 3.16/3.43 (r(s(s(z)), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1429, 44, 19430, 1416])).
% 3.16/3.43 tff(19432,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 3.16/3.43 tff(19433,plain,
% 3.16/3.43 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19434,plain,
% 3.16/3.43 (((~r(s(z), s(s(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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19435,plain,
% 3.16/3.43 (((~![X0: $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(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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19434])).
% 3.16/3.43 tff(19436,plain,
% 3.16/3.43 (((~![X0: $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(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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.43 inference(transitivity,[status(thm)],[19435, 19433])).
% 3.16/3.43 tff(19437,plain,
% 3.16/3.43 ((~![X0: $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(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.16/3.43 inference(quant_inst,[status(thm)],[])).
% 3.16/3.43 tff(19438,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19437, 19436])).
% 3.16/3.43 tff(19439,plain,
% 3.16/3.43 ($false),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19438, 333, 3193, 11546, 9770, 19432])).
% 3.16/3.43 tff(19440,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.43 tff(19441,plain,
% 3.16/3.43 (~r(s(s(s(z))), s(s(z)))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19440, 19431, 11546, 19416])).
% 3.16/3.43 tff(19442,plain,
% 3.16/3.43 ($false),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19441, 19412])).
% 3.16/3.43 tff(19443,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | r(s(s(s(z))), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.43 tff(19444,plain,
% 3.16/3.43 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19443, 490, 15126, 489, 670, 19384, 17787, 3, 54, 19386, 17789, 624])).
% 3.16/3.43 tff(19445,plain,
% 3.16/3.43 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[302, 19444])).
% 3.16/3.43 tff(19446,plain,
% 3.16/3.43 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19223, 19445, 670, 489, 490, 15126])).
% 3.16/3.43 tff(19447,plain,
% 3.16/3.43 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1137, 19446])).
% 3.16/3.43 tff(19448,plain,
% 3.16/3.43 (~b(s(s(s(z))), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[10110, 19447, 17787, 3, 54])).
% 3.16/3.43 tff(19449,plain,
% 3.16/3.43 (s(s(s(z))) = elem!1),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[704, 19448, 19384])).
% 3.16/3.43 tff(19450,plain,
% 3.16/3.43 (~(s(s(elem!1)) = elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[7595, 19449, 19208])).
% 3.16/3.43 tff(19451,plain,
% 3.16/3.43 (~(elem!1 = s(s(elem!1)))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[5603, 19450])).
% 3.16/3.43 tff(19452,plain,
% 3.16/3.43 (~(s(elem!1) = elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[5813, 19451])).
% 3.16/3.43 tff(19453,plain,
% 3.16/3.43 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19449])).
% 3.16/3.43 tff(19454,plain,
% 3.16/3.43 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.16/3.43 inference(symmetry,[status(thm)],[19453])).
% 3.16/3.43 tff(19455,plain,
% 3.16/3.43 (b(s(z), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19253, 19449, 19445, 489, 1, 15126, 17788, 17789, 670, 15133, 19382])).
% 3.16/3.43 tff(19456,plain,
% 3.16/3.43 (b(s(z), s(s(s(z))))),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[19455, 19454])).
% 3.16/3.43 tff(19457,plain,
% 3.16/3.43 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19449])).
% 3.16/3.43 tff(19458,plain,
% 3.16/3.43 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 3.16/3.43 inference(symmetry,[status(thm)],[19457])).
% 3.16/3.43 tff(19459,plain,
% 3.16/3.43 (b(s(s(s(z))), z)),
% 3.16/3.43 inference(modus_ponens,[status(thm)],[624, 19458])).
% 3.16/3.43 tff(19460,plain,
% 3.16/3.43 (~b(s(elem!1), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19276, 19459, 15126, 1229, 19445, 489, 19456, 19449, 17788, 17789])).
% 3.16/3.43 tff(19461,plain,
% 3.16/3.43 (r(s(elem!1), elem!1)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[448, 19460, 19452])).
% 3.16/3.43 tff(19462,plain,
% 3.16/3.43 (~r(z, s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1863, 19461, 670, 19383])).
% 3.16/3.43 tff(19463,plain,
% 3.16/3.43 (b(z, s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[583, 19462])).
% 3.16/3.43 tff(19464,plain,
% 3.16/3.43 (~r(s(elem!1), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[11139, 19461, 670, 19383])).
% 3.16/3.43 tff(19465,plain,
% 3.16/3.43 (b(s(elem!1), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[507, 19464])).
% 3.16/3.43 tff(19466,plain,
% 3.16/3.43 (~b(s(z), s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[2383, 19465, 489, 19463])).
% 3.16/3.43 tff(19467,plain,
% 3.16/3.43 (r(s(z), s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1244, 19466, 1229])).
% 3.16/3.43 tff(19468,plain,
% 3.16/3.43 (~b(s(elem!1), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[499, 19465, 489, 490])).
% 3.16/3.43 tff(19469,plain,
% 3.16/3.43 (r(s(elem!1), s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[486, 19468, 1])).
% 3.16/3.43 tff(19470,plain,
% 3.16/3.43 (~(elem!1 = s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[1569, 19452])).
% 3.16/3.43 tff(19471,plain,
% 3.16/3.43 (~b(elem!1, s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[949, 19465, 624, 19463])).
% 3.16/3.43 tff(19472,plain,
% 3.16/3.43 (r(elem!1, s(elem!1))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[560, 19471, 19470])).
% 3.16/3.43 tff(19473,plain,
% 3.16/3.43 ($false),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[7799, 19472, 19469, 19383, 19467])).
% 3.16/3.43 tff(19474,plain,((~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~r(z, elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.43 tff(19475,plain,
% 3.16/3.43 (~b(z, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19474, 19381, 4833, 1, 670, 3, 54, 623])).
% 3.16/3.43 tff(19476,plain,
% 3.16/3.43 (r(z, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[372, 19475])).
% 3.16/3.43 tff(19477,plain,
% 3.16/3.43 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[15183, 19476, 15126, 19293])).
% 3.16/3.43 tff(19478,plain,
% 3.16/3.43 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[302, 19477])).
% 3.16/3.43 tff(19479,plain,
% 3.16/3.43 (~r(elem!1, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[19174, 19476, 670, 15126])).
% 3.16/3.43 tff(19480,plain,
% 3.16/3.43 (b(elem!1, s(z))),
% 3.16/3.43 inference(unit_resolution,[status(thm)],[720, 19479, 15134])).
% 3.16/3.43 tff(19481,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19482,plain,
% 3.16/3.43 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(rewrite,[status(thm)],[])).
% 3.16/3.43 tff(19483,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.16/3.43 inference(monotonicity,[status(thm)],[19482])).
% 3.16/3.43 tff(19484,plain,
% 3.16/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.43 inference(transitivity,[status(thm)],[19483, 19481])).
% 3.16/3.43 tff(19485,plain,
% 3.16/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.16/3.43 inference(quant_inst,[status(thm)],[])).
% 3.16/3.44 tff(19486,plain,
% 3.16/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.44 inference(modus_ponens,[status(thm)],[19485, 19484])).
% 3.16/3.44 tff(19487,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19486, 144, 19381, 19480, 17788, 19478])).
% 3.16/3.44 tff(19488,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[319, 19487])).
% 3.16/3.44 tff(19489,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[18594, 333, 19476, 15126, 19488, 19293])).
% 3.16/3.44 tff(19490,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | r(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19491,plain,
% 3.16/3.44 (b(z, elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19490, 19199, 1, 3, 12930, 1378, 19164])).
% 3.16/3.44 tff(19492,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[880, 19491, 4833, 19200])).
% 3.16/3.44 tff(19493,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[302, 19492])).
% 3.16/3.44 tff(19494,plain,
% 3.16/3.44 (~r(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19065, 19493, 12930, 15126])).
% 3.16/3.44 tff(19495,plain,
% 3.16/3.44 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19291, 19199, 4833, 19164, 3, 1, 12930])).
% 3.16/3.44 tff(19496,plain,
% 3.16/3.44 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[279, 19495])).
% 3.16/3.44 tff(19497,plain,
% 3.16/3.44 (~r(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19019, 19491, 15126, 17787, 4833, 19496])).
% 3.16/3.44 tff(19498,plain,
% 3.16/3.44 (b(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[372, 19497])).
% 3.16/3.44 tff(19499,plain,
% 3.16/3.44 (~b(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19474, 19498, 4833, 1, 19164, 3, 19199, 12930])).
% 3.16/3.44 tff(19500,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[348, 19499, 19494])).
% 3.16/3.44 tff(19501,plain,(r(elem!1, z) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19502,plain,
% 3.16/3.44 (r(elem!1, z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19501, 255, 3, 1])).
% 3.16/3.44 tff(19503,plain,
% 3.16/3.44 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[8808, 251, 114, 3, 54])).
% 3.16/3.44 tff(19504,plain,
% 3.16/3.44 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[279, 19503])).
% 3.16/3.44 tff(19505,plain,
% 3.16/3.44 (~(s(s(s(z))) = elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[257, 251, 255])).
% 3.16/3.44 tff(19506,plain,
% 3.16/3.44 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[15633, 323, 11546, 51])).
% 3.16/3.44 tff(19507,plain,
% 3.16/3.44 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[319, 19506])).
% 3.16/3.44 tff(19508,plain,
% 3.16/3.44 (~r(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[417, 323, 408, 51])).
% 3.16/3.44 tff(19509,plain,
% 3.16/3.44 (b(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[406, 19508, 706])).
% 3.16/3.44 tff(19510,plain,
% 3.16/3.44 (~b(elem!1, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[3955, 19509, 133, 19507])).
% 3.16/3.44 tff(19511,plain,
% 3.16/3.44 (r(elem!1, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[720, 19510, 713])).
% 3.16/3.44 tff(19512,plain,
% 3.16/3.44 (((~![X0: $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(elem!1, 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(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 3.16/3.44 inference(rewrite,[status(thm)],[])).
% 3.16/3.44 tff(19513,plain,
% 3.16/3.44 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 3.16/3.44 inference(rewrite,[status(thm)],[])).
% 3.16/3.44 tff(19514,plain,
% 3.16/3.44 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z)))))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19513])).
% 3.16/3.44 tff(19515,plain,
% 3.16/3.44 (((~![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(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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))))),
% 3.16/3.44 inference(transitivity,[status(thm)],[19514, 19512])).
% 3.16/3.44 tff(19516,plain,
% 3.16/3.44 ((~![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(elem!1, z)) | (~r(elem!1, s(z))))),
% 3.16/3.44 inference(quant_inst,[status(thm)],[])).
% 3.16/3.44 tff(19517,plain,
% 3.16/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z)))))),
% 3.16/3.44 inference(modus_ponens,[status(thm)],[19516, 19515])).
% 3.16/3.44 tff(19518,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19517, 333, 323, 408, 19511, 623])).
% 3.16/3.44 tff(19519,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19520,plain,
% 3.16/3.44 (~r(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19519, 51, 623, 19417, 17796, 408, 11546])).
% 3.16/3.44 tff(19521,plain,
% 3.16/3.44 (b(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[348, 19520])).
% 3.16/3.44 tff(19522,plain,
% 3.16/3.44 (~b(s(s(s(z))), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[10110, 2254, 114, 3, 54])).
% 3.16/3.44 tff(19523,plain,
% 3.16/3.44 (r(s(s(s(z))), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[704, 19522, 698])).
% 3.16/3.44 tff(19524,plain,
% 3.16/3.44 (~r(elem!1, s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[7510, 19523, 623, 408])).
% 3.16/3.44 tff(19525,plain,
% 3.16/3.44 (b(elem!1, s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1538, 19524, 12398])).
% 3.16/3.44 tff(19526,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[18960, 19525, 132, 2254])).
% 3.16/3.44 tff(19527,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[249, 19526])).
% 3.16/3.44 tff(19528,plain,
% 3.16/3.44 (~r(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[15762, 19527, 623, 51])).
% 3.16/3.44 tff(19529,plain,
% 3.16/3.44 (b(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[396, 19528])).
% 3.16/3.44 tff(19530,plain,
% 3.16/3.44 (~b(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2273, 19529, 19521, 490])).
% 3.16/3.44 tff(19531,plain,
% 3.16/3.44 (r(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2794, 19530])).
% 3.16/3.44 tff(19532,plain,
% 3.16/3.44 (~r(s(z), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[15519, 19531, 11546, 19527])).
% 3.16/3.44 tff(19533,plain,
% 3.16/3.44 (b(s(z), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[172, 19532])).
% 3.16/3.44 tff(19534,plain,
% 3.16/3.44 (~r(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[9952, 19531, 408, 19523])).
% 3.16/3.44 tff(19535,plain,
% 3.16/3.44 (b(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[406, 19534, 17796])).
% 3.16/3.44 tff(19536,plain,
% 3.16/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 3.16/3.44 inference(rewrite,[status(thm)],[])).
% 3.16/3.44 tff(19537,plain,
% 3.16/3.44 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 3.16/3.44 inference(rewrite,[status(thm)],[])).
% 3.16/3.44 tff(19538,plain,
% 3.16/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19537])).
% 3.16/3.44 tff(19539,plain,
% 3.16/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 3.16/3.44 inference(transitivity,[status(thm)],[19538, 19536])).
% 3.16/3.44 tff(19540,plain,
% 3.16/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 3.16/3.44 inference(quant_inst,[status(thm)],[])).
% 3.16/3.44 tff(19541,plain,
% 3.16/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 3.16/3.44 inference(modus_ponens,[status(thm)],[19540, 19539])).
% 3.16/3.44 tff(19542,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19541, 144, 19535, 19521, 19525, 19529, 19533])).
% 3.16/3.44 tff(19543,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19544,plain,
% 3.16/3.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19543, 490, 408, 11546, 623, 51, 132, 698, 114, 3, 54])).
% 3.16/3.44 tff(19545,plain,
% 3.16/3.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1137, 19544])).
% 3.16/3.44 tff(19546,plain,
% 3.16/3.44 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19392, 19545, 51, 19521, 490, 11546])).
% 3.16/3.44 tff(19547,plain,
% 3.16/3.44 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[319, 19546])).
% 3.16/3.44 tff(19548,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[7093, 19547, 19521, 490])).
% 3.16/3.44 tff(19549,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[302, 19548])).
% 3.16/3.44 tff(19550,plain,
% 3.16/3.44 (~r(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[11754, 19549, 51, 19545])).
% 3.16/3.44 tff(19551,plain,
% 3.16/3.44 (b(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[396, 19550])).
% 3.16/3.44 tff(19552,plain,
% 3.16/3.44 (~b(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2273, 19551, 19521, 490])).
% 3.16/3.44 tff(19553,plain,
% 3.16/3.44 (r(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2794, 19552])).
% 3.16/3.44 tff(19554,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19217, 333, 19553, 11546, 19545, 19549])).
% 3.16/3.44 tff(19555,plain,((~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19556,plain,
% 3.16/3.44 (~b(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19555, 19504, 11546, 408, 12930, 132, 19505, 114, 3, 54])).
% 3.16/3.44 tff(19557,plain,
% 3.16/3.44 (r(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[372, 19556])).
% 3.16/3.44 tff(19558,plain,
% 3.16/3.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[15183, 19557, 11546, 19504])).
% 3.16/3.44 tff(19559,plain,
% 3.16/3.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[302, 19558])).
% 3.16/3.44 tff(19560,plain,
% 3.16/3.44 (~r(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19519, 19504, 12930, 19417, 17796, 408, 11546])).
% 3.16/3.44 tff(19561,plain,
% 3.16/3.44 (b(s(z), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[348, 19560])).
% 3.16/3.44 tff(19562,plain,
% 3.16/3.44 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[7634, 144, 251, 19561, 19417])).
% 3.16/3.44 tff(19563,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19562, 19559])).
% 3.16/3.44 tff(19564,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[319, 19563])).
% 3.16/3.44 tff(19565,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[18594, 333, 19557, 11546, 19564, 19504])).
% 3.16/3.44 tff(19566,plain,((~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19567,plain,
% 3.16/3.44 (~b(z, elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19566, 54, 19502, 17789, 17787, 3, 15126, 255])).
% 3.16/3.44 tff(19568,plain,
% 3.16/3.44 (r(z, elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[658, 19567, 71])).
% 3.16/3.44 tff(19569,plain,
% 3.16/3.44 (~r(s(s(s(z))), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2136, 670, 623, 408])).
% 3.16/3.44 tff(19570,plain,
% 3.16/3.44 (r(elem!1, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[720, 708, 15134])).
% 3.16/3.44 tff(19571,plain,
% 3.16/3.44 (~r(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19174, 19570, 670, 15126])).
% 3.16/3.44 tff(19572,plain,
% 3.16/3.44 (b(z, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[372, 19571])).
% 3.16/3.44 tff(19573,plain,
% 3.16/3.44 (~r(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[8094, 333, 670, 323, 408])).
% 3.16/3.44 tff(19574,plain,
% 3.16/3.44 (b(s(z), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[406, 19573, 15133])).
% 3.16/3.44 tff(19575,plain,
% 3.16/3.44 (b(elem!1, s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[720, 3945, 15134])).
% 3.16/3.44 tff(19576,plain,
% 3.16/3.44 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[3955, 305, 19417, 134])).
% 3.16/3.44 tff(19577,plain,
% 3.16/3.44 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[319, 19576])).
% 3.16/3.44 tff(19578,plain,
% 3.16/3.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[10110, 4367, 114, 3, 54])).
% 3.16/3.44 tff(19579,plain,
% 3.16/3.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1137, 19578])).
% 3.16/3.44 tff(19580,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[15720, 14013, 19579, 11546, 19577])).
% 3.16/3.44 tff(19581,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19582,plain,
% 3.16/3.44 (~b(s(s(s(z))), elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19581, 19575, 15126, 19574, 17787, 3, 54])).
% 3.16/3.44 tff(19583,plain,
% 3.16/3.44 (s(s(s(z))) = elem!1),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[704, 19582, 19569])).
% 3.16/3.44 tff(19584,plain,
% 3.16/3.44 (~(s(s(elem!1)) = elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[7595, 19583, 19208])).
% 3.16/3.44 tff(19585,plain,
% 3.16/3.44 (~(elem!1 = s(s(elem!1)))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[5603, 19584])).
% 3.16/3.44 tff(19586,plain,
% 3.16/3.44 (~(s(elem!1) = elem!1)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[5813, 19585])).
% 3.16/3.44 tff(19587,plain,
% 3.16/3.44 (~(elem!1 = s(elem!1))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1569, 19586])).
% 3.16/3.44 tff(19588,plain,
% 3.16/3.44 (~b(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[380, 19583, 377])).
% 3.16/3.44 tff(19589,plain,
% 3.16/3.44 (r(s(s(s(z))), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[396, 19588])).
% 3.16/3.44 tff(19590,plain,
% 3.16/3.44 (~r(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[11212, 19589, 670, 323])).
% 3.16/3.44 tff(19591,plain,
% 3.16/3.44 (b(s(s(s(z))), s(z))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[2794, 19590])).
% 3.16/3.44 tff(19592,plain,
% 3.16/3.44 (b(s(s(elem!1)), z)),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[5056, 19584, 408, 670, 19574, 323, 19575])).
% 3.16/3.44 tff(19593,plain,
% 3.16/3.44 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19519, 323, 623, 17788, 15133, 408, 15126])).
% 3.16/3.44 tff(19594,plain,
% 3.16/3.44 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[279, 19593])).
% 3.16/3.44 tff(19595,plain,
% 3.16/3.44 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[227, 19583, 54])).
% 3.16/3.44 tff(19596,plain,
% 3.16/3.44 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[249, 19595])).
% 3.16/3.44 tff(19597,plain,
% 3.16/3.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[78])).
% 3.16/3.44 tff(19598,plain,
% 3.16/3.44 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(symmetry,[status(thm)],[19597])).
% 3.16/3.44 tff(19599,plain,
% 3.16/3.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(modus_ponens,[status(thm)],[132, 19598])).
% 3.16/3.44 tff(19600,plain,
% 3.16/3.44 ($false),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[11541, 19599])).
% 3.16/3.44 tff(19601,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.44 tff(19602,plain,
% 3.16/3.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[19601, 19583, 17789])).
% 3.16/3.44 tff(19603,plain,
% 3.16/3.44 (~b(elem!1, s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[18960, 19602, 17789, 19596])).
% 3.16/3.44 tff(19604,plain,
% 3.16/3.44 (~r(elem!1, s(s(s(z))))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 19589])).
% 3.16/3.44 tff(19605,plain,
% 3.16/3.44 (elem!1 = s(s(s(z)))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1538, 19604, 19603])).
% 3.16/3.44 tff(19606,plain,
% 3.16/3.44 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[7608, 19583, 15133])).
% 3.16/3.44 tff(19607,plain,
% 3.16/3.44 (s(elem!1) = s(s(s(s(z))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[3238])).
% 3.16/3.44 tff(19608,plain,
% 3.16/3.44 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.44 tff(19609,plain,
% 3.16/3.44 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.16/3.44 inference(symmetry,[status(thm)],[19608])).
% 3.16/3.44 tff(19610,plain,
% 3.16/3.44 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19609])).
% 3.16/3.44 tff(19611,plain,
% 3.16/3.44 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.16/3.44 inference(transitivity,[status(thm)],[19610, 13328])).
% 3.16/3.44 tff(19612,plain,
% 3.16/3.44 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(symmetry,[status(thm)],[19611])).
% 3.16/3.44 tff(19613,plain,
% 3.16/3.44 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19612])).
% 3.16/3.44 tff(19614,plain,
% 3.16/3.44 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.44 inference(modus_ponens,[status(thm)],[2725, 19613])).
% 3.16/3.44 tff(19615,plain,
% 3.16/3.44 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19609])).
% 3.16/3.44 tff(19616,plain,
% 3.16/3.44 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.16/3.44 inference(symmetry,[status(thm)],[19615])).
% 3.16/3.44 tff(19617,plain,
% 3.16/3.44 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.16/3.44 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.44 tff(19618,plain,
% 3.16/3.44 (~(s(s(elem!1)) = s(elem!1))),
% 3.16/3.44 inference(unit_resolution,[status(thm)],[1196, 13979])).
% 3.16/3.44 tff(19619,plain,
% 3.16/3.45 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[3955, 305, 133, 134])).
% 3.16/3.45 tff(19620,plain,
% 3.16/3.45 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[319, 19619])).
% 3.16/3.45 tff(19621,plain,
% 3.16/3.45 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[16388, 353, 11546, 322])).
% 3.16/3.45 tff(19622,plain,
% 3.16/3.45 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1137, 19621])).
% 3.16/3.45 tff(19623,plain,
% 3.16/3.45 (~b(z, s(s(s(z))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[9071, 144, 283, 19622, 259])).
% 3.16/3.45 tff(19624,plain,
% 3.16/3.45 (r(z, s(s(s(z))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[619, 19623])).
% 3.16/3.45 tff(19625,plain,
% 3.16/3.45 ($false),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[11997, 333, 323, 1699, 19624, 353])).
% 3.16/3.45 tff(19626,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.45 tff(19627,plain,
% 3.16/3.45 (~r(s(z), s(s(s(z))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19626, 283, 11546, 323, 19620, 259, 1964])).
% 3.16/3.45 tff(19628,plain,
% 3.16/3.45 (b(s(z), s(s(s(z))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[172, 19627])).
% 3.16/3.45 tff(19629,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(monotonicity,[status(thm)],[3239])).
% 3.16/3.45 tff(19630,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19629])).
% 3.16/3.45 tff(19631,plain,
% 3.16/3.45 (s(s(s(s(z)))) = s(elem!1)),
% 3.16/3.45 inference(symmetry,[status(thm)],[19607])).
% 3.16/3.45 tff(19632,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19631, 3238])).
% 3.16/3.45 tff(19633,plain,
% 3.16/3.45 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(symmetry,[status(thm)],[19632])).
% 3.16/3.45 tff(19634,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19266, 19633])).
% 3.16/3.45 tff(19635,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19634, 19630])).
% 3.16/3.45 tff(19636,plain,
% 3.16/3.45 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.45 tff(19637,plain,
% 3.16/3.45 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19631])).
% 3.16/3.45 tff(19638,plain,
% 3.16/3.45 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19637, 174])).
% 3.16/3.45 tff(19639,plain,
% 3.16/3.45 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19638])).
% 3.16/3.45 tff(19640,plain,
% 3.16/3.45 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[196, 19639])).
% 3.16/3.45 tff(19641,plain,
% 3.16/3.45 (~r(s(elem!1), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[14129, 451, 133, 323, 305, 19640, 134, 354])).
% 3.16/3.45 tff(19642,plain,
% 3.16/3.45 (b(s(elem!1), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[486, 19641, 1])).
% 3.16/3.45 tff(19643,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), s(z))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19642, 19636])).
% 3.16/3.45 tff(19644,plain,
% 3.16/3.45 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[18487, 144, 56, 19643, 838])).
% 3.16/3.45 tff(19645,plain,
% 3.16/3.45 ($false),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19644, 19635])).
% 3.16/3.45 tff(19646,plain,((~b(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.45 tff(19647,plain,
% 3.16/3.45 (~b(s(elem!1), elem!1)),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19646, 354, 56, 19628, 1, 133, 323, 305, 134, 3238, 78])).
% 3.16/3.45 tff(19648,plain,
% 3.16/3.45 (r(s(elem!1), elem!1)),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[448, 19647, 13978])).
% 3.16/3.45 tff(19649,plain,
% 3.16/3.45 (~r(s(elem!1), z)),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[10865, 19648, 623, 408])).
% 3.16/3.45 tff(19650,plain,
% 3.16/3.45 (b(s(elem!1), z)),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[507, 19649])).
% 3.16/3.45 tff(19651,plain,
% 3.16/3.45 (~r(s(elem!1), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1670, 19650, 323, 19620, 19640, 354])).
% 3.16/3.45 tff(19652,plain,
% 3.16/3.45 (b(s(elem!1), s(z))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[486, 19651, 1])).
% 3.16/3.45 tff(19653,plain,
% 3.16/3.45 (~r(z, s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1990, 19652, 623, 323, 1963, 56, 19650])).
% 3.16/3.45 tff(19654,plain,
% 3.16/3.45 (b(z, s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[583, 19653])).
% 3.16/3.45 tff(19655,plain,
% 3.16/3.45 (~b(s(s(elem!1)), s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[5572, 19654, 2726, 19650])).
% 3.16/3.45 tff(19656,plain,
% 3.16/3.45 (r(s(s(elem!1)), s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1283, 19655, 19618])).
% 3.16/3.45 tff(19657,plain,
% 3.16/3.45 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19656, 19617])).
% 3.16/3.45 tff(19658,plain,
% 3.16/3.45 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19657, 19616])).
% 3.16/3.45 tff(19659,plain,
% 3.16/3.45 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19631])).
% 3.16/3.45 tff(19660,plain,
% 3.16/3.45 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19659])).
% 3.16/3.45 tff(19661,plain,
% 3.16/3.45 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[12069, 19654, 19067, 19650])).
% 3.16/3.45 tff(19662,plain,
% 3.16/3.45 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[542, 19661, 19640])).
% 3.16/3.45 tff(19663,plain,
% 3.16/3.45 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19662, 19660])).
% 3.16/3.45 tff(19664,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(monotonicity,[status(thm)],[3239])).
% 3.16/3.45 tff(19665,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19664])).
% 3.16/3.45 tff(19666,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19631, 3238])).
% 3.16/3.45 tff(19667,plain,
% 3.16/3.45 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(symmetry,[status(thm)],[19666])).
% 3.16/3.45 tff(19668,plain,
% 3.16/3.45 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[3238])).
% 3.16/3.45 tff(19669,plain,
% 3.16/3.45 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(transitivity,[status(thm)],[19668, 19667])).
% 3.16/3.45 tff(19670,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), elem!1)),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19648, 19669])).
% 3.16/3.45 tff(19671,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19670, 19665])).
% 3.16/3.45 tff(19672,plain,
% 3.16/3.45 (((~![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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19673,plain,
% 3.16/3.45 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19674,plain,
% 3.16/3.45 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), 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(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(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19673])).
% 3.16/3.45 tff(19675,plain,
% 3.16/3.45 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), 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(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(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19674, 19672])).
% 3.16/3.45 tff(19676,plain,
% 3.16/3.45 ((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(quant_inst,[status(thm)],[])).
% 3.16/3.45 tff(19677,plain,
% 3.16/3.45 ((~![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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19676, 19675])).
% 3.16/3.45 tff(19678,plain,
% 3.16/3.45 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19677, 333, 19671, 19663])).
% 3.16/3.45 tff(19679,plain,
% 3.16/3.45 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19678, 19658])).
% 3.16/3.45 tff(19680,plain,
% 3.16/3.45 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1159, 44, 19679])).
% 3.16/3.45 tff(19681,plain,
% 3.16/3.45 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19680, 19614])).
% 3.16/3.45 tff(19682,plain,
% 3.16/3.45 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19609])).
% 3.16/3.45 tff(19683,plain,
% 3.16/3.45 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19682, 15186])).
% 3.16/3.45 tff(19684,plain,
% 3.16/3.45 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19683])).
% 3.16/3.45 tff(19685,plain,
% 3.16/3.45 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19684])).
% 3.16/3.45 tff(19686,plain,
% 3.16/3.45 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[1184, 19685])).
% 3.16/3.45 tff(19687,plain,
% 3.16/3.45 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19609, 3239])).
% 3.16/3.45 tff(19688,plain,
% 3.16/3.45 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19687])).
% 3.16/3.45 tff(19689,plain,
% 3.16/3.45 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19688])).
% 3.16/3.45 tff(19690,plain,
% 3.16/3.45 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(elem!1))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[3238, 19631])).
% 3.16/3.45 tff(19691,plain,
% 3.16/3.45 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19690])).
% 3.16/3.45 tff(19692,plain,
% 3.16/3.45 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[3238])).
% 3.16/3.45 tff(19693,plain,
% 3.16/3.45 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19692, 19691])).
% 3.16/3.45 tff(19694,plain,
% 3.16/3.45 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.45 tff(19695,plain,
% 3.16/3.45 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 3.16/3.45 inference(symmetry,[status(thm)],[19694])).
% 3.16/3.45 tff(19696,plain,
% 3.16/3.45 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(elem!1)))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19695])).
% 3.16/3.45 tff(19697,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19631])).
% 3.16/3.45 tff(19698,plain,
% 3.16/3.45 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 3.16/3.45 inference(symmetry,[status(thm)],[19697])).
% 3.16/3.45 tff(19699,plain,
% 3.16/3.45 (b(s(s(s(s(z)))), z)),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19650, 19698])).
% 3.16/3.45 tff(19700,plain,
% 3.16/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19701,plain,
% 3.16/3.45 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19702,plain,
% 3.16/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19701])).
% 3.16/3.45 tff(19703,plain,
% 3.16/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19702, 19700])).
% 3.16/3.45 tff(19704,plain,
% 3.16/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 3.16/3.45 inference(quant_inst,[status(thm)],[])).
% 3.16/3.45 tff(19705,plain,
% 3.16/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19704, 19703])).
% 3.16/3.45 tff(19706,plain,
% 3.16/3.45 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19705, 144, 19067, 259])).
% 3.16/3.45 tff(19707,plain,
% 3.16/3.45 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19706, 19699])).
% 3.16/3.45 tff(19708,plain,
% 3.16/3.45 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[9761, 19707])).
% 3.16/3.45 tff(19709,plain,
% 3.16/3.45 (((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19710,plain,
% 3.16/3.45 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19711,plain,
% 3.16/3.45 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.45 inference(monotonicity,[status(thm)],[19710])).
% 3.16/3.45 tff(19712,plain,
% 3.16/3.45 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.45 inference(transitivity,[status(thm)],[19711, 19709])).
% 3.16/3.45 tff(19713,plain,
% 3.16/3.45 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.16/3.45 inference(quant_inst,[status(thm)],[])).
% 3.16/3.45 tff(19714,plain,
% 3.16/3.45 ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19713, 19712])).
% 3.16/3.45 tff(19715,plain,
% 3.16/3.45 (~r(s(z), s(s(s(s(z)))))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[19714, 333, 11546, 19620, 19708])).
% 3.16/3.45 tff(19716,plain,
% 3.16/3.45 (~r(s(z), s(elem!1))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19715, 19696])).
% 3.16/3.45 tff(19717,plain,
% 3.16/3.45 (b(s(z), s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[1244, 19716, 1229])).
% 3.16/3.45 tff(19718,plain,
% 3.16/3.45 (~b(elem!1, s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[4409, 19717, 305, 19652])).
% 3.16/3.45 tff(19719,plain,
% 3.16/3.45 (r(elem!1, s(elem!1))),
% 3.16/3.45 inference(unit_resolution,[status(thm)],[560, 19718, 13979])).
% 3.16/3.45 tff(19720,plain,
% 3.16/3.45 (r(elem!1, s(s(s(s(z)))))),
% 3.16/3.45 inference(modus_ponens,[status(thm)],[19719, 19693])).
% 3.16/3.45 tff(19721,plain,
% 3.16/3.45 (((~![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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19722,plain,
% 3.16/3.45 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.16/3.45 inference(rewrite,[status(thm)],[])).
% 3.16/3.45 tff(19723,plain,
% 3.16/3.45 (((~![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(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(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(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19722])).
% 3.16/3.46 tff(19724,plain,
% 3.16/3.46 (((~![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(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(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(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.16/3.46 inference(transitivity,[status(thm)],[19723, 19721])).
% 3.16/3.46 tff(19725,plain,
% 3.16/3.46 ((~![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(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 3.16/3.46 inference(quant_inst,[status(thm)],[])).
% 3.16/3.46 tff(19726,plain,
% 3.16/3.46 ((~![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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19725, 19724])).
% 3.16/3.46 tff(19727,plain,
% 3.16/3.46 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19726, 333])).
% 3.16/3.46 tff(19728,plain,
% 3.16/3.46 (~r(s(s(elem!1)), elem!1)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19727, 19720, 19657, 19670])).
% 3.16/3.46 tff(19729,plain,
% 3.16/3.46 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19728, 19689])).
% 3.16/3.46 tff(19730,plain,
% 3.16/3.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.16/3.46 inference(rewrite,[status(thm)],[])).
% 3.16/3.46 tff(19731,plain,
% 3.16/3.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.16/3.46 inference(quant_inst,[status(thm)],[])).
% 3.16/3.46 tff(19732,plain,
% 3.16/3.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19731, 19730])).
% 3.16/3.46 tff(19733,plain,
% 3.16/3.46 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19732, 44, 19729])).
% 3.16/3.46 tff(19734,plain,
% 3.16/3.46 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19733, 19686])).
% 3.16/3.46 tff(19735,plain,
% 3.16/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(rewrite,[status(thm)],[])).
% 3.16/3.46 tff(19736,plain,
% 3.16/3.46 (((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(rewrite,[status(thm)],[])).
% 3.16/3.46 tff(19737,plain,
% 3.16/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19736])).
% 3.16/3.46 tff(19738,plain,
% 3.16/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(transitivity,[status(thm)],[19737, 19735])).
% 3.16/3.46 tff(19739,plain,
% 3.16/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.16/3.46 inference(quant_inst,[status(thm)],[])).
% 3.16/3.46 tff(19740,plain,
% 3.16/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19739, 19738])).
% 3.16/3.46 tff(19741,plain,
% 3.16/3.46 ($false),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19740, 144, 283, 2254, 19734, 19681])).
% 3.16/3.46 tff(19742,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | b(s(s(s(z))), z) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.46 tff(19743,plain,
% 3.16/3.46 (~r(z, s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19742, 19596, 19602, 19606, 19605, 19208, 19575, 15126, 19594, 19592, 623, 323, 19588, 19591, 1, 408, 17788, 19574, 19583])).
% 3.16/3.46 tff(19744,plain,
% 3.16/3.46 (b(z, s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[372, 19743])).
% 3.16/3.46 tff(19745,plain,
% 3.16/3.46 (~r(s(elem!1), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[7112, 19744, 323, 19575, 19587, 1, 670])).
% 3.16/3.46 tff(19746,plain,
% 3.16/3.46 (b(s(elem!1), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[507, 19745])).
% 3.16/3.46 tff(19747,plain,
% 3.16/3.46 (s(elem!1) = s(s(s(s(z))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19605])).
% 3.16/3.46 tff(19748,plain,
% 3.16/3.46 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19747])).
% 3.16/3.46 tff(19749,plain,
% 3.16/3.46 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 3.16/3.46 inference(symmetry,[status(thm)],[19748])).
% 3.16/3.46 tff(19750,plain,
% 3.16/3.46 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19749])).
% 3.16/3.46 tff(19751,plain,
% 3.16/3.46 (s(s(s(s(z)))) = s(elem!1)),
% 3.16/3.46 inference(symmetry,[status(thm)],[19747])).
% 3.16/3.46 tff(19752,plain,
% 3.16/3.46 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19751])).
% 3.16/3.46 tff(19753,plain,
% 3.16/3.46 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 3.16/3.46 inference(symmetry,[status(thm)],[19752])).
% 3.16/3.46 tff(19754,plain,
% 3.16/3.46 (b(s(s(s(s(z)))), z)),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19746, 19753])).
% 3.16/3.46 tff(19755,plain,
% 3.16/3.46 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19705, 144, 19295, 19594])).
% 3.16/3.46 tff(19756,plain,
% 3.16/3.46 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19755, 19754])).
% 3.16/3.46 tff(19757,plain,
% 3.16/3.46 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[9761, 19756])).
% 3.16/3.46 tff(19758,plain,
% 3.16/3.46 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[3955, 19575, 17788, 19574])).
% 3.16/3.46 tff(19759,plain,
% 3.16/3.46 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[319, 19758])).
% 3.16/3.46 tff(19760,plain,
% 3.16/3.46 (((~![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(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(rewrite,[status(thm)],[])).
% 3.16/3.46 tff(19761,plain,
% 3.16/3.46 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(rewrite,[status(thm)],[])).
% 3.16/3.46 tff(19762,plain,
% 3.16/3.46 (((~![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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19761])).
% 3.16/3.46 tff(19763,plain,
% 3.16/3.46 (((~![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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.46 inference(transitivity,[status(thm)],[19762, 19760])).
% 3.16/3.46 tff(19764,plain,
% 3.16/3.46 ((~![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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.16/3.46 inference(quant_inst,[status(thm)],[])).
% 3.16/3.46 tff(19765,plain,
% 3.16/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19764, 19763])).
% 3.16/3.46 tff(19766,plain,
% 3.16/3.46 (~r(s(s(s(s(z)))), s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19765, 333, 15126, 19759, 19757])).
% 3.16/3.46 tff(19767,plain,
% 3.16/3.46 (~r(s(elem!1), s(z))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19766, 19750])).
% 3.16/3.46 tff(19768,plain,
% 3.16/3.46 (b(s(elem!1), s(z))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[486, 19767, 1])).
% 3.16/3.46 tff(19769,plain,
% 3.16/3.46 (~r(z, s(elem!1))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1990, 19768, 623, 323, 19588, 19591, 19746])).
% 3.16/3.46 tff(19770,plain,
% 3.16/3.46 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19747])).
% 3.16/3.46 tff(19771,plain,
% 3.16/3.46 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 3.16/3.46 inference(symmetry,[status(thm)],[19770])).
% 3.16/3.46 tff(19772,plain,
% 3.16/3.46 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(elem!1)))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19771])).
% 3.16/3.46 tff(19773,plain,
% 3.16/3.46 (~r(s(z), s(s(s(s(z)))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19714, 333, 15126, 19759, 19757])).
% 3.16/3.46 tff(19774,plain,
% 3.16/3.46 (~r(s(z), s(elem!1))),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[19773, 19772])).
% 3.16/3.46 tff(19775,plain,
% 3.16/3.46 (b(s(z), s(elem!1))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1244, 19774, 1229])).
% 3.16/3.46 tff(19776,plain,
% 3.16/3.46 (~b(z, s(elem!1))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1853, 19768, 19744, 19775])).
% 3.16/3.46 tff(19777,plain,
% 3.16/3.46 ($false),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[583, 19776, 19769])).
% 3.16/3.46 tff(19778,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | b(elem!1, z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.46 tff(19779,plain,
% 3.16/3.46 (~r(s(z), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19778, 670, 1, 623, 408, 377, 54, 3])).
% 3.16/3.46 tff(19780,plain,
% 3.16/3.46 (b(s(z), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[348, 19779])).
% 3.16/3.46 tff(19781,plain,
% 3.16/3.46 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[19223, 321, 670, 19780, 19572, 15126])).
% 3.16/3.46 tff(19782,plain,
% 3.16/3.46 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1137, 19781])).
% 3.16/3.46 tff(19783,plain,
% 3.16/3.46 (~b(s(s(s(z))), elem!1)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[10110, 19782, 17787, 3, 54])).
% 3.16/3.46 tff(19784,plain,
% 3.16/3.46 (s(s(s(z))) = elem!1),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[704, 19783, 19569])).
% 3.16/3.46 tff(19785,plain,
% 3.16/3.46 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[227, 19784, 54])).
% 3.16/3.46 tff(19786,plain,
% 3.16/3.46 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[249, 19785])).
% 3.16/3.46 tff(19787,plain,
% 3.16/3.46 (~b(elem!1, s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[18960, 19786, 17789, 19782])).
% 3.16/3.46 tff(19788,plain,
% 3.16/3.46 (~b(s(s(s(z))), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[380, 19784, 377])).
% 3.16/3.46 tff(19789,plain,
% 3.16/3.46 (r(s(s(s(z))), z)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[396, 19788])).
% 3.16/3.46 tff(19790,plain,
% 3.16/3.46 (~r(elem!1, s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 19789])).
% 3.16/3.46 tff(19791,plain,
% 3.16/3.46 (elem!1 = s(s(s(z)))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1538, 19790, 19787])).
% 3.16/3.46 tff(19792,plain,
% 3.16/3.46 (s(s(s(z))) = elem!1),
% 3.16/3.46 inference(symmetry,[status(thm)],[19791])).
% 3.16/3.46 tff(19793,plain,
% 3.16/3.46 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19792])).
% 3.16/3.46 tff(19794,plain,
% 3.16/3.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.46 inference(symmetry,[status(thm)],[19793])).
% 3.16/3.46 tff(19795,plain,
% 3.16/3.46 (s(elem!1) = s(s(s(s(z))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19791])).
% 3.16/3.46 tff(19796,plain,
% 3.16/3.46 (s(s(s(s(z)))) = s(elem!1)),
% 3.16/3.46 inference(symmetry,[status(thm)],[19795])).
% 3.16/3.46 tff(19797,plain,
% 3.16/3.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19796, 19791])).
% 3.16/3.46 tff(19798,plain,
% 3.16/3.46 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.16/3.46 inference(symmetry,[status(thm)],[19797])).
% 3.16/3.46 tff(19799,plain,
% 3.16/3.46 (~(s(s(z)) = elem!1)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[14611, 19784, 15133])).
% 3.16/3.46 tff(19800,plain,
% 3.16/3.46 (~(s(elem!1) = s(s(s(z))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[1508, 19799])).
% 3.16/3.46 tff(19801,plain,
% 3.16/3.46 (~(s(s(elem!1)) = elem!1)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[7595, 19784, 19208])).
% 3.16/3.46 tff(19802,plain,
% 3.16/3.46 (~(elem!1 = s(s(elem!1)))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[5603, 19801])).
% 3.16/3.46 tff(19803,plain,
% 3.16/3.46 (~(s(elem!1) = elem!1)),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[5813, 19802])).
% 3.16/3.46 tff(19804,plain,
% 3.16/3.46 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(unit_resolution,[status(thm)],[12214, 19784])).
% 3.16/3.46 tff(19805,plain,
% 3.16/3.46 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.46 tff(19806,plain,
% 3.16/3.46 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.46 inference(symmetry,[status(thm)],[19805])).
% 3.16/3.46 tff(19807,plain,
% 3.16/3.46 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19806])).
% 3.16/3.46 tff(19808,plain,
% 3.16/3.46 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.16/3.46 inference(monotonicity,[status(thm)],[19607])).
% 3.16/3.46 tff(19809,plain,
% 3.16/3.46 (r(s(s(s(s(z)))), z)),
% 3.16/3.46 inference(modus_ponens,[status(thm)],[509, 19808])).
% 3.16/3.46 tff(19810,plain,
% 3.16/3.46 (((~![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(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), 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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19811,plain,
% 3.16/3.47 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19812,plain,
% 3.16/3.47 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19811])).
% 3.16/3.47 tff(19813,plain,
% 3.16/3.47 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19812, 19810])).
% 3.16/3.47 tff(19814,plain,
% 3.16/3.47 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.47 inference(quant_inst,[status(thm)],[])).
% 3.16/3.47 tff(19815,plain,
% 3.16/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19814, 19813])).
% 3.16/3.47 tff(19816,plain,
% 3.16/3.47 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19815, 333, 623, 321, 19809])).
% 3.16/3.47 tff(19817,plain,
% 3.16/3.47 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19816, 19807])).
% 3.16/3.47 tff(19818,plain,
% 3.16/3.47 (~r(s(elem!1), elem!1)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[11139, 509, 670, 722])).
% 3.16/3.47 tff(19819,plain,
% 3.16/3.47 (b(s(elem!1), elem!1)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[448, 19818, 433])).
% 3.16/3.47 tff(19820,plain,
% 3.16/3.47 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[462, 19819, 133, 132])).
% 3.16/3.47 tff(19821,plain,
% 3.16/3.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[472, 19820, 432])).
% 3.16/3.47 tff(19822,plain,
% 3.16/3.47 ($false),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19821, 19817])).
% 3.16/3.47 tff(19823,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.47 tff(19824,plain,
% 3.16/3.47 (~r(s(elem!1), z)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19823, 19791, 623, 321, 19804, 17788, 17789, 19803, 670, 19570])).
% 3.16/3.47 tff(19825,plain,
% 3.16/3.47 (b(s(elem!1), z)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[507, 19824])).
% 3.16/3.47 tff(19826,plain,
% 3.16/3.47 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[7608, 19784, 15133])).
% 3.16/3.47 tff(19827,plain,
% 3.16/3.47 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19609])).
% 3.16/3.47 tff(19828,plain,
% 3.16/3.47 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19827])).
% 3.16/3.47 tff(19829,plain,
% 3.16/3.47 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19828])).
% 3.16/3.47 tff(19830,plain,
% 3.16/3.47 (r(s(s(elem!1)), z)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[5509, 5038])).
% 3.16/3.47 tff(19831,plain,
% 3.16/3.47 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[10243, 19830, 670, 321])).
% 3.16/3.47 tff(19832,plain,
% 3.16/3.47 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19831, 19829])).
% 3.16/3.47 tff(19833,plain,
% 3.16/3.47 (~r(s(s(elem!1)), elem!1)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[5047, 5038, 670, 408])).
% 3.16/3.47 tff(19834,plain,
% 3.16/3.47 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19833, 19689])).
% 3.16/3.47 tff(19835,plain,
% 3.16/3.47 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19732, 44])).
% 3.16/3.47 tff(19836,plain,
% 3.16/3.47 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19835, 19686, 19834])).
% 3.16/3.47 tff(19837,plain,
% 3.16/3.47 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19740, 144, 283, 2254, 19836])).
% 3.16/3.47 tff(19838,plain,
% 3.16/3.47 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[1159, 44, 19837])).
% 3.16/3.47 tff(19839,plain,
% 3.16/3.47 ($false),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19838, 19832, 19614])).
% 3.16/3.47 tff(19840,plain,(b(s(s(elem!1)), z) | (~(elem!1 = s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.47 tff(19841,plain,
% 3.16/3.47 (b(s(s(elem!1)), z)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19840, 19791, 19826, 19786, 19782, 19208, 670, 321, 408])).
% 3.16/3.47 tff(19842,plain,
% 3.16/3.47 (~(elem!1 = s(elem!1))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[1569, 19803])).
% 3.16/3.47 tff(19843,plain,
% 3.16/3.47 (~(s(s(elem!1)) = s(elem!1))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[1196, 19842])).
% 3.16/3.47 tff(19844,plain,
% 3.16/3.47 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19795])).
% 3.16/3.47 tff(19845,plain,
% 3.16/3.47 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19844])).
% 3.16/3.47 tff(19846,plain,
% 3.16/3.47 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19795])).
% 3.16/3.47 tff(19847,plain,
% 3.16/3.47 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19846])).
% 3.16/3.47 tff(19848,plain,
% 3.16/3.47 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19847])).
% 3.16/3.47 tff(19849,plain,
% 3.16/3.47 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19848, 19845])).
% 3.16/3.47 tff(19850,plain,
% 3.16/3.47 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19849])).
% 3.16/3.47 tff(19851,plain,
% 3.16/3.47 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19795])).
% 3.16/3.47 tff(19852,plain,
% 3.16/3.47 (~b(s(elem!1), s(z))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[499, 19825, 19780, 19572])).
% 3.16/3.47 tff(19853,plain,
% 3.16/3.47 (r(s(elem!1), s(z))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[486, 19852, 1])).
% 3.16/3.47 tff(19854,plain,
% 3.16/3.47 (r(s(s(s(s(z)))), s(z))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19853, 19851])).
% 3.16/3.47 tff(19855,plain,
% 3.16/3.47 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19847])).
% 3.16/3.47 tff(19856,plain,
% 3.16/3.47 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19855])).
% 3.16/3.47 tff(19857,plain,
% 3.16/3.47 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19856])).
% 3.16/3.47 tff(19858,plain,
% 3.16/3.47 (~(s(s(s(s(s(z))))) = s(z))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[107, 19857])).
% 3.16/3.47 tff(19859,plain,
% 3.16/3.47 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19847])).
% 3.16/3.47 tff(19860,plain,
% 3.16/3.47 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.16/3.47 inference(symmetry,[status(thm)],[19859])).
% 3.16/3.47 tff(19861,plain,
% 3.16/3.47 (b(s(s(s(s(s(z))))), z)),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19841, 19860])).
% 3.16/3.47 tff(19862,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19863,plain,
% 3.16/3.47 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19864,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19863])).
% 3.16/3.47 tff(19865,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19864, 19862])).
% 3.16/3.47 tff(19866,plain,
% 3.16/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.16/3.47 inference(quant_inst,[status(thm)],[])).
% 3.16/3.47 tff(19867,plain,
% 3.16/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19866, 19865])).
% 3.16/3.47 tff(19868,plain,
% 3.16/3.47 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19867, 144, 19572, 19780])).
% 3.16/3.47 tff(19869,plain,
% 3.16/3.47 (~b(s(s(s(s(s(z))))), s(z))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19868, 19861])).
% 3.16/3.47 tff(19870,plain,
% 3.16/3.47 (((~![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)))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19871,plain,
% 3.16/3.47 ((~![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)))),
% 3.16/3.47 inference(quant_inst,[status(thm)],[])).
% 3.16/3.47 tff(19872,plain,
% 3.16/3.47 ((~![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))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19871, 19870])).
% 3.16/3.47 tff(19873,plain,
% 3.16/3.47 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19872, 44, 19869])).
% 3.16/3.47 tff(19874,plain,
% 3.16/3.47 (r(s(s(s(s(s(z))))), s(z))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19873, 19858])).
% 3.16/3.47 tff(19875,plain,
% 3.16/3.47 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(elem!1))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19796])).
% 3.16/3.47 tff(19876,plain,
% 3.16/3.47 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(z))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19875, 1577])).
% 3.16/3.47 tff(19877,plain,
% 3.16/3.47 ((s(elem!1) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19876])).
% 3.16/3.47 tff(19878,plain,
% 3.16/3.47 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19877])).
% 3.16/3.47 tff(19879,plain,
% 3.16/3.47 (~(s(z) = s(s(s(s(z)))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[1, 19878])).
% 3.16/3.47 tff(19880,plain,
% 3.16/3.47 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19792])).
% 3.16/3.47 tff(19881,plain,
% 3.16/3.47 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19880])).
% 3.16/3.47 tff(19882,plain,
% 3.16/3.47 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(elem!1))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19791, 19796])).
% 3.16/3.47 tff(19883,plain,
% 3.16/3.47 (b(s(s(s(z))), s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.16/3.47 inference(symmetry,[status(thm)],[19882])).
% 3.16/3.47 tff(19884,plain,
% 3.16/3.47 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19791])).
% 3.16/3.47 tff(19885,plain,
% 3.16/3.47 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19884, 19883])).
% 3.16/3.47 tff(19886,plain,
% 3.16/3.47 (~r(elem!1, s(elem!1))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[11731, 19853, 670, 1229, 19780, 19570, 19825])).
% 3.16/3.47 tff(19887,plain,
% 3.16/3.47 (b(elem!1, s(elem!1))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[560, 19886, 19842])).
% 3.16/3.47 tff(19888,plain,
% 3.16/3.47 (b(elem!1, s(s(s(s(z)))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19887, 19885])).
% 3.16/3.47 tff(19889,plain,
% 3.16/3.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19888, 19881])).
% 3.16/3.47 tff(19890,plain,
% 3.16/3.47 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19796])).
% 3.16/3.47 tff(19891,plain,
% 3.16/3.47 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 3.16/3.47 inference(symmetry,[status(thm)],[19890])).
% 3.16/3.47 tff(19892,plain,
% 3.16/3.47 (b(s(s(s(s(z)))), z)),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19825, 19891])).
% 3.16/3.47 tff(19893,plain,
% 3.16/3.47 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19791])).
% 3.16/3.47 tff(19894,plain,
% 3.16/3.47 (b(s(z), elem!1)),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19253, 19784, 321, 19780, 1, 15126, 17788, 17789, 670, 15133, 708])).
% 3.16/3.47 tff(19895,plain,
% 3.16/3.47 (b(s(z), s(s(s(z))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19894, 19893])).
% 3.16/3.47 tff(19896,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19897,plain,
% 3.16/3.47 (((~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(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19898,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.16/3.47 inference(monotonicity,[status(thm)],[19897])).
% 3.16/3.47 tff(19899,plain,
% 3.16/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.16/3.47 inference(transitivity,[status(thm)],[19898, 19896])).
% 3.16/3.47 tff(19900,plain,
% 3.16/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 3.16/3.47 inference(quant_inst,[status(thm)],[])).
% 3.16/3.47 tff(19901,plain,
% 3.16/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19900, 19899])).
% 3.16/3.47 tff(19902,plain,
% 3.16/3.47 ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19901, 144, 19780, 19895])).
% 3.16/3.47 tff(19903,plain,
% 3.16/3.47 (~b(s(z), s(s(s(s(z)))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19902, 19892, 19889])).
% 3.16/3.47 tff(19904,plain,
% 3.16/3.47 (((~![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))))))),
% 3.16/3.47 inference(rewrite,[status(thm)],[])).
% 3.16/3.47 tff(19905,plain,
% 3.16/3.47 ((~![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))))))),
% 3.16/3.47 inference(quant_inst,[status(thm)],[])).
% 3.16/3.47 tff(19906,plain,
% 3.16/3.47 ((~![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)))))),
% 3.16/3.47 inference(modus_ponens,[status(thm)],[19905, 19904])).
% 3.16/3.47 tff(19907,plain,
% 3.16/3.47 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19906, 44, 19903])).
% 3.16/3.47 tff(19908,plain,
% 3.16/3.47 (r(s(z), s(s(s(s(z)))))),
% 3.16/3.47 inference(unit_resolution,[status(thm)],[19907, 19879])).
% 3.16/3.47 tff(19909,plain,
% 3.16/3.47 (((~![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(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(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)))))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19910,plain,
% 3.16/3.48 ((~![X0: $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(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19911,plain,
% 3.16/3.48 ((~![X0: $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(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19910, 19909])).
% 3.16/3.48 tff(19912,plain,
% 3.16/3.48 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19911, 333, 19908, 19874, 19854])).
% 3.16/3.48 tff(19913,plain,
% 3.16/3.48 (~r(s(s(elem!1)), s(elem!1))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19912, 19850])).
% 3.16/3.48 tff(19914,plain,
% 3.16/3.48 (b(s(s(elem!1)), s(elem!1))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1283, 19913, 19843])).
% 3.16/3.48 tff(19915,plain,
% 3.16/3.48 (~b(z, s(elem!1))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[5572, 19914, 19841, 19825])).
% 3.16/3.48 tff(19916,plain,
% 3.16/3.48 (r(z, s(elem!1))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[583, 19915])).
% 3.16/3.48 tff(19917,plain,
% 3.16/3.48 (~r(s(elem!1), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1972, 19916, 623, 19789])).
% 3.16/3.48 tff(19918,plain,
% 3.16/3.48 (b(s(elem!1), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[965, 19917, 19800])).
% 3.16/3.48 tff(19919,plain,
% 3.16/3.48 (b(s(s(s(s(z)))), elem!1)),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19918, 19798])).
% 3.16/3.48 tff(19920,plain,
% 3.16/3.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19919, 19794])).
% 3.16/3.48 tff(19921,plain,
% 3.16/3.48 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[18464, 144, 19786, 19782])).
% 3.16/3.48 tff(19922,plain,
% 3.16/3.48 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19921, 19920])).
% 3.16/3.48 tff(19923,plain,
% 3.16/3.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[9761, 19922])).
% 3.16/3.48 tff(19924,plain,
% 3.16/3.48 (((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19925,plain,
% 3.16/3.48 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19926,plain,
% 3.16/3.48 (((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19925])).
% 3.16/3.48 tff(19927,plain,
% 3.16/3.48 (((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(transitivity,[status(thm)],[19926, 19924])).
% 3.16/3.48 tff(19928,plain,
% 3.16/3.48 ((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19929,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19928, 19927])).
% 3.16/3.48 tff(19930,plain,
% 3.16/3.48 ($false),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19929, 333, 19854, 15126, 321, 19923])).
% 3.16/3.48 tff(19931,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | b(elem!1, z) | b(elem!1, s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.48 tff(19932,plain,
% 3.16/3.48 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19931, 708, 670, 408, 1, 377, 623, 54, 3])).
% 3.16/3.48 tff(19933,plain,
% 3.16/3.48 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[302, 19932])).
% 3.16/3.48 tff(19934,plain,
% 3.16/3.48 (~r(z, s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19174, 722, 670, 15126])).
% 3.16/3.48 tff(19935,plain,
% 3.16/3.48 (b(z, s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[372, 19934])).
% 3.16/3.48 tff(19936,plain,
% 3.16/3.48 (b(s(s(s(z))), elem!1)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[704, 698, 699])).
% 3.16/3.48 tff(19937,plain,
% 3.16/3.48 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[10110, 19936, 17787, 3, 54])).
% 3.16/3.48 tff(19938,plain,
% 3.16/3.48 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1137, 19937])).
% 3.16/3.48 tff(19939,plain,
% 3.16/3.48 (~r(s(s(s(z))), s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[15720, 19938, 15126, 19388])).
% 3.16/3.48 tff(19940,plain,
% 3.16/3.48 (b(s(s(s(z))), s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[2794, 19939])).
% 3.16/3.48 tff(19941,plain,
% 3.16/3.48 (~b(s(s(s(z))), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[2273, 19940, 489, 490])).
% 3.16/3.48 tff(19942,plain,
% 3.16/3.48 (r(s(s(s(z))), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[396, 19941])).
% 3.16/3.48 tff(19943,plain,
% 3.16/3.48 (~r(elem!1, s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 19942])).
% 3.16/3.48 tff(19944,plain,
% 3.16/3.48 (b(elem!1, s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1538, 19943, 12398])).
% 3.16/3.48 tff(19945,plain,
% 3.16/3.48 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[11026, 144, 19944, 17788, 19936])).
% 3.16/3.48 tff(19946,plain,
% 3.16/3.48 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[249, 19945])).
% 3.16/3.48 tff(19947,plain,
% 3.16/3.48 (~r(s(z), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[16042, 333, 11546, 224, 6107])).
% 3.16/3.48 tff(19948,plain,
% 3.16/3.48 (b(s(z), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[172, 19947])).
% 3.16/3.48 tff(19949,plain,
% 3.16/3.48 (((~![X0: $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(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19950,plain,
% 3.16/3.48 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19951,plain,
% 3.16/3.48 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19950])).
% 3.16/3.48 tff(19952,plain,
% 3.16/3.48 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(transitivity,[status(thm)],[19951, 19949])).
% 3.16/3.48 tff(19953,plain,
% 3.16/3.48 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19954,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19953, 19952])).
% 3.16/3.48 tff(19955,plain,
% 3.16/3.48 (~r(s(s(z)), s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19954, 333, 2671, 11546, 224])).
% 3.16/3.48 tff(19956,plain,
% 3.16/3.48 (b(s(s(z)), s(z))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1429, 44, 19955, 1416])).
% 3.16/3.48 tff(19957,plain,
% 3.16/3.48 (~r(s(s(z)), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[18163, 2671, 322, 6107])).
% 3.16/3.48 tff(19958,plain,
% 3.16/3.48 (b(s(s(z)), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1473, 44, 19957, 217])).
% 3.16/3.48 tff(19959,plain,
% 3.16/3.48 ($false),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[18113, 144, 56, 19958, 19956, 19948])).
% 3.16/3.48 tff(19960,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.48 tff(19961,plain,
% 3.16/3.48 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19960, 19946, 15126, 19940, 19388, 19938])).
% 3.16/3.48 tff(19962,plain,
% 3.16/3.48 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1451, 19961])).
% 3.16/3.48 tff(19963,plain,
% 3.16/3.48 (~b(s(s(z)), elem!1)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[11650, 144, 19962, 17788, 17789])).
% 3.16/3.48 tff(19964,plain,
% 3.16/3.48 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19965,plain,
% 3.16/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19964])).
% 3.16/3.48 tff(19966,plain,
% 3.16/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.16/3.48 inference(transitivity,[status(thm)],[19965, 18377])).
% 3.16/3.48 tff(19967,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19968,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19967, 19966])).
% 3.16/3.48 tff(19969,plain,
% 3.16/3.48 (~b(s(s(z)), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19968, 144, 19962, 286, 259])).
% 3.16/3.48 tff(19970,plain,
% 3.16/3.48 (r(s(s(z)), z)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[1462, 44, 164, 19969])).
% 3.16/3.48 tff(19971,plain,
% 3.16/3.48 (((~![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)), 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19972,plain,
% 3.16/3.48 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19973,plain,
% 3.16/3.48 (((~![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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19972])).
% 3.16/3.48 tff(19974,plain,
% 3.16/3.48 (((~![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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 3.16/3.48 inference(transitivity,[status(thm)],[19973, 19971])).
% 3.16/3.48 tff(19975,plain,
% 3.16/3.48 ((~![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)))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19976,plain,
% 3.16/3.48 ((~![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)), elem!1)) | (~r(s(s(z)), z))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19975, 19974])).
% 3.16/3.48 tff(19977,plain,
% 3.16/3.48 (~r(s(s(z)), elem!1)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19976, 333, 670, 408, 19970])).
% 3.16/3.48 tff(19978,plain,
% 3.16/3.48 (s(s(z)) = elem!1),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[7970, 19977, 19963])).
% 3.16/3.48 tff(19979,plain,
% 3.16/3.48 (s(elem!1) = s(s(s(z)))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[11670, 19978])).
% 3.16/3.48 tff(19980,plain,
% 3.16/3.48 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19979])).
% 3.16/3.48 tff(19981,plain,
% 3.16/3.48 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19980])).
% 3.16/3.48 tff(19982,plain,
% 3.16/3.48 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.16/3.48 inference(symmetry,[status(thm)],[19981])).
% 3.16/3.48 tff(19983,plain,
% 3.16/3.48 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19982])).
% 3.16/3.48 tff(19984,plain,
% 3.16/3.48 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.16/3.48 inference(symmetry,[status(thm)],[19983])).
% 3.16/3.48 tff(19985,plain,
% 3.16/3.48 (~r(s(z), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[16388, 19938, 15126, 19388])).
% 3.16/3.48 tff(19986,plain,
% 3.16/3.48 (b(s(z), s(s(s(z))))),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[172, 19985])).
% 3.16/3.48 tff(19987,plain,
% 3.16/3.48 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), 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(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(19988,plain,
% 3.16/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19987])).
% 3.16/3.48 tff(19989,plain,
% 3.16/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.16/3.48 inference(transitivity,[status(thm)],[19988, 10687])).
% 3.16/3.48 tff(19990,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 3.16/3.48 inference(quant_inst,[status(thm)],[])).
% 3.16/3.48 tff(19991,plain,
% 3.16/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19990, 19989])).
% 3.16/3.48 tff(19992,plain,
% 3.16/3.48 (~b(s(z), elem!1)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[19991, 144, 19944, 19986, 19936])).
% 3.16/3.48 tff(19993,plain,
% 3.16/3.48 (r(s(z), elem!1)),
% 3.16/3.48 inference(unit_resolution,[status(thm)],[406, 19992, 15133])).
% 3.16/3.48 tff(19994,plain,
% 3.16/3.48 (s(s(s(z))) = s(elem!1)),
% 3.16/3.48 inference(modus_ponens,[status(thm)],[19979, 998])).
% 3.16/3.48 tff(19995,plain,
% 3.16/3.48 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[1002])).
% 3.16/3.48 tff(19996,plain,
% 3.16/3.48 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.16/3.48 inference(symmetry,[status(thm)],[19995])).
% 3.16/3.48 tff(19997,plain,
% 3.16/3.48 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19996])).
% 3.16/3.48 tff(19998,plain,
% 3.16/3.48 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.16/3.48 inference(symmetry,[status(thm)],[19997])).
% 3.16/3.48 tff(19999,plain,
% 3.16/3.48 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.16/3.48 inference(monotonicity,[status(thm)],[19998])).
% 3.16/3.48 tff(20000,plain,
% 3.16/3.48 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 3.16/3.48 inference(symmetry,[status(thm)],[19999])).
% 3.16/3.48 tff(20001,plain,
% 3.16/3.48 (((~![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(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, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.16/3.48 inference(rewrite,[status(thm)],[])).
% 3.16/3.48 tff(20002,plain,
% 3.16/3.48 ((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20003,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20002, 20001])).
% 3.16/3.49 tff(20004,plain,
% 3.16/3.49 ($false),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20003, 333, 409, 3065, 1024, 408])).
% 3.16/3.49 tff(20005,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.49 tff(20006,plain,
% 3.16/3.49 (~r(s(s(s(elem!1))), s(z))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20005, 3065, 409, 408])).
% 3.16/3.49 tff(20007,plain,
% 3.16/3.49 (b(s(s(s(elem!1))), s(z))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[1101, 20006])).
% 3.16/3.49 tff(20008,plain,
% 3.16/3.49 (b(s(s(s(s(s(z))))), s(z))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20007, 20000])).
% 3.16/3.49 tff(20009,plain,
% 3.16/3.49 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20010,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[20009])).
% 3.16/3.49 tff(20011,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.49 inference(transitivity,[status(thm)],[20010, 19862])).
% 3.16/3.49 tff(20012,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20013,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20012, 20011])).
% 3.16/3.49 tff(20014,plain,
% 3.16/3.49 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20013, 144, 490, 489])).
% 3.16/3.49 tff(20015,plain,
% 3.16/3.49 (~b(s(s(s(s(s(z))))), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20014, 20008])).
% 3.16/3.49 tff(20016,plain,
% 3.16/3.49 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 3.16/3.49 inference(monotonicity,[status(thm)],[19998])).
% 3.16/3.49 tff(20017,plain,
% 3.16/3.49 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.16/3.49 inference(symmetry,[status(thm)],[20016])).
% 3.16/3.49 tff(20018,plain,
% 3.16/3.49 (r(s(s(s(s(s(z))))), elem!1)),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[3065, 20017])).
% 3.16/3.49 tff(20019,plain,
% 3.16/3.49 (((~![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(s(z))))), elem!1)) | (~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(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20020,plain,
% 3.16/3.49 ((~![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(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20021,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20020, 20019])).
% 3.16/3.49 tff(20022,plain,
% 3.16/3.49 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20021, 333, 670, 408])).
% 3.16/3.49 tff(20023,plain,
% 3.16/3.49 (~r(s(s(s(s(s(z))))), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20022, 20018])).
% 3.16/3.49 tff(20024,plain,
% 3.16/3.49 ($false),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 20023, 20015])).
% 3.16/3.49 tff(20025,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~(s(s(s(z))) = s(elem!1))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.16/3.49 tff(20026,plain,
% 3.16/3.49 (~r(s(s(s(elem!1))), elem!1)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20025, 19994, 408, 670, 489, 490, 19993])).
% 3.16/3.49 tff(20027,plain,
% 3.16/3.49 (~(s(s(s(elem!1))) = elem!1)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[1010, 19994])).
% 3.16/3.49 tff(20028,plain,
% 3.16/3.49 (b(s(s(s(elem!1))), elem!1)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[1079, 20027, 20026])).
% 3.16/3.49 tff(20029,plain,
% 3.16/3.49 (b(s(s(s(s(s(z))))), elem!1)),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20028, 19984])).
% 3.16/3.49 tff(20030,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20031,plain,
% 3.16/3.49 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20032,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[20031])).
% 3.16/3.49 tff(20033,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.16/3.49 inference(transitivity,[status(thm)],[20032, 20030])).
% 3.16/3.49 tff(20034,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20035,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20034, 20033])).
% 3.16/3.49 tff(20036,plain,
% 3.16/3.49 ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20035, 144, 17788, 17789])).
% 3.16/3.49 tff(20037,plain,
% 3.16/3.49 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20036, 20029])).
% 3.16/3.49 tff(20038,plain,
% 3.16/3.49 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[990, 19979, 1])).
% 3.16/3.49 tff(20039,plain,
% 3.16/3.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[12459, 20038])).
% 3.16/3.49 tff(20040,plain,
% 3.16/3.49 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[19979])).
% 3.16/3.49 tff(20041,plain,
% 3.16/3.49 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 3.16/3.49 inference(symmetry,[status(thm)],[20040])).
% 3.16/3.49 tff(20042,plain,
% 3.16/3.49 (b(elem!1, s(elem!1))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[19944, 20041])).
% 3.16/3.49 tff(20043,plain,
% 3.16/3.49 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[19979])).
% 3.16/3.49 tff(20044,plain,
% 3.16/3.49 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 3.16/3.49 inference(symmetry,[status(thm)],[20043])).
% 3.16/3.49 tff(20045,plain,
% 3.16/3.49 (b(s(elem!1), s(z))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[19940, 20044])).
% 3.16/3.49 tff(20046,plain,
% 3.16/3.49 (~b(s(elem!1), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[6057, 19979, 19941])).
% 3.16/3.49 tff(20047,plain,
% 3.16/3.49 (r(s(elem!1), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[507, 20046])).
% 3.16/3.49 tff(20048,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20049,plain,
% 3.16/3.49 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20050,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[20049])).
% 3.16/3.49 tff(20051,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.16/3.49 inference(transitivity,[status(thm)],[20050, 20048])).
% 3.16/3.49 tff(20052,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20053,plain,
% 3.16/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20052, 20051])).
% 3.16/3.49 tff(20054,plain,
% 3.16/3.49 (~b(s(s(s(elem!1))), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20053, 144, 490, 3584, 489])).
% 3.16/3.49 tff(20055,plain,
% 3.16/3.49 (r(s(s(s(elem!1))), z)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 20054])).
% 3.16/3.49 tff(20056,plain,
% 3.16/3.49 (((~![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))), 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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20057,plain,
% 3.16/3.49 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20058,plain,
% 3.16/3.49 (((~![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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 3.16/3.49 inference(monotonicity,[status(thm)],[20057])).
% 3.16/3.49 tff(20059,plain,
% 3.16/3.49 (((~![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(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.16/3.49 inference(transitivity,[status(thm)],[20058, 20056])).
% 3.16/3.49 tff(20060,plain,
% 3.16/3.49 ((~![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)))),
% 3.16/3.49 inference(quant_inst,[status(thm)],[])).
% 3.16/3.49 tff(20061,plain,
% 3.16/3.49 ((~![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))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 3.16/3.49 inference(modus_ponens,[status(thm)],[20060, 20059])).
% 3.16/3.49 tff(20062,plain,
% 3.16/3.49 (~r(s(s(s(elem!1))), elem!1)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[20061, 333, 670, 408, 20055])).
% 3.16/3.49 tff(20063,plain,
% 3.16/3.49 (b(s(s(s(elem!1))), elem!1)),
% 3.16/3.49 inference(unit_resolution,[status(thm)],[1079, 20062, 1012])).
% 3.16/3.49 tff(20064,plain,
% 3.16/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.16/3.49 tff(20065,plain,
% 3.16/3.49 (((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.16/3.49 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20066,plain,
% 3.25/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20065])).
% 3.25/3.50 tff(20067,plain,
% 3.25/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[20066, 20064])).
% 3.25/3.50 tff(20068,plain,
% 3.25/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(20069,plain,
% 3.25/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20068, 20067])).
% 3.25/3.50 tff(20070,plain,
% 3.25/3.50 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20069, 144, 547, 3584, 488])).
% 3.25/3.50 tff(20071,plain,
% 3.25/3.50 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20070, 20063])).
% 3.25/3.50 tff(20072,plain,
% 3.25/3.50 (((~![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(s(s(elem!1))), z)) | (~r(s(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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20073,plain,
% 3.25/3.50 ((~![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(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(20074,plain,
% 3.25/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20073, 20072])).
% 3.25/3.50 tff(20075,plain,
% 3.25/3.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20074, 333, 670, 509, 20055])).
% 3.25/3.50 tff(20076,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[3130, 44, 3127, 20075, 20071])).
% 3.25/3.50 tff(20077,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(20078,plain,
% 3.25/3.50 (~b(s(s(s(elem!1))), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20077, 20027, 408, 670, 490, 20047, 20045, 20042, 20039, 489])).
% 3.25/3.50 tff(20079,plain,
% 3.25/3.50 (r(s(s(s(elem!1))), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1101, 20078])).
% 3.25/3.50 tff(20080,plain,
% 3.25/3.50 (r(s(s(s(s(s(z))))), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[13206, 20079, 19979])).
% 3.25/3.50 tff(20081,plain,
% 3.25/3.50 (((~![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(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20082,plain,
% 3.25/3.50 (((~r(s(z), elem!1)) | (~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20083,plain,
% 3.25/3.50 (((~![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(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(s(s(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(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20082])).
% 3.25/3.50 tff(20084,plain,
% 3.25/3.50 (((~![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(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(s(s(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(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[20083, 20081])).
% 3.25/3.50 tff(20085,plain,
% 3.25/3.50 ((~![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(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(s(s(s(z))))))))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(20086,plain,
% 3.25/3.50 ((~![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(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20085, 20084])).
% 3.25/3.50 tff(20087,plain,
% 3.25/3.50 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20086, 333, 19993, 20080, 19388])).
% 3.25/3.50 tff(20088,plain,
% 3.25/3.50 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1159, 44, 20087])).
% 3.25/3.50 tff(20089,plain,
% 3.25/3.50 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20088, 20037])).
% 3.25/3.50 tff(20090,plain,
% 3.25/3.50 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 3.25/3.50 inference(symmetry,[status(thm)],[20089])).
% 3.25/3.50 tff(20091,plain,
% 3.25/3.50 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20090])).
% 3.25/3.50 tff(20092,plain,
% 3.25/3.50 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(symmetry,[status(thm)],[20091])).
% 3.25/3.50 tff(20093,plain,
% 3.25/3.50 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[239, 20092, 20])).
% 3.25/3.50 tff(20094,plain,
% 3.25/3.50 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20093])).
% 3.25/3.50 tff(20095,plain,
% 3.25/3.50 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 3.25/3.50 inference(symmetry,[status(thm)],[20094])).
% 3.25/3.50 tff(20096,plain,
% 3.25/3.50 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.25/3.50 inference(transitivity,[status(thm)],[19981, 93, 20095, 183])).
% 3.25/3.50 tff(20097,plain,
% 3.25/3.50 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[19979])).
% 3.25/3.50 tff(20098,plain,
% 3.25/3.50 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[20097, 972])).
% 3.25/3.50 tff(20099,plain,
% 3.25/3.50 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20098])).
% 3.25/3.50 tff(20100,plain,
% 3.25/3.50 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20038, 20099])).
% 3.25/3.50 tff(20101,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20100, 20096])).
% 3.25/3.50 tff(20102,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(20103,plain,
% 3.25/3.50 (s(s(s(z))) = elem!1),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20102, 259, 670, 19935, 489, 1, 286, 408, 3, 54, 19569])).
% 3.25/3.50 tff(20104,plain,
% 3.25/3.50 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[12214, 20103])).
% 3.25/3.50 tff(20105,plain,
% 3.25/3.50 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[7595, 20103, 19208])).
% 3.25/3.50 tff(20106,plain,
% 3.25/3.50 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[5603, 20105])).
% 3.25/3.50 tff(20107,plain,
% 3.25/3.50 (~(s(elem!1) = elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[5813, 20106])).
% 3.25/3.50 tff(20108,plain,
% 3.25/3.50 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[10345, 144, 491, 286, 259])).
% 3.25/3.50 tff(20109,plain,
% 3.25/3.50 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20110,plain,
% 3.25/3.50 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20111,plain,
% 3.25/3.50 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20110])).
% 3.25/3.50 tff(20112,plain,
% 3.25/3.50 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[20111, 20109])).
% 3.25/3.50 tff(20113,plain,
% 3.25/3.50 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(20114,plain,
% 3.25/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20113, 20112])).
% 3.25/3.50 tff(20115,plain,
% 3.25/3.50 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20114, 333, 9318, 11546, 19388])).
% 3.25/3.50 tff(20116,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[472, 20115, 20108, 432])).
% 3.25/3.50 tff(20117,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(20118,plain,
% 3.25/3.50 (~b(s(elem!1), z)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20117, 20104, 15126, 286, 259, 1, 489, 19935])).
% 3.25/3.50 tff(20119,plain,
% 3.25/3.50 (r(s(elem!1), z)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[507, 20118])).
% 3.25/3.50 tff(20120,plain,
% 3.25/3.50 (~r(s(elem!1), elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[11139, 20119, 670, 722])).
% 3.25/3.50 tff(20121,plain,
% 3.25/3.50 (b(s(elem!1), elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[448, 20120, 20107])).
% 3.25/3.50 tff(20122,plain,
% 3.25/3.50 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[462, 20121, 17788, 17789])).
% 3.25/3.50 tff(20123,plain,
% 3.25/3.50 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[472, 20122, 20104])).
% 3.25/3.50 tff(20124,plain,
% 3.25/3.50 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[7093, 286, 489, 19935])).
% 3.25/3.50 tff(20125,plain,
% 3.25/3.50 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[319, 20124])).
% 3.25/3.50 tff(20126,plain,
% 3.25/3.50 (~r(elem!1, s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[678, 20119, 408, 670])).
% 3.25/3.50 tff(20127,plain,
% 3.25/3.50 (~(elem!1 = s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1569, 20107])).
% 3.25/3.50 tff(20128,plain,
% 3.25/3.50 (~r(s(elem!1), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[481, 409, 17787, 408, 54, 20125, 3, 20107, 20104])).
% 3.25/3.50 tff(20129,plain,
% 3.25/3.50 (b(s(elem!1), s(z))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[486, 20128, 1])).
% 3.25/3.50 tff(20130,plain,
% 3.25/3.50 (~r(s(elem!1), elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[16793, 409, 623, 1, 408, 489, 19935])).
% 3.25/3.50 tff(20131,plain,
% 3.25/3.50 (b(s(elem!1), elem!1)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[448, 20130, 20107])).
% 3.25/3.50 tff(20132,plain,
% 3.25/3.50 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[462, 20131, 17788, 17789])).
% 3.25/3.50 tff(20133,plain,
% 3.25/3.50 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[472, 20132, 20104])).
% 3.25/3.50 tff(20134,plain,
% 3.25/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20135,plain,
% 3.25/3.50 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20136,plain,
% 3.25/3.50 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[20135])).
% 3.25/3.50 tff(20137,plain,
% 3.25/3.50 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[20136, 20134])).
% 3.25/3.50 tff(20138,plain,
% 3.25/3.50 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(20139,plain,
% 3.25/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[20138, 20137])).
% 3.25/3.50 tff(20140,plain,
% 3.25/3.50 (~r(s(z), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[20139, 333, 15126, 20125, 20133])).
% 3.25/3.50 tff(20141,plain,
% 3.25/3.50 (b(s(z), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1244, 20140, 1229])).
% 3.25/3.50 tff(20142,plain,
% 3.25/3.50 (~b(z, s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1853, 20141, 19935, 20129])).
% 3.25/3.50 tff(20143,plain,
% 3.25/3.50 (r(z, s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[583, 20142])).
% 3.25/3.50 tff(20144,plain,
% 3.25/3.50 (~b(s(elem!1), z)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[499, 20129, 489, 19935])).
% 3.25/3.50 tff(20145,plain,
% 3.25/3.50 (r(s(elem!1), z)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[507, 20144])).
% 3.25/3.50 tff(20146,plain,
% 3.25/3.50 (~(s(s(elem!1)) = s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1196, 20127])).
% 3.25/3.50 tff(20147,plain,
% 3.25/3.50 (~r(elem!1, s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[678, 20145, 408, 670])).
% 3.25/3.50 tff(20148,plain,
% 3.25/3.50 (b(elem!1, s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[560, 20147, 20127])).
% 3.25/3.50 tff(20149,plain,
% 3.25/3.50 (~b(s(s(elem!1)), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1278, 20141, 722, 20131, 20148, 20105, 20129, 409])).
% 3.25/3.50 tff(20150,plain,
% 3.25/3.50 (r(s(s(elem!1)), s(elem!1))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[1283, 20149, 20146])).
% 3.25/3.50 tff(20151,plain,
% 3.25/3.50 (((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), 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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(20152,plain,
% 3.25/3.50 (((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20153,plain,
% 3.25/3.51 (((~![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(elem!1))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20152])).
% 3.25/3.51 tff(20154,plain,
% 3.25/3.51 (((~![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(elem!1))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20153, 20151])).
% 3.25/3.51 tff(20155,plain,
% 3.25/3.51 ((~![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(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(20156,plain,
% 3.25/3.51 ((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20155, 20154])).
% 3.25/3.51 tff(20157,plain,
% 3.25/3.51 (~r(s(s(elem!1)), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20156, 333, 20150, 20145, 20143])).
% 3.25/3.51 tff(20158,plain,
% 3.25/3.51 (b(s(s(elem!1)), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[5509, 20157])).
% 3.25/3.51 tff(20159,plain,
% 3.25/3.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7608, 20103, 15133])).
% 3.25/3.51 tff(20160,plain,
% 3.25/3.51 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7776, 20159])).
% 3.25/3.51 tff(20161,plain,
% 3.25/3.51 (s(s(s(s(z)))) = s(elem!1)),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20103])).
% 3.25/3.51 tff(20162,plain,
% 3.25/3.51 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20161])).
% 3.25/3.51 tff(20163,plain,
% 3.25/3.51 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20162, 174])).
% 3.25/3.51 tff(20164,plain,
% 3.25/3.51 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20163])).
% 3.25/3.51 tff(20165,plain,
% 3.25/3.51 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[196, 20164])).
% 3.25/3.51 tff(20166,plain,
% 3.25/3.51 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[555, 20148, 17788, 20131])).
% 3.25/3.51 tff(20167,plain,
% 3.25/3.51 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[542, 20166, 20165])).
% 3.25/3.51 tff(20168,plain,
% 3.25/3.51 (((~![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(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20169,plain,
% 3.25/3.51 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20170,plain,
% 3.25/3.51 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20169])).
% 3.25/3.51 tff(20171,plain,
% 3.25/3.51 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20170, 20168])).
% 3.25/3.51 tff(20172,plain,
% 3.25/3.51 ((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(20173,plain,
% 3.25/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20172, 20171])).
% 3.25/3.51 tff(20174,plain,
% 3.25/3.51 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20173, 333, 20150, 20145, 20167])).
% 3.25/3.51 tff(20175,plain,
% 3.25/3.51 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7819, 44, 20174, 20160])).
% 3.25/3.51 tff(20176,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[8153, 144, 286, 20175, 259, 20158])).
% 3.25/3.51 tff(20177,plain,((~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(20178,plain,
% 3.25/3.51 (~r(s(z), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20177, 259, 286, 722, 408, 670, 489, 1, 54, 3, 623])).
% 3.25/3.51 tff(20179,plain,
% 3.25/3.51 (b(s(z), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[406, 20178, 15133])).
% 3.25/3.51 tff(20180,plain,
% 3.25/3.51 (~b(s(z), s(elem!1))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1732, 20120, 20179, 20127, 20126])).
% 3.25/3.51 tff(20181,plain,
% 3.25/3.51 (r(s(z), s(elem!1))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1244, 20180, 1229])).
% 3.25/3.51 tff(20182,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20139, 333, 20181, 15126, 20125, 20123])).
% 3.25/3.51 tff(20183,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(20184,plain,
% 3.25/3.51 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20183, 19570, 670, 408, 19933, 1, 19780, 54, 3, 623])).
% 3.25/3.51 tff(20185,plain,
% 3.25/3.51 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[279, 20184])).
% 3.25/3.51 tff(20186,plain,
% 3.25/3.51 (s(s(s(z))) = elem!1),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19555, 20185, 15126, 408, 623, 17789, 19572, 17787, 3, 54])).
% 3.25/3.51 tff(20187,plain,
% 3.25/3.51 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19601, 20186, 17789])).
% 3.25/3.51 tff(20188,plain,
% 3.25/3.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[227, 20186, 54])).
% 3.25/3.51 tff(20189,plain,
% 3.25/3.51 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[249, 20188])).
% 3.25/3.51 tff(20190,plain,
% 3.25/3.51 (~b(elem!1, s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[18960, 20189, 17789, 20187])).
% 3.25/3.51 tff(20191,plain,
% 3.25/3.51 (~b(s(s(s(z))), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[380, 20186, 377])).
% 3.25/3.51 tff(20192,plain,
% 3.25/3.51 (r(s(s(s(z))), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[396, 20191])).
% 3.25/3.51 tff(20193,plain,
% 3.25/3.51 (~r(elem!1, s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[11956, 333, 408, 20192, 20185])).
% 3.25/3.51 tff(20194,plain,
% 3.25/3.51 (elem!1 = s(s(s(z)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1538, 20193, 20190])).
% 3.25/3.51 tff(20195,plain,
% 3.25/3.51 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20194])).
% 3.25/3.51 tff(20196,plain,
% 3.25/3.51 (~(s(s(z)) = elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[14611, 20186, 15133])).
% 3.25/3.51 tff(20197,plain,
% 3.25/3.51 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7093, 19933, 19780, 19572])).
% 3.25/3.51 tff(20198,plain,
% 3.25/3.51 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[319, 20197])).
% 3.25/3.51 tff(20199,plain,
% 3.25/3.51 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19392, 20185, 19572, 19780, 20198, 15126])).
% 3.25/3.51 tff(20200,plain,
% 3.25/3.51 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[17920, 20185, 19572, 19780, 20198, 15126])).
% 3.25/3.51 tff(20201,plain,
% 3.25/3.51 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1451, 20200])).
% 3.25/3.51 tff(20202,plain,
% 3.25/3.51 (~b(s(s(z)), s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7952, 20201, 20188, 20199])).
% 3.25/3.51 tff(20203,plain,
% 3.25/3.51 (~b(s(s(z)), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7936, 20202, 20186])).
% 3.25/3.51 tff(20204,plain,
% 3.25/3.51 (r(s(s(z)), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7970, 20203, 20196])).
% 3.25/3.51 tff(20205,plain,
% 3.25/3.51 (r(s(s(z)), s(s(s(z))))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20204, 20195])).
% 3.25/3.51 tff(20206,plain,
% 3.25/3.51 (((~![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)), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20207,plain,
% 3.25/3.51 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20208,plain,
% 3.25/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20207])).
% 3.25/3.51 tff(20209,plain,
% 3.25/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20208, 20206])).
% 3.25/3.51 tff(20210,plain,
% 3.25/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(20211,plain,
% 3.25/3.51 ((~![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)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20210, 20209])).
% 3.25/3.51 tff(20212,plain,
% 3.25/3.51 (~r(s(s(z)), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20211, 333, 20192, 623, 20205])).
% 3.25/3.51 tff(20213,plain,
% 3.25/3.51 (b(s(s(z)), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1462, 44, 164, 20212])).
% 3.25/3.51 tff(20214,plain,
% 3.25/3.51 (~b(s(s(z)), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19429, 144, 19572, 19780, 20213])).
% 3.25/3.51 tff(20215,plain,
% 3.25/3.51 (r(s(s(z)), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1429, 44, 20214, 1416])).
% 3.25/3.51 tff(20216,plain,
% 3.25/3.51 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20194])).
% 3.25/3.51 tff(20217,plain,
% 3.25/3.51 (r(s(s(s(z))), s(z))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[19570, 20216])).
% 3.25/3.51 tff(20218,plain,
% 3.25/3.51 (((~![X0: $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(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20219,plain,
% 3.25/3.51 (((~r(s(z), s(s(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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(rewrite,[status(thm)],[])).
% 3.25/3.51 tff(20220,plain,
% 3.25/3.51 (((~![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(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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20219])).
% 3.25/3.51 tff(20221,plain,
% 3.25/3.51 (((~![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(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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20220, 20218])).
% 3.25/3.51 tff(20222,plain,
% 3.25/3.51 ((~![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(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))))))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(20223,plain,
% 3.25/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20222, 20221])).
% 3.25/3.51 tff(20224,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20223, 333, 20217, 15126, 20205, 20215])).
% 3.25/3.51 tff(20225,plain,(b(elem!1, s(z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)) | b(elem!1, z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(20226,plain,
% 3.25/3.51 (b(elem!1, s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20225, 54, 408, 377, 623, 3, 670, 1])).
% 3.25/3.51 tff(20227,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[690, 333, 670, 409, 354, 408])).
% 3.25/3.51 tff(20228,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(20229,plain,
% 3.25/3.51 (~r(s(z), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20228, 354, 670, 408])).
% 3.25/3.51 tff(20230,plain,
% 3.25/3.51 (b(s(z), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[406, 20229, 15133])).
% 3.25/3.51 tff(20231,plain,
% 3.25/3.51 (~b(s(s(s(z))), elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19581, 20230, 15126, 20226, 17787, 3, 54])).
% 3.25/3.51 tff(20232,plain,
% 3.25/3.51 (s(s(s(z))) = elem!1),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[704, 20231, 19569])).
% 3.25/3.51 tff(20233,plain,
% 3.25/3.51 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[19601, 20232, 17789])).
% 3.25/3.51 tff(20234,plain,
% 3.25/3.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[227, 20232, 54])).
% 3.25/3.51 tff(20235,plain,
% 3.25/3.51 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[249, 20234])).
% 3.25/3.51 tff(20236,plain,
% 3.25/3.51 (~b(elem!1, s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[18960, 20235, 17789, 20233])).
% 3.25/3.51 tff(20237,plain,
% 3.25/3.51 (~b(s(s(s(z))), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[380, 20232, 377])).
% 3.25/3.51 tff(20238,plain,
% 3.25/3.51 (r(s(s(s(z))), z)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[396, 20237])).
% 3.25/3.51 tff(20239,plain,
% 3.25/3.51 (~r(elem!1, s(s(s(z))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 20238])).
% 3.25/3.51 tff(20240,plain,
% 3.25/3.51 (elem!1 = s(s(s(z)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[1538, 20239, 20236])).
% 3.25/3.51 tff(20241,plain,
% 3.25/3.51 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20240])).
% 3.25/3.51 tff(20242,plain,
% 3.25/3.51 (s(s(s(s(z)))) = s(elem!1)),
% 3.25/3.51 inference(symmetry,[status(thm)],[20241])).
% 3.25/3.51 tff(20243,plain,
% 3.25/3.51 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(elem!1))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20242])).
% 3.25/3.51 tff(20244,plain,
% 3.25/3.51 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(z))),
% 3.25/3.51 inference(transitivity,[status(thm)],[20243, 1577])).
% 3.25/3.51 tff(20245,plain,
% 3.25/3.51 ((s(elem!1) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 3.25/3.51 inference(symmetry,[status(thm)],[20244])).
% 3.25/3.51 tff(20246,plain,
% 3.25/3.51 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20245])).
% 3.25/3.51 tff(20247,plain,
% 3.25/3.51 (~(s(z) = s(s(s(s(z)))))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[1, 20246])).
% 3.25/3.51 tff(20248,plain,
% 3.25/3.51 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20242])).
% 3.25/3.51 tff(20249,plain,
% 3.25/3.51 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 3.25/3.51 inference(symmetry,[status(thm)],[20248])).
% 3.25/3.51 tff(20250,plain,
% 3.25/3.51 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[7595, 20232, 19208])).
% 3.25/3.51 tff(20251,plain,
% 3.25/3.51 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[5603, 20250])).
% 3.25/3.51 tff(20252,plain,
% 3.25/3.51 (~(s(elem!1) = elem!1)),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[5813, 20251])).
% 3.25/3.51 tff(20253,plain,
% 3.25/3.51 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20240])).
% 3.25/3.51 tff(20254,plain,
% 3.25/3.51 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 3.25/3.51 inference(symmetry,[status(thm)],[20253])).
% 3.25/3.51 tff(20255,plain,
% 3.25/3.51 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20242, 20240])).
% 3.25/3.51 tff(20256,plain,
% 3.25/3.51 (s(s(s(z))) = elem!1),
% 3.25/3.51 inference(symmetry,[status(thm)],[20240])).
% 3.25/3.51 tff(20257,plain,
% 3.25/3.51 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20256])).
% 3.25/3.51 tff(20258,plain,
% 3.25/3.51 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 3.25/3.51 inference(transitivity,[status(thm)],[20257, 20255, 20254])).
% 3.25/3.51 tff(20259,plain,
% 3.25/3.51 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(elem!1), elem!1))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20258])).
% 3.25/3.51 tff(20260,plain,
% 3.25/3.51 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20240])).
% 3.25/3.51 tff(20261,plain,
% 3.25/3.51 (b(s(z), s(s(s(z))))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20230, 20260])).
% 3.25/3.51 tff(20262,plain,
% 3.25/3.51 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20240])).
% 3.25/3.51 tff(20263,plain,
% 3.25/3.51 (b(s(s(s(z))), s(z))),
% 3.25/3.51 inference(modus_ponens,[status(thm)],[20226, 20262])).
% 3.25/3.51 tff(20264,plain,
% 3.25/3.51 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[3955, 20230, 17788, 20226])).
% 3.25/3.51 tff(20265,plain,
% 3.25/3.51 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[319, 20264])).
% 3.25/3.51 tff(20266,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.25/3.51 tff(20267,plain,
% 3.25/3.51 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[18464, 144, 283, 2254])).
% 3.25/3.51 tff(20268,plain,
% 3.25/3.51 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[20267, 20266])).
% 3.25/3.51 tff(20269,plain,
% 3.25/3.51 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[9761, 20268])).
% 3.25/3.51 tff(20270,plain,
% 3.25/3.51 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[19607])).
% 3.25/3.51 tff(20271,plain,
% 3.25/3.51 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 3.25/3.51 inference(symmetry,[status(thm)],[19636])).
% 3.25/3.51 tff(20272,plain,
% 3.25/3.51 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 3.25/3.51 inference(monotonicity,[status(thm)],[20271])).
% 3.25/3.51 tff(20273,plain,
% 3.25/3.51 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18487, 144, 56, 838])).
% 3.25/3.52 tff(20274,plain,
% 3.25/3.52 (~b(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20273, 20266])).
% 3.25/3.52 tff(20275,plain,
% 3.25/3.52 (~b(s(elem!1), s(z))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20274, 20272])).
% 3.25/3.52 tff(20276,plain,
% 3.25/3.52 (r(s(elem!1), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[486, 20275, 1])).
% 3.25/3.52 tff(20277,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20276, 20270])).
% 3.25/3.52 tff(20278,plain,
% 3.25/3.52 ($false),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19765, 333, 20277, 11546, 322, 20269])).
% 3.25/3.52 tff(20279,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(elem!1 = s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.52 tff(20280,plain,
% 3.25/3.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20279, 20265, 15126, 20240, 1, 20235, 20233, 20263, 20261])).
% 3.25/3.52 tff(20281,plain,
% 3.25/3.52 (~b(s(elem!1), elem!1)),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20280, 20259])).
% 3.25/3.52 tff(20282,plain,
% 3.25/3.52 (r(s(elem!1), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[448, 20281, 20252])).
% 3.25/3.52 tff(20283,plain,
% 3.25/3.52 (~r(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[10865, 20282, 623, 408])).
% 3.25/3.52 tff(20284,plain,
% 3.25/3.52 (b(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[507, 20283])).
% 3.25/3.52 tff(20285,plain,
% 3.25/3.52 (b(s(s(s(s(z)))), z)),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20284, 20249])).
% 3.25/3.52 tff(20286,plain,
% 3.25/3.52 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18594, 333, 354, 15126, 20265])).
% 3.25/3.52 tff(20287,plain,
% 3.25/3.52 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[279, 20286])).
% 3.25/3.52 tff(20288,plain,
% 3.25/3.52 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18394, 333, 354, 15126, 20265])).
% 3.25/3.52 tff(20289,plain,
% 3.25/3.52 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[302, 20288])).
% 3.25/3.52 tff(20290,plain,
% 3.25/3.52 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19705, 144, 20289, 20287])).
% 3.25/3.52 tff(20291,plain,
% 3.25/3.52 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20290, 20285])).
% 3.25/3.52 tff(20292,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[9761, 20291])).
% 3.25/3.52 tff(20293,plain,
% 3.25/3.52 (~r(s(z), s(s(s(s(z)))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19714, 333, 15126, 20265, 20292])).
% 3.25/3.52 tff(20294,plain,
% 3.25/3.52 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20241])).
% 3.25/3.52 tff(20295,plain,
% 3.25/3.52 (~(s(s(z)) = elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[14611, 20232, 15133])).
% 3.25/3.52 tff(20296,plain,
% 3.25/3.52 (~(s(elem!1) = s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1508, 20295])).
% 3.25/3.52 tff(20297,plain,
% 3.25/3.52 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(transitivity,[status(thm)],[20257, 20255])).
% 3.25/3.52 tff(20298,plain,
% 3.25/3.52 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20297])).
% 3.25/3.52 tff(20299,plain,
% 3.25/3.52 (~b(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20280, 20298])).
% 3.25/3.52 tff(20300,plain,
% 3.25/3.52 (r(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[965, 20299, 20296])).
% 3.25/3.52 tff(20301,plain,
% 3.25/3.52 (~r(z, s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1972, 20300, 623, 20238])).
% 3.25/3.52 tff(20302,plain,
% 3.25/3.52 (b(z, s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[583, 20301])).
% 3.25/3.52 tff(20303,plain,
% 3.25/3.52 (b(z, s(s(s(s(z)))))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20302, 20294])).
% 3.25/3.52 tff(20304,plain,
% 3.25/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.25/3.52 inference(rewrite,[status(thm)],[])).
% 3.25/3.52 tff(20305,plain,
% 3.25/3.52 (((~b(s(s(s(s(z)))), z)) | (~b(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(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.25/3.52 inference(rewrite,[status(thm)],[])).
% 3.25/3.52 tff(20306,plain,
% 3.25/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20305])).
% 3.25/3.52 tff(20307,plain,
% 3.25/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.25/3.52 inference(transitivity,[status(thm)],[20306, 20304])).
% 3.25/3.52 tff(20308,plain,
% 3.25/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 3.25/3.52 inference(quant_inst,[status(thm)],[])).
% 3.25/3.52 tff(20309,plain,
% 3.25/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20308, 20307])).
% 3.25/3.52 tff(20310,plain,
% 3.25/3.52 ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20309, 144, 19780, 20303])).
% 3.25/3.52 tff(20311,plain,
% 3.25/3.52 (~b(s(z), s(s(s(s(z)))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20310, 20285])).
% 3.25/3.52 tff(20312,plain,
% 3.25/3.52 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19906, 44, 20311])).
% 3.25/3.52 tff(20313,plain,
% 3.25/3.52 ($false),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20312, 20293, 20247])).
% 3.25/3.52 tff(20314,plain,((~r(z, s(z))) | (s(elem!1) = s(z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | b(elem!1, z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.52 tff(20315,plain,
% 3.25/3.52 (~r(z, s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20314, 670, 623, 408, 1, 377, 54, 3])).
% 3.25/3.52 tff(20316,plain,
% 3.25/3.52 (b(z, s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[372, 20315])).
% 3.25/3.52 tff(20317,plain,
% 3.25/3.52 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[7093, 304, 19780, 20316])).
% 3.25/3.52 tff(20318,plain,
% 3.25/3.52 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[302, 20317])).
% 3.25/3.52 tff(20319,plain,
% 3.25/3.52 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19223, 20318, 670, 19780, 20316, 15126])).
% 3.25/3.52 tff(20320,plain,
% 3.25/3.52 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1137, 20319])).
% 3.25/3.52 tff(20321,plain,
% 3.25/3.52 (~b(s(s(s(z))), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[10110, 20320, 17787, 3, 54])).
% 3.25/3.52 tff(20322,plain,
% 3.25/3.52 (s(s(s(z))) = elem!1),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[704, 20321, 19569])).
% 3.25/3.52 tff(20323,plain,
% 3.25/3.52 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[227, 20322, 54])).
% 3.25/3.52 tff(20324,plain,
% 3.25/3.52 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[249, 20323])).
% 3.25/3.52 tff(20325,plain,
% 3.25/3.52 (~b(elem!1, s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18960, 20324, 17789, 20320])).
% 3.25/3.52 tff(20326,plain,
% 3.25/3.52 (~b(s(s(s(z))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[380, 20322, 377])).
% 3.25/3.52 tff(20327,plain,
% 3.25/3.52 (r(s(s(s(z))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[396, 20326])).
% 3.25/3.52 tff(20328,plain,
% 3.25/3.52 (~r(elem!1, s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 20327])).
% 3.25/3.52 tff(20329,plain,
% 3.25/3.52 (elem!1 = s(s(s(z)))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1538, 20328, 20325])).
% 3.25/3.52 tff(20330,plain,
% 3.25/3.52 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20329])).
% 3.25/3.52 tff(20331,plain,
% 3.25/3.52 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20330])).
% 3.25/3.52 tff(20332,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 3.25/3.52 inference(symmetry,[status(thm)],[20331])).
% 3.25/3.52 tff(20333,plain,
% 3.25/3.52 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20332])).
% 3.25/3.52 tff(20334,plain,
% 3.25/3.52 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20330])).
% 3.25/3.52 tff(20335,plain,
% 3.25/3.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[12214, 20322])).
% 3.25/3.52 tff(20336,plain,
% 3.25/3.52 (~b(s(z), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[3955, 304, 17788, 20226])).
% 3.25/3.52 tff(20337,plain,
% 3.25/3.52 (r(s(z), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[406, 20336, 15133])).
% 3.25/3.52 tff(20338,plain,
% 3.25/3.52 (~r(s(elem!1), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[16793, 20337, 623, 1, 408, 19780, 20316])).
% 3.25/3.52 tff(20339,plain,
% 3.25/3.52 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[7595, 20322, 19208])).
% 3.25/3.52 tff(20340,plain,
% 3.25/3.52 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[5603, 20339])).
% 3.25/3.52 tff(20341,plain,
% 3.25/3.52 (~(s(elem!1) = elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[5813, 20340])).
% 3.25/3.52 tff(20342,plain,
% 3.25/3.52 (b(s(elem!1), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[448, 20341, 20338])).
% 3.25/3.52 tff(20343,plain,
% 3.25/3.52 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[462, 20342, 17788, 17789])).
% 3.25/3.52 tff(20344,plain,
% 3.25/3.52 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[472, 20343, 20335])).
% 3.25/3.52 tff(20345,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20344, 20334])).
% 3.25/3.52 tff(20346,plain,
% 3.25/3.52 (~r(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19929, 333, 15126, 20318, 20345])).
% 3.25/3.52 tff(20347,plain,
% 3.25/3.52 (~r(s(elem!1), s(z))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20346, 20333])).
% 3.25/3.52 tff(20348,plain,
% 3.25/3.52 (b(s(elem!1), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[486, 20347, 1])).
% 3.25/3.52 tff(20349,plain,
% 3.25/3.52 (~b(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[499, 20348, 19780, 20316])).
% 3.25/3.52 tff(20350,plain,
% 3.25/3.52 (r(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[507, 20349])).
% 3.25/3.52 tff(20351,plain,
% 3.25/3.52 (~(elem!1 = s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1569, 20341])).
% 3.25/3.52 tff(20352,plain,
% 3.25/3.52 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20330])).
% 3.25/3.52 tff(20353,plain,
% 3.25/3.52 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 3.25/3.52 inference(symmetry,[status(thm)],[20352])).
% 3.25/3.52 tff(20354,plain,
% 3.25/3.52 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(elem!1)))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20353])).
% 3.25/3.52 tff(20355,plain,
% 3.25/3.52 (~r(s(z), s(s(s(s(z)))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18706, 333, 15126, 20318, 20345])).
% 3.25/3.52 tff(20356,plain,
% 3.25/3.52 (~r(s(z), s(elem!1))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20355, 20354])).
% 3.25/3.52 tff(20357,plain,
% 3.25/3.52 (b(s(z), s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1244, 20356, 1229])).
% 3.25/3.52 tff(20358,plain,
% 3.25/3.52 (~b(elem!1, s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[4409, 20357, 20226, 20348])).
% 3.25/3.52 tff(20359,plain,
% 3.25/3.52 (r(elem!1, s(elem!1))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[560, 20358, 20351])).
% 3.25/3.52 tff(20360,plain,
% 3.25/3.52 ($false),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[678, 20359, 20350, 408, 670])).
% 3.25/3.52 tff(20361,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | b(elem!1, z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.52 tff(20362,plain,
% 3.25/3.52 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20361, 19568, 19502, 1, 377, 54, 3, 12930])).
% 3.25/3.52 tff(20363,plain,
% 3.25/3.52 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[319, 20362])).
% 3.25/3.52 tff(20364,plain,
% 3.25/3.52 (~r(s(s(s(z))), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[2136, 19568, 12930, 19502])).
% 3.25/3.52 tff(20365,plain,
% 3.25/3.52 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[19223, 321, 670, 19780, 20316, 15126])).
% 3.25/3.52 tff(20366,plain,
% 3.25/3.52 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1137, 20365])).
% 3.25/3.52 tff(20367,plain,
% 3.25/3.52 (~b(s(s(s(z))), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[10110, 20366, 17787, 3, 54])).
% 3.25/3.52 tff(20368,plain,
% 3.25/3.52 (s(s(s(z))) = elem!1),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[704, 20367, 19569])).
% 3.25/3.52 tff(20369,plain,
% 3.25/3.52 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[227, 20368, 54])).
% 3.25/3.52 tff(20370,plain,
% 3.25/3.52 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[249, 20369])).
% 3.25/3.52 tff(20371,plain,
% 3.25/3.52 (~b(elem!1, s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18960, 20370, 17789, 20366])).
% 3.25/3.52 tff(20372,plain,
% 3.25/3.52 (~b(s(s(s(z))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[380, 20368, 377])).
% 3.25/3.52 tff(20373,plain,
% 3.25/3.52 (r(s(s(s(z))), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[396, 20372])).
% 3.25/3.52 tff(20374,plain,
% 3.25/3.52 (~r(elem!1, s(s(s(z))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 20373])).
% 3.25/3.52 tff(20375,plain,
% 3.25/3.52 (elem!1 = s(s(s(z)))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[1538, 20374, 20371])).
% 3.25/3.52 tff(20376,plain,
% 3.25/3.52 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20375])).
% 3.25/3.52 tff(20377,plain,
% 3.25/3.52 (s(s(s(s(z)))) = s(elem!1)),
% 3.25/3.52 inference(symmetry,[status(thm)],[20376])).
% 3.25/3.52 tff(20378,plain,
% 3.25/3.52 (s(s(s(z))) = elem!1),
% 3.25/3.52 inference(symmetry,[status(thm)],[20375])).
% 3.25/3.52 tff(20379,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20378])).
% 3.25/3.52 tff(20380,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.52 inference(symmetry,[status(thm)],[20379])).
% 3.25/3.52 tff(20381,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20377, 20375])).
% 3.25/3.52 tff(20382,plain,
% 3.25/3.52 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.25/3.52 inference(symmetry,[status(thm)],[20381])).
% 3.25/3.52 tff(20383,plain,
% 3.25/3.52 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20375])).
% 3.25/3.52 tff(20384,plain,
% 3.25/3.52 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.25/3.52 inference(transitivity,[status(thm)],[20383, 20382])).
% 3.25/3.52 tff(20385,plain,
% 3.25/3.52 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[7595, 20368, 19208])).
% 3.25/3.52 tff(20386,plain,
% 3.25/3.52 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[5603, 20385])).
% 3.25/3.52 tff(20387,plain,
% 3.25/3.52 (~(s(elem!1) = elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[5813, 20386])).
% 3.25/3.52 tff(20388,plain,
% 3.25/3.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[12214, 20368])).
% 3.25/3.52 tff(20389,plain,
% 3.25/3.52 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20376])).
% 3.25/3.52 tff(20390,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(symmetry,[status(thm)],[20389])).
% 3.25/3.52 tff(20391,plain,
% 3.25/3.52 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20390])).
% 3.25/3.52 tff(20392,plain,
% 3.25/3.52 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20361, 670, 408, 1, 377, 54, 3, 623])).
% 3.25/3.52 tff(20393,plain,
% 3.25/3.52 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[319, 20392])).
% 3.25/3.52 tff(20394,plain,
% 3.25/3.52 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20376])).
% 3.25/3.52 tff(20395,plain,
% 3.25/3.52 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[19607])).
% 3.25/3.52 tff(20396,plain,
% 3.25/3.52 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[3238])).
% 3.25/3.52 tff(20397,plain,
% 3.25/3.52 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.52 inference(transitivity,[status(thm)],[20396, 20395])).
% 3.25/3.52 tff(20398,plain,
% 3.25/3.52 (~r(s(elem!1), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[10865, 509, 623, 408])).
% 3.25/3.52 tff(20399,plain,
% 3.25/3.52 (b(s(elem!1), elem!1)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[448, 20398, 433])).
% 3.25/3.52 tff(20400,plain,
% 3.25/3.52 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20399, 20397])).
% 3.25/3.52 tff(20401,plain,
% 3.25/3.52 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[18464, 144, 283, 2254, 20400])).
% 3.25/3.52 tff(20402,plain,
% 3.25/3.52 ($false),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[9761, 20401, 19816])).
% 3.25/3.52 tff(20403,plain,((~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.52 tff(20404,plain,
% 3.25/3.52 (~r(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[20403, 20370, 20366, 623, 321, 20375, 20387, 408])).
% 3.25/3.52 tff(20405,plain,
% 3.25/3.52 (b(s(elem!1), z)),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[507, 20404])).
% 3.25/3.52 tff(20406,plain,
% 3.25/3.52 (~b(s(elem!1), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[499, 20405, 19780, 20316])).
% 3.25/3.52 tff(20407,plain,
% 3.25/3.52 (r(s(elem!1), s(z))),
% 3.25/3.52 inference(unit_resolution,[status(thm)],[486, 20406, 1])).
% 3.25/3.52 tff(20408,plain,
% 3.25/3.52 (r(s(s(s(s(z)))), s(z))),
% 3.25/3.52 inference(modus_ponens,[status(thm)],[20407, 20394])).
% 3.25/3.52 tff(20409,plain,
% 3.25/3.52 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.52 inference(rewrite,[status(thm)],[])).
% 3.25/3.52 tff(20410,plain,
% 3.25/3.52 (((~![X0: $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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.52 inference(monotonicity,[status(thm)],[20409])).
% 3.25/3.52 tff(20411,plain,
% 3.25/3.52 (((~![X0: $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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.52 inference(transitivity,[status(thm)],[20410, 19760])).
% 3.25/3.52 tff(20412,plain,
% 3.25/3.52 ((~![X0: $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(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.52 inference(quant_inst,[status(thm)],[])).
% 3.25/3.52 tff(20413,plain,
% 3.25/3.53 ((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20412, 20411])).
% 3.25/3.53 tff(20414,plain,
% 3.25/3.53 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20413, 333, 20408, 15126, 20393])).
% 3.25/3.53 tff(20415,plain,
% 3.25/3.53 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20414, 20391])).
% 3.25/3.53 tff(20416,plain,
% 3.25/3.53 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[472, 20415, 20388])).
% 3.25/3.53 tff(20417,plain,
% 3.25/3.53 (~b(s(elem!1), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[464, 20416, 17787, 54, 3])).
% 3.25/3.53 tff(20418,plain,
% 3.25/3.53 (r(s(elem!1), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[448, 20417, 20387])).
% 3.25/3.53 tff(20419,plain,
% 3.25/3.53 (r(s(s(s(s(z)))), elem!1)),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20418, 20384])).
% 3.25/3.53 tff(20420,plain,
% 3.25/3.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20419, 20380])).
% 3.25/3.53 tff(20421,plain,
% 3.25/3.53 (~(elem!1 = s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1569, 20387])).
% 3.25/3.53 tff(20422,plain,
% 3.25/3.53 (r(s(s(s(s(z)))), s(z))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[434, 20270])).
% 3.25/3.53 tff(20423,plain,
% 3.25/3.53 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20413, 333, 20422, 11546, 322])).
% 3.25/3.53 tff(20424,plain,
% 3.25/3.53 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20423, 19807])).
% 3.25/3.53 tff(20425,plain,
% 3.25/3.53 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[19659])).
% 3.25/3.53 tff(20426,plain,
% 3.25/3.53 (((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20427,plain,
% 3.25/3.53 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20428,plain,
% 3.25/3.53 (((~![X0: $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(z))))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20427])).
% 3.25/3.53 tff(20429,plain,
% 3.25/3.53 (((~![X0: $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(z))))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.25/3.53 inference(transitivity,[status(thm)],[20428, 20426])).
% 3.25/3.53 tff(20430,plain,
% 3.25/3.53 ((~![X0: $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(z))))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.25/3.53 inference(quant_inst,[status(thm)],[])).
% 3.25/3.53 tff(20431,plain,
% 3.25/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20430, 20429])).
% 3.25/3.53 tff(20432,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20431, 333, 20422, 11546, 322])).
% 3.25/3.53 tff(20433,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20432, 20425])).
% 3.25/3.53 tff(20434,plain,
% 3.25/3.53 (~b(elem!1, s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[5467, 20433, 132, 19640, 20424])).
% 3.25/3.53 tff(20435,plain,
% 3.25/3.53 (r(elem!1, s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[560, 20434, 902])).
% 3.25/3.53 tff(20436,plain,
% 3.25/3.53 (~b(z, s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[8386, 20433, 259, 19640, 20424])).
% 3.25/3.53 tff(20437,plain,
% 3.25/3.53 (r(z, s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[583, 20436])).
% 3.25/3.53 tff(20438,plain,
% 3.25/3.53 ($false),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[2393, 20437, 20435, 670, 434])).
% 3.25/3.53 tff(20439,plain,((~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.53 tff(20440,plain,
% 3.25/3.53 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20439, 20407, 20421, 670, 17789, 20375, 15126, 20393])).
% 3.25/3.53 tff(20441,plain,
% 3.25/3.53 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[279, 20440])).
% 3.25/3.53 tff(20442,plain,
% 3.25/3.53 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[17920, 20441, 20316, 19780, 20393, 15126])).
% 3.25/3.53 tff(20443,plain,
% 3.25/3.53 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1451, 20442])).
% 3.25/3.53 tff(20444,plain,
% 3.25/3.53 (~b(s(s(z)), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[7952, 20443, 20369, 20365])).
% 3.25/3.53 tff(20445,plain,
% 3.25/3.53 (r(s(s(z)), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1473, 44, 20444, 217])).
% 3.25/3.53 tff(20446,plain,
% 3.25/3.53 (((~![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(s(z)), 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(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20447,plain,
% 3.25/3.53 ((~![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(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.25/3.53 inference(quant_inst,[status(thm)],[])).
% 3.25/3.53 tff(20448,plain,
% 3.25/3.53 ((~![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(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20447, 20446])).
% 3.25/3.53 tff(20449,plain,
% 3.25/3.53 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20448, 333, 20373, 20445])).
% 3.25/3.53 tff(20450,plain,
% 3.25/3.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20449, 20420])).
% 3.25/3.53 tff(20451,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20377])).
% 3.25/3.53 tff(20452,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.25/3.53 inference(symmetry,[status(thm)],[20451])).
% 3.25/3.53 tff(20453,plain,
% 3.25/3.53 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20377])).
% 3.25/3.53 tff(20454,plain,
% 3.25/3.53 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.53 inference(transitivity,[status(thm)],[20453, 174])).
% 3.25/3.53 tff(20455,plain,
% 3.25/3.53 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20454])).
% 3.25/3.53 tff(20456,plain,
% 3.25/3.53 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[196, 20455])).
% 3.25/3.53 tff(20457,plain,
% 3.25/3.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20377])).
% 3.25/3.53 tff(20458,plain,
% 3.25/3.53 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20457])).
% 3.25/3.53 tff(20459,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20431, 333, 20408, 15126, 20393])).
% 3.25/3.53 tff(20460,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20459, 20458])).
% 3.25/3.53 tff(20461,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[542, 20460, 20456])).
% 3.25/3.53 tff(20462,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20461, 20452])).
% 3.25/3.53 tff(20463,plain,
% 3.25/3.53 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[9761, 20414])).
% 3.25/3.53 tff(20464,plain,
% 3.25/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20465,plain,
% 3.25/3.53 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20466,plain,
% 3.25/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20465])).
% 3.25/3.53 tff(20467,plain,
% 3.25/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.25/3.53 inference(transitivity,[status(thm)],[20466, 20464])).
% 3.25/3.53 tff(20468,plain,
% 3.25/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.53 inference(quant_inst,[status(thm)],[])).
% 3.25/3.53 tff(20469,plain,
% 3.25/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20468, 20467])).
% 3.25/3.53 tff(20470,plain,
% 3.25/3.53 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20469, 144, 20443, 20463, 20462])).
% 3.25/3.53 tff(20471,plain,
% 3.25/3.53 (((~![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))))))),
% 3.25/3.53 inference(rewrite,[status(thm)],[])).
% 3.25/3.53 tff(20472,plain,
% 3.25/3.53 ((~![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))))))),
% 3.25/3.53 inference(quant_inst,[status(thm)],[])).
% 3.25/3.53 tff(20473,plain,
% 3.25/3.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20472, 20471])).
% 3.25/3.53 tff(20474,plain,
% 3.25/3.53 (s(s(z)) = s(s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20473, 44, 20470, 20450])).
% 3.25/3.53 tff(20475,plain,
% 3.25/3.53 (s(s(z)) = s(elem!1)),
% 3.25/3.53 inference(transitivity,[status(thm)],[20474, 20377])).
% 3.25/3.53 tff(20476,plain,
% 3.25/3.53 ($false),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[19207, 20475])).
% 3.25/3.53 tff(20477,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 3.25/3.53 tff(20478,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20477, 54, 3, 19568, 1, 12930, 19502, 377])).
% 3.25/3.53 tff(20479,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[302, 20478])).
% 3.25/3.53 tff(20480,plain,
% 3.25/3.53 (~r(s(z), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[19778, 19568, 1, 12930, 19502, 377, 54, 3])).
% 3.25/3.53 tff(20481,plain,
% 3.25/3.53 (b(s(z), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[348, 20480])).
% 3.25/3.53 tff(20482,plain,
% 3.25/3.53 (~r(z, s(z))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20314, 19568, 12930, 19502, 1, 377, 54, 3])).
% 3.25/3.53 tff(20483,plain,
% 3.25/3.53 (b(z, s(z))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[372, 20482])).
% 3.25/3.53 tff(20484,plain,
% 3.25/3.53 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[19392, 17204, 490, 489, 322, 15126])).
% 3.25/3.53 tff(20485,plain,
% 3.25/3.53 (~(s(s(s(z))) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[19601, 11541, 17789])).
% 3.25/3.53 tff(20486,plain,
% 3.25/3.53 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20102, 20485, 670, 490, 489, 1, 286, 408, 3, 54, 699])).
% 3.25/3.53 tff(20487,plain,
% 3.25/3.53 ($false),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[279, 20486, 20484])).
% 3.25/3.53 tff(20488,plain,(b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.53 tff(20489,plain,
% 3.25/3.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20488, 19568, 20483, 20481, 1, 20479, 19502, 3, 54, 20364, 20363])).
% 3.25/3.53 tff(20490,plain,
% 3.25/3.53 (~b(s(s(s(z))), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[10110, 20489, 17787, 3, 54])).
% 3.25/3.53 tff(20491,plain,
% 3.25/3.53 (s(s(s(z))) = elem!1),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[704, 20490, 20364])).
% 3.25/3.53 tff(20492,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[227, 20491, 54])).
% 3.25/3.53 tff(20493,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[249, 20492])).
% 3.25/3.53 tff(20494,plain,
% 3.25/3.53 (~b(elem!1, s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[18960, 20493, 17789, 20489])).
% 3.25/3.53 tff(20495,plain,
% 3.25/3.53 (~b(s(s(s(z))), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[380, 20491, 377])).
% 3.25/3.53 tff(20496,plain,
% 3.25/3.53 (r(s(s(s(z))), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[396, 20495])).
% 3.25/3.53 tff(20497,plain,
% 3.25/3.53 (~r(elem!1, s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[6311, 333, 19568, 19502, 20496])).
% 3.25/3.53 tff(20498,plain,
% 3.25/3.53 (elem!1 = s(s(s(z)))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1538, 20497, 20494])).
% 3.25/3.53 tff(20499,plain,
% 3.25/3.53 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20498])).
% 3.25/3.53 tff(20500,plain,
% 3.25/3.53 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20499])).
% 3.25/3.53 tff(20501,plain,
% 3.25/3.53 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 3.25/3.53 inference(symmetry,[status(thm)],[20500])).
% 3.25/3.53 tff(20502,plain,
% 3.25/3.53 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(elem!1)))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20501])).
% 3.25/3.53 tff(20503,plain,
% 3.25/3.53 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20499])).
% 3.25/3.53 tff(20504,plain,
% 3.25/3.53 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20498])).
% 3.25/3.53 tff(20505,plain,
% 3.25/3.53 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.53 inference(transitivity,[status(thm)],[20504, 20503])).
% 3.25/3.53 tff(20506,plain,
% 3.25/3.53 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[7595, 20491, 19208])).
% 3.25/3.53 tff(20507,plain,
% 3.25/3.53 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[5603, 20506])).
% 3.25/3.53 tff(20508,plain,
% 3.25/3.53 (~(s(elem!1) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[5813, 20507])).
% 3.25/3.53 tff(20509,plain,
% 3.25/3.53 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[12214, 20491])).
% 3.25/3.53 tff(20510,plain,
% 3.25/3.53 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20498])).
% 3.25/3.53 tff(20511,plain,
% 3.25/3.53 (b(elem!1, s(z))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20225, 54, 19502, 377, 12930, 3, 19568, 1])).
% 3.25/3.53 tff(20512,plain,
% 3.25/3.53 (b(s(s(s(z))), s(z))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20511, 20510])).
% 3.25/3.53 tff(20513,plain,
% 3.25/3.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20488, 670, 490, 489, 1, 286, 408, 3, 54, 19569, 322])).
% 3.25/3.53 tff(20514,plain,
% 3.25/3.53 (~b(s(s(s(z))), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[10110, 20513, 17787, 3, 54])).
% 3.25/3.53 tff(20515,plain,
% 3.25/3.53 (s(s(s(z))) = elem!1),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[704, 20514, 19569])).
% 3.25/3.53 tff(20516,plain,
% 3.25/3.53 (~(s(s(z)) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[14611, 20515, 15133])).
% 3.25/3.53 tff(20517,plain,
% 3.25/3.53 (~(s(elem!1) = s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1508, 20516])).
% 3.25/3.53 tff(20518,plain,
% 3.25/3.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[227, 20515, 54])).
% 3.25/3.53 tff(20519,plain,
% 3.25/3.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[249, 20518])).
% 3.25/3.53 tff(20520,plain,
% 3.25/3.53 (~b(elem!1, s(s(s(z))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[18960, 20519, 17789, 20513])).
% 3.25/3.53 tff(20521,plain,
% 3.25/3.53 (elem!1 = s(s(s(z)))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[1538, 11461, 20520])).
% 3.25/3.53 tff(20522,plain,
% 3.25/3.53 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20521])).
% 3.25/3.53 tff(20523,plain,
% 3.25/3.53 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20522])).
% 3.25/3.53 tff(20524,plain,
% 3.25/3.53 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.53 inference(symmetry,[status(thm)],[20523])).
% 3.25/3.53 tff(20525,plain,
% 3.25/3.53 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20524])).
% 3.25/3.53 tff(20526,plain,
% 3.25/3.53 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20521])).
% 3.25/3.53 tff(20527,plain,
% 3.25/3.53 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[7595, 20515, 19208])).
% 3.25/3.53 tff(20528,plain,
% 3.25/3.53 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[5603, 20527])).
% 3.25/3.53 tff(20529,plain,
% 3.25/3.53 (~(s(elem!1) = elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[5813, 20528])).
% 3.25/3.53 tff(20530,plain,
% 3.25/3.53 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[12214, 20515])).
% 3.25/3.53 tff(20531,plain,
% 3.25/3.53 (s(s(s(s(z)))) = s(elem!1)),
% 3.25/3.53 inference(symmetry,[status(thm)],[20522])).
% 3.25/3.53 tff(20532,plain,
% 3.25/3.53 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20531])).
% 3.25/3.53 tff(20533,plain,
% 3.25/3.53 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.53 inference(transitivity,[status(thm)],[20532, 174])).
% 3.25/3.53 tff(20534,plain,
% 3.25/3.53 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.25/3.53 inference(monotonicity,[status(thm)],[20533])).
% 3.25/3.53 tff(20535,plain,
% 3.25/3.53 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[196, 20534])).
% 3.25/3.53 tff(20536,plain,
% 3.25/3.53 (~r(s(elem!1), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[16793, 409, 623, 1, 408, 489, 490])).
% 3.25/3.53 tff(20537,plain,
% 3.25/3.53 (b(s(elem!1), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[448, 20536, 433])).
% 3.25/3.53 tff(20538,plain,
% 3.25/3.53 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[462, 20537, 17788, 17789])).
% 3.25/3.53 tff(20539,plain,
% 3.25/3.53 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[472, 20538, 432])).
% 3.25/3.53 tff(20540,plain,
% 3.25/3.53 (~r(s(elem!1), s(z))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[481, 409, 17787, 408, 54, 322, 3, 433, 432])).
% 3.25/3.53 tff(20541,plain,
% 3.25/3.53 (b(s(elem!1), s(z))),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[486, 20540, 1])).
% 3.25/3.53 tff(20542,plain,
% 3.25/3.53 (~b(s(elem!1), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[499, 20541, 489, 490])).
% 3.25/3.53 tff(20543,plain,
% 3.25/3.53 (r(s(elem!1), z)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[507, 20542])).
% 3.25/3.53 tff(20544,plain,
% 3.25/3.53 ($false),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[7622, 20543, 20539, 408, 17788, 51, 20537, 1722, 537])).
% 3.25/3.53 tff(20545,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.53 tff(20546,plain,
% 3.25/3.53 (~r(s(z), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[20545, 51, 408, 20535, 20530, 489, 490, 1, 20529, 54, 322, 3, 623])).
% 3.25/3.53 tff(20547,plain,
% 3.25/3.53 (b(s(z), elem!1)),
% 3.25/3.53 inference(unit_resolution,[status(thm)],[406, 20546, 15133])).
% 3.25/3.53 tff(20548,plain,
% 3.25/3.53 (b(s(z), s(s(s(z))))),
% 3.25/3.53 inference(modus_ponens,[status(thm)],[20547, 20526])).
% 3.25/3.54 tff(20549,plain,
% 3.25/3.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20279, 20548, 322, 20521, 1, 20519, 20513, 56, 15126])).
% 3.25/3.54 tff(20550,plain,
% 3.25/3.54 (~b(s(elem!1), s(s(s(z))))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20549, 20525])).
% 3.25/3.54 tff(20551,plain,
% 3.25/3.54 (r(s(elem!1), s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[965, 20550, 20517])).
% 3.25/3.54 tff(20552,plain,
% 3.25/3.54 (~r(z, s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1972, 20551, 623, 1699])).
% 3.25/3.54 tff(20553,plain,
% 3.25/3.54 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[462, 20399, 133, 132])).
% 3.25/3.54 tff(20554,plain,
% 3.25/3.54 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[4578, 20399, 670, 51, 1722, 537, 509, 408, 133])).
% 3.25/3.54 tff(20555,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[472, 20554, 20553, 432])).
% 3.25/3.54 tff(20556,plain,((~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20557,plain,
% 3.25/3.54 (~r(s(elem!1), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20556, 51, 670, 20530, 20535, 408, 17788, 17789, 20529, 623])).
% 3.25/3.54 tff(20558,plain,
% 3.25/3.54 (b(s(elem!1), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[507, 20557])).
% 3.25/3.54 tff(20559,plain,
% 3.25/3.54 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20531])).
% 3.25/3.54 tff(20560,plain,
% 3.25/3.54 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20559])).
% 3.25/3.54 tff(20561,plain,
% 3.25/3.54 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20522])).
% 3.25/3.54 tff(20562,plain,
% 3.25/3.54 (~b(s(elem!1), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[499, 20558, 489, 490])).
% 3.25/3.54 tff(20563,plain,
% 3.25/3.54 (r(s(elem!1), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[486, 20562, 1])).
% 3.25/3.54 tff(20564,plain,
% 3.25/3.54 (r(s(s(s(s(z)))), s(z))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20563, 20561])).
% 3.25/3.54 tff(20565,plain,
% 3.25/3.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20431, 333, 20564, 15126, 322])).
% 3.25/3.54 tff(20566,plain,
% 3.25/3.54 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20565, 20560])).
% 3.25/3.54 tff(20567,plain,
% 3.25/3.54 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[542, 20566, 20535])).
% 3.25/3.54 tff(20568,plain,
% 3.25/3.54 (~b(z, s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[12069, 20567, 286, 20558])).
% 3.25/3.54 tff(20569,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[583, 20568, 20552])).
% 3.25/3.54 tff(20570,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20571,plain,
% 3.25/3.54 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20570, 20479, 12930, 20496, 20363, 1, 20512, 20481, 20483, 19568, 19502, 54, 3])).
% 3.25/3.54 tff(20572,plain,
% 3.25/3.54 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[279, 20571])).
% 3.25/3.54 tff(20573,plain,
% 3.25/3.54 (~b(s(elem!1), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20117, 20572, 15126, 20483, 20479, 1, 20481, 20509])).
% 3.25/3.54 tff(20574,plain,
% 3.25/3.54 (r(s(elem!1), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[507, 20573])).
% 3.25/3.54 tff(20575,plain,
% 3.25/3.54 (~r(s(elem!1), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[10865, 20574, 12930, 19502])).
% 3.25/3.54 tff(20576,plain,
% 3.25/3.54 (b(s(elem!1), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[448, 20575, 20508])).
% 3.25/3.54 tff(20577,plain,
% 3.25/3.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20576, 20505])).
% 3.25/3.54 tff(20578,plain,
% 3.25/3.54 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[18464, 144, 20493, 20489, 20577])).
% 3.25/3.54 tff(20579,plain,
% 3.25/3.54 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[9761, 20578])).
% 3.25/3.54 tff(20580,plain,
% 3.25/3.54 (~r(s(z), s(s(s(s(z)))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[19714, 333, 15126, 20363, 20579])).
% 3.25/3.54 tff(20581,plain,
% 3.25/3.54 (~r(s(z), s(elem!1))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20580, 20502])).
% 3.25/3.54 tff(20582,plain,
% 3.25/3.54 (~(elem!1 = s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1569, 20508])).
% 3.25/3.54 tff(20583,plain,
% 3.25/3.54 (~r(s(elem!1), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20439, 20572, 20582, 19568, 17789, 20498, 15126, 20363])).
% 3.25/3.54 tff(20584,plain,
% 3.25/3.54 (b(s(elem!1), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[486, 20583, 1])).
% 3.25/3.54 tff(20585,plain,
% 3.25/3.54 (~r(elem!1, s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[678, 20574, 19502, 19568])).
% 3.25/3.54 tff(20586,plain,
% 3.25/3.54 (b(elem!1, s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[560, 20585, 20582])).
% 3.25/3.54 tff(20587,plain,
% 3.25/3.54 (~b(s(z), s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[4409, 20586, 20511, 20584])).
% 3.25/3.54 tff(20588,plain,
% 3.25/3.54 (r(s(z), s(elem!1))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1244, 20587, 1229])).
% 3.25/3.54 tff(20589,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20588, 20581])).
% 3.25/3.54 tff(20590,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(elem!1, z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20591,plain,
% 3.25/3.54 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20590, 377, 3, 1, 255])).
% 3.25/3.54 tff(20592,plain,
% 3.25/3.54 (((~![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, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20593,plain,
% 3.25/3.54 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20594,plain,
% 3.25/3.54 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20593])).
% 3.25/3.54 tff(20595,plain,
% 3.25/3.54 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), 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(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(transitivity,[status(thm)],[20594, 20592])).
% 3.25/3.54 tff(20596,plain,
% 3.25/3.54 ((~![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(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(quant_inst,[status(thm)],[])).
% 3.25/3.54 tff(20597,plain,
% 3.25/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20596, 20595])).
% 3.25/3.54 tff(20598,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20597, 333, 409, 408, 11546, 2484])).
% 3.25/3.54 tff(20599,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20600,plain,
% 3.25/3.54 (~r(s(z), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20599, 20591, 15126, 19502])).
% 3.25/3.54 tff(20601,plain,
% 3.25/3.54 (b(s(z), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[406, 20600, 15133])).
% 3.25/3.54 tff(20602,plain,
% 3.25/3.54 (((~![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(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), 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(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20603,plain,
% 3.25/3.54 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20604,plain,
% 3.25/3.54 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(elem!1, 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, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20603])).
% 3.25/3.54 tff(20605,plain,
% 3.25/3.54 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(elem!1, 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, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(transitivity,[status(thm)],[20604, 20602])).
% 3.25/3.54 tff(20606,plain,
% 3.25/3.54 ((~![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(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 3.25/3.54 inference(quant_inst,[status(thm)],[])).
% 3.25/3.54 tff(20607,plain,
% 3.25/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20606, 20605])).
% 3.25/3.54 tff(20608,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20607, 333, 354, 408, 722, 11546])).
% 3.25/3.54 tff(20609,plain,((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20610,plain,
% 3.25/3.54 (~r(elem!1, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20609, 354, 408, 11546])).
% 3.25/3.54 tff(20611,plain,
% 3.25/3.54 (b(elem!1, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[720, 20610, 714])).
% 3.25/3.54 tff(20612,plain,
% 3.25/3.54 (~b(s(s(s(z))), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[4375, 56, 305, 134])).
% 3.25/3.54 tff(20613,plain,
% 3.25/3.54 (r(s(s(s(z))), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[704, 20612, 698])).
% 3.25/3.54 tff(20614,plain,
% 3.25/3.54 (~r(s(z), s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1519, 20613, 623, 354])).
% 3.25/3.54 tff(20615,plain,
% 3.25/3.54 (b(s(z), s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[172, 20614])).
% 3.25/3.54 tff(20616,plain,
% 3.25/3.54 (~r(elem!1, s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[7510, 20613, 623, 408])).
% 3.25/3.54 tff(20617,plain,
% 3.25/3.54 (b(elem!1, s(s(s(z))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1538, 20616, 12398])).
% 3.25/3.54 tff(20618,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[18973, 144, 20617, 305, 56, 20615])).
% 3.25/3.54 tff(20619,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20620,plain,
% 3.25/3.54 (~b(s(s(s(z))), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20619, 20611, 623, 354, 408, 698, 134])).
% 3.25/3.54 tff(20621,plain,
% 3.25/3.54 (r(s(s(s(z))), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[2794, 20620])).
% 3.25/3.54 tff(20622,plain,
% 3.25/3.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[17809, 20621, 11546, 2484])).
% 3.25/3.54 tff(20623,plain,
% 3.25/3.54 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[1137, 20622])).
% 3.25/3.54 tff(20624,plain,
% 3.25/3.54 (~r(elem!1, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[19517, 333, 323, 408, 623])).
% 3.25/3.54 tff(20625,plain,
% 3.25/3.54 (b(elem!1, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[720, 20624, 714])).
% 3.25/3.54 tff(20626,plain,
% 3.25/3.54 (~b(z, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[7079, 20625, 251, 134])).
% 3.25/3.54 tff(20627,plain,
% 3.25/3.54 (r(z, s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[372, 20626])).
% 3.25/3.54 tff(20628,plain,
% 3.25/3.54 (~b(s(s(s(z))), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20619, 20625, 623, 20627, 408, 698, 134])).
% 3.25/3.54 tff(20629,plain,
% 3.25/3.54 (r(s(s(s(z))), s(z))),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[2794, 20628])).
% 3.25/3.54 tff(20630,plain,
% 3.25/3.54 ($false),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[8841, 333, 20627, 323, 623, 20629])).
% 3.25/3.54 tff(20631,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.54 tff(20632,plain,
% 3.25/3.54 (~r(s(z), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20631, 698, 408, 623, 134, 251, 714])).
% 3.25/3.54 tff(20633,plain,
% 3.25/3.54 (b(s(z), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[348, 20632])).
% 3.25/3.54 tff(20634,plain,
% 3.25/3.54 (~r(s(s(s(z))), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[2146, 354, 623, 71, 408, 134, 20633])).
% 3.25/3.54 tff(20635,plain,
% 3.25/3.54 (b(s(s(s(z))), elem!1)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[704, 20634, 698])).
% 3.25/3.54 tff(20636,plain,
% 3.25/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20637,plain,
% 3.25/3.54 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(rewrite,[status(thm)],[])).
% 3.25/3.54 tff(20638,plain,
% 3.25/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.54 inference(monotonicity,[status(thm)],[20637])).
% 3.25/3.54 tff(20639,plain,
% 3.25/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.54 inference(transitivity,[status(thm)],[20638, 20636])).
% 3.25/3.54 tff(20640,plain,
% 3.25/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 3.25/3.54 inference(quant_inst,[status(thm)],[])).
% 3.25/3.54 tff(20641,plain,
% 3.25/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.54 inference(modus_ponens,[status(thm)],[20640, 20639])).
% 3.25/3.54 tff(20642,plain,
% 3.25/3.54 (~b(s(s(s(z))), z)),
% 3.25/3.54 inference(unit_resolution,[status(thm)],[20641, 144, 251, 132, 20623, 20635])).
% 3.25/3.55 tff(20643,plain,
% 3.25/3.55 (r(s(s(s(z))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[396, 20642])).
% 3.25/3.55 tff(20644,plain,
% 3.25/3.55 (((~![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(s(s(z))), 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(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20645,plain,
% 3.25/3.55 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20646,plain,
% 3.25/3.55 (((~![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(z))), z)) | (~r(elem!1, 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(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20645])).
% 3.25/3.55 tff(20647,plain,
% 3.25/3.55 (((~![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(z))), z)) | (~r(elem!1, 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(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.25/3.55 inference(transitivity,[status(thm)],[20646, 20644])).
% 3.25/3.55 tff(20648,plain,
% 3.25/3.55 ((~![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(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 3.25/3.55 inference(quant_inst,[status(thm)],[])).
% 3.25/3.55 tff(20649,plain,
% 3.25/3.55 ((~![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(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20648, 20647])).
% 3.25/3.55 tff(20650,plain,
% 3.25/3.55 (~r(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20649, 333, 354, 408, 20643])).
% 3.25/3.55 tff(20651,plain,
% 3.25/3.55 (b(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1538, 20650, 12398])).
% 3.25/3.55 tff(20652,plain,
% 3.25/3.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[18960, 20651, 132, 20623])).
% 3.25/3.55 tff(20653,plain,
% 3.25/3.55 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[249, 20652])).
% 3.25/3.55 tff(20654,plain,
% 3.25/3.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[15576, 20653, 11546, 354])).
% 3.25/3.55 tff(20655,plain,
% 3.25/3.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[279, 20654])).
% 3.25/3.55 tff(20656,plain,
% 3.25/3.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[14348, 354, 408, 2484])).
% 3.25/3.55 tff(20657,plain,
% 3.25/3.55 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[302, 20656])).
% 3.25/3.55 tff(20658,plain,
% 3.25/3.55 (~r(s(z), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[15519, 20653, 11546, 20621])).
% 3.25/3.55 tff(20659,plain,
% 3.25/3.55 (b(s(z), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[172, 20658])).
% 3.25/3.55 tff(20660,plain,
% 3.25/3.55 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[6165])).
% 3.25/3.55 tff(20661,plain,
% 3.25/3.55 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.55 inference(symmetry,[status(thm)],[20660])).
% 3.25/3.55 tff(20662,plain,
% 3.25/3.55 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[6165])).
% 3.25/3.55 tff(20663,plain,
% 3.25/3.55 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20662])).
% 3.25/3.55 tff(20664,assumption,(~b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.25/3.55 tff(20665,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20664, 18852])).
% 3.25/3.55 tff(20666,plain,(b(z, s(s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20667,plain,
% 3.25/3.55 (b(z, s(s(s(s(s(s(z)))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20666, 927, 251])).
% 3.25/3.55 tff(20668,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.25/3.55 tff(20669,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20670,plain,
% 3.25/3.55 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20671,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20670])).
% 3.25/3.55 tff(20672,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(transitivity,[status(thm)],[20671, 20669])).
% 3.25/3.55 tff(20673,plain,
% 3.25/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 3.25/3.55 inference(quant_inst,[status(thm)],[])).
% 3.25/3.55 tff(20674,plain,
% 3.25/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20673, 20672])).
% 3.25/3.55 tff(20675,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20674, 144, 489, 285, 838, 6169, 20668])).
% 3.25/3.55 tff(20676,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20677,plain,
% 3.25/3.55 (~b(s(s(s(z))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20676, 14200, 838, 489, 20667])).
% 3.25/3.55 tff(20678,plain,
% 3.25/3.55 (r(s(s(s(z))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[396, 20677])).
% 3.25/3.55 tff(20679,plain,
% 3.25/3.55 (((~![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(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20680,plain,
% 3.25/3.55 ((~![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(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.25/3.55 inference(quant_inst,[status(thm)],[])).
% 3.25/3.55 tff(20681,plain,
% 3.25/3.55 ((~![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(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20680, 20679])).
% 3.25/3.55 tff(20682,plain,
% 3.25/3.55 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20681, 333, 354, 20678])).
% 3.25/3.55 tff(20683,plain,
% 3.25/3.55 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20682, 17997])).
% 3.25/3.55 tff(20684,plain,
% 3.25/3.55 (~r(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20683, 20663])).
% 3.25/3.55 tff(20685,plain,
% 3.25/3.55 (b(elem!1, s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1538, 20684, 1524])).
% 3.25/3.55 tff(20686,plain,
% 3.25/3.55 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20685, 20661])).
% 3.25/3.55 tff(20687,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20688,plain,
% 3.25/3.55 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20689,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20688])).
% 3.25/3.55 tff(20690,plain,
% 3.25/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.55 inference(transitivity,[status(thm)],[20689, 20687])).
% 3.25/3.55 tff(20691,plain,
% 3.25/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 3.25/3.55 inference(quant_inst,[status(thm)],[])).
% 3.25/3.55 tff(20692,plain,
% 3.25/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20691, 20690])).
% 3.25/3.55 tff(20693,plain,
% 3.25/3.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20692, 144, 489, 838, 14200, 20667])).
% 3.25/3.55 tff(20694,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20693, 20686])).
% 3.25/3.55 tff(20695,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20696,plain,
% 3.25/3.55 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20695, 20659, 20633, 12398, 354, 408, 251, 134])).
% 3.25/3.55 tff(20697,plain,
% 3.25/3.55 (~b(s(z), s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[8892, 144, 251, 491, 134, 489])).
% 3.25/3.55 tff(20698,plain,
% 3.25/3.55 (r(s(z), s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1244, 20697, 1229])).
% 3.25/3.55 tff(20699,plain,
% 3.25/3.55 (~(s(elem!1) = elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[3262, 20697, 134])).
% 3.25/3.55 tff(20700,plain,
% 3.25/3.55 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[267, 259, 132, 251])).
% 3.25/3.55 tff(20701,plain,
% 3.25/3.55 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[472, 20108, 432])).
% 3.25/3.55 tff(20702,plain,
% 3.25/3.55 (~r(s(elem!1), elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[13988, 20701, 286, 377, 20700, 77])).
% 3.25/3.55 tff(20703,plain,
% 3.25/3.55 (b(s(elem!1), elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[448, 20702, 20699])).
% 3.25/3.55 tff(20704,plain,
% 3.25/3.55 (~b(z, s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[14718, 144, 20703, 251, 132, 259])).
% 3.25/3.55 tff(20705,plain,
% 3.25/3.55 (r(z, s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[583, 20704])).
% 3.25/3.55 tff(20706,plain,
% 3.25/3.55 (~b(s(elem!1), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[10716, 144, 20703, 251, 491, 489])).
% 3.25/3.55 tff(20707,plain,
% 3.25/3.55 (r(s(elem!1), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[486, 20706, 1])).
% 3.25/3.55 tff(20708,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1651, 333, 354, 20707, 20705, 20698])).
% 3.25/3.55 tff(20709,plain,((~b(s(elem!1), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(elem!1, z) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20710,plain,
% 3.25/3.55 (~b(s(elem!1), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20709, 20696, 1, 251, 20633, 132, 354, 20657, 377, 20655, 134])).
% 3.25/3.55 tff(20711,plain,
% 3.25/3.55 (r(s(elem!1), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[507, 20710])).
% 3.25/3.55 tff(20712,plain,
% 3.25/3.55 (~r(elem!1, s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1620, 20711, 354, 408])).
% 3.25/3.55 tff(20713,plain,
% 3.25/3.55 (~r(s(z), s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[6565, 20643, 354, 20621])).
% 3.25/3.55 tff(20714,plain,
% 3.25/3.55 (b(s(z), s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1244, 20713, 1229])).
% 3.25/3.55 tff(20715,plain,
% 3.25/3.55 (~r(s(elem!1), elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[10865, 20711, 623, 408])).
% 3.25/3.55 tff(20716,plain,
% 3.25/3.55 (elem!1 = s(elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1732, 20715, 134, 20714, 20712])).
% 3.25/3.55 tff(20717,plain,
% 3.25/3.55 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20716])).
% 3.25/3.55 tff(20718,plain,
% 3.25/3.55 (b(s(s(s(z))), s(elem!1))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20635, 20717])).
% 3.25/3.55 tff(20719,plain,
% 3.25/3.55 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.55 inference(monotonicity,[status(thm)],[20716])).
% 3.25/3.55 tff(20720,plain,
% 3.25/3.55 (b(s(elem!1), s(s(s(z))))),
% 3.25/3.55 inference(modus_ponens,[status(thm)],[20651, 20719])).
% 3.25/3.55 tff(20721,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[12255, 144, 20714, 20659, 20720, 20718])).
% 3.25/3.55 tff(20722,plain,((~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20723,plain,
% 3.25/3.55 (~r(z, s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20722, 251, 408, 12930, 1, 134, 132, 377, 11546, 2484, 19505, 714])).
% 3.25/3.55 tff(20724,plain,
% 3.25/3.55 (b(z, s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[372, 20723])).
% 3.25/3.55 tff(20725,plain,
% 3.25/3.55 (~b(elem!1, s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[7079, 20724, 251, 134])).
% 3.25/3.55 tff(20726,plain,
% 3.25/3.55 (r(elem!1, s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[720, 20725, 714])).
% 3.25/3.55 tff(20727,plain,
% 3.25/3.55 (~(elem!1 = s(s(s(z))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[10997, 19505])).
% 3.25/3.55 tff(20728,plain,
% 3.25/3.55 (~r(s(z), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20631, 19505, 408, 12930, 134, 251, 714])).
% 3.25/3.55 tff(20729,plain,
% 3.25/3.55 (b(s(z), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[348, 20728])).
% 3.25/3.55 tff(20730,plain,
% 3.25/3.55 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[14578, 20724, 132, 134, 251])).
% 3.25/3.55 tff(20731,plain,
% 3.25/3.55 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[279, 20730])).
% 3.25/3.55 tff(20732,plain,
% 3.25/3.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[12025, 20731, 408, 2484])).
% 3.25/3.55 tff(20733,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[432, 12841])).
% 3.25/3.55 tff(20734,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20735,plain,
% 3.25/3.55 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20734, 432])).
% 3.25/3.55 tff(20736,plain,
% 3.25/3.55 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[14578, 490, 132, 134, 251])).
% 3.25/3.55 tff(20737,plain,
% 3.25/3.55 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[279, 20736])).
% 3.25/3.55 tff(20738,plain,
% 3.25/3.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[12025, 20737, 408, 2484])).
% 3.25/3.55 tff(20739,plain,
% 3.25/3.55 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[302, 20738])).
% 3.25/3.55 tff(20740,plain,
% 3.25/3.55 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[7093, 20739, 489, 490])).
% 3.25/3.55 tff(20741,plain,
% 3.25/3.55 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[319, 20740])).
% 3.25/3.55 tff(20742,plain,
% 3.25/3.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20114, 333, 9318, 11546, 20741])).
% 3.25/3.55 tff(20743,plain,
% 3.25/3.55 (elem!1 = s(elem!1)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[12081, 20742, 132, 2484, 20739, 408, 432, 20735, 491])).
% 3.25/3.55 tff(20744,plain,
% 3.25/3.55 ($false),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[1569, 20743, 20699])).
% 3.25/3.55 tff(20745,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.55 tff(20746,plain,
% 3.25/3.55 (~b(s(elem!1), z)),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[20745, 432, 2484, 408, 132, 134, 11546, 251, 489, 1, 490])).
% 3.25/3.55 tff(20747,plain,
% 3.25/3.55 (~b(elem!1, s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[7079, 490, 251, 134])).
% 3.25/3.55 tff(20748,plain,
% 3.25/3.55 (~b(s(elem!1), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[890, 885, 708])).
% 3.25/3.55 tff(20749,plain,
% 3.25/3.55 (r(s(elem!1), s(z))),
% 3.25/3.55 inference(unit_resolution,[status(thm)],[486, 20748, 1])).
% 3.25/3.55 tff(20750,plain,
% 3.25/3.55 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.55 inference(rewrite,[status(thm)],[])).
% 3.25/3.55 tff(20751,plain,
% 3.25/3.55 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20752,plain,
% 3.25/3.56 (((~![X0: $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(z))))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20751])).
% 3.25/3.56 tff(20753,plain,
% 3.25/3.56 (((~![X0: $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(z))))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.56 inference(transitivity,[status(thm)],[20752, 20750])).
% 3.25/3.56 tff(20754,plain,
% 3.25/3.56 ((~![X0: $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(z))))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.25/3.56 inference(quant_inst,[status(thm)],[])).
% 3.25/3.56 tff(20755,plain,
% 3.25/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20754, 20753])).
% 3.25/3.56 tff(20756,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20755, 333, 20749, 11546, 322, 4127])).
% 3.25/3.56 tff(20757,plain,((~(elem!1 = s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20758,plain,
% 3.25/3.56 (~(elem!1 = s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20757, 20741, 11546, 2484, 1, 20747])).
% 3.25/3.56 tff(20759,plain,
% 3.25/3.56 (~r(s(elem!1), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[12050, 20735, 132, 408, 2484, 251, 20737, 20758])).
% 3.25/3.56 tff(20760,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[507, 20759, 20746])).
% 3.25/3.56 tff(20761,plain,((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20762,plain,
% 3.25/3.56 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20761, 251, 408, 2484, 132, 134, 11546, 20729, 1, 20724])).
% 3.25/3.56 tff(20763,plain,
% 3.25/3.56 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[930, 20762])).
% 3.25/3.56 tff(20764,plain,
% 3.25/3.56 (~r(s(elem!1), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2899, 20763, 20732])).
% 3.25/3.56 tff(20765,plain,
% 3.25/3.56 (b(s(elem!1), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[507, 20764])).
% 3.25/3.56 tff(20766,plain,
% 3.25/3.56 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[302, 20732])).
% 3.25/3.56 tff(20767,plain,
% 3.25/3.56 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[7093, 20766, 20729, 20724])).
% 3.25/3.56 tff(20768,plain,
% 3.25/3.56 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[319, 20767])).
% 3.25/3.56 tff(20769,plain,
% 3.25/3.56 (~(elem!1 = s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20757, 20768, 11546, 2484, 1, 20725])).
% 3.25/3.56 tff(20770,plain,
% 3.25/3.56 (~(s(elem!1) = elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[906, 20769])).
% 3.25/3.56 tff(20771,plain,
% 3.25/3.56 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[19392, 20768, 20724, 20729, 20731, 11546])).
% 3.25/3.56 tff(20772,plain,
% 3.25/3.56 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1137, 20771])).
% 3.25/3.56 tff(20773,plain,
% 3.25/3.56 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.56 inference(symmetry,[status(thm)],[20662])).
% 3.25/3.56 tff(20774,plain,
% 3.25/3.56 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[927])).
% 3.25/3.56 tff(20775,plain,
% 3.25/3.56 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.25/3.56 inference(symmetry,[status(thm)],[20774])).
% 3.25/3.56 tff(20776,plain,
% 3.25/3.56 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20775])).
% 3.25/3.56 tff(20777,plain,
% 3.25/3.56 (~(s(elem!1) = s(s(s(z))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[244, 20776])).
% 3.25/3.56 tff(20778,plain,
% 3.25/3.56 (~r(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[8903, 3193, 251, 1229, 134, 722, 491])).
% 3.25/3.56 tff(20779,plain,
% 3.25/3.56 (b(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[704, 20778, 698])).
% 3.25/3.56 tff(20780,plain,
% 3.25/3.56 (~b(s(s(s(z))), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[10937, 20779, 377, 251, 490, 722, 1, 433, 3193, 489, 408, 134, 20777, 12398])).
% 3.25/3.56 tff(20781,plain,
% 3.25/3.56 (r(s(s(s(z))), z)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[396, 20780])).
% 3.25/3.56 tff(20782,plain,
% 3.25/3.56 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[15762, 20781, 623, 20737])).
% 3.25/3.56 tff(20783,plain,
% 3.25/3.56 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[249, 20782])).
% 3.25/3.56 tff(20784,plain,
% 3.25/3.56 (~b(elem!1, s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[18960, 20783, 132, 2254])).
% 3.25/3.56 tff(20785,plain,
% 3.25/3.56 (r(elem!1, s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1538, 20784, 12398])).
% 3.25/3.56 tff(20786,plain,
% 3.25/3.56 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20785, 20773])).
% 3.25/3.56 tff(20787,plain,
% 3.25/3.56 (((~![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(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20788,plain,
% 3.25/3.56 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20789,plain,
% 3.25/3.56 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(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(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20788])).
% 3.25/3.56 tff(20790,plain,
% 3.25/3.56 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(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(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.25/3.56 inference(transitivity,[status(thm)],[20789, 20787])).
% 3.25/3.56 tff(20791,plain,
% 3.25/3.56 ((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.25/3.56 inference(quant_inst,[status(thm)],[])).
% 3.25/3.56 tff(20792,plain,
% 3.25/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20791, 20790])).
% 3.25/3.56 tff(20793,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20792, 333, 623, 3193, 17997, 20786])).
% 3.25/3.56 tff(20794,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20795,plain,
% 3.25/3.56 (~r(s(s(s(z))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20794, 20762, 12930, 408, 132, 20772, 377, 251, 20724, 20726, 1, 20770, 20729, 134, 19505, 20765])).
% 3.25/3.56 tff(20796,plain,
% 3.25/3.56 (b(s(s(s(z))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2794, 20795])).
% 3.25/3.56 tff(20797,plain,
% 3.25/3.56 (~r(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2094, 20796, 408, 134, 71, 20729, 20724, 20727, 20726])).
% 3.25/3.56 tff(20798,plain,
% 3.25/3.56 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[17864, 144, 134, 132, 20772])).
% 3.25/3.56 tff(20799,plain,
% 3.25/3.56 (~b(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20798, 20796])).
% 3.25/3.56 tff(20800,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[704, 20799, 20797, 19505])).
% 3.25/3.56 tff(20801,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | b(elem!1, z) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20802,plain,
% 3.25/3.56 (~b(z, elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20801, 20601, 17789, 19502, 377, 1, 20591, 15126, 15134, 255])).
% 3.25/3.56 tff(20803,plain,
% 3.25/3.56 (~r(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2136, 7265, 623, 408])).
% 3.25/3.56 tff(20804,plain,
% 3.25/3.56 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2938, 7265, 408, 2484])).
% 3.25/3.56 tff(20805,plain,
% 3.25/3.56 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[279, 20804])).
% 3.25/3.56 tff(20806,plain,
% 3.25/3.56 (~r(elem!1, s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[3944, 333, 7265, 323, 408])).
% 3.25/3.56 tff(20807,plain,
% 3.25/3.56 (b(elem!1, s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[720, 20806, 713])).
% 3.25/3.56 tff(20808,plain,
% 3.25/3.56 (~r(s(z), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20599, 2484, 11546, 408])).
% 3.25/3.56 tff(20809,plain,
% 3.25/3.56 (b(s(z), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[406, 20808, 706])).
% 3.25/3.56 tff(20810,plain,
% 3.25/3.56 (~r(elem!1, s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[678, 509, 408, 7265])).
% 3.25/3.56 tff(20811,plain,
% 3.25/3.56 (~r(s(z), s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1235, 509, 323, 354])).
% 3.25/3.56 tff(20812,plain,
% 3.25/3.56 (b(s(z), s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1244, 20811, 1229])).
% 3.25/3.56 tff(20813,plain,
% 3.25/3.56 (elem!1 = s(elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1732, 20812, 20809, 20398, 20810])).
% 3.25/3.56 tff(20814,plain,
% 3.25/3.56 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20813])).
% 3.25/3.56 tff(20815,plain,
% 3.25/3.56 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[132, 20814])).
% 3.25/3.56 tff(20816,plain,
% 3.25/3.56 (s(s(s(elem!1))) = elem!1),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2482, 20813])).
% 3.25/3.56 tff(20817,plain,
% 3.25/3.56 (~(s(s(s(z))) = s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1010, 20816])).
% 3.25/3.56 tff(20818,plain,
% 3.25/3.56 (~r(s(elem!1), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1365, 509, 323, 354])).
% 3.25/3.56 tff(20819,plain,
% 3.25/3.56 (b(s(elem!1), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[486, 20818, 1])).
% 3.25/3.56 tff(20820,plain,
% 3.25/3.56 (~b(z, s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2974, 20813, 606])).
% 3.25/3.56 tff(20821,plain,
% 3.25/3.56 (r(z, s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[583, 20820])).
% 3.25/3.56 tff(20822,plain,
% 3.25/3.56 (~b(s(s(s(z))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1960, 20821, 623, 323, 509, 20819, 1229, 20817])).
% 3.25/3.56 tff(20823,plain,
% 3.25/3.56 (r(s(s(s(z))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2794, 20822])).
% 3.25/3.56 tff(20824,plain,
% 3.25/3.56 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[17809, 20823, 11546, 2484])).
% 3.25/3.56 tff(20825,plain,
% 3.25/3.56 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1137, 20824])).
% 3.25/3.56 tff(20826,plain,
% 3.25/3.56 (s(elem!1) = s(s(s(elem!1)))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[2584, 20816, 20813])).
% 3.25/3.56 tff(20827,plain,
% 3.25/3.56 (s(s(s(elem!1))) = s(elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[3254, 20826])).
% 3.25/3.56 tff(20828,plain,
% 3.25/3.56 (~(elem!1 = s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[3246, 20827, 706])).
% 3.25/3.56 tff(20829,plain,
% 3.25/3.56 (~r(elem!1, s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[3201, 20823, 623, 7265])).
% 3.25/3.56 tff(20830,plain,
% 3.25/3.56 (b(elem!1, s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[1538, 20829, 20828])).
% 3.25/3.56 tff(20831,plain,
% 3.25/3.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[18960, 20830, 132, 20825])).
% 3.25/3.56 tff(20832,plain,
% 3.25/3.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[249, 20831])).
% 3.25/3.56 tff(20833,plain,
% 3.25/3.56 (((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20834,plain,
% 3.25/3.56 ((~![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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.25/3.56 inference(quant_inst,[status(thm)],[])).
% 3.25/3.56 tff(20835,plain,
% 3.25/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20834, 20833])).
% 3.25/3.56 tff(20836,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20835, 333, 323, 3193, 224, 322])).
% 3.25/3.56 tff(20837,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20838,plain,
% 3.25/3.56 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20837, 20832, 323, 20823])).
% 3.25/3.56 tff(20839,plain,
% 3.25/3.56 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[319, 20838])).
% 3.25/3.56 tff(20840,plain,
% 3.25/3.56 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20813])).
% 3.25/3.56 tff(20841,plain,
% 3.25/3.56 (b(s(elem!1), s(s(s(z))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20830, 20840])).
% 3.25/3.56 tff(20842,plain,
% 3.25/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20843,plain,
% 3.25/3.56 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.56 inference(rewrite,[status(thm)],[])).
% 3.25/3.56 tff(20844,plain,
% 3.25/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[20843])).
% 3.25/3.56 tff(20845,plain,
% 3.25/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.56 inference(transitivity,[status(thm)],[20844, 20842])).
% 3.25/3.56 tff(20846,plain,
% 3.25/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.25/3.56 inference(quant_inst,[status(thm)],[])).
% 3.25/3.56 tff(20847,plain,
% 3.25/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20846, 20845])).
% 3.25/3.56 tff(20848,plain,
% 3.25/3.56 ($false),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20847, 144, 20819, 20841, 20825, 20839, 20815])).
% 3.25/3.56 tff(20849,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | b(z, elem!1) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.56 tff(20850,plain,
% 3.25/3.56 (~r(z, s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[20849, 509, 323, 623, 11546, 2484, 706, 606, 1, 132, 408])).
% 3.25/3.56 tff(20851,plain,
% 3.25/3.56 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[132, 4119])).
% 3.25/3.56 tff(20852,plain,
% 3.25/3.56 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 3.25/3.56 inference(monotonicity,[status(thm)],[885])).
% 3.25/3.56 tff(20853,plain,
% 3.25/3.56 (elem!1 = s(s(elem!1))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[5813, 3674])).
% 3.25/3.56 tff(20854,plain,
% 3.25/3.56 (s(s(elem!1)) = elem!1),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[5603, 20853])).
% 3.25/3.56 tff(20855,plain,
% 3.25/3.56 (~(s(s(s(z))) = elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[7595, 20854, 1184])).
% 3.25/3.56 tff(20856,plain,
% 3.25/3.56 (b(s(s(s(z))), elem!1)),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[704, 20855, 699])).
% 3.25/3.56 tff(20857,plain,
% 3.25/3.56 (b(s(s(s(z))), s(elem!1))),
% 3.25/3.56 inference(modus_ponens,[status(thm)],[20856, 20852])).
% 3.25/3.56 tff(20858,plain,
% 3.25/3.56 (~b(s(s(s(z))), s(z))),
% 3.25/3.56 inference(unit_resolution,[status(thm)],[4375, 20856, 305, 134])).
% 3.25/3.57 tff(20859,plain,
% 3.25/3.57 (r(s(s(s(z))), s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[2794, 20858])).
% 3.25/3.57 tff(20860,plain,
% 3.25/3.57 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[17809, 20859, 11546, 2484])).
% 3.25/3.57 tff(20861,plain,
% 3.25/3.57 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[1137, 20860])).
% 3.25/3.57 tff(20862,plain,
% 3.25/3.57 (~r(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[11212, 20859, 670, 323])).
% 3.25/3.57 tff(20863,plain,
% 3.25/3.57 (b(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[396, 20862])).
% 3.25/3.57 tff(20864,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20865,plain,
% 3.25/3.57 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20866,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.25/3.57 inference(monotonicity,[status(thm)],[20865])).
% 3.25/3.57 tff(20867,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(transitivity,[status(thm)],[20866, 20864])).
% 3.25/3.57 tff(20868,plain,
% 3.25/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 3.25/3.57 inference(quant_inst,[status(thm)],[])).
% 3.25/3.57 tff(20869,plain,
% 3.25/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20868, 20867])).
% 3.25/3.57 tff(20870,plain,
% 3.25/3.57 ($false),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20869, 144, 20863, 20861, 20857, 286, 20851])).
% 3.25/3.57 tff(20871,plain,((~(elem!1 = s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.57 tff(20872,plain,
% 3.25/3.57 (~(elem!1 = s(elem!1))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20871, 323, 132, 11546, 2484, 7265, 13798, 20807, 20809, 20803, 863])).
% 3.25/3.57 tff(20873,plain,
% 3.25/3.57 (~b(z, s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[7112, 509, 323, 20807, 20872, 1, 7265])).
% 3.25/3.57 tff(20874,plain,
% 3.25/3.57 ($false),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[372, 20873, 20850])).
% 3.25/3.57 tff(20875,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | b(z, elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.57 tff(20876,plain,
% 3.25/3.57 (~r(s(elem!1), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20875, 323, 1, 623, 11546, 2484, 706, 606, 132, 408])).
% 3.25/3.57 tff(20877,plain,
% 3.25/3.57 (b(s(elem!1), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[507, 20876])).
% 3.25/3.57 tff(20878,plain,
% 3.25/3.57 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20879,plain,
% 3.25/3.57 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20880,plain,
% 3.25/3.57 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.57 inference(monotonicity,[status(thm)],[20879])).
% 3.25/3.57 tff(20881,plain,
% 3.25/3.57 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(transitivity,[status(thm)],[20880, 20878])).
% 3.25/3.57 tff(20882,plain,
% 3.25/3.57 ((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 3.25/3.57 inference(quant_inst,[status(thm)],[])).
% 3.25/3.57 tff(20883,plain,
% 3.25/3.57 ((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20882, 20881])).
% 3.25/3.57 tff(20884,plain,
% 3.25/3.57 (~r(s(z), s(elem!1))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20883, 333, 11546, 2484, 20701])).
% 3.25/3.57 tff(20885,plain,
% 3.25/3.57 (b(s(z), s(elem!1))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[1244, 20884, 1229])).
% 3.25/3.57 tff(20886,plain,
% 3.25/3.57 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20887,plain,
% 3.25/3.57 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20888,plain,
% 3.25/3.57 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.57 inference(monotonicity,[status(thm)],[20887])).
% 3.25/3.57 tff(20889,plain,
% 3.25/3.57 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.57 inference(transitivity,[status(thm)],[20888, 20886])).
% 3.25/3.57 tff(20890,plain,
% 3.25/3.57 ((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))))),
% 3.25/3.57 inference(quant_inst,[status(thm)],[])).
% 3.25/3.57 tff(20891,plain,
% 3.25/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20890, 20889])).
% 3.25/3.57 tff(20892,plain,
% 3.25/3.57 (~r(s(elem!1), s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20891, 333, 11546, 2484, 20701])).
% 3.25/3.57 tff(20893,plain,
% 3.25/3.57 (b(s(elem!1), s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[486, 20892, 1])).
% 3.25/3.57 tff(20894,plain,
% 3.25/3.57 (~b(elem!1, s(elem!1))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[4409, 20893, 305, 20885])).
% 3.25/3.57 tff(20895,plain,
% 3.25/3.57 (~b(s(elem!1), elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[7338, 144, 134, 20893, 305])).
% 3.25/3.57 tff(20896,plain,
% 3.25/3.57 ($false),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[12698, 12525, 5787, 2484, 525])).
% 3.25/3.57 tff(20897,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.57 tff(20898,plain,
% 3.25/3.57 (elem!1 = s(elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20897, 20701, 2484, 20895, 20894])).
% 3.25/3.57 tff(20899,plain,
% 3.25/3.57 (b(elem!1, z) <=> b(s(elem!1), z)),
% 3.25/3.57 inference(monotonicity,[status(thm)],[20898])).
% 3.25/3.57 tff(20900,plain,
% 3.25/3.57 (b(s(elem!1), z) <=> b(elem!1, z)),
% 3.25/3.57 inference(symmetry,[status(thm)],[20899])).
% 3.25/3.57 tff(20901,plain,
% 3.25/3.57 (b(elem!1, z)),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[491, 20900])).
% 3.25/3.57 tff(20902,plain,
% 3.25/3.57 ($false),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[377, 20901])).
% 3.25/3.57 tff(20903,plain,((~b(s(elem!1), z)) | b(elem!1, z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.57 tff(20904,plain,
% 3.25/3.57 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20903, 20877, 2484, 20809, 20807, 1, 11546, 377, 13798, 20805])).
% 3.25/3.57 tff(20905,plain,
% 3.25/3.57 (~(s(s(s(z))) = elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[12214, 20904])).
% 3.25/3.57 tff(20906,plain,
% 3.25/3.57 (b(s(s(s(z))), elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[704, 20905, 20803])).
% 3.25/3.57 tff(20907,plain,
% 3.25/3.57 (~b(s(s(s(z))), s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[4375, 20906, 20807, 20809])).
% 3.25/3.57 tff(20908,plain,
% 3.25/3.57 (r(s(s(s(z))), s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[2794, 20907])).
% 3.25/3.57 tff(20909,plain,
% 3.25/3.57 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[17809, 20908, 11546, 2484])).
% 3.25/3.57 tff(20910,plain,
% 3.25/3.57 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[1137, 20909])).
% 3.25/3.57 tff(20911,plain,
% 3.25/3.57 (~r(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[11212, 20908, 7265, 323])).
% 3.25/3.57 tff(20912,plain,
% 3.25/3.57 (b(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[396, 20911])).
% 3.25/3.57 tff(20913,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20914,plain,
% 3.25/3.57 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20915,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.25/3.57 inference(monotonicity,[status(thm)],[20914])).
% 3.25/3.57 tff(20916,plain,
% 3.25/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.25/3.57 inference(transitivity,[status(thm)],[20915, 20913])).
% 3.25/3.57 tff(20917,plain,
% 3.25/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 3.25/3.57 inference(quant_inst,[status(thm)],[])).
% 3.25/3.57 tff(20918,plain,
% 3.25/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20917, 20916])).
% 3.25/3.57 tff(20919,plain,
% 3.25/3.57 ($false),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20918, 144, 20912, 132, 20910, 20906, 13798])).
% 3.25/3.57 tff(20920,plain,((~r(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | b(elem!1, z) | (~r(z, s(s(s(z))))) | (s(z) = elem!1) | b(z, elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.57 tff(20921,plain,
% 3.25/3.57 (~r(s(z), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20920, 20591, 15126, 17789, 1, 377, 12930, 15133, 20802, 19502])).
% 3.25/3.57 tff(20922,plain,
% 3.25/3.57 (b(s(z), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[348, 20921])).
% 3.25/3.57 tff(20923,plain,
% 3.25/3.57 (r(z, elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[658, 20802, 71])).
% 3.25/3.57 tff(20924,plain,
% 3.25/3.57 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[13796, 333, 20923, 19502, 20591])).
% 3.25/3.57 tff(20925,plain,
% 3.25/3.57 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[302, 20924])).
% 3.25/3.57 tff(20926,plain,
% 3.25/3.57 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[13796, 333, 670, 408, 2484])).
% 3.25/3.57 tff(20927,plain,
% 3.25/3.57 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[302, 20926])).
% 3.25/3.57 tff(20928,plain,
% 3.25/3.57 (r(s(elem!1), elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[12390, 3326, 2484])).
% 3.25/3.57 tff(20929,plain,
% 3.25/3.57 (~(s(s(s(z))) = elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[12214, 927])).
% 3.25/3.57 tff(20930,plain,
% 3.25/3.57 (~(elem!1 = s(s(s(z))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[10997, 20929])).
% 3.25/3.57 tff(20931,plain,
% 3.25/3.57 (b(s(s(s(z))), elem!1)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[704, 20929, 19569])).
% 3.25/3.57 tff(20932,plain,
% 3.25/3.57 (~b(elem!1, s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[4375, 56, 20931, 134])).
% 3.25/3.57 tff(20933,plain,
% 3.25/3.57 (r(elem!1, s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[720, 20932, 714])).
% 3.25/3.57 tff(20934,plain,
% 3.25/3.57 (~r(z, s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[19174, 20933, 670, 11546])).
% 3.25/3.57 tff(20935,plain,
% 3.25/3.57 (b(z, s(z))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[372, 20934])).
% 3.25/3.57 tff(20936,plain,
% 3.25/3.57 (~b(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[2273, 20935, 489, 56])).
% 3.25/3.57 tff(20937,plain,
% 3.25/3.57 (r(s(s(s(z))), z)),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[396, 20936])).
% 3.25/3.57 tff(20938,plain,
% 3.25/3.57 (((~![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(s(s(z)))))), z)) | (~r(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.25/3.57 inference(rewrite,[status(thm)],[])).
% 3.25/3.57 tff(20939,plain,
% 3.25/3.57 ((~![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(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.25/3.57 inference(quant_inst,[status(thm)],[])).
% 3.25/3.57 tff(20940,plain,
% 3.25/3.57 ((~![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(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20939, 20938])).
% 3.25/3.57 tff(20941,plain,
% 3.25/3.57 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20940, 333, 20937, 623])).
% 3.25/3.57 tff(20942,plain,
% 3.25/3.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[20941, 17997])).
% 3.25/3.57 tff(20943,plain,
% 3.25/3.57 (~r(elem!1, s(s(s(z))))),
% 3.25/3.57 inference(modus_ponens,[status(thm)],[20942, 20663])).
% 3.25/3.57 tff(20944,plain,
% 3.25/3.57 (b(elem!1, s(s(s(z))))),
% 3.25/3.57 inference(unit_resolution,[status(thm)],[1538, 20943, 20930])).
% 3.25/3.57 tff(20945,plain,
% 3.25/3.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[20944, 20661])).
% 3.25/3.58 tff(20946,plain,
% 3.25/3.58 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), elem!1)),
% 3.25/3.58 inference(monotonicity,[status(thm)],[6165])).
% 3.25/3.58 tff(20947,plain,
% 3.25/3.58 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.25/3.58 inference(symmetry,[status(thm)],[20946])).
% 3.25/3.58 tff(20948,plain,
% 3.25/3.58 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[20931, 20947])).
% 3.25/3.58 tff(20949,plain,
% 3.25/3.58 (~r(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[7731, 20935, 670, 1, 489, 435, 20933])).
% 3.25/3.58 tff(20950,plain,
% 3.25/3.58 (b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[172, 20949])).
% 3.25/3.58 tff(20951,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(20952,plain,
% 3.25/3.58 (((~b(s(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(s(z)))))))) | (~b(s(z), s(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(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(20953,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[20952])).
% 3.25/3.58 tff(20954,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 3.25/3.58 inference(transitivity,[status(thm)],[20953, 20951])).
% 3.25/3.58 tff(20955,plain,
% 3.25/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))),
% 3.25/3.58 inference(quant_inst,[status(thm)],[])).
% 3.25/3.58 tff(20956,plain,
% 3.25/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[20955, 20954])).
% 3.25/3.58 tff(20957,plain,
% 3.25/3.58 ($false),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[20956, 144, 20950, 14200, 20948, 20945])).
% 3.25/3.58 tff(20958,plain,((~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.58 tff(20959,plain,
% 3.25/3.58 (~b(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[20958, 927, 623, 408, 670, 1, 489, 20928, 11546, 714, 134])).
% 3.25/3.58 tff(20960,plain,
% 3.25/3.58 (r(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[2794, 20959])).
% 3.25/3.58 tff(20961,plain,
% 3.25/3.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[2938, 670, 408, 2484])).
% 3.25/3.58 tff(20962,plain,
% 3.25/3.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[279, 20961])).
% 3.25/3.58 tff(20963,plain,
% 3.25/3.58 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[17809, 20960, 11546, 2484])).
% 3.25/3.58 tff(20964,plain,
% 3.25/3.58 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1137, 20963])).
% 3.25/3.58 tff(20965,plain,
% 3.25/3.58 (~b(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[14036, 144, 20964, 20927, 20962])).
% 3.25/3.58 tff(20966,plain,
% 3.25/3.58 (r(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[396, 20965])).
% 3.25/3.58 tff(20967,plain,
% 3.25/3.58 (~r(z, s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[6565, 20966, 20960, 18556])).
% 3.25/3.58 tff(20968,plain,
% 3.25/3.58 (b(z, s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[372, 20967])).
% 3.25/3.58 tff(20969,plain,
% 3.25/3.58 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[7093, 20968, 20927, 489])).
% 3.25/3.58 tff(20970,plain,
% 3.25/3.58 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[319, 20969])).
% 3.25/3.58 tff(20971,plain,
% 3.25/3.58 (~r(elem!1, s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[3201, 20960, 623, 670])).
% 3.25/3.58 tff(20972,plain,
% 3.25/3.58 (b(elem!1, s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1538, 20971, 20930])).
% 3.25/3.58 tff(20973,plain,
% 3.25/3.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[18960, 20964, 132, 20972])).
% 3.25/3.58 tff(20974,plain,
% 3.25/3.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[249, 20973])).
% 3.25/3.58 tff(20975,plain,
% 3.25/3.58 ($false),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[15703, 333, 20960, 11546, 20974, 20970])).
% 3.25/3.58 tff(20976,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.58 tff(20977,plain,
% 3.25/3.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[20976, 20922, 15126, 17789, 12930, 20923, 20591, 19502, 1, 15134, 20601])).
% 3.25/3.58 tff(20978,plain,
% 3.25/3.58 (~b(s(elem!1), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[20117, 490, 11546, 20962, 20927, 1, 489, 432])).
% 3.25/3.58 tff(20979,plain,
% 3.25/3.58 (r(s(elem!1), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[507, 20978])).
% 3.25/3.58 tff(20980,plain,
% 3.25/3.58 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[7093, 490, 20927, 489])).
% 3.25/3.58 tff(20981,plain,
% 3.25/3.58 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[319, 20980])).
% 3.25/3.58 tff(20982,plain,
% 3.25/3.58 (~r(elem!1, s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[678, 20979, 408, 670])).
% 3.25/3.58 tff(20983,plain,
% 3.25/3.58 (b(elem!1, s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[560, 20982, 902])).
% 3.25/3.58 tff(20984,plain,
% 3.25/3.58 (~r(s(elem!1), elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[10865, 20979, 623, 408])).
% 3.25/3.58 tff(20985,plain,
% 3.25/3.58 (b(s(elem!1), elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[448, 20984, 907])).
% 3.25/3.58 tff(20986,plain,
% 3.25/3.58 (~b(s(z), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1732, 20984, 20809, 902, 20982])).
% 3.25/3.58 tff(20987,plain,
% 3.25/3.58 (~r(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[17809, 17204, 11546, 2484])).
% 3.25/3.58 tff(20988,plain,
% 3.25/3.58 (b(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[2794, 20987])).
% 3.25/3.58 tff(20989,plain,
% 3.25/3.58 (~b(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[2273, 20988, 489, 490])).
% 3.25/3.58 tff(20990,plain,
% 3.25/3.58 (r(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[396, 20989])).
% 3.25/3.58 tff(20991,plain,
% 3.25/3.58 (~r(s(s(s(z))), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[5824, 333, 670, 509, 20990])).
% 3.25/3.58 tff(20992,plain,
% 3.25/3.58 (~(s(s(s(z))) = elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[19601, 11541, 132])).
% 3.25/3.58 tff(20993,plain,
% 3.25/3.58 (b(s(s(s(z))), elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[704, 20992, 699])).
% 3.25/3.58 tff(20994,plain,
% 3.25/3.58 (~b(s(s(s(z))), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[4819, 20993, 451, 547])).
% 3.25/3.58 tff(20995,plain,
% 3.25/3.58 (s(s(s(z))) = s(elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1951, 44, 20994, 20991])).
% 3.25/3.58 tff(20996,plain,
% 3.25/3.58 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[20995])).
% 3.25/3.58 tff(20997,plain,
% 3.25/3.58 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(symmetry,[status(thm)],[20996])).
% 3.25/3.58 tff(20998,plain,
% 3.25/3.58 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[20997])).
% 3.25/3.58 tff(20999,plain,
% 3.25/3.58 (~b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[1239, 20998])).
% 3.25/3.58 tff(21000,plain,
% 3.25/3.58 (~r(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[16388, 17204, 11546, 322])).
% 3.25/3.58 tff(21001,plain,
% 3.25/3.58 (b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[172, 21000])).
% 3.25/3.58 tff(21002,plain,
% 3.25/3.58 ($false),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21001, 20999])).
% 3.25/3.58 tff(21003,plain,(b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | b(s(z), s(elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | r(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.58 tff(21004,plain,
% 3.25/3.58 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21003, 20986, 670, 20979, 489, 490, 20985, 20983, 19569, 11546, 20981, 2484, 132])).
% 3.25/3.58 tff(21005,plain,
% 3.25/3.58 (~b(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[14036, 144, 21004, 20927, 20962])).
% 3.25/3.58 tff(21006,plain,
% 3.25/3.58 (r(s(s(s(z))), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[396, 21005])).
% 3.25/3.58 tff(21007,plain,
% 3.25/3.58 (~r(elem!1, s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[6311, 333, 670, 408, 21006])).
% 3.25/3.58 tff(21008,plain,
% 3.25/3.58 (~r(s(s(s(z))), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[5824, 333, 670, 20979, 21006])).
% 3.25/3.58 tff(21009,plain,
% 3.25/3.58 (~b(s(s(s(z))), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[4819, 19936, 451, 547])).
% 3.25/3.58 tff(21010,plain,
% 3.25/3.58 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1951, 44, 5995])).
% 3.25/3.58 tff(21011,plain,
% 3.25/3.58 (s(s(s(z))) = s(elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21010, 21009])).
% 3.25/3.58 tff(21012,plain,
% 3.25/3.58 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[21011])).
% 3.25/3.58 tff(21013,plain,
% 3.25/3.58 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(symmetry,[status(thm)],[21012])).
% 3.25/3.58 tff(21014,plain,
% 3.25/3.58 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[21013])).
% 3.25/3.58 tff(21015,plain,
% 3.25/3.58 (~b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[1239, 21014])).
% 3.25/3.58 tff(21016,plain,
% 3.25/3.58 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[17864, 144, 134, 132, 2254])).
% 3.25/3.58 tff(21017,plain,
% 3.25/3.58 (~b(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21016, 19936])).
% 3.25/3.58 tff(21018,plain,
% 3.25/3.58 (r(s(s(s(z))), s(z))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[2794, 21017])).
% 3.25/3.58 tff(21019,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 3.25/3.58 tff(21020,plain,
% 3.25/3.58 (b(elem!1, s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1538, 12398, 21019])).
% 3.25/3.58 tff(21021,plain,
% 3.25/3.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[18960, 21020, 132, 2254])).
% 3.25/3.58 tff(21022,plain,
% 3.25/3.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[249, 21021])).
% 3.25/3.58 tff(21023,plain,
% 3.25/3.58 (~r(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[15519, 21022, 11546, 21018])).
% 3.25/3.58 tff(21024,plain,
% 3.25/3.58 (b(s(z), s(s(s(z))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[172, 21023])).
% 3.25/3.58 tff(21025,plain,
% 3.25/3.58 ($false),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21024, 21015])).
% 3.25/3.58 tff(21026,plain,((s(s(s(z))) = elem!1) | b(s(z), s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.25/3.58 tff(21027,plain,
% 3.25/3.58 (s(s(s(z))) = elem!1),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21026, 20986, 11546, 21008, 132, 21004, 20809, 20985, 20983, 21007, 19569])).
% 3.25/3.58 tff(21028,plain,
% 3.25/3.58 (~(s(s(z)) = elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[14611, 21027, 706])).
% 3.25/3.58 tff(21029,plain,
% 3.25/3.58 (~b(s(s(z)), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[19968, 144, 1398, 286, 259])).
% 3.25/3.58 tff(21030,plain,
% 3.25/3.58 (r(s(s(z)), z)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1462, 44, 164, 21029])).
% 3.25/3.58 tff(21031,plain,
% 3.25/3.58 (((~![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(s(z)), 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(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(21032,plain,
% 3.25/3.58 ((~![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(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(quant_inst,[status(thm)],[])).
% 3.25/3.58 tff(21033,plain,
% 3.25/3.58 ((~![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(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[21032, 21031])).
% 3.25/3.58 tff(21034,plain,
% 3.25/3.58 (~r(s(s(z)), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21033, 333, 670, 509, 21030])).
% 3.25/3.58 tff(21035,plain,
% 3.25/3.58 (~r(s(s(z)), elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[19976, 333, 670, 408, 21030])).
% 3.25/3.58 tff(21036,plain,
% 3.25/3.58 (b(s(s(z)), elem!1)),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[7970, 21035, 1506])).
% 3.25/3.58 tff(21037,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(21038,plain,
% 3.25/3.58 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(21039,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1)))))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[21038])).
% 3.25/3.58 tff(21040,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(transitivity,[status(thm)],[21039, 21037])).
% 3.25/3.58 tff(21041,plain,
% 3.25/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 3.25/3.58 inference(quant_inst,[status(thm)],[])).
% 3.25/3.58 tff(21042,plain,
% 3.25/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1)))),
% 3.25/3.58 inference(modus_ponens,[status(thm)],[21041, 21040])).
% 3.25/3.58 tff(21043,plain,
% 3.25/3.58 ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21042, 144, 451, 1398, 132])).
% 3.25/3.58 tff(21044,plain,
% 3.25/3.58 (~b(s(s(z)), s(elem!1))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21043, 21036])).
% 3.25/3.58 tff(21045,plain,
% 3.25/3.58 ($false),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1408, 44, 860, 21044, 21034])).
% 3.25/3.58 tff(21046,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.58 tff(21047,plain,
% 3.25/3.58 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[21046, 20985, 856, 132, 21028, 670, 20979, 408, 20927, 20962])).
% 3.25/3.58 tff(21048,plain,
% 3.25/3.58 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.58 inference(unit_resolution,[status(thm)],[1451, 21047])).
% 3.25/3.58 tff(21049,plain,
% 3.25/3.58 (((~![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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(21050,plain,
% 3.25/3.58 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.58 inference(rewrite,[status(thm)],[])).
% 3.25/3.58 tff(21051,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.58 inference(monotonicity,[status(thm)],[21050])).
% 3.25/3.58 tff(21052,plain,
% 3.25/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.59 inference(transitivity,[status(thm)],[21051, 21049])).
% 3.25/3.59 tff(21053,plain,
% 3.25/3.59 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 3.25/3.59 inference(quant_inst,[status(thm)],[])).
% 3.25/3.59 tff(21054,plain,
% 3.25/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21053, 21052])).
% 3.25/3.59 tff(21055,plain,
% 3.25/3.59 ($false),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21054, 333, 2671, 11546, 2484, 9770])).
% 3.25/3.59 tff(21056,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.59 tff(21057,plain,
% 3.25/3.59 (~r(s(s(z)), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21056, 21048, 11546, 2484])).
% 3.25/3.59 tff(21058,plain,
% 3.25/3.59 (b(s(s(z)), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1429, 44, 21057, 1416])).
% 3.25/3.59 tff(21059,plain,
% 3.25/3.59 (elem!1 = s(s(s(z)))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21027, 2])).
% 3.25/3.59 tff(21060,plain,
% 3.25/3.59 (~r(s(elem!1), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[20439, 21059, 670, 20962, 132, 902, 11546, 20981])).
% 3.25/3.59 tff(21061,plain,
% 3.25/3.59 (b(s(elem!1), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[486, 21060, 1])).
% 3.25/3.59 tff(21062,plain,
% 3.25/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.25/3.59 inference(rewrite,[status(thm)],[])).
% 3.25/3.59 tff(21063,plain,
% 3.25/3.59 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.25/3.59 inference(rewrite,[status(thm)],[])).
% 3.25/3.59 tff(21064,plain,
% 3.25/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))))),
% 3.25/3.59 inference(monotonicity,[status(thm)],[21063])).
% 3.25/3.59 tff(21065,plain,
% 3.25/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.25/3.59 inference(transitivity,[status(thm)],[21064, 21062])).
% 3.25/3.59 tff(21066,plain,
% 3.25/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.25/3.59 inference(quant_inst,[status(thm)],[])).
% 3.25/3.59 tff(21067,plain,
% 3.25/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21066, 21065])).
% 3.25/3.59 tff(21068,plain,
% 3.25/3.59 (~b(s(elem!1), s(s(z)))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21067, 144, 20985, 20809, 21061, 21058])).
% 3.25/3.59 tff(21069,plain,
% 3.25/3.59 (r(s(elem!1), s(s(z)))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[7466, 44, 7435, 21068])).
% 3.25/3.59 tff(21070,plain,
% 3.25/3.59 (~b(s(s(z)), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[17918, 144, 490, 489, 21058])).
% 3.25/3.59 tff(21071,plain,
% 3.25/3.59 (r(s(s(z)), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1462, 44, 164, 21070])).
% 3.25/3.59 tff(21072,plain,
% 3.25/3.59 (((~![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(elem!1), 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, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.25/3.59 inference(rewrite,[status(thm)],[])).
% 3.25/3.59 tff(21073,plain,
% 3.25/3.59 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.25/3.59 inference(rewrite,[status(thm)],[])).
% 3.25/3.59 tff(21074,plain,
% 3.25/3.59 (((~![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(elem!1), z)) | (~r(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, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.25/3.59 inference(monotonicity,[status(thm)],[21073])).
% 3.25/3.59 tff(21075,plain,
% 3.25/3.59 (((~![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(elem!1), z)) | (~r(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, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.25/3.59 inference(transitivity,[status(thm)],[21074, 21072])).
% 3.25/3.59 tff(21076,plain,
% 3.25/3.59 ((~![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(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 3.25/3.59 inference(quant_inst,[status(thm)],[])).
% 3.25/3.59 tff(21077,plain,
% 3.25/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21076, 21075])).
% 3.25/3.59 tff(21078,plain,
% 3.25/3.59 ($false),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21077, 333, 670, 20979, 21071, 21069])).
% 3.25/3.59 tff(21079,plain,((~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.59 tff(21080,plain,
% 3.25/3.59 (~b(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21079, 432, 489, 11546, 2484, 132, 408, 1, 902, 706, 623, 670])).
% 3.25/3.59 tff(21081,plain,
% 3.25/3.59 (r(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[372, 21080])).
% 3.25/3.59 tff(21082,plain,
% 3.25/3.59 (~r(elem!1, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[20609, 21081, 408, 11546])).
% 3.25/3.59 tff(21083,plain,
% 3.25/3.59 (b(elem!1, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[720, 21082, 713])).
% 3.25/3.59 tff(21084,plain,
% 3.25/3.59 (~b(s(elem!1), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[20903, 21083, 2484, 20809, 432, 1, 11546, 377, 20927, 20962])).
% 3.25/3.59 tff(21085,plain,
% 3.25/3.59 (r(s(elem!1), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[507, 21084])).
% 3.25/3.59 tff(21086,plain,
% 3.25/3.59 (~r(elem!1, s(elem!1))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[678, 21085, 408, 670])).
% 3.25/3.59 tff(21087,plain,
% 3.25/3.59 (~r(s(elem!1), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[10865, 21085, 623, 408])).
% 3.25/3.59 tff(21088,plain,
% 3.25/3.59 (~b(s(z), s(elem!1))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1732, 21087, 20809, 902, 21086])).
% 3.25/3.59 tff(21089,plain,
% 3.25/3.59 (r(s(z), s(elem!1))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1244, 21088, 1229])).
% 3.25/3.59 tff(21090,plain,
% 3.25/3.59 (b(s(elem!1), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[448, 21087, 907])).
% 3.25/3.59 tff(21091,plain,
% 3.25/3.59 (~b(s(elem!1), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[4344, 144, 21090, 20809, 21083])).
% 3.25/3.59 tff(21092,plain,
% 3.25/3.59 (r(s(elem!1), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[486, 21091, 1])).
% 3.25/3.59 tff(21093,plain,
% 3.25/3.59 ($false),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[2918, 333, 21081, 21092, 21085, 21089])).
% 3.25/3.59 tff(21094,plain,((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.25/3.59 tff(21095,plain,
% 3.25/3.59 (elem!1 = s(elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21094, 20977, 1, 19502, 20923, 12930, 20591, 15126, 377, 20922, 17789, 15133])).
% 3.25/3.59 tff(21096,plain,
% 3.25/3.59 (~r(s(s(s(z))), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[2136, 20923, 12930, 19502])).
% 3.25/3.59 tff(21097,plain,
% 3.25/3.59 (s(elem!1) = elem!1),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1569, 21095])).
% 3.25/3.59 tff(21098,plain,
% 3.25/3.59 (elem!1 = s(s(elem!1))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[5813, 21097])).
% 3.25/3.59 tff(21099,plain,
% 3.25/3.59 (s(s(elem!1)) = elem!1),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[5603, 21098])).
% 3.25/3.59 tff(21100,plain,
% 3.25/3.59 (~(s(s(s(z))) = elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[7595, 21099, 19208])).
% 3.25/3.59 tff(21101,plain,
% 3.25/3.59 (b(s(s(s(z))), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[704, 21100, 21096])).
% 3.25/3.59 tff(21102,plain,
% 3.25/3.59 (s(s(s(elem!1))) = elem!1),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[2482, 21095])).
% 3.25/3.59 tff(21103,plain,
% 3.25/3.59 (s(elem!1) = s(s(s(elem!1)))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[2584, 21102, 21095])).
% 3.25/3.59 tff(21104,plain,
% 3.25/3.59 (s(s(s(elem!1))) = s(elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[3254, 21103])).
% 3.25/3.59 tff(21105,plain,
% 3.25/3.59 (~(elem!1 = s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[3246, 21104, 15133])).
% 3.25/3.59 tff(21106,plain,
% 3.25/3.59 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 3.25/3.59 inference(monotonicity,[status(thm)],[21095])).
% 3.25/3.59 tff(21107,plain,
% 3.25/3.59 (b(s(s(s(z))), s(elem!1))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21101, 21106])).
% 3.25/3.59 tff(21108,plain,
% 3.25/3.59 (b(s(z), s(elem!1))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[3262, 21097, 20601])).
% 3.25/3.59 tff(21109,plain,
% 3.25/3.59 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.25/3.59 inference(monotonicity,[status(thm)],[885])).
% 3.25/3.59 tff(21110,plain,
% 3.25/3.59 (~r(elem!1, s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[3201, 3193, 623, 670])).
% 3.25/3.59 tff(21111,plain,
% 3.25/3.59 (b(elem!1, s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1538, 21110, 1524])).
% 3.25/3.59 tff(21112,plain,
% 3.25/3.59 (b(s(elem!1), s(s(s(z))))),
% 3.25/3.59 inference(modus_ponens,[status(thm)],[21111, 21109])).
% 3.25/3.59 tff(21113,plain,
% 3.25/3.59 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[17809, 3193, 11546, 2484])).
% 3.25/3.59 tff(21114,plain,
% 3.25/3.59 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[1137, 21113])).
% 3.25/3.59 tff(21115,plain,
% 3.25/3.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[18960, 21114, 132, 21111])).
% 3.25/3.59 tff(21116,plain,
% 3.25/3.59 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[249, 21115])).
% 3.25/3.59 tff(21117,plain,
% 3.25/3.59 (~r(s(z), s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[15519, 21116, 11546, 3193])).
% 3.25/3.59 tff(21118,plain,
% 3.25/3.59 (b(s(z), s(s(s(z))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[172, 21117])).
% 3.25/3.59 tff(21119,plain,
% 3.25/3.59 ($false),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[12255, 144, 1262, 21118, 21112, 4811])).
% 3.25/3.59 tff(21120,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~(elem!1 = s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.59 tff(21121,plain,
% 3.25/3.59 (~r(s(s(s(z))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21120, 21108, 21107, 21095, 15126, 17789, 21105, 12930, 20923, 20591])).
% 3.25/3.59 tff(21122,plain,
% 3.25/3.59 (b(s(s(s(z))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[2794, 21121])).
% 3.25/3.59 tff(21123,plain,
% 3.25/3.59 (~b(elem!1, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[4375, 21122, 21101, 20601])).
% 3.25/3.59 tff(21124,plain,
% 3.25/3.59 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[20757, 21123, 15126, 20591, 1, 21095])).
% 3.25/3.59 tff(21125,plain,
% 3.25/3.59 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[319, 21124])).
% 3.25/3.59 tff(21126,plain,
% 3.25/3.59 (r(elem!1, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[720, 21123, 15134])).
% 3.25/3.59 tff(21127,plain,
% 3.25/3.59 (~r(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19174, 21126, 20923, 15126])).
% 3.25/3.59 tff(21128,plain,
% 3.25/3.59 (b(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[372, 21127])).
% 3.25/3.59 tff(21129,plain,
% 3.25/3.59 ($false),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[7093, 21128, 21125, 20925, 20922])).
% 3.25/3.59 tff(21130,plain,(b(elem!1, z) | (s(elem!1) = s(z)) | b(z, s(s(s(z)))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.59 tff(21131,plain,
% 3.25/3.59 (b(elem!1, z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[21130, 255, 1, 3])).
% 3.25/3.59 tff(21132,plain,
% 3.25/3.59 (r(z, elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19163, 21131, 3, 1, 255])).
% 3.25/3.59 tff(21133,plain,
% 3.25/3.59 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19198, 21131, 17789, 21132, 15134, 15126, 12930])).
% 3.25/3.59 tff(21134,plain,
% 3.25/3.59 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19291, 21131, 21133, 21132, 3, 1, 12930])).
% 3.25/3.59 tff(21135,plain,
% 3.25/3.59 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[279, 21134])).
% 3.25/3.59 tff(21136,plain,
% 3.25/3.59 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[130, 21133, 17787])).
% 3.25/3.59 tff(21137,plain,
% 3.25/3.59 (~r(s(z), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19519, 21135, 12930, 21136, 15133, 19502, 15126])).
% 3.25/3.59 tff(21138,plain,
% 3.25/3.59 (b(s(z), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[348, 21137])).
% 3.25/3.59 tff(21139,plain,
% 3.25/3.59 (~b(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[19474, 21138, 21131, 1, 21132, 3, 21133, 12930])).
% 3.25/3.59 tff(21140,plain,
% 3.25/3.59 (r(z, s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[372, 21139])).
% 3.25/3.59 tff(21141,plain,
% 3.25/3.59 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[15183, 21140, 15126, 21135])).
% 3.25/3.59 tff(21142,plain,
% 3.25/3.59 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[302, 21141])).
% 3.25/3.59 tff(21143,plain,
% 3.25/3.59 (~r(s(z), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[20228, 21140, 21132, 19502])).
% 3.25/3.59 tff(21144,plain,
% 3.25/3.59 (b(s(z), elem!1)),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[406, 21143, 15133])).
% 3.25/3.59 tff(21145,plain,
% 3.25/3.59 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[3988, 21144, 21131, 21136, 21142])).
% 3.25/3.59 tff(21146,plain,
% 3.25/3.59 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.25/3.59 inference(unit_resolution,[status(thm)],[319, 21145])).
% 3.25/3.59 tff(21147,plain,
% 3.25/3.59 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.59 inference(rewrite,[status(thm)],[])).
% 3.25/3.59 tff(21148,plain,
% 3.25/3.59 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[21147])).
% 3.35/3.60 tff(21149,plain,
% 3.35/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(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(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.60 inference(transitivity,[status(thm)],[21148, 18589])).
% 3.35/3.60 tff(21150,plain,
% 3.35/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 3.35/3.60 inference(quant_inst,[status(thm)],[])).
% 3.35/3.60 tff(21151,plain,
% 3.35/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21150, 21149])).
% 3.35/3.60 tff(21152,plain,
% 3.35/3.60 ($false),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21151, 333, 21140, 15126, 21146, 21135])).
% 3.35/3.60 tff(21153,plain,(b(z, s(s(s(z)))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.60 tff(21154,plain,
% 3.35/3.60 (b(z, s(s(s(z))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21153, 1, 3])).
% 3.35/3.60 tff(21155,plain,
% 3.35/3.60 (~b(z, s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[2176, 144, 284, 19219, 16744])).
% 3.35/3.60 tff(21156,plain,
% 3.35/3.60 (r(z, s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[372, 21155])).
% 3.35/3.60 tff(21157,plain,
% 3.35/3.60 ($false),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[19029, 333, 21156, 323, 11546, 321])).
% 3.35/3.60 tff(21158,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.60 tff(21159,plain,
% 3.35/3.60 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21158, 323, 15126, 284, 17204])).
% 3.35/3.60 tff(21160,plain,
% 3.35/3.60 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[302, 21159])).
% 3.35/3.60 tff(21161,plain,
% 3.35/3.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[294, 21160, 284, 285])).
% 3.35/3.60 tff(21162,plain,
% 3.35/3.60 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[249, 21161])).
% 3.35/3.60 tff(21163,plain,
% 3.35/3.60 (~r(s(z), s(s(s(z))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[16042, 333, 15126, 21162, 17204])).
% 3.35/3.60 tff(21164,plain,
% 3.35/3.60 (b(s(z), s(s(s(z))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[172, 21163])).
% 3.35/3.60 tff(21165,plain,
% 3.35/3.60 (~r(s(s(s(z))), s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[16045, 21161, 15126, 11541])).
% 3.35/3.60 tff(21166,plain,
% 3.35/3.60 (b(s(s(s(z))), s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[2794, 21165])).
% 3.35/3.60 tff(21167,plain,
% 3.35/3.60 (~b(z, s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[2176, 144, 284, 21166, 21164])).
% 3.35/3.60 tff(21168,plain,
% 3.35/3.60 (r(z, s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[372, 21167])).
% 3.35/3.60 tff(21169,plain,
% 3.35/3.60 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[15576, 21168, 15126, 21162])).
% 3.35/3.60 tff(21170,plain,
% 3.35/3.60 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[279, 21169])).
% 3.35/3.60 tff(21171,plain,
% 3.35/3.60 (~b(elem!1, z)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[14405, 21170, 17789, 21160])).
% 3.35/3.60 tff(21172,plain,
% 3.35/3.60 (r(elem!1, z)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[653, 21171, 77])).
% 3.35/3.60 tff(21173,plain,
% 3.35/3.60 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[10345, 144, 491, 21160, 21170])).
% 3.35/3.60 tff(21174,plain,
% 3.35/3.60 (~(s(s(s(z))) = elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[380, 21171, 285])).
% 3.35/3.60 tff(21175,plain,
% 3.35/3.60 (~r(s(z), elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[1376, 21172, 323, 21168])).
% 3.35/3.60 tff(21176,plain,
% 3.35/3.60 (~r(elem!1, s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[747, 21172, 323, 21168])).
% 3.35/3.60 tff(21177,plain,
% 3.35/3.60 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[6102])).
% 3.35/3.60 tff(21178,plain,
% 3.35/3.60 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(elem!1))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[928])).
% 3.35/3.60 tff(21179,plain,
% 3.35/3.60 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = s(elem!1)))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[21178])).
% 3.35/3.60 tff(21180,plain,
% 3.35/3.60 (~(s(s(z)) = s(elem!1))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[1446, 21179])).
% 3.35/3.60 tff(21181,plain,
% 3.35/3.60 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[862, 21180])).
% 3.35/3.60 tff(21182,plain,
% 3.35/3.60 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[6102])).
% 3.35/3.60 tff(21183,plain,
% 3.35/3.60 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.35/3.60 inference(symmetry,[status(thm)],[21182])).
% 3.35/3.60 tff(21184,plain,
% 3.35/3.60 ((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[21183])).
% 3.35/3.60 tff(21185,plain,
% 3.35/3.60 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(transitivity,[status(thm)],[6223, 6222])).
% 3.35/3.60 tff(21186,plain,
% 3.35/3.60 (~(s(s(s(elem!1))) = elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[12928, 3326])).
% 3.35/3.60 tff(21187,plain,
% 3.35/3.60 (~(elem!1 = s(elem!1))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[2482, 21186])).
% 3.35/3.60 tff(21188,plain,
% 3.35/3.60 (~(s(s(elem!1)) = s(elem!1))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[1196, 21187])).
% 3.35/3.60 tff(21189,plain,
% 3.35/3.60 (~(s(elem!1) = elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[5813, 14202])).
% 3.35/3.60 tff(21190,plain,
% 3.35/3.60 (b(s(elem!1), elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[448, 21189, 1727])).
% 3.35/3.60 tff(21191,plain,
% 3.35/3.60 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[12390, 3326, 1727])).
% 3.35/3.60 tff(21192,plain,
% 3.35/3.60 (~b(z, elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[8808, 21191, 114, 3, 259])).
% 3.35/3.60 tff(21193,plain,
% 3.35/3.60 (r(z, elem!1)),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[658, 21192, 74])).
% 3.35/3.60 tff(21194,plain,
% 3.35/3.60 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 3.35/3.60 inference(symmetry,[status(thm)],[3403])).
% 3.35/3.60 tff(21195,plain,
% 3.35/3.60 (b(elem!1, s(elem!1))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[132, 21194])).
% 3.35/3.60 tff(21196,plain,
% 3.35/3.60 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[927])).
% 3.35/3.60 tff(21197,plain,
% 3.35/3.60 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(elem!1))),
% 3.35/3.60 inference(symmetry,[status(thm)],[21196])).
% 3.35/3.60 tff(21198,plain,
% 3.35/3.60 (b(z, s(elem!1))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[259, 21197])).
% 3.35/3.60 tff(21199,plain,
% 3.35/3.60 (~b(s(s(elem!1)), s(elem!1))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[7807, 21198, 21195, 21193, 491, 21190, 14203, 408])).
% 3.35/3.60 tff(21200,plain,
% 3.35/3.60 (r(s(s(elem!1)), s(elem!1))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[1283, 21199, 21188])).
% 3.35/3.60 tff(21201,plain,
% 3.35/3.60 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21200, 21185])).
% 3.35/3.60 tff(21202,plain,
% 3.35/3.60 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[1294, 333, 224, 6107, 21201])).
% 3.35/3.60 tff(21203,plain,
% 3.35/3.60 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21202, 21184])).
% 3.35/3.60 tff(21204,plain,
% 3.35/3.60 (b(s(s(s(z))), s(s(elem!1)))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[1301, 21203, 21181])).
% 3.35/3.60 tff(21205,plain,
% 3.35/3.60 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21204, 21177])).
% 3.35/3.60 tff(21206,plain,
% 3.35/3.60 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[6102])).
% 3.35/3.60 tff(21207,plain,
% 3.35/3.60 (r(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(z), s(s(elem!1)))),
% 3.35/3.60 inference(symmetry,[status(thm)],[6160])).
% 3.35/3.60 tff(21208,plain,
% 3.35/3.60 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(z), s(s(elem!1))))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[21207])).
% 3.35/3.60 tff(21209,plain,
% 3.35/3.60 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[15981, 333, 11546, 224, 21201])).
% 3.35/3.60 tff(21210,plain,
% 3.35/3.60 (~r(s(z), s(s(elem!1)))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21209, 21208])).
% 3.35/3.60 tff(21211,plain,
% 3.35/3.60 (b(s(z), s(s(elem!1)))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[5484, 21210])).
% 3.35/3.60 tff(21212,plain,
% 3.35/3.60 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21211, 21206])).
% 3.35/3.60 tff(21213,plain,
% 3.35/3.60 ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[6103])).
% 3.35/3.60 tff(21214,plain,
% 3.35/3.60 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(z))),
% 3.35/3.60 inference(symmetry,[status(thm)],[21213])).
% 3.35/3.60 tff(21215,plain,
% 3.35/3.60 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(z)))),
% 3.35/3.60 inference(monotonicity,[status(thm)],[21214])).
% 3.35/3.60 tff(21216,plain,
% 3.35/3.60 (~(s(s(s(s(s(s(s(s(z)))))))) = s(z))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[107, 21215])).
% 3.35/3.60 tff(21217,plain,
% 3.35/3.60 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[16053, 333, 11546, 224, 21201])).
% 3.35/3.60 tff(21218,plain,
% 3.35/3.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 3.35/3.60 inference(rewrite,[status(thm)],[])).
% 3.35/3.60 tff(21219,plain,
% 3.35/3.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 3.35/3.60 inference(quant_inst,[status(thm)],[])).
% 3.35/3.60 tff(21220,plain,
% 3.35/3.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.35/3.60 inference(modus_ponens,[status(thm)],[21219, 21218])).
% 3.35/3.60 tff(21221,plain,
% 3.35/3.60 ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21220, 44, 21217])).
% 3.35/3.60 tff(21222,plain,
% 3.35/3.60 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21221, 21216])).
% 3.35/3.60 tff(21223,plain,
% 3.35/3.60 ($false),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[17645, 144, 56, 21222, 21212, 21205])).
% 3.35/3.60 tff(21224,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | r(s(elem!1), elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.60 tff(21225,plain,
% 3.35/3.60 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[21224, 1727, 224, 6107, 11546, 491, 408, 259, 132, 74, 56, 114, 3])).
% 3.35/3.60 tff(21226,plain,
% 3.35/3.60 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.60 inference(unit_resolution,[status(thm)],[472, 21225, 467])).
% 3.35/3.60 tff(21227,plain,
% 3.35/3.60 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.60 inference(rewrite,[status(thm)],[])).
% 3.35/3.60 tff(21228,plain,
% 3.35/3.60 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.61 inference(rewrite,[status(thm)],[])).
% 3.35/3.61 tff(21229,plain,
% 3.35/3.61 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21228])).
% 3.35/3.61 tff(21230,plain,
% 3.35/3.61 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(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(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.61 inference(transitivity,[status(thm)],[21229, 21227])).
% 3.35/3.61 tff(21231,plain,
% 3.35/3.61 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 3.35/3.61 inference(quant_inst,[status(thm)],[])).
% 3.35/3.61 tff(21232,plain,
% 3.35/3.61 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21231, 21230])).
% 3.35/3.61 tff(21233,plain,
% 3.35/3.61 (~r(s(elem!1), s(s(s(z))))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[21232, 333, 224, 6107, 21226])).
% 3.35/3.61 tff(21234,plain,
% 3.35/3.61 (s(elem!1) = s(s(s(z)))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[965, 21233, 901])).
% 3.35/3.61 tff(21235,plain,
% 3.35/3.61 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21234])).
% 3.35/3.61 tff(21236,plain,
% 3.35/3.61 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21235])).
% 3.35/3.61 tff(21237,plain,
% 3.35/3.61 (~r(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[1727, 21236])).
% 3.35/3.61 tff(21238,plain,
% 3.35/3.61 (b(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[704, 21237, 698])).
% 3.35/3.61 tff(21239,plain,
% 3.35/3.61 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21234])).
% 3.35/3.61 tff(21240,plain,
% 3.35/3.61 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.35/3.61 inference(symmetry,[status(thm)],[21239])).
% 3.35/3.61 tff(21241,plain,
% 3.35/3.61 (s(s(z)) = elem!1),
% 3.35/3.61 inference(transitivity,[status(thm)],[87, 21240, 850])).
% 3.35/3.61 tff(21242,plain,
% 3.35/3.61 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21241])).
% 3.35/3.61 tff(21243,plain,
% 3.35/3.61 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 3.35/3.61 inference(transitivity,[status(thm)],[21242, 52])).
% 3.35/3.61 tff(21244,plain,
% 3.35/3.61 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21243])).
% 3.35/3.61 tff(21245,plain,
% 3.35/3.61 (~(s(z) = elem!1)),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[1416, 21244])).
% 3.35/3.61 tff(21246,plain,
% 3.35/3.61 (b(s(z), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[406, 21245, 2310])).
% 3.35/3.61 tff(21247,plain,
% 3.35/3.61 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.35/3.61 inference(transitivity,[status(thm)],[21243, 53])).
% 3.35/3.61 tff(21248,plain,
% 3.35/3.61 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21247])).
% 3.35/3.61 tff(21249,plain,
% 3.35/3.61 (~(elem!1 = s(z))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[1416, 21248])).
% 3.35/3.61 tff(21250,plain,
% 3.35/3.61 (b(elem!1, s(z))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[720, 21249, 715])).
% 3.35/3.61 tff(21251,plain,
% 3.35/3.61 ($false),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[4375, 21250, 21246, 21238, 56])).
% 3.35/3.61 tff(21252,plain,(r(s(elem!1), elem!1) | (~b(s(s(s(z))), s(z))) | r(elem!1, s(z)) | r(s(z), elem!1) | (s(s(s(z))) = elem!1) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.61 tff(21253,plain,
% 3.35/3.61 (r(s(elem!1), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[21252, 21166, 21176, 21175, 21174, 13309, 21162, 17204, 21173, 15126, 491, 21172, 21170, 17789, 71, 17787, 3])).
% 3.35/3.61 tff(21254,plain,
% 3.35/3.61 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[472, 466, 467])).
% 3.35/3.61 tff(21255,plain,
% 3.35/3.61 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21254])).
% 3.35/3.61 tff(21256,plain,
% 3.35/3.61 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 3.35/3.61 inference(symmetry,[status(thm)],[21255])).
% 3.35/3.61 tff(21257,plain,
% 3.35/3.61 (s(s(s(s(s(s(z)))))) = elem!1),
% 3.35/3.61 inference(transitivity,[status(thm)],[21, 21256, 850])).
% 3.35/3.61 tff(21258,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21257])).
% 3.35/3.61 tff(21259,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.35/3.61 inference(symmetry,[status(thm)],[21258])).
% 3.35/3.61 tff(21260,plain,
% 3.35/3.61 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21254])).
% 3.35/3.61 tff(21261,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[435, 21260])).
% 3.35/3.61 tff(21262,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21261, 21259])).
% 3.35/3.61 tff(21263,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21257])).
% 3.35/3.61 tff(21264,plain,
% 3.35/3.61 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.35/3.61 inference(symmetry,[status(thm)],[21263])).
% 3.35/3.61 tff(21265,plain,
% 3.35/3.61 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21257])).
% 3.35/3.61 tff(21266,plain,
% 3.35/3.61 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21265])).
% 3.35/3.61 tff(21267,plain,
% 3.35/3.61 (elem!1 = s(s(s(s(s(s(z))))))),
% 3.35/3.61 inference(transitivity,[status(thm)],[1193, 21255, 20])).
% 3.35/3.61 tff(21268,plain,
% 3.35/3.61 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21267])).
% 3.35/3.61 tff(21269,plain,
% 3.35/3.61 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[2689, 57, 467])).
% 3.35/3.61 tff(21270,plain,
% 3.35/3.61 ($false),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[1451, 21269, 2675])).
% 3.35/3.61 tff(21271,plain,((~(s(z) = elem!1)) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.61 tff(21272,plain,
% 3.35/3.61 (~(s(z) = elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[21271, 466, 467])).
% 3.35/3.61 tff(21273,plain,
% 3.35/3.61 (~(elem!1 = s(z))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[712, 21272])).
% 3.35/3.61 tff(21274,plain,
% 3.35/3.61 (b(elem!1, s(z))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[720, 21273, 715])).
% 3.35/3.61 tff(21275,plain,
% 3.35/3.61 (b(s(s(s(s(s(s(z)))))), s(z))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21274, 21268])).
% 3.35/3.61 tff(21276,plain,
% 3.35/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.61 inference(rewrite,[status(thm)],[])).
% 3.35/3.61 tff(21277,plain,
% 3.35/3.61 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.61 inference(rewrite,[status(thm)],[])).
% 3.35/3.61 tff(21278,plain,
% 3.35/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21277])).
% 3.35/3.61 tff(21279,plain,
% 3.35/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.61 inference(transitivity,[status(thm)],[21278, 21276])).
% 3.35/3.61 tff(21280,plain,
% 3.35/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.61 inference(quant_inst,[status(thm)],[])).
% 3.35/3.61 tff(21281,plain,
% 3.35/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21280, 21279])).
% 3.35/3.61 tff(21282,plain,
% 3.35/3.61 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[21281, 144, 56, 21275, 838])).
% 3.35/3.61 tff(21283,plain,
% 3.35/3.61 (~b(elem!1, s(s(s(z))))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21282, 21266])).
% 3.35/3.61 tff(21284,plain,
% 3.35/3.61 (r(elem!1, s(s(s(z))))),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[1538, 21283, 12398])).
% 3.35/3.61 tff(21285,plain,
% 3.35/3.61 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21284, 21264])).
% 3.35/3.61 tff(21286,plain,
% 3.35/3.61 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(monotonicity,[status(thm)],[21257])).
% 3.35/3.61 tff(21287,plain,
% 3.35/3.61 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.35/3.61 inference(symmetry,[status(thm)],[21286])).
% 3.35/3.61 tff(21288,plain,
% 3.35/3.61 (b(s(z), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[406, 21272, 2310])).
% 3.35/3.61 tff(21289,plain,
% 3.35/3.61 (~b(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[4375, 21274, 21288, 56])).
% 3.35/3.61 tff(21290,plain,
% 3.35/3.61 (r(s(s(s(z))), elem!1)),
% 3.35/3.61 inference(unit_resolution,[status(thm)],[704, 21289, 698])).
% 3.35/3.61 tff(21291,plain,
% 3.35/3.61 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.35/3.61 inference(modus_ponens,[status(thm)],[21290, 21287])).
% 3.35/3.61 tff(21292,plain,
% 3.35/3.61 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.35/3.62 inference(rewrite,[status(thm)],[])).
% 3.35/3.62 tff(21293,plain,
% 3.35/3.62 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.35/3.62 inference(rewrite,[status(thm)],[])).
% 3.35/3.62 tff(21294,plain,
% 3.35/3.62 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21293])).
% 3.35/3.62 tff(21295,plain,
% 3.35/3.62 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.35/3.62 inference(transitivity,[status(thm)],[21294, 21292])).
% 3.35/3.62 tff(21296,plain,
% 3.35/3.62 ((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(quant_inst,[status(thm)],[])).
% 3.35/3.62 tff(21297,plain,
% 3.35/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21296, 21295])).
% 3.35/3.62 tff(21298,plain,
% 3.35/3.62 ($false),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[21297, 333, 6107, 21291, 21285, 21262])).
% 3.35/3.62 tff(21299,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | r(elem!1, s(z)) | r(s(z), elem!1) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.62 tff(21300,plain,
% 3.35/3.62 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[21299, 21166, 17204, 21164, 21174, 21176, 21175, 21173, 21253])).
% 3.35/3.62 tff(21301,plain,
% 3.35/3.62 (~r(s(elem!1), s(s(s(z))))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[21232, 333, 21162, 17204, 21300])).
% 3.35/3.62 tff(21302,plain,
% 3.35/3.62 (s(elem!1) = s(s(s(z)))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[965, 21301, 13309])).
% 3.35/3.62 tff(21303,plain,
% 3.35/3.62 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21302])).
% 3.35/3.62 tff(21304,plain,
% 3.35/3.62 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21303])).
% 3.35/3.62 tff(21305,plain,
% 3.35/3.62 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 3.35/3.62 inference(symmetry,[status(thm)],[21304])).
% 3.35/3.62 tff(21306,plain,
% 3.35/3.62 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21302])).
% 3.35/3.62 tff(21307,plain,
% 3.35/3.62 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.35/3.62 inference(symmetry,[status(thm)],[21306])).
% 3.35/3.62 tff(21308,plain,
% 3.35/3.62 (s(s(z)) = elem!1),
% 3.35/3.62 inference(transitivity,[status(thm)],[87, 21307, 850])).
% 3.35/3.62 tff(21309,plain,
% 3.35/3.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21308])).
% 3.35/3.62 tff(21310,plain,
% 3.35/3.62 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.35/3.62 inference(transitivity,[status(thm)],[21309, 203])).
% 3.35/3.62 tff(21311,plain,
% 3.35/3.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 3.35/3.62 inference(transitivity,[status(thm)],[21310, 21305, 4572])).
% 3.35/3.62 tff(21312,plain,
% 3.35/3.62 (s(s(s(z))) = s(elem!1)),
% 3.35/3.62 inference(symmetry,[status(thm)],[21302])).
% 3.35/3.62 tff(21313,plain,
% 3.35/3.62 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21312])).
% 3.35/3.62 tff(21314,plain,
% 3.35/3.62 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.35/3.62 inference(symmetry,[status(thm)],[21313])).
% 3.35/3.62 tff(21315,plain,
% 3.35/3.62 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21303])).
% 3.35/3.62 tff(21316,plain,
% 3.35/3.62 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[13988, 21300, 21160, 21171, 21253, 77])).
% 3.35/3.62 tff(21317,plain,
% 3.35/3.62 (~b(z, elem!1)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[267, 21316, 17789, 21170])).
% 3.35/3.62 tff(21318,plain,
% 3.35/3.62 (r(z, elem!1)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[658, 21317, 71])).
% 3.35/3.62 tff(21319,plain,
% 3.35/3.62 (~r(z, s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[2453, 333, 21253, 21318, 21172])).
% 3.35/3.62 tff(21320,plain,
% 3.35/3.62 (b(z, s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[583, 21319])).
% 3.35/3.62 tff(21321,plain,
% 3.35/3.62 (~(elem!1 = s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[2974, 21320, 21317])).
% 3.35/3.62 tff(21322,plain,
% 3.35/3.62 (~(s(s(elem!1)) = s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[1196, 21321])).
% 3.35/3.62 tff(21323,plain,
% 3.35/3.62 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21308])).
% 3.35/3.62 tff(21324,plain,
% 3.35/3.62 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 3.35/3.62 inference(transitivity,[status(thm)],[21323, 52])).
% 3.35/3.62 tff(21325,plain,
% 3.35/3.62 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.35/3.62 inference(transitivity,[status(thm)],[21324, 53])).
% 3.35/3.62 tff(21326,plain,
% 3.35/3.62 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21325])).
% 3.35/3.62 tff(21327,plain,
% 3.35/3.62 (~(elem!1 = s(z))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[1416, 21326])).
% 3.35/3.62 tff(21328,plain,
% 3.35/3.62 (b(elem!1, s(z))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[720, 21327, 21176])).
% 3.35/3.62 tff(21329,plain,
% 3.35/3.62 (s(s(s(z))) = s(elem!1)),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21302, 998])).
% 3.35/3.62 tff(21330,plain,
% 3.35/3.62 (~(s(s(elem!1)) = elem!1)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[11095, 21329, 1])).
% 3.35/3.62 tff(21331,plain,
% 3.35/3.62 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21324])).
% 3.35/3.62 tff(21332,plain,
% 3.35/3.62 (~(s(z) = elem!1)),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[1416, 21331])).
% 3.35/3.62 tff(21333,plain,
% 3.35/3.62 (b(s(z), elem!1)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[406, 21332, 21175])).
% 3.35/3.62 tff(21334,plain,
% 3.35/3.62 (b(s(s(elem!1)), z)),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[5056, 21333, 21318, 21172, 21330, 21328, 323])).
% 3.35/3.62 tff(21335,plain,
% 3.35/3.62 (~b(s(s(elem!1)), s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[5572, 21334, 491, 21320])).
% 3.35/3.62 tff(21336,plain,
% 3.35/3.62 (r(s(s(elem!1)), s(elem!1))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[1283, 21335, 21322])).
% 3.35/3.62 tff(21337,plain,
% 3.35/3.62 (r(s(s(s(s(z)))), s(elem!1))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21336, 21315])).
% 3.35/3.62 tff(21338,plain,
% 3.35/3.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21337, 21314])).
% 3.35/3.62 tff(21339,plain,
% 3.35/3.62 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(rewrite,[status(thm)],[])).
% 3.35/3.62 tff(21340,plain,
% 3.35/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21339])).
% 3.35/3.62 tff(21341,plain,
% 3.35/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(transitivity,[status(thm)],[21340, 9812])).
% 3.35/3.62 tff(21342,plain,
% 3.35/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(quant_inst,[status(thm)],[])).
% 3.35/3.62 tff(21343,plain,
% 3.35/3.62 ((~![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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21342, 21341])).
% 3.35/3.62 tff(21344,plain,
% 3.35/3.62 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[21343, 333, 21162, 17204])).
% 3.35/3.62 tff(21345,plain,
% 3.35/3.62 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[21344, 21338])).
% 3.35/3.62 tff(21346,plain,
% 3.35/3.62 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[9761, 21345])).
% 3.35/3.62 tff(21347,plain,
% 3.35/3.62 (elem!1 = s(s(z))),
% 3.35/3.62 inference(transitivity,[status(thm)],[1193, 21306, 86])).
% 3.35/3.62 tff(21348,plain,
% 3.35/3.62 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21347])).
% 3.35/3.62 tff(21349,plain,
% 3.35/3.62 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[21316, 21348])).
% 3.35/3.62 tff(21350,plain,
% 3.35/3.62 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21347])).
% 3.35/3.62 tff(21351,plain,
% 3.35/3.62 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.62 inference(modus_ponens,[status(thm)],[17789, 21350])).
% 3.35/3.62 tff(21352,plain,
% 3.35/3.62 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.35/3.62 inference(unit_resolution,[status(thm)],[9745, 144, 21351, 21349, 21346])).
% 3.35/3.62 tff(21353,plain,
% 3.35/3.62 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21308])).
% 3.35/3.62 tff(21354,plain,
% 3.35/3.62 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.35/3.62 inference(symmetry,[status(thm)],[21353])).
% 3.35/3.62 tff(21355,plain,
% 3.35/3.62 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 3.35/3.62 inference(monotonicity,[status(thm)],[21302])).
% 3.35/3.62 tff(21356,plain,
% 3.35/3.62 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 3.35/3.62 inference(transitivity,[status(thm)],[21355, 21354])).
% 3.35/3.62 tff(21357,plain,
% 3.35/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.62 inference(rewrite,[status(thm)],[])).
% 3.35/3.62 tff(21358,plain,
% 3.35/3.62 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21359,plain,
% 3.35/3.63 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21358])).
% 3.35/3.63 tff(21360,plain,
% 3.35/3.63 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(transitivity,[status(thm)],[21359, 21357])).
% 3.35/3.63 tff(21361,plain,
% 3.35/3.63 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21362,plain,
% 3.35/3.63 ((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21361, 21360])).
% 3.35/3.63 tff(21363,plain,
% 3.35/3.63 (~r(s(z), s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21362, 333, 15126, 21162, 21300])).
% 3.35/3.63 tff(21364,plain,
% 3.35/3.63 (b(s(z), s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[1244, 21363, 1229])).
% 3.35/3.63 tff(21365,plain,
% 3.35/3.63 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21366,plain,
% 3.35/3.63 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21367,plain,
% 3.35/3.63 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21366])).
% 3.35/3.63 tff(21368,plain,
% 3.35/3.63 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(transitivity,[status(thm)],[21367, 21365])).
% 3.35/3.63 tff(21369,plain,
% 3.35/3.63 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21370,plain,
% 3.35/3.63 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21369, 21368])).
% 3.35/3.63 tff(21371,plain,
% 3.35/3.63 (~r(s(elem!1), s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21370, 333, 15126, 21162, 21300])).
% 3.35/3.63 tff(21372,plain,
% 3.35/3.63 (b(s(elem!1), s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[486, 21371, 1])).
% 3.35/3.63 tff(21373,plain,
% 3.35/3.63 (~b(elem!1, s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[4409, 21328, 21372, 21364])).
% 3.35/3.63 tff(21374,plain,
% 3.35/3.63 (r(elem!1, s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[560, 21373, 21321])).
% 3.35/3.63 tff(21375,plain,
% 3.35/3.63 (r(s(s(z)), s(s(s(z))))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21374, 21356])).
% 3.35/3.63 tff(21376,plain,
% 3.35/3.63 (((~![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(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $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(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21377,plain,
% 3.35/3.63 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21378,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(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(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21377])).
% 3.35/3.63 tff(21379,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(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(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.35/3.63 inference(transitivity,[status(thm)],[21378, 21376])).
% 3.35/3.63 tff(21380,plain,
% 3.35/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21381,plain,
% 3.35/3.63 ((~![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(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21380, 21379])).
% 3.35/3.63 tff(21382,plain,
% 3.35/3.63 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21381, 333, 17204, 21375])).
% 3.35/3.63 tff(21383,plain,
% 3.35/3.63 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21382, 21338])).
% 3.35/3.63 tff(21384,plain,
% 3.35/3.63 (((~![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))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21385,plain,
% 3.35/3.63 ((~![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))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21386,plain,
% 3.35/3.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21385, 21384])).
% 3.35/3.63 tff(21387,plain,
% 3.35/3.63 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21386, 44, 21383])).
% 3.35/3.63 tff(21388,plain,
% 3.35/3.63 (s(s(s(s(z)))) = s(s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21387, 21352])).
% 3.35/3.63 tff(21389,plain,
% 3.35/3.63 (s(s(elem!1)) = elem!1),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21388, 21311])).
% 3.35/3.63 tff(21390,plain,
% 3.35/3.63 ($false),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21330, 21389])).
% 3.35/3.63 tff(21391,plain,((~r(s(z), z)) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.63 tff(21392,plain,
% 3.35/3.63 (~r(s(z), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21391, 285, 1, 3, 491, 284, 11541])).
% 3.35/3.63 tff(21393,plain,
% 3.35/3.63 (b(s(z), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[348, 21392])).
% 3.35/3.63 tff(21394,plain,
% 3.35/3.63 (~b(s(z), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[2156, 21393, 284, 285])).
% 3.35/3.63 tff(21395,plain,
% 3.35/3.63 (r(s(z), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[172, 21394])).
% 3.35/3.63 tff(21396,plain,
% 3.35/3.63 ($false),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[16742, 333, 353, 11546, 6107, 321])).
% 3.35/3.63 tff(21397,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.63 tff(21398,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21397, 21395, 15126, 17204])).
% 3.35/3.63 tff(21399,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[302, 21398])).
% 3.35/3.63 tff(21400,plain,
% 3.35/3.63 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[294, 21399, 284, 285])).
% 3.35/3.63 tff(21401,plain,
% 3.35/3.63 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[249, 21400])).
% 3.35/3.63 tff(21402,plain,
% 3.35/3.63 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21403,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21402])).
% 3.35/3.63 tff(21404,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(transitivity,[status(thm)],[21403, 16037])).
% 3.35/3.63 tff(21405,plain,
% 3.35/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21406,plain,
% 3.35/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21405, 21404])).
% 3.35/3.63 tff(21407,plain,
% 3.35/3.63 ($false),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21406, 333, 21395, 15126, 21401, 17204])).
% 3.35/3.63 tff(21408,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), z)) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.63 tff(21409,plain,
% 3.35/3.63 (~b(s(s(s(z))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21408, 491, 1, 3, 284, 11541])).
% 3.35/3.63 tff(21410,plain,
% 3.35/3.63 (r(s(s(s(z))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[396, 21409])).
% 3.35/3.63 tff(21411,plain,
% 3.35/3.63 (~r(s(z), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21397, 321, 11546, 6107])).
% 3.35/3.63 tff(21412,plain,
% 3.35/3.63 (b(s(z), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[172, 21411])).
% 3.35/3.63 tff(21413,plain,
% 3.35/3.63 (~b(z, s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[2176, 144, 284, 19219, 21412])).
% 3.35/3.63 tff(21414,plain,
% 3.35/3.63 (r(z, s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[372, 21413])).
% 3.35/3.63 tff(21415,plain,
% 3.35/3.63 ($false),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[12296, 333, 21414, 1699, 6107, 321])).
% 3.35/3.63 tff(21416,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.63 tff(21417,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21416, 21410, 17204, 284, 15126])).
% 3.35/3.63 tff(21418,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[302, 21417])).
% 3.35/3.63 tff(21419,plain,
% 3.35/3.63 (~(s(elem!1) = s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[6057, 21409, 491])).
% 3.35/3.63 tff(21420,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21416, 1699, 17204, 284, 11546])).
% 3.35/3.63 tff(21421,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[302, 21420])).
% 3.35/3.63 tff(21422,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[16045, 3193, 11546, 11541])).
% 3.35/3.63 tff(21423,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21424,plain,
% 3.35/3.63 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.63 inference(rewrite,[status(thm)],[])).
% 3.35/3.63 tff(21425,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21424])).
% 3.35/3.63 tff(21426,plain,
% 3.35/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.63 inference(transitivity,[status(thm)],[21425, 21423])).
% 3.35/3.63 tff(21427,plain,
% 3.35/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.63 inference(quant_inst,[status(thm)],[])).
% 3.35/3.63 tff(21428,plain,
% 3.35/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.35/3.63 inference(modus_ponens,[status(thm)],[21427, 21426])).
% 3.35/3.63 tff(21429,plain,
% 3.35/3.63 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21428, 144, 491, 284, 21422, 21421])).
% 3.35/3.63 tff(21430,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[17809, 3193, 11546, 17204])).
% 3.35/3.63 tff(21431,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[130, 21430, 114])).
% 3.35/3.63 tff(21432,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[15720, 3193, 11546, 17204])).
% 3.35/3.63 tff(21433,plain,
% 3.35/3.63 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[319, 21432])).
% 3.35/3.63 tff(21434,plain,
% 3.35/3.63 ($false),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[17265, 144, 489, 284, 283, 304, 286])).
% 3.35/3.63 tff(21435,plain,((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.63 tff(21436,plain,
% 3.35/3.63 (~b(s(z), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[21435, 21422, 284, 21433, 21421])).
% 3.35/3.63 tff(21437,plain,
% 3.35/3.63 (r(s(z), z)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[348, 21436])).
% 3.35/3.63 tff(21438,plain,
% 3.35/3.63 (~r(z, elem!1)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[11212, 21437, 1699, 3193])).
% 3.35/3.63 tff(21439,plain,
% 3.35/3.63 (b(z, elem!1)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[658, 21438, 74])).
% 3.35/3.63 tff(21440,plain,
% 3.35/3.63 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[267, 21439, 132, 21431])).
% 3.35/3.63 tff(21441,plain,
% 3.35/3.63 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[279, 21440])).
% 3.35/3.63 tff(21442,plain,
% 3.35/3.63 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[13763, 21441, 17204, 1699])).
% 3.35/3.63 tff(21443,plain,
% 3.35/3.63 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.35/3.63 inference(unit_resolution,[status(thm)],[542, 21442, 21429])).
% 3.35/3.63 tff(21444,plain,
% 3.35/3.63 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 3.35/3.63 inference(monotonicity,[status(thm)],[21443])).
% 3.35/3.64 tff(21445,plain,
% 3.35/3.64 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(symmetry,[status(thm)],[21444])).
% 3.35/3.64 tff(21446,plain,
% 3.35/3.64 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21445])).
% 3.35/3.64 tff(21447,plain,
% 3.35/3.64 (~r(z, s(elem!1))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[8030, 21437, 3193, 1699])).
% 3.35/3.64 tff(21448,plain,
% 3.35/3.64 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21447, 21446])).
% 3.35/3.64 tff(21449,plain,
% 3.35/3.64 ($false),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21441, 21448])).
% 3.35/3.64 tff(21450,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.64 tff(21451,plain,
% 3.35/3.64 (~r(s(s(s(z))), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21450, 21410, 17789, 71, 284, 491, 17787, 15126, 11541])).
% 3.35/3.64 tff(21452,plain,
% 3.35/3.64 (b(s(s(s(z))), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[2794, 21451])).
% 3.35/3.64 tff(21453,plain,
% 3.35/3.64 (~b(z, s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[2176, 144, 284, 56, 19948])).
% 3.35/3.64 tff(21454,plain,
% 3.35/3.64 (r(z, s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[372, 21453])).
% 3.35/3.64 tff(21455,plain,
% 3.35/3.64 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[15576, 21454, 11546, 224])).
% 3.35/3.64 tff(21456,plain,
% 3.35/3.64 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[279, 21455])).
% 3.35/3.64 tff(21457,plain,
% 3.35/3.64 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21416, 1699, 6107, 284, 11546])).
% 3.35/3.64 tff(21458,plain,
% 3.35/3.64 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[302, 21457])).
% 3.35/3.64 tff(21459,plain,
% 3.35/3.64 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[10345, 144, 491, 21458, 21456])).
% 3.35/3.64 tff(21460,plain,
% 3.35/3.64 (~r(s(elem!1), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21232, 333, 224, 6107, 525])).
% 3.35/3.64 tff(21461,plain,
% 3.35/3.64 (b(s(elem!1), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[965, 21460, 960])).
% 3.35/3.64 tff(21462,plain,
% 3.35/3.64 (~r(s(elem!1), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21370, 333, 11546, 224, 525])).
% 3.35/3.64 tff(21463,plain,
% 3.35/3.64 (b(s(elem!1), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[486, 21462, 1])).
% 3.35/3.64 tff(21464,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21465,plain,
% 3.35/3.64 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21466,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21465])).
% 3.35/3.64 tff(21467,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(transitivity,[status(thm)],[21466, 21464])).
% 3.35/3.64 tff(21468,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))),
% 3.35/3.64 inference(quant_inst,[status(thm)],[])).
% 3.35/3.64 tff(21469,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21468, 21467])).
% 3.35/3.64 tff(21470,plain,
% 3.35/3.64 ($false),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21469, 144, 491, 21463, 284, 56, 21461])).
% 3.35/3.64 tff(21471,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(s(s(z)))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.64 tff(21472,plain,
% 3.35/3.64 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21471, 224, 284, 56, 960, 1, 491, 6107, 11546])).
% 3.35/3.64 tff(21473,plain,
% 3.35/3.64 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[472, 21472, 21459])).
% 3.35/3.64 tff(21474,plain,
% 3.35/3.64 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21473])).
% 3.35/3.64 tff(21475,plain,
% 3.35/3.64 (elem!1 = s(s(s(s(s(s(z))))))),
% 3.35/3.64 inference(transitivity,[status(thm)],[1193, 21474, 20])).
% 3.35/3.64 tff(21476,plain,
% 3.35/3.64 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21475])).
% 3.35/3.64 tff(21477,plain,
% 3.35/3.64 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(elem!1, s(z))),
% 3.35/3.64 inference(symmetry,[status(thm)],[21476])).
% 3.35/3.64 tff(21478,plain,
% 3.35/3.64 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(elem!1, s(z)))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21477])).
% 3.35/3.64 tff(21479,plain,
% 3.35/3.64 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 3.35/3.64 inference(symmetry,[status(thm)],[21474])).
% 3.35/3.64 tff(21480,plain,
% 3.35/3.64 (s(s(s(s(s(s(z)))))) = elem!1),
% 3.35/3.64 inference(transitivity,[status(thm)],[21, 21479, 850])).
% 3.35/3.64 tff(21481,plain,
% 3.35/3.64 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21480])).
% 3.35/3.64 tff(21482,plain,
% 3.35/3.64 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.35/3.64 inference(symmetry,[status(thm)],[21481])).
% 3.35/3.64 tff(21483,plain,
% 3.35/3.64 (~b(elem!1, z)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[14405, 21456, 132, 21458])).
% 3.35/3.64 tff(21484,plain,
% 3.35/3.64 (r(elem!1, z)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[653, 21483, 77])).
% 3.35/3.64 tff(21485,plain,
% 3.35/3.64 (~r(elem!1, s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[20649, 333, 21454, 21484, 1699])).
% 3.35/3.64 tff(21486,plain,
% 3.35/3.64 (~(s(s(s(z))) = elem!1)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[12214, 21473])).
% 3.35/3.64 tff(21487,plain,
% 3.35/3.64 (~(elem!1 = s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[10997, 21486])).
% 3.35/3.64 tff(21488,plain,
% 3.35/3.64 (b(elem!1, s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[1538, 21487, 21485])).
% 3.35/3.64 tff(21489,plain,
% 3.35/3.64 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21488, 21482])).
% 3.35/3.64 tff(21490,plain,
% 3.35/3.64 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21491,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21490])).
% 3.35/3.64 tff(21492,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.35/3.64 inference(transitivity,[status(thm)],[21491, 21276])).
% 3.35/3.64 tff(21493,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.35/3.64 inference(quant_inst,[status(thm)],[])).
% 3.35/3.64 tff(21494,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21493, 21492])).
% 3.35/3.64 tff(21495,plain,
% 3.35/3.64 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21494, 144, 56, 19948])).
% 3.35/3.64 tff(21496,plain,
% 3.35/3.64 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21495, 21489])).
% 3.35/3.64 tff(21497,plain,
% 3.35/3.64 (~b(elem!1, s(z))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21496, 21478])).
% 3.35/3.64 tff(21498,plain,
% 3.35/3.64 (~(s(z) = elem!1)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21271, 21472, 21459])).
% 3.35/3.64 tff(21499,plain,
% 3.35/3.64 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21475])).
% 3.35/3.64 tff(21500,plain,
% 3.35/3.64 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), elem!1)),
% 3.35/3.64 inference(symmetry,[status(thm)],[21499])).
% 3.35/3.64 tff(21501,plain,
% 3.35/3.64 ((~b(s(z), s(s(s(s(s(s(z)))))))) <=> (~b(s(z), elem!1))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21500])).
% 3.35/3.64 tff(21502,plain,
% 3.35/3.64 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), elem!1)),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21480])).
% 3.35/3.64 tff(21503,plain,
% 3.35/3.64 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(symmetry,[status(thm)],[21502])).
% 3.35/3.64 tff(21504,plain,
% 3.35/3.64 (~r(s(s(s(z))), elem!1)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[2122, 21484, 1699, 21454])).
% 3.35/3.64 tff(21505,plain,
% 3.35/3.64 (b(s(s(s(z))), elem!1)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[704, 21486, 21504])).
% 3.35/3.64 tff(21506,plain,
% 3.35/3.64 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21505, 21503])).
% 3.35/3.64 tff(21507,plain,
% 3.35/3.64 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[20956, 144, 19948])).
% 3.35/3.64 tff(21508,plain,
% 3.35/3.64 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21507, 21489, 21506])).
% 3.35/3.64 tff(21509,plain,
% 3.35/3.64 (~b(s(z), elem!1)),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21508, 21501])).
% 3.35/3.64 tff(21510,plain,
% 3.35/3.64 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, elem!1)),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21480])).
% 3.35/3.64 tff(21511,plain,
% 3.35/3.64 ((~b(z, s(s(s(s(s(s(z)))))))) <=> (~b(z, elem!1))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21510])).
% 3.35/3.64 tff(21512,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21513,plain,
% 3.35/3.64 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21514,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21513])).
% 3.35/3.64 tff(21515,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(transitivity,[status(thm)],[21514, 21512])).
% 3.35/3.64 tff(21516,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 3.35/3.64 inference(quant_inst,[status(thm)],[])).
% 3.35/3.64 tff(21517,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21516, 21515])).
% 3.35/3.64 tff(21518,plain,
% 3.35/3.64 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21517, 144, 284])).
% 3.35/3.64 tff(21519,plain,
% 3.35/3.64 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21518, 21489, 21506])).
% 3.35/3.64 tff(21520,plain,
% 3.35/3.64 (~b(z, elem!1)),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21519, 21511])).
% 3.35/3.64 tff(21521,plain,
% 3.35/3.64 (r(z, elem!1)),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[658, 21520, 71])).
% 3.35/3.64 tff(21522,plain,
% 3.35/3.64 ($false),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[13826, 21521, 21509, 21454, 21498, 21497])).
% 3.35/3.64 tff(21523,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.64 tff(21524,plain,
% 3.35/3.64 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21523, 21452, 284, 21419, 1, 491, 17204, 15126, 21410, 17789])).
% 3.35/3.64 tff(21525,plain,
% 3.35/3.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[249, 21524])).
% 3.35/3.64 tff(21526,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21527,plain,
% 3.35/3.64 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.64 inference(rewrite,[status(thm)],[])).
% 3.35/3.64 tff(21528,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.35/3.64 inference(monotonicity,[status(thm)],[21527])).
% 3.35/3.64 tff(21529,plain,
% 3.35/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.64 inference(transitivity,[status(thm)],[21528, 21526])).
% 3.35/3.64 tff(21530,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.64 inference(quant_inst,[status(thm)],[])).
% 3.35/3.64 tff(21531,plain,
% 3.35/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.35/3.64 inference(modus_ponens,[status(thm)],[21530, 21529])).
% 3.35/3.64 tff(21532,plain,
% 3.35/3.64 ($false),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21531, 144, 284, 56, 283, 304, 286])).
% 3.35/3.64 tff(21533,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.64 tff(21534,plain,
% 3.35/3.64 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[21533, 21452, 284, 21525, 21418])).
% 3.35/3.64 tff(21535,plain,
% 3.35/3.64 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[319, 21534])).
% 3.35/3.64 tff(21536,plain,
% 3.35/3.64 (~r(s(z), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[16388, 21535, 15126, 17204])).
% 3.35/3.64 tff(21537,plain,
% 3.35/3.64 (b(s(z), s(s(s(z))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[172, 21536])).
% 3.35/3.64 tff(21538,plain,
% 3.35/3.64 (~b(z, s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[16453, 21535, 284, 15126, 17204])).
% 3.35/3.64 tff(21539,plain,
% 3.35/3.64 (r(z, s(z))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[372, 21538])).
% 3.35/3.64 tff(21540,plain,
% 3.35/3.64 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[18594, 333, 21539, 15126, 21535])).
% 3.35/3.64 tff(21541,plain,
% 3.35/3.64 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.64 inference(unit_resolution,[status(thm)],[279, 21540])).
% 3.35/3.65 tff(21542,plain,
% 3.35/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.65 inference(rewrite,[status(thm)],[])).
% 3.35/3.65 tff(21543,plain,
% 3.35/3.65 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.65 inference(rewrite,[status(thm)],[])).
% 3.35/3.65 tff(21544,plain,
% 3.35/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21543])).
% 3.35/3.65 tff(21545,plain,
% 3.35/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.65 inference(transitivity,[status(thm)],[21544, 21542])).
% 3.35/3.65 tff(21546,plain,
% 3.35/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 3.35/3.65 inference(quant_inst,[status(thm)],[])).
% 3.35/3.65 tff(21547,plain,
% 3.35/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[21546, 21545])).
% 3.35/3.65 tff(21548,plain,
% 3.35/3.65 ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21547, 144, 284, 17789, 21525])).
% 3.35/3.65 tff(21549,plain,
% 3.35/3.65 (~b(z, elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21548, 21541])).
% 3.35/3.65 tff(21550,plain,
% 3.35/3.65 (~(s(s(s(z))) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[609, 21549, 284])).
% 3.35/3.65 tff(21551,plain,
% 3.35/3.65 (~(elem!1 = s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[10997, 21550])).
% 3.35/3.65 tff(21552,plain,
% 3.35/3.65 (~b(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[14405, 21541, 17789, 21418])).
% 3.35/3.65 tff(21553,plain,
% 3.35/3.65 (r(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[653, 21552, 77])).
% 3.35/3.65 tff(21554,plain,
% 3.35/3.65 (r(z, elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[658, 21549, 71])).
% 3.35/3.65 tff(21555,plain,
% 3.35/3.65 (~r(elem!1, s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[6311, 333, 21554, 21553, 21410])).
% 3.35/3.65 tff(21556,plain,
% 3.35/3.65 (b(elem!1, s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1538, 21555, 21551])).
% 3.35/3.65 tff(21557,plain,
% 3.35/3.65 (~b(elem!1, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[18973, 144, 21556, 21452, 21537])).
% 3.35/3.65 tff(21558,plain,
% 3.35/3.65 (~r(s(s(s(z))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2122, 21553, 21410, 21539])).
% 3.35/3.65 tff(21559,plain,
% 3.35/3.65 (b(s(s(s(z))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[704, 21550, 21558])).
% 3.35/3.65 tff(21560,plain,
% 3.35/3.65 (~b(s(z), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[19991, 144, 21556, 21537, 21559])).
% 3.35/3.65 tff(21561,plain,
% 3.35/3.65 (s(z) = elem!1),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[13826, 21560, 21539, 21554, 21557])).
% 3.35/3.65 tff(21562,plain,
% 3.35/3.65 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21561])).
% 3.35/3.65 tff(21563,plain,
% 3.35/3.65 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(symmetry,[status(thm)],[21562])).
% 3.35/3.65 tff(21564,plain,
% 3.35/3.65 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[17789, 21563])).
% 3.35/3.65 tff(21565,plain,
% 3.35/3.65 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.35/3.65 inference(rewrite,[status(thm)],[])).
% 3.35/3.65 tff(21566,plain,
% 3.35/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21565])).
% 3.35/3.65 tff(21567,plain,
% 3.35/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.35/3.65 inference(transitivity,[status(thm)],[21566, 11021])).
% 3.35/3.65 tff(21568,plain,
% 3.35/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.35/3.65 inference(quant_inst,[status(thm)],[])).
% 3.35/3.65 tff(21569,plain,
% 3.35/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[21568, 21567])).
% 3.35/3.65 tff(21570,plain,
% 3.35/3.65 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21569, 144, 21556, 21525, 21559])).
% 3.35/3.65 tff(21571,plain,
% 3.35/3.65 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[130, 21570, 17787])).
% 3.35/3.65 tff(21572,plain,
% 3.35/3.65 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[14783, 21571, 21552, 3, 1, 21540])).
% 3.35/3.65 tff(21573,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21572, 21564])).
% 3.35/3.65 tff(21574,plain,((~b(s(elem!1), z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21575,plain,
% 3.35/3.65 (~b(s(elem!1), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21574, 11541, 1, 284, 3])).
% 3.35/3.65 tff(21576,plain,
% 3.35/3.65 (r(s(elem!1), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[507, 21575])).
% 3.35/3.65 tff(21577,plain,
% 3.35/3.65 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[17785, 1, 11546])).
% 3.35/3.65 tff(21578,plain,
% 3.35/3.65 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[3398, 21577])).
% 3.35/3.65 tff(21579,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[130, 21430, 21578])).
% 3.35/3.65 tff(21580,plain,
% 3.35/3.65 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[294, 21422, 284, 285])).
% 3.35/3.65 tff(21581,plain,
% 3.35/3.65 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[302, 21580])).
% 3.35/3.65 tff(21582,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[19217, 333, 3193, 11546, 17204, 21581])).
% 3.35/3.65 tff(21583,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21584,plain,
% 3.35/3.65 (~b(s(s(s(z))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21583, 3193, 284, 11546, 11541])).
% 3.35/3.65 tff(21585,plain,
% 3.35/3.65 (r(s(s(s(z))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[396, 21584])).
% 3.35/3.65 tff(21586,plain,
% 3.35/3.65 (~r(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21158, 321, 11546, 284, 6107])).
% 3.35/3.65 tff(21587,plain,
% 3.35/3.65 (b(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[348, 21586])).
% 3.35/3.65 tff(21588,plain,
% 3.35/3.65 (~r(s(s(s(z))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21416, 321, 6107, 284, 11546])).
% 3.35/3.65 tff(21589,plain,
% 3.35/3.65 (b(s(s(s(z))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[396, 21588])).
% 3.35/3.65 tff(21590,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2156, 21589, 21412, 284, 21587])).
% 3.35/3.65 tff(21591,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21592,plain,
% 3.35/3.65 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21591, 17204, 284, 11546])).
% 3.35/3.65 tff(21593,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[302, 21592])).
% 3.35/3.65 tff(21594,plain,
% 3.35/3.65 (~b(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21435, 21433, 284, 21422, 21593])).
% 3.35/3.65 tff(21595,plain,
% 3.35/3.65 (r(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[348, 21594])).
% 3.35/3.65 tff(21596,plain,
% 3.35/3.65 (~r(z, elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[11212, 21595, 3193, 21585])).
% 3.35/3.65 tff(21597,plain,
% 3.35/3.65 (b(z, elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[658, 21596, 71])).
% 3.35/3.65 tff(21598,plain,
% 3.35/3.65 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[267, 21597, 132, 21579])).
% 3.35/3.65 tff(21599,plain,
% 3.35/3.65 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[279, 21598])).
% 3.35/3.65 tff(21600,plain,
% 3.35/3.65 (~b(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[880, 21597, 21579, 21593])).
% 3.35/3.65 tff(21601,plain,
% 3.35/3.65 (r(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[653, 21600, 77])).
% 3.35/3.65 tff(21602,plain,
% 3.35/3.65 (~r(s(elem!1), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[517, 21601, 509, 21599])).
% 3.35/3.65 tff(21603,plain,
% 3.35/3.65 (~r(z, s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[8030, 21595, 3193, 21585])).
% 3.35/3.65 tff(21604,plain,
% 3.35/3.65 (b(z, s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[583, 21603])).
% 3.35/3.65 tff(21605,plain,
% 3.35/3.65 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2899, 21592, 509])).
% 3.35/3.65 tff(21606,plain,
% 3.35/3.65 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[13763, 21599, 17204, 21585])).
% 3.35/3.65 tff(21607,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[542, 21606, 21605])).
% 3.35/3.65 tff(21608,plain,
% 3.35/3.65 (~b(s(elem!1), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[593, 21607, 21593, 21604, 21579])).
% 3.35/3.65 tff(21609,plain,
% 3.35/3.65 (s(elem!1) = elem!1),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[448, 21608, 21602])).
% 3.35/3.65 tff(21610,plain,
% 3.35/3.65 (b(s(elem!1), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21609])).
% 3.35/3.65 tff(21611,plain,
% 3.35/3.65 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(symmetry,[status(thm)],[21610])).
% 3.35/3.65 tff(21612,plain,
% 3.35/3.65 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21611])).
% 3.35/3.65 tff(21613,plain,
% 3.35/3.65 (~r(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[6555, 21595, 3193, 21585])).
% 3.35/3.65 tff(21614,plain,
% 3.35/3.65 (b(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[372, 21613])).
% 3.35/3.65 tff(21615,plain,
% 3.35/3.65 (~r(s(z), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[417, 21599, 21595, 21601])).
% 3.35/3.65 tff(21616,plain,
% 3.35/3.65 (elem!1 = s(elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[906, 21609])).
% 3.35/3.65 tff(21617,plain,
% 3.35/3.65 (s(s(s(elem!1))) = elem!1),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2482, 21616])).
% 3.35/3.65 tff(21618,plain,
% 3.35/3.65 (~(s(z) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2468, 21617])).
% 3.35/3.65 tff(21619,plain,
% 3.35/3.65 (b(s(z), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[406, 21618, 21615])).
% 3.35/3.65 tff(21620,plain,
% 3.35/3.65 (~b(elem!1, s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2090, 21619, 284, 21597, 21614])).
% 3.35/3.65 tff(21621,plain,
% 3.35/3.65 (~b(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[21620, 21612])).
% 3.35/3.65 tff(21622,plain,
% 3.35/3.65 (s(elem!1) = s(s(s(elem!1)))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2584, 21617, 21616])).
% 3.35/3.65 tff(21623,plain,
% 3.35/3.65 (~(s(elem!1) = s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[990, 21622, 1])).
% 3.35/3.65 tff(21624,plain,
% 3.35/3.65 (~b(elem!1, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[7079, 21619, 21614, 21597])).
% 3.35/3.65 tff(21625,plain,
% 3.35/3.65 (~b(s(elem!1), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[890, 21624, 21616])).
% 3.35/3.65 tff(21626,plain,
% 3.35/3.65 (r(s(elem!1), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[486, 21625, 1])).
% 3.35/3.65 tff(21627,plain,
% 3.35/3.65 (~r(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[11237, 21626, 3193, 21595])).
% 3.35/3.65 tff(21628,plain,
% 3.35/3.65 (b(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[965, 21627, 21623])).
% 3.35/3.65 tff(21629,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21628, 21621])).
% 3.35/3.65 tff(21630,plain,((~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21631,plain,
% 3.35/3.65 (~r(s(s(s(z))), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21630, 21576, 284, 1, 17789, 15126, 11541])).
% 3.35/3.65 tff(21632,plain,
% 3.35/3.65 (b(s(s(s(z))), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2794, 21631])).
% 3.35/3.65 tff(21633,plain,
% 3.35/3.65 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21591, 6107, 284, 11546])).
% 3.35/3.65 tff(21634,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[302, 21633])).
% 3.35/3.65 tff(21635,plain,
% 3.35/3.65 (~b(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[16453, 322, 284, 11546, 6107])).
% 3.35/3.65 tff(21636,plain,
% 3.35/3.65 (r(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[372, 21635])).
% 3.35/3.65 tff(21637,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[18594, 333, 21636, 11546, 322, 51])).
% 3.35/3.65 tff(21638,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21639,plain,
% 3.35/3.65 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21638, 51, 11546, 284, 6107])).
% 3.35/3.65 tff(21640,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[319, 21639])).
% 3.35/3.65 tff(21641,plain,
% 3.35/3.65 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21533, 21640, 284, 56, 21634])).
% 3.35/3.65 tff(21642,plain,
% 3.35/3.65 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[249, 21641])).
% 3.35/3.65 tff(21643,plain,
% 3.35/3.65 (~r(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[15576, 21642, 11546, 51])).
% 3.35/3.65 tff(21644,plain,
% 3.35/3.65 (b(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[372, 21643])).
% 3.35/3.65 tff(21645,plain,
% 3.35/3.65 (~b(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[7093, 21644, 21634, 21640])).
% 3.35/3.65 tff(21646,plain,
% 3.35/3.65 (r(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[348, 21645])).
% 3.35/3.65 tff(21647,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[19046, 333, 21646, 11546, 21642, 51])).
% 3.35/3.65 tff(21648,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21649,plain,
% 3.35/3.65 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21648, 21632, 284, 15126, 17204])).
% 3.35/3.65 tff(21650,plain,
% 3.35/3.65 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[279, 21649])).
% 3.35/3.65 tff(21651,plain,
% 3.35/3.65 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21591, 6107, 284, 15126])).
% 3.35/3.65 tff(21652,plain,
% 3.35/3.65 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[302, 21651])).
% 3.35/3.65 tff(21653,plain,
% 3.35/3.65 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21648, 56, 284, 15126, 6107])).
% 3.35/3.65 tff(21654,plain,
% 3.35/3.65 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[279, 21653])).
% 3.35/3.65 tff(21655,plain,
% 3.35/3.65 (~b(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[14405, 21654, 17789, 21652])).
% 3.35/3.65 tff(21656,plain,
% 3.35/3.65 (r(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[653, 21655, 77])).
% 3.35/3.65 tff(21657,plain,
% 3.35/3.65 (~r(s(elem!1), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[8063, 333, 7265, 21656, 509])).
% 3.35/3.65 tff(21658,plain,
% 3.35/3.65 (~r(s(z), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[16042, 333, 15126, 224, 6107])).
% 3.35/3.65 tff(21659,plain,
% 3.35/3.65 (b(s(z), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[172, 21658])).
% 3.35/3.65 tff(21660,plain,
% 3.35/3.65 (~b(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2176, 144, 284, 56, 21659])).
% 3.35/3.65 tff(21661,plain,
% 3.35/3.65 (r(z, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[372, 21660])).
% 3.35/3.65 tff(21662,plain,
% 3.35/3.65 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[15576, 21661, 15126, 224])).
% 3.35/3.65 tff(21663,plain,
% 3.35/3.65 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[279, 21662])).
% 3.35/3.65 tff(21664,plain,
% 3.35/3.65 (~b(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[14405, 21663, 17789, 21652])).
% 3.35/3.65 tff(21665,plain,
% 3.35/3.65 (r(elem!1, z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[653, 21664, 77])).
% 3.35/3.65 tff(21666,plain,
% 3.35/3.65 (~r(elem!1, s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1620, 21665, 509, 21661])).
% 3.35/3.65 tff(21667,plain,
% 3.35/3.65 (~b(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2156, 285, 284, 21659])).
% 3.35/3.65 tff(21668,plain,
% 3.35/3.65 (r(s(z), z)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[348, 21667])).
% 3.35/3.65 tff(21669,plain,
% 3.35/3.65 (~r(s(z), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1235, 21668, 509, 21661])).
% 3.35/3.65 tff(21670,plain,
% 3.35/3.65 (b(s(z), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1244, 21669, 1229])).
% 3.35/3.65 tff(21671,plain,
% 3.35/3.65 (~r(s(elem!1), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1610, 333, 21661, 21665, 509])).
% 3.35/3.65 tff(21672,plain,
% 3.35/3.65 (~r(s(z), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1376, 21668, 21665, 21661])).
% 3.35/3.65 tff(21673,plain,
% 3.35/3.65 (~r(elem!1, s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[747, 21668, 21661, 21665])).
% 3.35/3.65 tff(21674,plain,
% 3.35/3.65 (~(s(s(s(z))) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[380, 285, 21664])).
% 3.35/3.65 tff(21675,plain,
% 3.35/3.65 (~r(s(elem!1), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1365, 21668, 509, 21661])).
% 3.35/3.65 tff(21676,plain,
% 3.35/3.65 (b(s(elem!1), s(z))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[486, 21675, 1])).
% 3.35/3.65 tff(21677,plain,
% 3.35/3.65 (~b(s(s(s(z))), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1946, 144, 21676, 21670, 56])).
% 3.35/3.65 tff(21678,plain,
% 3.35/3.65 (~b(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[899, 144, 21676, 56, 21659])).
% 3.35/3.65 tff(21679,plain,
% 3.35/3.65 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2899, 21651, 509])).
% 3.35/3.65 tff(21680,plain,
% 3.35/3.65 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[132, 6020])).
% 3.35/3.65 tff(21681,plain,
% 3.35/3.65 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[8651, 57, 259, 1727, 606, 1368, 1237, 114, 670])).
% 3.35/3.65 tff(21682,plain,
% 3.35/3.65 ($false),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21681, 21680])).
% 3.35/3.65 tff(21683,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | b(z, elem!1) | (elem!1 = z) | (s(z) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.65 tff(21684,plain,
% 3.35/3.65 (~(s(z) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[21683, 606, 259, 1727, 132, 77, 1229, 21578, 7265])).
% 3.35/3.65 tff(21685,plain,
% 3.35/3.65 (b(s(z), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[406, 21684, 2310])).
% 3.35/3.65 tff(21686,plain,
% 3.35/3.65 (elem!1 = s(elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1732, 21685, 1727, 1262, 1725])).
% 3.35/3.65 tff(21687,plain,
% 3.35/3.65 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21686])).
% 3.35/3.65 tff(21688,plain,
% 3.35/3.65 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.65 inference(symmetry,[status(thm)],[21687])).
% 3.35/3.65 tff(21689,plain,
% 3.35/3.65 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21688])).
% 3.35/3.65 tff(21690,plain,
% 3.35/3.65 (elem!1 = s(elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1732, 6060, 1727, 1262, 1725])).
% 3.35/3.65 tff(21691,plain,
% 3.35/3.65 (s(elem!1) = elem!1),
% 3.35/3.65 inference(symmetry,[status(thm)],[21690])).
% 3.35/3.65 tff(21692,plain,
% 3.35/3.65 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 3.35/3.65 inference(monotonicity,[status(thm)],[21691])).
% 3.35/3.65 tff(21693,plain,
% 3.35/3.65 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 3.35/3.65 inference(symmetry,[status(thm)],[21692])).
% 3.35/3.65 tff(21694,plain,
% 3.35/3.65 (~b(s(s(s(z))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[4375, 14286, 6060, 56])).
% 3.35/3.65 tff(21695,plain,
% 3.35/3.65 (r(s(s(s(z))), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[704, 21694, 698])).
% 3.35/3.65 tff(21696,plain,
% 3.35/3.65 (~r(s(s(z)), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[7175, 21695, 408, 670, 285])).
% 3.35/3.65 tff(21697,plain,
% 3.35/3.65 (s(s(s(elem!1))) = elem!1),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2482, 21690])).
% 3.35/3.65 tff(21698,plain,
% 3.35/3.65 (s(elem!1) = s(s(s(elem!1)))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[2584, 21697, 21690])).
% 3.35/3.65 tff(21699,plain,
% 3.35/3.65 (~(s(elem!1) = s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[990, 21698, 1])).
% 3.35/3.65 tff(21700,plain,
% 3.35/3.65 (~(s(s(z)) = elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[11670, 21699])).
% 3.35/3.65 tff(21701,plain,
% 3.35/3.65 (b(s(s(z)), elem!1)),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[7970, 21700, 21696])).
% 3.35/3.65 tff(21702,plain,
% 3.35/3.65 (b(s(s(z)), s(elem!1))),
% 3.35/3.65 inference(modus_ponens,[status(thm)],[21701, 21693])).
% 3.35/3.65 tff(21703,plain,
% 3.35/3.65 (~(s(s(s(z))) = s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[1010, 21697])).
% 3.35/3.65 tff(21704,plain,
% 3.35/3.65 (r(s(s(s(z))), s(elem!1))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[3297, 21703])).
% 3.35/3.65 tff(21705,plain,
% 3.35/3.65 (r(s(elem!1), s(s(s(z))))),
% 3.35/3.65 inference(unit_resolution,[status(thm)],[965, 21699, 901])).
% 3.35/3.65 tff(21706,plain,
% 3.35/3.65 (((~![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(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.65 inference(rewrite,[status(thm)],[])).
% 3.35/3.65 tff(21707,plain,
% 3.35/3.65 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21708,plain,
% 3.35/3.66 (((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21707])).
% 3.35/3.66 tff(21709,plain,
% 3.35/3.66 (((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(transitivity,[status(thm)],[21708, 21706])).
% 3.35/3.66 tff(21710,plain,
% 3.35/3.66 ((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(quant_inst,[status(thm)],[])).
% 3.35/3.66 tff(21711,plain,
% 3.35/3.66 ((~![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(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21710, 21709])).
% 3.35/3.66 tff(21712,plain,
% 3.35/3.66 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21711, 333, 21705, 224, 21704])).
% 3.35/3.66 tff(21713,plain,
% 3.35/3.66 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[542, 21712, 537])).
% 3.35/3.66 tff(21714,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21690])).
% 3.35/3.66 tff(21715,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.66 inference(symmetry,[status(thm)],[21714])).
% 3.35/3.66 tff(21716,plain,
% 3.35/3.66 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21715])).
% 3.35/3.66 tff(21717,plain,
% 3.35/3.66 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21712, 21716])).
% 3.35/3.66 tff(21718,plain,
% 3.35/3.66 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[130, 21717, 21578])).
% 3.35/3.66 tff(21719,plain,
% 3.35/3.66 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[3955, 21718, 6060, 14286])).
% 3.35/3.66 tff(21720,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[319, 21719])).
% 3.35/3.66 tff(21721,plain,
% 3.35/3.66 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[19960, 21720, 11546, 224, 56, 6107])).
% 3.35/3.66 tff(21722,plain,
% 3.35/3.66 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1451, 21721])).
% 3.35/3.66 tff(21723,plain,
% 3.35/3.66 (~b(s(s(z)), s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1404, 144, 21722, 21713, 450])).
% 3.35/3.66 tff(21724,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21723, 21702])).
% 3.35/3.66 tff(21725,plain,((s(z) = elem!1) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | r(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | r(elem!1, s(elem!1)) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21726,plain,
% 3.35/3.66 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21725, 21684, 11546, 224, 56, 6107, 537, 901, 1, 3296, 408, 7265, 285, 698, 1727, 1262, 1725, 715, 2310])).
% 3.35/3.66 tff(21727,plain,
% 3.35/3.66 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21726, 21689])).
% 3.35/3.66 tff(21728,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[132, 21727])).
% 3.35/3.66 tff(21729,plain,(b(z, elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | r(elem!1, s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | r(elem!1, s(z)) | r(s(z), elem!1) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21730,plain,
% 3.35/3.66 (b(z, elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21729, 21670, 21671, 17789, 21666, 15126, 224, 56, 6107, 21679, 21678, 1, 21677, 21665, 285, 21674, 21673, 21672, 21663])).
% 3.35/3.66 tff(21731,plain,
% 3.35/3.66 (~(s(z) = elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[9366, 21730, 21660])).
% 3.35/3.66 tff(21732,plain,
% 3.35/3.66 (b(s(z), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[406, 21731, 21672])).
% 3.35/3.66 tff(21733,plain,
% 3.35/3.66 (elem!1 = s(elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1732, 21732, 21671, 21670, 21666])).
% 3.35/3.66 tff(21734,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21733])).
% 3.35/3.66 tff(21735,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[8808, 21730, 17787, 3, 21663])).
% 3.35/3.66 tff(21736,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21735, 21734])).
% 3.35/3.66 tff(21737,plain,
% 3.35/3.66 (s(s(s(elem!1))) = elem!1),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[2482, 21733])).
% 3.35/3.66 tff(21738,plain,
% 3.35/3.66 (~(s(s(s(z))) = s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1010, 21737])).
% 3.35/3.66 tff(21739,plain,
% 3.35/3.66 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1951, 44, 21677])).
% 3.35/3.66 tff(21740,plain,
% 3.35/3.66 (r(s(s(s(z))), s(elem!1))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21739, 21738])).
% 3.35/3.66 tff(21741,plain,
% 3.35/3.66 (((~![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(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21742,plain,
% 3.35/3.66 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21743,plain,
% 3.35/3.66 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21742])).
% 3.35/3.66 tff(21744,plain,
% 3.35/3.66 (((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(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(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.66 inference(transitivity,[status(thm)],[21743, 21741])).
% 3.35/3.66 tff(21745,plain,
% 3.35/3.66 ((~![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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.66 inference(quant_inst,[status(thm)],[])).
% 3.35/3.66 tff(21746,plain,
% 3.35/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21745, 21744])).
% 3.35/3.66 tff(21747,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21746, 333, 509, 6107, 21740, 21736])).
% 3.35/3.66 tff(21748,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21749,plain,
% 3.35/3.66 (~b(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21748, 224, 6107, 3, 509, 56, 1, 284])).
% 3.35/3.66 tff(21750,plain,
% 3.35/3.66 (r(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[396, 21749])).
% 3.35/3.66 tff(21751,plain,
% 3.35/3.66 (~r(s(s(s(z))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[2079, 21750, 21656, 7265])).
% 3.35/3.66 tff(21752,plain,
% 3.35/3.66 (~r(elem!1, s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[6311, 333, 7265, 21656, 21750])).
% 3.35/3.66 tff(21753,plain,
% 3.35/3.66 (~(s(z) = elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21683, 606, 259, 1727, 132, 730, 1237, 114, 8715])).
% 3.35/3.66 tff(21754,plain,
% 3.35/3.66 (~(s(s(s(z))) = elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[609, 606, 284])).
% 3.35/3.66 tff(21755,plain,
% 3.35/3.66 (b(s(s(s(z))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[704, 21754, 699])).
% 3.35/3.66 tff(21756,plain,
% 3.35/3.66 (~(elem!1 = s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[10997, 21754])).
% 3.35/3.66 tff(21757,plain,
% 3.35/3.66 (b(elem!1, s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[1538, 21756, 21019])).
% 3.35/3.66 tff(21758,plain,
% 3.35/3.66 (~b(s(z), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[19991, 144, 21757, 838, 21755])).
% 3.35/3.66 tff(21759,plain,
% 3.35/3.66 (~b(elem!1, s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[18973, 144, 21757, 56, 838])).
% 3.35/3.66 tff(21760,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[13826, 21759, 21758, 2178, 8715, 21753])).
% 3.35/3.66 tff(21761,plain,(b(z, elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21762,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21761, 21659, 21752, 56, 606, 21751, 21654, 21657, 17789, 1229, 17787, 284, 71])).
% 3.35/3.66 tff(21763,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | b(z, elem!1) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21764,plain,
% 3.35/3.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21763, 606, 56, 284, 6107, 3, 509, 1])).
% 3.35/3.66 tff(21765,plain,
% 3.35/3.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[249, 21764])).
% 3.35/3.66 tff(21766,plain,
% 3.35/3.66 (~b(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[294, 21765, 284, 21652])).
% 3.35/3.66 tff(21767,plain,
% 3.35/3.66 (r(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[396, 21766])).
% 3.35/3.66 tff(21768,plain,
% 3.35/3.66 (~r(s(s(s(z))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[14255, 21765, 21656, 7265, 21652])).
% 3.35/3.66 tff(21769,plain,
% 3.35/3.66 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21533, 21765, 284, 56, 21652])).
% 3.35/3.66 tff(21770,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[319, 21769])).
% 3.35/3.66 tff(21771,plain,
% 3.35/3.66 (~r(s(z), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[16388, 21770, 15126, 6107])).
% 3.35/3.66 tff(21772,plain,
% 3.35/3.66 (b(s(z), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[172, 21771])).
% 3.35/3.66 tff(21773,plain,
% 3.35/3.66 (r(elem!1, s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21761, 21772, 56, 606, 21768, 21654, 21657, 17789, 1229, 17787, 284, 71])).
% 3.35/3.66 tff(21774,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[6311, 333, 7265, 21656, 21773, 21767])).
% 3.35/3.66 tff(21775,plain,(b(z, elem!1) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21776,plain,
% 3.35/3.66 (b(z, elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21775, 21632, 284, 17204, 3, 21576, 1])).
% 3.35/3.66 tff(21777,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21547, 144, 251, 284, 132, 283, 259])).
% 3.35/3.66 tff(21778,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21779,plain,
% 3.35/3.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21778, 21776, 284, 17789, 21650])).
% 3.35/3.66 tff(21780,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[249, 21779])).
% 3.35/3.66 tff(21781,plain,
% 3.35/3.66 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[8808, 21776, 17787, 3, 21650])).
% 3.35/3.66 tff(21782,plain,
% 3.35/3.66 (~b(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21748, 21780, 17204, 3, 21576, 21632, 1, 284])).
% 3.35/3.66 tff(21783,plain,
% 3.35/3.66 (r(s(s(s(z))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[396, 21782])).
% 3.35/3.66 tff(21784,plain,
% 3.35/3.66 (~r(s(z), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[17817, 333, 15126, 21781, 17204])).
% 3.35/3.66 tff(21785,plain,
% 3.35/3.66 (b(s(z), s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[172, 21784])).
% 3.35/3.66 tff(21786,plain,
% 3.35/3.66 (~b(z, s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[2176, 144, 284, 21632, 21785])).
% 3.35/3.66 tff(21787,plain,
% 3.35/3.66 (r(z, s(z))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[372, 21786])).
% 3.35/3.66 tff(21788,plain,
% 3.35/3.66 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21591, 17204, 284, 15126])).
% 3.35/3.66 tff(21789,plain,
% 3.35/3.66 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[302, 21788])).
% 3.35/3.66 tff(21790,plain,
% 3.35/3.66 (~b(elem!1, z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[14405, 21650, 17789, 21789])).
% 3.35/3.66 tff(21791,plain,
% 3.35/3.66 (r(elem!1, z)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[653, 21790, 77])).
% 3.35/3.66 tff(21792,plain,
% 3.35/3.66 (~r(s(s(s(z))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[2122, 21783, 21791, 21787])).
% 3.35/3.66 tff(21793,plain,
% 3.35/3.66 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21794,plain,
% 3.35/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 3.35/3.66 inference(monotonicity,[status(thm)],[21793])).
% 3.35/3.66 tff(21795,plain,
% 3.35/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 3.35/3.66 inference(transitivity,[status(thm)],[21794, 10679])).
% 3.35/3.66 tff(21796,plain,
% 3.35/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 3.35/3.66 inference(quant_inst,[status(thm)],[])).
% 3.35/3.66 tff(21797,plain,
% 3.35/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21796, 21795])).
% 3.35/3.66 tff(21798,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21797, 144, 251, 21020, 284, 19936])).
% 3.35/3.66 tff(21799,plain,((s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21800,plain,
% 3.35/3.66 (r(elem!1, s(s(s(z))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21799, 21792, 284, 20485, 21776])).
% 3.35/3.66 tff(21801,plain,
% 3.35/3.66 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21802,plain,
% 3.35/3.66 ((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.35/3.66 inference(quant_inst,[status(thm)],[])).
% 3.35/3.66 tff(21803,plain,
% 3.35/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.35/3.66 inference(modus_ponens,[status(thm)],[21802, 21801])).
% 3.35/3.66 tff(21804,plain,
% 3.35/3.66 ($false),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21803, 333, 21800, 21783, 21781, 21780])).
% 3.35/3.66 tff(21805,plain,(b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.66 tff(21806,plain,
% 3.35/3.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[21805, 21154, 3, 1])).
% 3.35/3.66 tff(21807,plain,
% 3.35/3.66 (~b(s(s(s(z))), elem!1)),
% 3.35/3.66 inference(unit_resolution,[status(thm)],[10110, 54, 17787, 3, 21806])).
% 3.35/3.66 tff(21808,plain,
% 3.35/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.66 inference(rewrite,[status(thm)],[])).
% 3.35/3.66 tff(21809,plain,
% 3.35/3.66 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21810,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[21809])).
% 3.35/3.67 tff(21811,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.67 inference(transitivity,[status(thm)],[21810, 21808])).
% 3.35/3.67 tff(21812,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 3.35/3.67 inference(quant_inst,[status(thm)],[])).
% 3.35/3.67 tff(21813,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[21812, 21811])).
% 3.35/3.67 tff(21814,plain,
% 3.35/3.67 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21813, 144, 21154, 17789, 21806])).
% 3.35/3.67 tff(21815,plain,
% 3.35/3.67 (~b(elem!1, s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21814, 624])).
% 3.35/3.67 tff(21816,plain,
% 3.35/3.67 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[880, 251, 624, 17788])).
% 3.35/3.67 tff(21817,plain,
% 3.35/3.67 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[302, 21816])).
% 3.35/3.67 tff(21818,plain,
% 3.35/3.67 (~r(s(z), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[17877, 333, 15126, 21817, 17791])).
% 3.35/3.67 tff(21819,plain,
% 3.35/3.67 (b(s(z), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[348, 21818])).
% 3.35/3.67 tff(21820,plain,
% 3.35/3.67 (~r(z, s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[19019, 17791, 15126, 17787, 624, 251])).
% 3.35/3.67 tff(21821,plain,
% 3.35/3.67 (b(z, s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[372, 21820])).
% 3.35/3.67 tff(21822,plain,
% 3.35/3.67 (~b(elem!1, s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[387, 144, 624, 21821, 21819])).
% 3.35/3.67 tff(21823,plain,
% 3.35/3.67 (r(elem!1, s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[720, 21822, 15134])).
% 3.35/3.67 tff(21824,plain,
% 3.35/3.67 (~b(s(z), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1602, 21819, 624, 251])).
% 3.35/3.67 tff(21825,plain,
% 3.35/3.67 (r(s(z), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[406, 21824, 15133])).
% 3.35/3.67 tff(21826,plain,
% 3.35/3.67 (~r(s(z), s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[12402, 698, 55, 722, 12397])).
% 3.35/3.67 tff(21827,plain,
% 3.35/3.67 (b(s(z), s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[172, 21826])).
% 3.35/3.67 tff(21828,plain,
% 3.35/3.67 (~r(s(s(s(z))), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[9910, 12399, 409, 722])).
% 3.35/3.67 tff(21829,plain,
% 3.35/3.67 (b(s(s(s(z))), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[2794, 21828])).
% 3.35/3.67 tff(21830,plain,
% 3.35/3.67 ($false),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[2176, 144, 490, 284, 21829, 21827])).
% 3.35/3.67 tff(21831,plain,((s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.67 tff(21832,plain,
% 3.35/3.67 (s(s(s(z))) = elem!1),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21831, 21821, 21154, 21825, 21823, 21807, 21815])).
% 3.35/3.67 tff(21833,plain,
% 3.35/3.67 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[12214, 21832])).
% 3.35/3.67 tff(21834,plain,
% 3.35/3.67 (~b(s(elem!1), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7692, 907, 17789, 1, 251, 17791, 15133, 21824, 21819, 20735, 21822, 902, 432, 21817, 624])).
% 3.35/3.67 tff(21835,plain,
% 3.35/3.67 (r(s(elem!1), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[507, 21834])).
% 3.35/3.67 tff(21836,plain,
% 3.35/3.67 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[601, 333, 21835, 21817, 17791])).
% 3.35/3.67 tff(21837,plain,
% 3.35/3.67 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[472, 21836, 432])).
% 3.35/3.67 tff(21838,plain,
% 3.35/3.67 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7702, 333, 21835, 21817, 17791])).
% 3.35/3.67 tff(21839,plain,
% 3.35/3.67 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[542, 21838, 20735])).
% 3.35/3.67 tff(21840,plain,
% 3.35/3.67 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7710, 902, 17787, 15133, 251, 54, 21819, 3, 20735, 21822, 907, 1, 432, 21823])).
% 3.35/3.67 tff(21841,plain,
% 3.35/3.67 (~b(s(elem!1), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[464, 21837, 17787, 54, 3])).
% 3.35/3.67 tff(21842,plain,
% 3.35/3.67 (r(s(elem!1), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[448, 21841, 907])).
% 3.35/3.67 tff(21843,plain,
% 3.35/3.67 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7093, 489, 490, 304])).
% 3.35/3.67 tff(21844,plain,
% 3.35/3.67 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[302, 21843])).
% 3.35/3.67 tff(21845,plain,
% 3.35/3.67 (~r(s(z), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7675, 19382, 706, 435, 2205])).
% 3.35/3.67 tff(21846,plain,
% 3.35/3.67 (b(s(z), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1244, 21845, 1229])).
% 3.35/3.67 tff(21847,plain,
% 3.35/3.67 (r(elem!1, s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[720, 19382, 713])).
% 3.35/3.67 tff(21848,plain,
% 3.35/3.67 (~r(s(elem!1), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7864, 333, 435, 2206, 21847])).
% 3.35/3.67 tff(21849,plain,
% 3.35/3.67 (b(s(elem!1), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[486, 21848, 1])).
% 3.35/3.67 tff(21850,plain,
% 3.35/3.67 (~b(z, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1853, 21849, 490, 21846])).
% 3.35/3.67 tff(21851,plain,
% 3.35/3.67 (r(z, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[583, 21850])).
% 3.35/3.67 tff(21852,plain,
% 3.35/3.67 (((~![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), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, 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), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21853,plain,
% 3.35/3.67 ((~![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), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.67 inference(quant_inst,[status(thm)],[])).
% 3.35/3.67 tff(21854,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[21853, 21852])).
% 3.35/3.67 tff(21855,plain,
% 3.35/3.67 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21854, 333, 509, 21851, 21844])).
% 3.35/3.67 tff(21856,plain,
% 3.35/3.67 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7888, 144, 21849, 21846, 304])).
% 3.35/3.67 tff(21857,plain,
% 3.35/3.67 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[540, 44, 21856, 21855])).
% 3.35/3.67 tff(21858,plain,
% 3.35/3.67 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(elem!1))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[21857])).
% 3.35/3.67 tff(21859,plain,
% 3.35/3.67 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(symmetry,[status(thm)],[21858])).
% 3.35/3.67 tff(21860,plain,
% 3.35/3.67 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[21846, 21859])).
% 3.35/3.67 tff(21861,assumption,(~b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.35/3.67 tff(21862,plain,
% 3.35/3.67 ($false),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21861, 21860])).
% 3.35/3.67 tff(21863,plain,((~b(s(z), z)) | b(s(z), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.67 tff(21864,plain,
% 3.35/3.67 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21863, 21842, 21819, 21821, 21835, 1, 21840, 15133, 624, 251])).
% 3.35/3.67 tff(21865,plain,
% 3.35/3.67 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[319, 21864])).
% 3.35/3.67 tff(21866,plain,
% 3.35/3.67 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[17920, 21865, 17791, 21821, 21819, 15126])).
% 3.35/3.67 tff(21867,plain,
% 3.35/3.67 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1451, 21866])).
% 3.35/3.67 tff(21868,plain,
% 3.35/3.67 (~b(s(s(z)), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1404, 144, 21867, 21839, 21837])).
% 3.35/3.67 tff(21869,plain,
% 3.35/3.67 (r(s(s(z)), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1408, 44, 19207, 21868])).
% 3.35/3.67 tff(21870,plain,
% 3.35/3.67 (~b(s(s(z)), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[11650, 144, 21867, 17788, 17789])).
% 3.35/3.67 tff(21871,plain,
% 3.35/3.67 (~b(elem!1, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[5467, 21838, 17789, 20735, 21836])).
% 3.35/3.67 tff(21872,plain,
% 3.35/3.67 (r(elem!1, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[560, 21871, 902])).
% 3.35/3.67 tff(21873,plain,
% 3.35/3.67 (~r(s(elem!1), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1390, 21872, 21825, 21842])).
% 3.35/3.67 tff(21874,plain,
% 3.35/3.67 (b(s(elem!1), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[486, 21873, 1])).
% 3.35/3.67 tff(21875,plain,
% 3.35/3.67 (~r(s(z), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7675, 21842, 15133, 21824, 21822])).
% 3.35/3.67 tff(21876,plain,
% 3.35/3.67 (b(s(z), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1244, 21875, 1229])).
% 3.35/3.67 tff(21877,plain,
% 3.35/3.67 (~b(z, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1853, 21876, 21821, 21874])).
% 3.35/3.67 tff(21878,plain,
% 3.35/3.67 (r(z, s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[583, 21877])).
% 3.35/3.67 tff(21879,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21880,plain,
% 3.35/3.67 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21881,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[21880])).
% 3.35/3.67 tff(21882,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.35/3.67 inference(transitivity,[status(thm)],[21881, 21879])).
% 3.35/3.67 tff(21883,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.67 inference(quant_inst,[status(thm)],[])).
% 3.35/3.67 tff(21884,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[21883, 21882])).
% 3.35/3.67 tff(21885,plain,
% 3.35/3.67 (~b(s(s(s(z))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21884, 144, 21806, 21839, 21837])).
% 3.35/3.67 tff(21886,plain,
% 3.35/3.67 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[1002])).
% 3.35/3.67 tff(21887,plain,
% 3.35/3.67 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 3.35/3.67 inference(symmetry,[status(thm)],[21886])).
% 3.35/3.67 tff(21888,plain,
% 3.35/3.67 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[21887])).
% 3.35/3.67 tff(21889,plain,
% 3.35/3.67 (~b(z, s(s(s(z))))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[578, 21888])).
% 3.35/3.67 tff(21890,plain,
% 3.35/3.67 ($false),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[284, 21889])).
% 3.35/3.67 tff(21891,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(z, s(s(s(z))))) | b(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.67 tff(21892,plain,
% 3.35/3.67 (~(s(s(s(z))) = s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21891, 21877, 21154])).
% 3.35/3.67 tff(21893,plain,
% 3.35/3.67 (r(s(s(s(z))), s(elem!1))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1951, 44, 21892, 21885])).
% 3.35/3.67 tff(21894,plain,
% 3.35/3.67 (~r(s(s(s(z))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[12891, 21893, 21842, 21878])).
% 3.35/3.67 tff(21895,plain,
% 3.35/3.67 (b(s(s(s(z))), z)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[396, 21894])).
% 3.35/3.67 tff(21896,plain,
% 3.35/3.67 (~b(s(s(s(z))), s(z))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[2273, 21895, 21821, 21819])).
% 3.35/3.67 tff(21897,plain,
% 3.35/3.67 (~(s(elem!1) = s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[8633, 21896, 21874])).
% 3.35/3.67 tff(21898,plain,
% 3.35/3.67 (~(s(s(z)) = elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[11670, 21897])).
% 3.35/3.67 tff(21899,plain,
% 3.35/3.67 (r(s(s(z)), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7970, 21898, 21870])).
% 3.35/3.67 tff(21900,plain,
% 3.35/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~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(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21901,plain,
% 3.35/3.67 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21902,plain,
% 3.35/3.67 (((~![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(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))))),
% 3.35/3.67 inference(monotonicity,[status(thm)],[21901])).
% 3.35/3.67 tff(21903,plain,
% 3.35/3.67 (((~![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(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 3.35/3.67 inference(transitivity,[status(thm)],[21902, 21900])).
% 3.35/3.67 tff(21904,plain,
% 3.35/3.67 ((~![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(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 3.35/3.67 inference(quant_inst,[status(thm)],[])).
% 3.35/3.67 tff(21905,plain,
% 3.35/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 3.35/3.67 inference(modus_ponens,[status(thm)],[21904, 21903])).
% 3.35/3.67 tff(21906,plain,
% 3.35/3.67 ($false),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21905, 333, 21872, 21842, 21899, 21869])).
% 3.35/3.67 tff(21907,plain,((elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.67 tff(21908,plain,
% 3.35/3.67 (elem!1 = s(elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21907, 21833, 624, 251, 54, 3, 1])).
% 3.35/3.67 tff(21909,plain,
% 3.35/3.67 (~(s(s(elem!1)) = elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[7595, 21832, 19208])).
% 3.35/3.67 tff(21910,plain,
% 3.35/3.67 (~(elem!1 = s(s(elem!1)))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[5603, 21909])).
% 3.35/3.67 tff(21911,plain,
% 3.35/3.67 (~(s(elem!1) = elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[5813, 21910])).
% 3.35/3.67 tff(21912,plain,
% 3.35/3.67 ($false),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1569, 21911, 21908])).
% 3.35/3.67 tff(21913,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.67 tff(21914,plain,
% 3.35/3.67 (~b(z, elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[21913, 624, 54, 3, 1])).
% 3.35/3.67 tff(21915,plain,
% 3.35/3.67 (r(z, elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[658, 21914, 71])).
% 3.35/3.67 tff(21916,plain,
% 3.35/3.67 (~(s(s(s(z))) = elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[609, 21914, 21154])).
% 3.35/3.67 tff(21917,plain,
% 3.35/3.67 (r(s(s(s(z))), elem!1)),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[704, 21916, 21807])).
% 3.35/3.67 tff(21918,plain,
% 3.35/3.67 (~(elem!1 = s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[10997, 21916])).
% 3.35/3.67 tff(21919,plain,
% 3.35/3.67 (r(elem!1, s(s(s(z))))),
% 3.35/3.67 inference(unit_resolution,[status(thm)],[1538, 21918, 21815])).
% 3.35/3.67 tff(21920,plain,
% 3.35/3.67 (((~![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))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), 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(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.67 inference(rewrite,[status(thm)],[])).
% 3.35/3.67 tff(21921,plain,
% 3.35/3.67 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21922,plain,
% 3.35/3.68 (((~![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(s(s(z))), elem!1)) | (~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))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 3.35/3.68 inference(monotonicity,[status(thm)],[21921])).
% 3.35/3.68 tff(21923,plain,
% 3.35/3.68 (((~![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(s(s(z))), elem!1)) | (~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))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.68 inference(transitivity,[status(thm)],[21922, 21920])).
% 3.35/3.68 tff(21924,plain,
% 3.35/3.68 ((~![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(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 3.35/3.68 inference(quant_inst,[status(thm)],[])).
% 3.35/3.68 tff(21925,plain,
% 3.35/3.68 ((~![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))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 3.35/3.68 inference(modus_ponens,[status(thm)],[21924, 21923])).
% 3.35/3.68 tff(21926,plain,
% 3.35/3.68 (~r(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21925, 333, 670, 1525, 707])).
% 3.35/3.68 tff(21927,plain,
% 3.35/3.68 (b(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[396, 21926])).
% 3.35/3.68 tff(21928,plain,
% 3.35/3.68 (((~![X0: $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), elem!1)) | (~r(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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21929,plain,
% 3.35/3.68 (((~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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21930,plain,
% 3.35/3.68 (((~![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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 3.35/3.68 inference(monotonicity,[status(thm)],[21929])).
% 3.35/3.68 tff(21931,plain,
% 3.35/3.68 (((~![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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.35/3.68 inference(transitivity,[status(thm)],[21930, 21928])).
% 3.35/3.68 tff(21932,plain,
% 3.35/3.68 ((~![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)))),
% 3.35/3.68 inference(quant_inst,[status(thm)],[])).
% 3.35/3.68 tff(21933,plain,
% 3.35/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 3.35/3.68 inference(modus_ponens,[status(thm)],[21932, 21931])).
% 3.35/3.68 tff(21934,plain,
% 3.35/3.68 (~r(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21933, 333, 670, 409, 1525])).
% 3.35/3.68 tff(21935,plain,
% 3.35/3.68 (b(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[348, 21934])).
% 3.35/3.68 tff(21936,plain,
% 3.35/3.68 (~r(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[7032, 333, 409, 1525, 707])).
% 3.35/3.68 tff(21937,plain,
% 3.35/3.68 (b(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[172, 21936])).
% 3.35/3.68 tff(21938,plain,
% 3.35/3.68 ($false),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[2156, 21937, 21935, 284, 21927])).
% 3.35/3.68 tff(21939,plain,((~r(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.68 tff(21940,plain,
% 3.35/3.68 (~r(s(z), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21939, 21919, 21154, 21917, 21915])).
% 3.35/3.68 tff(21941,plain,
% 3.35/3.68 (b(s(z), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[406, 21940, 15133])).
% 3.35/3.68 tff(21942,plain,
% 3.35/3.68 (((~![X0: $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(s(s(z))))))), z)) | (~r(s(z), 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(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21943,plain,
% 3.35/3.68 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21944,plain,
% 3.35/3.68 (((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), 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(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.68 inference(monotonicity,[status(thm)],[21943])).
% 3.35/3.68 tff(21945,plain,
% 3.35/3.68 (((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), 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(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(transitivity,[status(thm)],[21944, 21942])).
% 3.35/3.68 tff(21946,plain,
% 3.35/3.68 ((~![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(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(quant_inst,[status(thm)],[])).
% 3.35/3.68 tff(21947,plain,
% 3.35/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.68 inference(modus_ponens,[status(thm)],[21946, 21945])).
% 3.35/3.68 tff(21948,plain,
% 3.35/3.68 ($false),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21947, 333, 670, 323, 11546, 321])).
% 3.35/3.68 tff(21949,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.68 tff(21950,plain,
% 3.35/3.68 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21949, 323, 670, 11546])).
% 3.35/3.68 tff(21951,plain,
% 3.35/3.68 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[302, 21950])).
% 3.35/3.68 tff(21952,plain,
% 3.35/3.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[14405, 21951, 132, 624])).
% 3.35/3.68 tff(21953,plain,
% 3.35/3.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[279, 21952])).
% 3.35/3.68 tff(21954,plain,
% 3.35/3.68 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[3988, 21951, 624, 133, 134])).
% 3.35/3.68 tff(21955,plain,
% 3.35/3.68 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[319, 21954])).
% 3.35/3.68 tff(21956,plain,
% 3.35/3.68 ($false),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[15633, 21955, 21953, 11546, 323])).
% 3.35/3.68 tff(21957,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.68 tff(21958,plain,
% 3.35/3.68 (~r(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21957, 624, 15126, 17788, 21941, 17789, 21915])).
% 3.35/3.68 tff(21959,plain,
% 3.35/3.68 (b(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[348, 21958])).
% 3.35/3.68 tff(21960,plain,
% 3.35/3.68 (~r(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21925, 333, 21915, 21919, 21917])).
% 3.35/3.68 tff(21961,plain,
% 3.35/3.68 (b(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[396, 21960])).
% 3.35/3.68 tff(21962,plain,
% 3.35/3.68 (~b(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[2156, 21959, 21154, 21961])).
% 3.35/3.68 tff(21963,plain,
% 3.35/3.68 (r(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[172, 21962])).
% 3.35/3.68 tff(21964,plain,
% 3.35/3.68 (~r(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[12402, 21963, 21807, 21916, 21815])).
% 3.35/3.68 tff(21965,plain,
% 3.35/3.68 (b(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[720, 21964, 15134])).
% 3.35/3.68 tff(21966,plain,
% 3.35/3.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[19178, 21965, 624, 21959, 17789])).
% 3.35/3.68 tff(21967,plain,
% 3.35/3.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[279, 21966])).
% 3.35/3.68 tff(21968,plain,
% 3.35/3.68 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21805, 284, 3, 1])).
% 3.35/3.68 tff(21969,plain,
% 3.35/3.68 (~b(elem!1, s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[8765, 144, 17789, 283, 21968])).
% 3.35/3.68 tff(21970,plain,
% 3.35/3.68 (r(elem!1, s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[1538, 21969, 21756])).
% 3.35/3.68 tff(21971,plain,
% 3.35/3.68 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21972,plain,
% 3.35/3.68 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(21973,plain,
% 3.35/3.68 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.68 inference(monotonicity,[status(thm)],[21972])).
% 3.35/3.68 tff(21974,plain,
% 3.35/3.68 (((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(transitivity,[status(thm)],[21973, 21971])).
% 3.35/3.68 tff(21975,plain,
% 3.35/3.68 ((~![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(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.68 inference(quant_inst,[status(thm)],[])).
% 3.35/3.68 tff(21976,plain,
% 3.35/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.35/3.68 inference(modus_ponens,[status(thm)],[21975, 21974])).
% 3.35/3.68 tff(21977,plain,
% 3.35/3.68 ($false),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21976, 333, 670, 1525, 2484, 51])).
% 3.35/3.68 tff(21978,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.68 tff(21979,plain,
% 3.35/3.68 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21978, 21970, 7265, 51])).
% 3.35/3.68 tff(21980,plain,
% 3.35/3.68 (~b(s(s(s(z))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[10110, 21979, 17787, 3, 21968])).
% 3.35/3.68 tff(21981,plain,
% 3.35/3.68 (r(s(s(s(z))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[704, 21980, 21754])).
% 3.35/3.68 tff(21982,plain,
% 3.35/3.68 (~r(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[21925, 333, 7265, 21970, 21981])).
% 3.35/3.68 tff(21983,plain,
% 3.35/3.68 (b(s(s(s(z))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[396, 21982])).
% 3.35/3.68 tff(21984,plain,
% 3.35/3.68 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[294, 21983, 284, 283])).
% 3.35/3.68 tff(21985,plain,
% 3.35/3.68 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[302, 21984])).
% 3.35/3.68 tff(21986,plain,
% 3.35/3.68 (~r(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[17877, 333, 15126, 21985, 51])).
% 3.35/3.68 tff(21987,plain,
% 3.35/3.68 (b(s(z), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[348, 21986])).
% 3.35/3.68 tff(21988,plain,
% 3.35/3.68 (~r(z, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[15183, 21985, 15126, 51])).
% 3.35/3.68 tff(21989,plain,
% 3.35/3.68 (b(z, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[372, 21988])).
% 3.35/3.68 tff(21990,plain,
% 3.35/3.68 (~b(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[2156, 21987, 284, 21983])).
% 3.35/3.68 tff(21991,plain,
% 3.35/3.68 (r(s(z), s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[172, 21990])).
% 3.35/3.68 tff(21992,plain,
% 3.35/3.68 (~r(z, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[15183, 321, 11546, 51])).
% 3.35/3.68 tff(21993,plain,
% 3.35/3.68 (b(z, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[372, 21992])).
% 3.35/3.68 tff(21994,plain,
% 3.35/3.68 (~(s(z) = elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[8102, 21993, 606])).
% 3.35/3.68 tff(21995,plain,
% 3.35/3.68 (~(elem!1 = s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[712, 21994])).
% 3.35/3.68 tff(21996,plain,
% 3.35/3.68 (~b(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[387, 144, 624, 21993, 489])).
% 3.35/3.68 tff(21997,plain,
% 3.35/3.68 (r(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[720, 21996, 21995])).
% 3.35/3.68 tff(21998,plain,
% 3.35/3.68 (b(s(s(s(z))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[12402, 21997, 12397, 698, 353])).
% 3.35/3.68 tff(21999,plain,
% 3.35/3.68 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[10110, 21998, 114, 3, 2254])).
% 3.35/3.68 tff(22000,plain,
% 3.35/3.68 (r(elem!1, s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[1538, 12397, 12398])).
% 3.35/3.68 tff(22001,plain,
% 3.35/3.68 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(22002,plain,
% 3.35/3.68 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.68 inference(rewrite,[status(thm)],[])).
% 3.35/3.68 tff(22003,plain,
% 3.35/3.68 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.35/3.68 inference(monotonicity,[status(thm)],[22002])).
% 3.35/3.68 tff(22004,plain,
% 3.35/3.68 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.68 inference(transitivity,[status(thm)],[22003, 22001])).
% 3.35/3.68 tff(22005,plain,
% 3.35/3.68 ((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.35/3.68 inference(quant_inst,[status(thm)],[])).
% 3.35/3.68 tff(22006,plain,
% 3.35/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.35/3.68 inference(modus_ponens,[status(thm)],[22005, 22004])).
% 3.35/3.68 tff(22007,plain,
% 3.35/3.68 ($false),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[22006, 333, 670, 22000, 21999, 321])).
% 3.35/3.68 tff(22008,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), z)) | b(z, elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.68 tff(22009,plain,
% 3.35/3.68 (~b(elem!1, z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[22008, 21991, 17787, 3, 21968, 21969, 21754, 7265, 21985, 21987, 606, 15126, 51])).
% 3.35/3.68 tff(22010,plain,
% 3.35/3.68 (r(elem!1, z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[653, 22009, 77])).
% 3.35/3.68 tff(22011,plain,
% 3.35/3.68 (~(s(z) = elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[8102, 21989, 606])).
% 3.35/3.68 tff(22012,plain,
% 3.35/3.68 (~(elem!1 = s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[712, 22011])).
% 3.35/3.68 tff(22013,plain,
% 3.35/3.68 (~r(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[12402, 21991, 21969, 21754, 21980])).
% 3.35/3.68 tff(22014,plain,
% 3.35/3.68 (b(elem!1, s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[720, 22013, 22012])).
% 3.35/3.68 tff(22015,plain,
% 3.35/3.68 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[130, 21979, 17787])).
% 3.35/3.68 tff(22016,plain,
% 3.35/3.68 (~r(s(z), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[11876, 21991, 21970, 3193])).
% 3.35/3.68 tff(22017,plain,
% 3.35/3.68 (b(s(z), elem!1)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[406, 22016, 22011])).
% 3.35/3.68 tff(22018,plain,
% 3.35/3.68 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[3955, 22017, 22015, 22014])).
% 3.35/3.68 tff(22019,plain,
% 3.35/3.68 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[319, 22018])).
% 3.35/3.68 tff(22020,plain,
% 3.35/3.68 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[18624, 22019, 15126, 51, 21989])).
% 3.35/3.68 tff(22021,plain,
% 3.35/3.68 (~(s(s(z)) = s(elem!1))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[855, 22011])).
% 3.35/3.68 tff(22022,plain,
% 3.35/3.68 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[862, 22021])).
% 3.35/3.68 tff(22023,plain,
% 3.35/3.68 (~(s(s(elem!1)) = s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[4917, 22022])).
% 3.35/3.68 tff(22024,plain,
% 3.35/3.68 (~(s(elem!1) = s(s(s(z))))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[17954, 1727, 55, 1])).
% 3.35/3.68 tff(22025,plain,
% 3.35/3.68 (~r(elem!1, s(elem!1))),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[7151, 22024, 1525, 707, 670, 408, 21927])).
% 3.35/3.68 tff(22026,plain,
% 3.35/3.68 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[294, 21927, 284, 283])).
% 3.35/3.68 tff(22027,plain,
% 3.35/3.68 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.35/3.68 inference(unit_resolution,[status(thm)],[302, 22026])).
% 3.35/3.69 tff(22028,plain,
% 3.35/3.69 (~b(s(elem!1), z)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[9320, 22024, 1, 707, 21927, 490, 489, 284])).
% 3.35/3.69 tff(22029,plain,
% 3.35/3.69 (r(s(elem!1), z)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[507, 22028])).
% 3.35/3.69 tff(22030,plain,
% 3.35/3.69 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[3508, 333, 670, 22029, 22027])).
% 3.35/3.69 tff(22031,assumption,(~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.35/3.69 tff(22032,plain,
% 3.35/3.69 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[4779, 333, 670, 22029, 22027])).
% 3.35/3.69 tff(22033,plain,
% 3.35/3.69 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[5467, 1726, 132, 535, 466])).
% 3.35/3.69 tff(22034,plain,
% 3.35/3.69 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(elem!1))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22033])).
% 3.35/3.69 tff(22035,plain,
% 3.35/3.69 (b(s(s(s(z))), s(elem!1))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[2254, 22034])).
% 3.35/3.69 tff(22036,plain,
% 3.35/3.69 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22033])).
% 3.35/3.69 tff(22037,plain,
% 3.35/3.69 (b(s(elem!1), s(s(s(z))))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[283, 22036])).
% 3.35/3.69 tff(22038,plain,
% 3.35/3.69 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22033])).
% 3.35/3.69 tff(22039,plain,
% 3.35/3.69 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22038])).
% 3.35/3.69 tff(22040,plain,
% 3.35/3.69 (~r(s(s(elem!1)), s(elem!1))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22031, 22039])).
% 3.35/3.69 tff(22041,plain,
% 3.35/3.69 (b(s(s(elem!1)), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1283, 22040, 2727])).
% 3.35/3.69 tff(22042,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22043,plain,
% 3.35/3.69 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22044,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22043])).
% 3.35/3.69 tff(22045,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.35/3.69 inference(transitivity,[status(thm)],[22044, 22042])).
% 3.35/3.69 tff(22046,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.35/3.69 inference(quant_inst,[status(thm)],[])).
% 3.35/3.69 tff(22047,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22046, 22045])).
% 3.35/3.69 tff(22048,plain,
% 3.35/3.69 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22047, 144, 22041, 22037, 22035])).
% 3.35/3.69 tff(22049,plain,
% 3.35/3.69 (r(s(s(elem!1)), s(s(s(z))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[5022, 44, 4959, 22048])).
% 3.35/3.69 tff(22050,plain,
% 3.35/3.69 (~b(s(z), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1732, 902, 1725, 134, 1727])).
% 3.35/3.69 tff(22051,plain,
% 3.35/3.69 (r(s(z), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1244, 22050, 1237])).
% 3.35/3.69 tff(22052,plain,
% 3.35/3.69 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(elem!1), s(z))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22033])).
% 3.35/3.69 tff(22053,plain,
% 3.35/3.69 (r(s(elem!1), s(z))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[322, 22052])).
% 3.35/3.69 tff(22054,plain,
% 3.35/3.69 (~b(s(s(elem!1)), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[4996, 22053, 134, 22051, 2727, 1726, 305, 1728])).
% 3.35/3.69 tff(22055,plain,
% 3.35/3.69 (~(elem!1 = s(s(elem!1)))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1216, 22033])).
% 3.35/3.69 tff(22056,plain,
% 3.35/3.69 (~(s(s(elem!1)) = elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1223, 22055])).
% 3.35/3.69 tff(22057,plain,
% 3.35/3.69 (r(s(s(elem!1)), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1260, 44, 22056, 22054])).
% 3.35/3.69 tff(22058,plain,
% 3.35/3.69 ($false),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[5018, 333, 408, 22057, 707, 22049])).
% 3.35/3.69 tff(22059,plain,((elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.69 tff(22060,plain,
% 3.35/3.69 (elem!1 = s(elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22059, 22032, 707, 4959, 134, 305, 22031, 322, 2254, 283, 1229, 132, 408, 22030, 1727, 22025])).
% 3.35/3.69 tff(22061,plain,
% 3.35/3.69 (~r(s(s(z)), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[7175, 408, 707, 670, 21927])).
% 3.35/3.69 tff(22062,plain,
% 3.35/3.69 (~(s(s(z)) = elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[11670, 22024])).
% 3.35/3.69 tff(22063,plain,
% 3.35/3.69 (b(s(s(z)), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[7970, 22062, 22061])).
% 3.35/3.69 tff(22064,plain,
% 3.35/3.69 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 3.35/3.69 inference(monotonicity,[status(thm)],[2470])).
% 3.35/3.69 tff(22065,plain,
% 3.35/3.69 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22064])).
% 3.35/3.69 tff(22066,plain,
% 3.35/3.69 (b(s(s(z)), s(elem!1))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[7928, 22065])).
% 3.35/3.69 tff(22067,assumption,(~b(s(s(z)), s(elem!1))), introduced(assumption)).
% 3.35/3.69 tff(22068,plain,
% 3.35/3.69 ($false),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22067, 22066])).
% 3.35/3.69 tff(22069,plain,(b(s(s(z)), s(elem!1)) | (~b(s(s(z)), elem!1)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.35/3.69 tff(22070,plain,
% 3.35/3.69 (b(s(s(z)), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22069, 22063, 22060])).
% 3.35/3.69 tff(22071,plain,
% 3.35/3.69 (s(elem!1) = elem!1),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1569, 22060])).
% 3.35/3.69 tff(22072,plain,
% 3.35/3.69 (b(s(z), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[3262, 22071, 134])).
% 3.35/3.69 tff(22073,plain,
% 3.35/3.69 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22060])).
% 3.35/3.69 tff(22074,plain,
% 3.35/3.69 (b(s(elem!1), s(z))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[305, 22073])).
% 3.35/3.69 tff(22075,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22076,plain,
% 3.35/3.69 (((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22077,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22076])).
% 3.35/3.69 tff(22078,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(transitivity,[status(thm)],[22077, 22075])).
% 3.35/3.69 tff(22079,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(quant_inst,[status(thm)],[])).
% 3.35/3.69 tff(22080,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22079, 22078])).
% 3.35/3.69 tff(22081,plain,
% 3.35/3.69 (~b(s(s(z)), s(z))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22080, 144, 22074, 22072, 22070])).
% 3.35/3.69 tff(22082,plain,
% 3.35/3.69 (r(s(s(z)), s(z))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1429, 44, 22081, 1416])).
% 3.35/3.69 tff(22083,plain,
% 3.35/3.69 (s(s(s(elem!1))) = elem!1),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[2482, 22060])).
% 3.35/3.69 tff(22084,plain,
% 3.35/3.69 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[12928, 22083])).
% 3.35/3.69 tff(22085,plain,
% 3.35/3.69 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[930, 22084])).
% 3.35/3.69 tff(22086,plain,
% 3.35/3.69 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[472, 22085, 22030])).
% 3.35/3.69 tff(22087,plain,
% 3.35/3.69 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[542, 22084, 22032])).
% 3.35/3.69 tff(22088,plain,
% 3.35/3.69 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22089,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22088])).
% 3.35/3.69 tff(22090,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(transitivity,[status(thm)],[22089, 1399])).
% 3.35/3.69 tff(22091,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))),
% 3.35/3.69 inference(quant_inst,[status(thm)],[])).
% 3.35/3.69 tff(22092,plain,
% 3.35/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22091, 22090])).
% 3.35/3.69 tff(22093,plain,
% 3.35/3.69 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22092, 144, 22087, 22086, 22070])).
% 3.35/3.69 tff(22094,plain,
% 3.35/3.69 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1451, 22093])).
% 3.35/3.69 tff(22095,plain,
% 3.35/3.69 ($false),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[17910, 333, 22094, 11546, 322, 22082])).
% 3.35/3.69 tff(22096,plain,(r(s(elem!1), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.35/3.69 tff(22097,plain,
% 3.35/3.69 (r(s(elem!1), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[22096, 22019, 15126, 22014, 22017, 21981, 22023, 22020, 21968, 283, 17789, 22010, 7265, 21970, 1, 21989, 21987, 284, 21980])).
% 3.35/3.69 tff(22098,plain,
% 3.35/3.69 (~r(s(elem!1), z)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[517, 22097, 51, 22010])).
% 3.35/3.69 tff(22099,plain,
% 3.35/3.69 (b(s(elem!1), z)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[507, 22098])).
% 3.35/3.69 tff(22100,plain,
% 3.35/3.69 (s(elem!1) = s(s(s(z)))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[9320, 22099, 1, 21981, 21983, 21989, 21987, 284])).
% 3.35/3.69 tff(22101,plain,
% 3.35/3.69 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22100])).
% 3.35/3.69 tff(22102,plain,
% 3.35/3.69 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22101])).
% 3.35/3.69 tff(22103,plain,
% 3.35/3.69 (s(s(z)) = elem!1),
% 3.35/3.69 inference(transitivity,[status(thm)],[87, 22102, 850])).
% 3.35/3.69 tff(22104,plain,
% 3.35/3.69 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22100])).
% 3.35/3.69 tff(22105,plain,
% 3.35/3.69 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22104])).
% 3.35/3.69 tff(22106,plain,
% 3.35/3.69 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22105])).
% 3.35/3.69 tff(22107,plain,
% 3.35/3.69 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22106, 22103])).
% 3.35/3.69 tff(22108,plain,
% 3.35/3.69 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22107])).
% 3.35/3.69 tff(22109,plain,
% 3.35/3.69 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22100])).
% 3.35/3.69 tff(22110,plain,
% 3.35/3.69 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22109])).
% 3.35/3.69 tff(22111,plain,
% 3.35/3.69 (r(elem!1, s(elem!1))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[21970, 22110])).
% 3.35/3.69 tff(22112,plain,
% 3.35/3.69 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[990, 22100, 1])).
% 3.35/3.69 tff(22113,plain,
% 3.35/3.69 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22100])).
% 3.35/3.69 tff(22114,plain,
% 3.35/3.69 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 3.35/3.69 inference(symmetry,[status(thm)],[22113])).
% 3.35/3.69 tff(22115,plain,
% 3.35/3.69 (r(s(z), s(elem!1))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[21991, 22114])).
% 3.35/3.69 tff(22116,plain,
% 3.35/3.69 (~r(s(s(s(elem!1))), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[3101, 22115, 7265, 21987, 22112, 22099, 22111])).
% 3.35/3.69 tff(22117,plain,
% 3.35/3.69 (s(s(s(z))) = s(elem!1)),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22100, 998])).
% 3.35/3.69 tff(22118,plain,
% 3.35/3.69 (~(s(s(s(elem!1))) = elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1010, 22117])).
% 3.35/3.69 tff(22119,plain,
% 3.35/3.69 (b(s(s(s(elem!1))), elem!1)),
% 3.35/3.69 inference(unit_resolution,[status(thm)],[1079, 22118, 22116])).
% 3.35/3.69 tff(22120,plain,
% 3.35/3.69 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22119, 22108])).
% 3.35/3.69 tff(22121,plain,
% 3.35/3.69 (elem!1 = s(s(z))),
% 3.35/3.69 inference(transitivity,[status(thm)],[1193, 22101, 86])).
% 3.35/3.69 tff(22122,plain,
% 3.35/3.69 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22121])).
% 3.35/3.69 tff(22123,plain,
% 3.35/3.69 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[22015, 22122])).
% 3.35/3.69 tff(22124,plain,
% 3.35/3.69 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22121])).
% 3.35/3.69 tff(22125,plain,
% 3.35/3.69 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.35/3.69 inference(modus_ponens,[status(thm)],[17789, 22124])).
% 3.35/3.69 tff(22126,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22127,plain,
% 3.35/3.69 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.35/3.69 inference(rewrite,[status(thm)],[])).
% 3.35/3.69 tff(22128,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.35/3.69 inference(monotonicity,[status(thm)],[22127])).
% 3.35/3.69 tff(22129,plain,
% 3.35/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22128, 22126])).
% 3.44/3.70 tff(22130,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.44/3.70 inference(quant_inst,[status(thm)],[])).
% 3.44/3.70 tff(22131,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22130, 22129])).
% 3.44/3.70 tff(22132,plain,
% 3.44/3.70 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22131, 144, 22125, 22123])).
% 3.44/3.70 tff(22133,plain,
% 3.44/3.70 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22132, 22120])).
% 3.44/3.70 tff(22134,plain,
% 3.44/3.70 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[12459, 22112])).
% 3.44/3.70 tff(22135,plain,
% 3.44/3.70 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22136,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22135])).
% 3.44/3.70 tff(22137,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22136, 3104])).
% 3.44/3.70 tff(22138,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.44/3.70 inference(quant_inst,[status(thm)],[])).
% 3.44/3.70 tff(22139,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22138, 22137])).
% 3.44/3.70 tff(22140,plain,
% 3.44/3.70 (~b(s(s(s(elem!1))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22139, 144, 134, 3584, 305])).
% 3.44/3.70 tff(22141,plain,
% 3.44/3.70 (r(s(s(s(elem!1))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1079, 22140, 1012])).
% 3.44/3.70 tff(22142,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22143,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.44/3.70 inference(quant_inst,[status(thm)],[])).
% 3.44/3.70 tff(22144,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22143, 22142])).
% 3.44/3.70 tff(22145,plain,
% 3.44/3.70 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22144, 333, 563, 435, 22141])).
% 3.44/3.70 tff(22146,plain,
% 3.44/3.70 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[3130, 44, 3127, 22145])).
% 3.44/3.70 tff(22147,plain,
% 3.44/3.70 (~r(s(s(s(elem!1))), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[3077, 333, 563, 670, 22141])).
% 3.44/3.70 tff(22148,plain,
% 3.44/3.70 (b(s(s(s(elem!1))), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1043, 44, 1022, 22147])).
% 3.44/3.70 tff(22149,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22150,plain,
% 3.44/3.70 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22151,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z)))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22150])).
% 3.44/3.70 tff(22152,plain,
% 3.44/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22151, 22149])).
% 3.44/3.70 tff(22153,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.44/3.70 inference(quant_inst,[status(thm)],[])).
% 3.44/3.70 tff(22154,plain,
% 3.44/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z)))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22153, 22152])).
% 3.44/3.70 tff(22155,plain,
% 3.44/3.70 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22154, 144, 491, 490, 3584])).
% 3.44/3.70 tff(22156,plain,
% 3.44/3.70 ($false),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22155, 22148, 22146])).
% 3.44/3.70 tff(22157,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.70 tff(22158,plain,
% 3.44/3.70 (~b(s(s(s(elem!1))), s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22157, 22111, 7265, 21989, 22097, 22134, 22099, 22118, 22017, 22014])).
% 3.44/3.70 tff(22159,plain,
% 3.44/3.70 (r(s(s(s(elem!1))), s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1101, 22158])).
% 3.44/3.70 tff(22160,plain,
% 3.44/3.70 (r(s(s(s(s(s(z))))), s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[13206, 22159, 22100])).
% 3.44/3.70 tff(22161,plain,
% 3.44/3.70 (((~![X0: $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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22162,plain,
% 3.44/3.70 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22163,plain,
% 3.44/3.70 (((~![X0: $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(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(s(s(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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22162])).
% 3.44/3.70 tff(22164,plain,
% 3.44/3.70 (((~![X0: $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(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(s(s(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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22163, 22161])).
% 3.44/3.70 tff(22165,plain,
% 3.44/3.70 ((~![X0: $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(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(s(s(s(z))))))))))),
% 3.44/3.70 inference(quant_inst,[status(thm)],[])).
% 3.44/3.70 tff(22166,plain,
% 3.44/3.70 ((~![X0: $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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22165, 22164])).
% 3.44/3.70 tff(22167,plain,
% 3.44/3.70 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22166, 333, 22160, 21991, 22019])).
% 3.44/3.70 tff(22168,plain,
% 3.44/3.70 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1159, 44, 22167])).
% 3.44/3.70 tff(22169,plain,
% 3.44/3.70 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22168, 22133])).
% 3.44/3.70 tff(22170,plain,
% 3.44/3.70 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 3.44/3.70 inference(symmetry,[status(thm)],[22169])).
% 3.44/3.70 tff(22171,plain,
% 3.44/3.70 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22170])).
% 3.44/3.70 tff(22172,plain,
% 3.44/3.70 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.44/3.70 inference(symmetry,[status(thm)],[22171])).
% 3.44/3.70 tff(22173,plain,
% 3.44/3.70 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 3.44/3.70 inference(transitivity,[status(thm)],[239, 22172, 20])).
% 3.44/3.70 tff(22174,plain,
% 3.44/3.70 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22173])).
% 3.44/3.70 tff(22175,plain,
% 3.44/3.70 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 3.44/3.70 inference(symmetry,[status(thm)],[22174])).
% 3.44/3.70 tff(22176,plain,
% 3.44/3.70 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22105, 93, 22175, 183])).
% 3.44/3.70 tff(22177,plain,
% 3.44/3.70 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22100])).
% 3.44/3.70 tff(22178,plain,
% 3.44/3.70 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.44/3.70 inference(transitivity,[status(thm)],[22177, 972])).
% 3.44/3.70 tff(22179,plain,
% 3.44/3.70 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22178])).
% 3.44/3.70 tff(22180,plain,
% 3.44/3.70 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22112, 22179])).
% 3.44/3.70 tff(22181,plain,
% 3.44/3.70 ($false),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22180, 22176])).
% 3.44/3.70 tff(22182,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(z, elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.70 tff(22183,plain,
% 3.44/3.70 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22182, 51, 284, 1, 3, 606, 3193])).
% 3.44/3.70 tff(22184,plain,
% 3.44/3.70 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[249, 22183])).
% 3.44/3.70 tff(22185,plain,
% 3.44/3.70 (~r(s(z), s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[15519, 22184, 15126, 3193])).
% 3.44/3.70 tff(22186,plain,
% 3.44/3.70 (b(s(z), s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[172, 22185])).
% 3.44/3.70 tff(22187,plain,
% 3.44/3.70 (~r(s(z), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[19046, 333, 15126, 22184, 51])).
% 3.44/3.70 tff(22188,plain,
% 3.44/3.70 (b(s(z), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[348, 22187])).
% 3.44/3.70 tff(22189,plain,
% 3.44/3.70 (~b(s(s(s(z))), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[2156, 22188, 284, 22186])).
% 3.44/3.70 tff(22190,plain,
% 3.44/3.70 (r(s(s(s(z))), z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[396, 22189])).
% 3.44/3.70 tff(22191,plain,
% 3.44/3.70 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[2938, 408, 51, 670])).
% 3.44/3.70 tff(22192,plain,
% 3.44/3.70 ($false),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[10110, 6548, 22191, 114, 3, 2254])).
% 3.44/3.70 tff(22193,plain,((~r(elem!1, z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.70 tff(22194,plain,
% 3.44/3.70 (~r(elem!1, z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22193, 51, 3, 21968, 21754, 17787, 7265, 22190])).
% 3.44/3.70 tff(22195,plain,
% 3.44/3.70 (b(elem!1, z)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1380, 22194, 77])).
% 3.44/3.70 tff(22196,plain,
% 3.44/3.70 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[21813, 144, 284, 17789, 21968])).
% 3.44/3.70 tff(22197,plain,
% 3.44/3.70 (~b(elem!1, s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22196, 22195])).
% 3.44/3.70 tff(22198,plain,
% 3.44/3.70 (r(elem!1, s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1538, 22197, 21756])).
% 3.44/3.70 tff(22199,plain,
% 3.44/3.70 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[21978, 22198, 7265, 51])).
% 3.44/3.70 tff(22200,plain,
% 3.44/3.70 (~b(s(s(s(z))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[10110, 22199, 17787, 3, 21968])).
% 3.44/3.70 tff(22201,plain,
% 3.44/3.70 (r(s(s(s(z))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[704, 22200, 21754])).
% 3.44/3.70 tff(22202,plain,
% 3.44/3.70 (~r(z, s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[15576, 22184, 15126, 51])).
% 3.44/3.70 tff(22203,plain,
% 3.44/3.70 (b(z, s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[372, 22202])).
% 3.44/3.70 tff(22204,plain,
% 3.44/3.70 (~(s(z) = elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[8102, 22203, 606])).
% 3.44/3.70 tff(22205,plain,
% 3.44/3.70 (~(elem!1 = s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[712, 22204])).
% 3.44/3.70 tff(22206,plain,
% 3.44/3.70 (~b(elem!1, s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[387, 144, 22195, 22203, 22188])).
% 3.44/3.70 tff(22207,plain,
% 3.44/3.70 (r(elem!1, s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[720, 22206, 22205])).
% 3.44/3.70 tff(22208,plain,
% 3.44/3.70 (~r(s(z), s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[8957, 22207, 3193, 22201])).
% 3.44/3.70 tff(22209,plain,
% 3.44/3.70 (~b(elem!1, s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[22196, 624])).
% 3.44/3.70 tff(22210,plain,
% 3.44/3.70 (r(elem!1, s(s(s(z))))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1538, 22209, 12398])).
% 3.44/3.70 tff(22211,plain,
% 3.44/3.70 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[21978, 22210, 670, 51])).
% 3.44/3.70 tff(22212,plain,
% 3.44/3.70 (~b(s(s(s(z))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[10110, 22211, 17787, 3, 21968])).
% 3.44/3.70 tff(22213,plain,
% 3.44/3.70 (r(s(s(s(z))), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[704, 22212, 698])).
% 3.44/3.70 tff(22214,plain,
% 3.44/3.70 (~r(s(z), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[9910, 21847, 3193, 22213])).
% 3.44/3.70 tff(22215,plain,
% 3.44/3.70 (b(s(z), elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[406, 22214, 706])).
% 3.44/3.70 tff(22216,plain,
% 3.44/3.70 (~r(elem!1, s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[6585, 22213, 1699, 670])).
% 3.44/3.70 tff(22217,plain,
% 3.44/3.70 (~r(s(z), s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[8957, 21847, 3193, 22213])).
% 3.44/3.70 tff(22218,plain,
% 3.44/3.70 (b(s(z), s(elem!1))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1244, 22217, 1229])).
% 3.44/3.70 tff(22219,plain,
% 3.44/3.70 (elem!1 = s(elem!1)),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[1732, 22218, 22216, 22215, 1727])).
% 3.44/3.70 tff(22220,plain,
% 3.44/3.70 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22219])).
% 3.44/3.70 tff(22221,plain,
% 3.44/3.70 (r(s(elem!1), s(s(s(z))))),
% 3.44/3.70 inference(modus_ponens,[status(thm)],[22210, 22220])).
% 3.44/3.70 tff(22222,plain,
% 3.44/3.70 (~b(s(elem!1), s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[890, 22219, 19382])).
% 3.44/3.70 tff(22223,plain,
% 3.44/3.70 (r(s(elem!1), s(z))),
% 3.44/3.70 inference(unit_resolution,[status(thm)],[486, 22222, 1])).
% 3.44/3.70 tff(22224,plain,
% 3.44/3.70 (((~![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(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22225,plain,
% 3.44/3.70 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.70 inference(rewrite,[status(thm)],[])).
% 3.44/3.70 tff(22226,plain,
% 3.44/3.70 (((~![X0: $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(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.70 inference(monotonicity,[status(thm)],[22225])).
% 3.44/3.70 tff(22227,plain,
% 3.44/3.70 (((~![X0: $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(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.71 inference(transitivity,[status(thm)],[22226, 22224])).
% 3.44/3.71 tff(22228,plain,
% 3.44/3.71 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 3.44/3.71 inference(quant_inst,[status(thm)],[])).
% 3.44/3.71 tff(22229,plain,
% 3.44/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.71 inference(modus_ponens,[status(thm)],[22228, 22227])).
% 3.44/3.71 tff(22230,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22229, 333, 22223, 3193, 22221, 15126])).
% 3.44/3.71 tff(22231,plain,((~b(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | (s(z) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22232,plain,
% 3.44/3.71 (r(s(elem!1), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22231, 22195, 1, 3193, 22204, 22203, 22188, 22190, 7265, 21754, 3, 51, 284])).
% 3.44/3.71 tff(22233,plain,
% 3.44/3.71 (~r(s(elem!1), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[3895, 333, 22232, 7265, 22198])).
% 3.44/3.71 tff(22234,plain,
% 3.44/3.71 (b(s(elem!1), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[507, 22233])).
% 3.44/3.71 tff(22235,plain,
% 3.44/3.71 (~r(z, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[3875, 333, 22232, 7265, 22198])).
% 3.44/3.71 tff(22236,plain,
% 3.44/3.71 (b(z, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[583, 22235])).
% 3.44/3.71 tff(22237,plain,
% 3.44/3.71 (~b(s(z), s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2383, 22236, 22188, 22234])).
% 3.44/3.71 tff(22238,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[1244, 22237, 22208, 1229])).
% 3.44/3.71 tff(22239,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(z))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22240,plain,
% 3.44/3.71 (~r(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22239, 21967, 3, 1, 21154, 21914])).
% 3.44/3.71 tff(22241,plain,
% 3.44/3.71 (b(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2794, 22240])).
% 3.44/3.71 tff(22242,plain,
% 3.44/3.71 (~b(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2273, 22241, 21961, 21959])).
% 3.44/3.71 tff(22243,plain,
% 3.44/3.71 (r(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[372, 22242])).
% 3.44/3.71 tff(22244,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22008, 21967, 17787, 3, 624, 21815, 21806, 21915, 21916, 21959, 21914, 15126, 21963])).
% 3.44/3.71 tff(22245,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[302, 22244])).
% 3.44/3.71 tff(22246,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[294, 22245, 21154, 21961])).
% 3.44/3.71 tff(22247,plain,
% 3.44/3.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[249, 22246])).
% 3.44/3.71 tff(22248,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[15576, 22247, 22243, 15126, 21967])).
% 3.44/3.71 tff(22249,plain,((~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22250,plain,
% 3.44/3.71 (~b(elem!1, z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22249, 54, 1, 3])).
% 3.44/3.71 tff(22251,plain,
% 3.44/3.71 (r(elem!1, z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[653, 22250, 77])).
% 3.44/3.71 tff(22252,plain,
% 3.44/3.71 (~r(s(elem!1), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[15216, 490, 1, 22251, 17791, 409])).
% 3.44/3.71 tff(22253,plain,
% 3.44/3.71 (~(s(s(elem!1)) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7595, 78, 19208])).
% 3.44/3.71 tff(22254,plain,
% 3.44/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[5603, 22253])).
% 3.44/3.71 tff(22255,plain,
% 3.44/3.71 (~(s(elem!1) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[5813, 22254])).
% 3.44/3.71 tff(22256,plain,
% 3.44/3.71 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[20734, 14872])).
% 3.44/3.71 tff(22257,plain,
% 3.44/3.71 (~(elem!1 = s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[1569, 22255])).
% 3.44/3.71 tff(22258,plain,
% 3.44/3.71 (~r(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[417, 409, 22251, 17791])).
% 3.44/3.71 tff(22259,plain,
% 3.44/3.71 (b(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[348, 22258])).
% 3.44/3.71 tff(22260,plain,
% 3.44/3.71 (~b(s(elem!1), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7653, 22255, 17787, 22251, 54, 251, 22259, 490, 3, 22257, 14872, 1, 409, 22256])).
% 3.44/3.71 tff(22261,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[448, 22260, 22255, 22252])).
% 3.44/3.71 tff(22262,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, elem!1)) | (~b(z, s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22263,plain,
% 3.44/3.71 (~(s(s(s(z))) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22262, 490, 251, 54, 3, 1, 409])).
% 3.44/3.71 tff(22264,plain,
% 3.44/3.71 (r(s(s(s(z))), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[704, 22263, 21807])).
% 3.44/3.71 tff(22265,plain,
% 3.44/3.71 (~r(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[9952, 22264, 22251, 409])).
% 3.44/3.71 tff(22266,plain,
% 3.44/3.71 (b(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2794, 22265])).
% 3.44/3.71 tff(22267,plain,
% 3.44/3.71 (~b(s(z), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2055, 22266, 22251, 490, 22259, 22264])).
% 3.44/3.71 tff(22268,plain,
% 3.44/3.71 (r(s(z), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[172, 22267])).
% 3.44/3.71 tff(22269,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2035, 333, 409, 22251, 22264, 22268])).
% 3.44/3.71 tff(22270,plain,((~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22271,plain,
% 3.44/3.71 (~b(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22270, 409, 251, 54, 3, 1])).
% 3.44/3.71 tff(22272,plain,
% 3.44/3.71 (r(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[372, 22271])).
% 3.44/3.71 tff(22273,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[15183, 22272, 15126, 17791])).
% 3.44/3.71 tff(22274,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[302, 22273])).
% 3.44/3.71 tff(22275,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[429, 22272, 409, 17791])).
% 3.44/3.71 tff(22276,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[319, 22275])).
% 3.44/3.71 tff(22277,plain,
% 3.44/3.71 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7634, 144, 251, 22259, 17788])).
% 3.44/3.71 tff(22278,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22277, 22276, 22274])).
% 3.44/3.71 tff(22279,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22280,plain,
% 3.44/3.71 (~r(s(z), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22279, 251, 54, 3, 1])).
% 3.44/3.71 tff(22281,plain,
% 3.44/3.71 (b(s(z), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[406, 22280, 15133])).
% 3.44/3.71 tff(22282,plain,
% 3.44/3.71 (~b(elem!1, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[3955, 19507, 133, 134])).
% 3.44/3.71 tff(22283,plain,
% 3.44/3.71 (r(elem!1, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[720, 22282, 714])).
% 3.44/3.71 tff(22284,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[12125, 333, 323, 408, 22283, 51])).
% 3.44/3.71 tff(22285,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22286,plain,
% 3.44/3.71 (~r(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22285, 17791, 22251, 15134, 17788, 22281, 15126])).
% 3.44/3.71 tff(22287,plain,
% 3.44/3.71 (b(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[348, 22286])).
% 3.44/3.71 tff(22288,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[15183, 354, 11546, 51])).
% 3.44/3.71 tff(22289,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[302, 22288])).
% 3.44/3.71 tff(22290,plain,
% 3.44/3.71 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7634, 144, 251, 489, 133])).
% 3.44/3.71 tff(22291,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22290, 22289])).
% 3.44/3.71 tff(22292,plain,
% 3.44/3.71 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[319, 22291])).
% 3.44/3.71 tff(22293,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[18594, 333, 354, 11546, 22292, 51])).
% 3.44/3.71 tff(22294,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22295,plain,
% 3.44/3.71 (~r(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22294, 17791, 15126, 251, 22287, 17788])).
% 3.44/3.71 tff(22296,plain,
% 3.44/3.71 (b(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[372, 22295])).
% 3.44/3.71 tff(22297,plain,
% 3.44/3.71 (~b(elem!1, s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2090, 22296, 21154, 251, 22281])).
% 3.44/3.71 tff(22298,plain,
% 3.44/3.71 (~b(elem!1, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7079, 22296, 251, 22281])).
% 3.44/3.71 tff(22299,plain,
% 3.44/3.71 (r(elem!1, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[720, 22298, 15134])).
% 3.44/3.71 tff(22300,plain,
% 3.44/3.71 (~b(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2156, 21827, 284, 489])).
% 3.44/3.71 tff(22301,plain,
% 3.44/3.71 (r(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[396, 22300])).
% 3.44/3.71 tff(22302,plain,
% 3.44/3.71 (((~![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))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, 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(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.71 inference(rewrite,[status(thm)],[])).
% 3.44/3.71 tff(22303,plain,
% 3.44/3.71 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.71 inference(rewrite,[status(thm)],[])).
% 3.44/3.71 tff(22304,plain,
% 3.44/3.71 (((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.71 inference(monotonicity,[status(thm)],[22303])).
% 3.44/3.71 tff(22305,plain,
% 3.44/3.71 (((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.71 inference(transitivity,[status(thm)],[22304, 22302])).
% 3.44/3.71 tff(22306,plain,
% 3.44/3.71 ((~![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(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 3.44/3.71 inference(quant_inst,[status(thm)],[])).
% 3.44/3.71 tff(22307,plain,
% 3.44/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.71 inference(modus_ponens,[status(thm)],[22306, 22305])).
% 3.44/3.71 tff(22308,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22307, 333, 408, 22301, 12399, 51])).
% 3.44/3.71 tff(22309,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | b(s(s(s(z))), elem!1) | (~r(elem!1, s(z))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22310,plain,
% 3.44/3.71 (s(s(s(z))) = elem!1),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22309, 17791, 22251, 21154, 22287, 21807, 22299, 22297])).
% 3.44/3.71 tff(22311,plain,
% 3.44/3.71 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[12214, 22310])).
% 3.44/3.71 tff(22312,plain,
% 3.44/3.71 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[20734, 22311])).
% 3.44/3.71 tff(22313,plain,
% 3.44/3.71 (~(s(s(elem!1)) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7595, 22310, 19208])).
% 3.44/3.71 tff(22314,plain,
% 3.44/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[5603, 22313])).
% 3.44/3.71 tff(22315,plain,
% 3.44/3.71 (~(s(elem!1) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[5813, 22314])).
% 3.44/3.71 tff(22316,plain,
% 3.44/3.71 (~(elem!1 = s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[1569, 22315])).
% 3.44/3.71 tff(22317,plain,
% 3.44/3.71 (~r(s(elem!1), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[517, 509, 408, 51])).
% 3.44/3.71 tff(22318,plain,
% 3.44/3.71 (b(s(elem!1), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[448, 22317, 433])).
% 3.44/3.71 tff(22319,plain,
% 3.44/3.71 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[464, 22318, 114, 54, 3])).
% 3.44/3.71 tff(22320,plain,
% 3.44/3.71 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7622, 22318, 408, 19417, 51, 509, 1722, 20735])).
% 3.44/3.71 tff(22321,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[472, 22320, 22319, 432])).
% 3.44/3.71 tff(22322,plain,((~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22323,plain,
% 3.44/3.71 (~r(s(elem!1), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22322, 22311, 22251, 17791, 17787, 54, 3, 22315])).
% 3.44/3.71 tff(22324,plain,
% 3.44/3.71 (b(s(elem!1), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[507, 22323])).
% 3.44/3.71 tff(22325,plain,
% 3.44/3.71 (~r(elem!1, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7799, 20698, 722, 10902])).
% 3.44/3.71 tff(22326,plain,
% 3.44/3.71 (b(elem!1, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[560, 22325, 902])).
% 3.44/3.71 tff(22327,plain,
% 3.44/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 3.44/3.71 inference(rewrite,[status(thm)],[])).
% 3.44/3.71 tff(22328,plain,
% 3.44/3.71 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 3.44/3.71 inference(rewrite,[status(thm)],[])).
% 3.44/3.71 tff(22329,plain,
% 3.44/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 3.44/3.71 inference(monotonicity,[status(thm)],[22328])).
% 3.44/3.71 tff(22330,plain,
% 3.44/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 3.44/3.71 inference(transitivity,[status(thm)],[22329, 22327])).
% 3.44/3.71 tff(22331,plain,
% 3.44/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 3.44/3.71 inference(quant_inst,[status(thm)],[])).
% 3.44/3.71 tff(22332,plain,
% 3.44/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 3.44/3.71 inference(modus_ponens,[status(thm)],[22331, 22330])).
% 3.44/3.71 tff(22333,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22332, 144, 547, 251, 585, 134, 490])).
% 3.44/3.71 tff(22334,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22335,plain,
% 3.44/3.71 (~b(z, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22334, 22326, 251, 134, 490])).
% 3.44/3.71 tff(22336,plain,
% 3.44/3.71 (r(z, s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[583, 22335])).
% 3.44/3.71 tff(22337,plain,
% 3.44/3.71 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[940, 22336, 51, 321])).
% 3.44/3.71 tff(22338,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[13736, 22336, 51, 10902])).
% 3.44/3.71 tff(22339,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[5467, 22338, 22337, 132, 537, 22326])).
% 3.44/3.71 tff(22340,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22341,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22340, 22324, 22312, 17791, 17789, 251, 22281, 22296, 22316, 22299, 22287, 1])).
% 3.44/3.71 tff(22342,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[302, 22341])).
% 3.44/3.71 tff(22343,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[9997, 144, 251, 22324, 17788, 22342])).
% 3.44/3.71 tff(22344,plain,
% 3.44/3.71 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[7634, 144, 251, 22287, 17788])).
% 3.44/3.71 tff(22345,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22344, 22342])).
% 3.44/3.71 tff(22346,plain,
% 3.44/3.71 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[319, 22345])).
% 3.44/3.71 tff(22347,plain,
% 3.44/3.71 (~b(s(elem!1), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[499, 22324, 22296, 22287])).
% 3.44/3.71 tff(22348,plain,
% 3.44/3.71 (r(s(elem!1), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[486, 22347, 1])).
% 3.44/3.71 tff(22349,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[20755, 333, 22348, 15126, 22346])).
% 3.44/3.71 tff(22350,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[542, 22349, 22343, 22312])).
% 3.44/3.71 tff(22351,plain,((~b(z, elem!1)) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22352,plain,
% 3.44/3.71 (~b(z, elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22351, 54, 1, 3])).
% 3.44/3.71 tff(22353,plain,
% 3.44/3.71 (r(z, elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[658, 22352, 71])).
% 3.44/3.71 tff(22354,plain,
% 3.44/3.71 (~(s(s(s(z))) = elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[609, 22352, 21154])).
% 3.44/3.71 tff(22355,plain,
% 3.44/3.71 (r(s(s(s(z))), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[704, 22354, 21807])).
% 3.44/3.71 tff(22356,plain,
% 3.44/3.71 (~r(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2079, 22355, 22251, 22353])).
% 3.44/3.71 tff(22357,plain,
% 3.44/3.71 (b(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[396, 22356])).
% 3.44/3.71 tff(22358,plain,
% 3.44/3.71 (b(s(z), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[406, 19573, 706])).
% 3.44/3.71 tff(22359,plain,
% 3.44/3.71 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22285, 22358, 408, 713, 133, 323, 11546])).
% 3.44/3.71 tff(22360,plain,
% 3.44/3.71 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[279, 22359])).
% 3.44/3.71 tff(22361,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[14138, 144, 285, 2254, 21951, 22360])).
% 3.44/3.71 tff(22362,plain,((~r(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22363,plain,
% 3.44/3.71 (~r(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22362, 22357, 21806, 22251, 17788, 15126, 15133, 22353])).
% 3.44/3.71 tff(22364,plain,
% 3.44/3.71 (b(s(z), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[348, 22363])).
% 3.44/3.71 tff(22365,plain,
% 3.44/3.71 (~r(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2079, 707, 408, 670])).
% 3.44/3.71 tff(22366,plain,
% 3.44/3.71 (b(s(s(s(z))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[396, 22365])).
% 3.44/3.71 tff(22367,plain,
% 3.44/3.71 (~r(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[9952, 409, 408, 707])).
% 3.44/3.71 tff(22368,plain,
% 3.44/3.71 (b(s(s(s(z))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2794, 22367])).
% 3.44/3.71 tff(22369,plain,
% 3.44/3.71 (~r(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[20228, 409, 408, 670])).
% 3.44/3.71 tff(22370,plain,
% 3.44/3.71 (b(z, s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[372, 22369])).
% 3.44/3.71 tff(22371,plain,
% 3.44/3.71 ($false),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2273, 22370, 22368, 22366, 489])).
% 3.44/3.71 tff(22372,plain,((~r(s(z), elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.71 tff(22373,plain,
% 3.44/3.71 (~r(s(z), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[22372, 22364, 22251, 22353, 22355])).
% 3.44/3.71 tff(22374,plain,
% 3.44/3.71 (b(s(z), elem!1)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[406, 22373, 15133])).
% 3.44/3.71 tff(22375,plain,
% 3.44/3.71 (~b(s(z), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[2156, 22364, 21154, 22357])).
% 3.44/3.71 tff(22376,plain,
% 3.44/3.71 (r(s(z), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[172, 22375])).
% 3.44/3.71 tff(22377,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[3955, 19176, 133, 134])).
% 3.44/3.71 tff(22378,plain,
% 3.44/3.71 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[319, 22377])).
% 3.44/3.71 tff(22379,plain,
% 3.44/3.71 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[362, 22378, 353, 354])).
% 3.44/3.71 tff(22380,plain,
% 3.44/3.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[302, 22379])).
% 3.44/3.71 tff(22381,plain,
% 3.44/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[14255, 22380, 408, 670, 707])).
% 3.44/3.71 tff(22382,plain,
% 3.44/3.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.71 inference(unit_resolution,[status(thm)],[249, 22381])).
% 3.44/3.71 tff(22383,plain,
% 3.44/3.71 (((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.44/3.71 inference(rewrite,[status(thm)],[])).
% 3.44/3.71 tff(22384,plain,
% 3.44/3.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.44/3.72 inference(rewrite,[status(thm)],[])).
% 3.44/3.72 tff(22385,plain,
% 3.44/3.72 (((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 3.44/3.72 inference(monotonicity,[status(thm)],[22384])).
% 3.44/3.72 tff(22386,plain,
% 3.44/3.72 (((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.44/3.72 inference(transitivity,[status(thm)],[22385, 22383])).
% 3.44/3.72 tff(22387,plain,
% 3.44/3.72 ((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.44/3.72 inference(quant_inst,[status(thm)],[])).
% 3.44/3.72 tff(22388,plain,
% 3.44/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.44/3.72 inference(modus_ponens,[status(thm)],[22387, 22386])).
% 3.44/3.72 tff(22389,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22388, 333, 707, 353, 22382, 22378])).
% 3.44/3.72 tff(22390,plain,((~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22391,plain,
% 3.44/3.72 (~r(z, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22390, 22355, 22376, 22251, 22353, 17788, 22374, 15134, 15126])).
% 3.44/3.72 tff(22392,plain,
% 3.44/3.72 (b(z, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[372, 22391])).
% 3.44/3.72 tff(22393,plain,
% 3.44/3.72 (~b(s(s(s(z))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2273, 22392, 22357, 22364])).
% 3.44/3.72 tff(22394,plain,
% 3.44/3.72 (r(s(s(s(z))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2794, 22393])).
% 3.44/3.72 tff(22395,plain,
% 3.44/3.72 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22239, 22394, 3, 1, 21154, 22352])).
% 3.44/3.72 tff(22396,plain,
% 3.44/3.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[16228, 259, 284, 2254])).
% 3.44/3.72 tff(22397,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[249, 22396])).
% 3.44/3.72 tff(22398,plain,
% 3.44/3.72 (~r(s(z), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[15519, 22397, 11546, 3193])).
% 3.44/3.72 tff(22399,plain,
% 3.44/3.72 (b(s(z), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[172, 22398])).
% 3.44/3.72 tff(22400,plain,
% 3.44/3.72 (~r(s(z), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[15519, 224, 11546, 3193])).
% 3.44/3.72 tff(22401,plain,
% 3.44/3.72 (b(s(z), s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[172, 22400])).
% 3.44/3.72 tff(22402,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[10110, 4367, 114, 3, 2254])).
% 3.44/3.72 tff(22403,plain,
% 3.44/3.72 (((~![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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(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(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.72 inference(rewrite,[status(thm)],[])).
% 3.44/3.72 tff(22404,plain,
% 3.44/3.72 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.72 inference(rewrite,[status(thm)],[])).
% 3.44/3.72 tff(22405,plain,
% 3.44/3.72 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.44/3.72 inference(monotonicity,[status(thm)],[22404])).
% 3.44/3.72 tff(22406,plain,
% 3.44/3.72 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.72 inference(transitivity,[status(thm)],[22405, 22403])).
% 3.44/3.72 tff(22407,plain,
% 3.44/3.72 ((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.72 inference(quant_inst,[status(thm)],[])).
% 3.44/3.72 tff(22408,plain,
% 3.44/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.72 inference(modus_ponens,[status(thm)],[22407, 22406])).
% 3.44/3.72 tff(22409,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22408, 333, 1525, 3193, 2484, 224])).
% 3.44/3.72 tff(22410,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22411,plain,
% 3.44/3.72 (~r(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22410, 22402, 3193, 224])).
% 3.44/3.72 tff(22412,plain,
% 3.44/3.72 (b(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[1538, 22411, 1524])).
% 3.44/3.72 tff(22413,plain,
% 3.44/3.72 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[21813, 144, 284, 132, 2254])).
% 3.44/3.72 tff(22414,plain,
% 3.44/3.72 (~b(elem!1, z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22413, 22412])).
% 3.44/3.72 tff(22415,plain,
% 3.44/3.72 (r(elem!1, z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[653, 22414, 1368])).
% 3.44/3.72 tff(22416,plain,
% 3.44/3.72 (~r(s(z), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[20599, 22415, 11546, 22402])).
% 3.44/3.72 tff(22417,plain,
% 3.44/3.72 (b(s(z), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[406, 22416, 706])).
% 3.44/3.72 tff(22418,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[10692, 144, 22417, 22412, 22401, 4367])).
% 3.44/3.72 tff(22419,plain,((~b(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22420,plain,
% 3.44/3.72 (~b(s(s(s(z))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22419, 706, 11546, 1368, 284, 132, 2254, 12398, 3193, 22397, 114, 3])).
% 3.44/3.72 tff(22421,plain,
% 3.44/3.72 (r(s(s(s(z))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[704, 22420, 698])).
% 3.44/3.72 tff(22422,plain,
% 3.44/3.72 (~r(s(z), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[9952, 408, 3193, 707])).
% 3.44/3.72 tff(22423,plain,
% 3.44/3.72 (b(s(z), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[406, 22422, 706])).
% 3.44/3.72 tff(22424,plain,
% 3.44/3.72 (~r(s(s(s(z))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2079, 408, 670, 707])).
% 3.44/3.72 tff(22425,plain,
% 3.44/3.72 (b(s(s(s(z))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[396, 22424])).
% 3.44/3.72 tff(22426,plain,
% 3.44/3.72 (~b(s(z), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2156, 22425, 284, 838])).
% 3.44/3.72 tff(22427,plain,
% 3.44/3.72 (r(s(z), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[348, 22426])).
% 3.44/3.72 tff(22428,plain,
% 3.44/3.72 (~r(elem!1, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[8824, 22427, 707, 3193])).
% 3.44/3.72 tff(22429,plain,
% 3.44/3.72 (b(elem!1, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[720, 22428, 713])).
% 3.44/3.72 tff(22430,plain,
% 3.44/3.72 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[20837, 22427, 3193, 224])).
% 3.44/3.72 tff(22431,plain,
% 3.44/3.72 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[319, 22430])).
% 3.44/3.72 tff(22432,plain,
% 3.44/3.72 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[3955, 22431, 22429, 22423])).
% 3.44/3.72 tff(22433,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[130, 22432, 114])).
% 3.44/3.72 tff(22434,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[14260, 333, 408, 707, 22433, 224])).
% 3.44/3.72 tff(22435,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22436,plain,
% 3.44/3.72 (~r(elem!1, z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22435, 22421, 22397, 114, 3193, 284, 22399, 706, 670])).
% 3.44/3.72 tff(22437,plain,
% 3.44/3.72 (b(elem!1, z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[1380, 22436, 1368])).
% 3.44/3.72 tff(22438,plain,
% 3.44/3.72 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[14405, 22437, 132, 259])).
% 3.44/3.72 tff(22439,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[302, 22438])).
% 3.44/3.72 tff(22440,plain,
% 3.44/3.72 (~b(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22413, 22437])).
% 3.44/3.72 tff(22441,plain,
% 3.44/3.72 (r(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[1538, 22440, 12398])).
% 3.44/3.72 tff(22442,plain,
% 3.44/3.72 (~r(s(s(s(z))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[21925, 333, 670, 22441, 22421])).
% 3.44/3.72 tff(22443,plain,
% 3.44/3.72 (b(s(s(s(z))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[396, 22442])).
% 3.44/3.72 tff(22444,plain,
% 3.44/3.72 (~b(s(z), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2156, 22443, 284, 22399])).
% 3.44/3.72 tff(22445,plain,
% 3.44/3.72 (r(s(z), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[348, 22444])).
% 3.44/3.72 tff(22446,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[21947, 333, 670, 22445, 11546, 22439])).
% 3.44/3.72 tff(22447,plain,((s(z) = elem!1) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22448,plain,
% 3.44/3.72 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22447, 22394, 15126, 15133, 17789, 21806, 21154, 77, 17787, 22353, 22354, 3])).
% 3.44/3.72 tff(22449,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[279, 22448, 22395])).
% 3.44/3.72 tff(22450,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22451,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22450, 1, 3])).
% 3.44/3.72 tff(22452,plain,
% 3.44/3.72 (~b(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22413, 624])).
% 3.44/3.72 tff(22453,plain,
% 3.44/3.72 (~r(elem!1, s(s(s(z))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[17853, 409, 11546, 2484])).
% 3.44/3.72 tff(22454,plain,
% 3.44/3.72 (elem!1 = s(s(s(z)))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[1538, 22453, 22452])).
% 3.44/3.72 tff(22455,plain,
% 3.44/3.72 (s(s(s(z))) = elem!1),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[10997, 22454])).
% 3.44/3.72 tff(22456,plain,
% 3.44/3.72 (~(s(s(elem!1)) = elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[7595, 22455, 1184])).
% 3.44/3.72 tff(22457,plain,
% 3.44/3.72 (~(elem!1 = s(s(elem!1)))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[5603, 22456])).
% 3.44/3.72 tff(22458,plain,
% 3.44/3.72 (~(s(elem!1) = elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[5813, 22457])).
% 3.44/3.72 tff(22459,plain,
% 3.44/3.72 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 3.44/3.72 inference(monotonicity,[status(thm)],[22454])).
% 3.44/3.72 tff(22460,plain,
% 3.44/3.72 (r(s(z), s(s(s(z))))),
% 3.44/3.72 inference(modus_ponens,[status(thm)],[409, 22459])).
% 3.44/3.72 tff(22461,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.72 inference(monotonicity,[status(thm)],[22454])).
% 3.44/3.72 tff(22462,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.72 inference(modus_ponens,[status(thm)],[2484, 22461])).
% 3.44/3.72 tff(22463,plain,
% 3.44/3.72 (~r(s(s(s(z))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[15519, 22462, 11546, 22460])).
% 3.44/3.72 tff(22464,plain,
% 3.44/3.72 (b(s(s(s(z))), s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[2794, 22463])).
% 3.44/3.72 tff(22465,plain,
% 3.44/3.72 (s(s(s(z))) = elem!1),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[10997, 3238])).
% 3.44/3.72 tff(22466,plain,
% 3.44/3.72 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[12214, 22465])).
% 3.44/3.72 tff(22467,plain,
% 3.44/3.72 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[20734, 22466])).
% 3.44/3.72 tff(22468,plain,
% 3.44/3.72 (b(z, elem!1)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[609, 22465, 284])).
% 3.44/3.72 tff(22469,plain,
% 3.44/3.72 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[19019, 354, 11546, 114, 624, 251])).
% 3.44/3.72 tff(22470,plain,
% 3.44/3.72 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[279, 22469])).
% 3.44/3.72 tff(22471,plain,
% 3.44/3.72 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[14405, 22470, 132, 624])).
% 3.44/3.72 tff(22472,plain,
% 3.44/3.72 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[302, 22471])).
% 3.44/3.72 tff(22473,plain,
% 3.44/3.72 ($false),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[19029, 333, 354, 323, 11546, 22472])).
% 3.44/3.72 tff(22474,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.72 tff(22475,plain,
% 3.44/3.72 (~r(z, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[22474, 22468, 11546, 132, 624, 21578, 323])).
% 3.44/3.72 tff(22476,plain,
% 3.44/3.72 (b(z, s(z))),
% 3.44/3.72 inference(unit_resolution,[status(thm)],[372, 22475])).
% 3.44/3.72 tff(22477,plain,
% 3.44/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.72 inference(rewrite,[status(thm)],[])).
% 3.44/3.72 tff(22478,plain,
% 3.44/3.72 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.72 inference(rewrite,[status(thm)],[])).
% 3.44/3.72 tff(22479,plain,
% 3.44/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22478])).
% 3.44/3.73 tff(22480,plain,
% 3.44/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(transitivity,[status(thm)],[22479, 22477])).
% 3.44/3.73 tff(22481,plain,
% 3.44/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))),
% 3.44/3.73 inference(quant_inst,[status(thm)],[])).
% 3.44/3.73 tff(22482,plain,
% 3.44/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22481, 22480])).
% 3.44/3.73 tff(22483,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22482, 144, 490, 284, 2254, 304, 259])).
% 3.44/3.73 tff(22484,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22485,plain,
% 3.44/3.73 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22484, 259, 284, 2254, 22476])).
% 3.44/3.73 tff(22486,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[319, 22485])).
% 3.44/3.73 tff(22487,plain,
% 3.44/3.73 (~r(z, s(elem!1))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[8274, 22486, 323, 19081])).
% 3.44/3.73 tff(22488,plain,
% 3.44/3.73 (b(z, s(elem!1))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[583, 22487])).
% 3.44/3.73 tff(22489,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[3238])).
% 3.44/3.73 tff(22490,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[2484, 22489])).
% 3.44/3.73 tff(22491,plain,
% 3.44/3.73 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 3.44/3.73 inference(symmetry,[status(thm)],[20270])).
% 3.44/3.73 tff(22492,plain,
% 3.44/3.73 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22491])).
% 3.44/3.73 tff(22493,plain,
% 3.44/3.73 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22494,plain,
% 3.44/3.73 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22495,plain,
% 3.44/3.73 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22494])).
% 3.44/3.73 tff(22496,plain,
% 3.44/3.73 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(transitivity,[status(thm)],[22495, 22493])).
% 3.44/3.73 tff(22497,plain,
% 3.44/3.73 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.44/3.73 inference(quant_inst,[status(thm)],[])).
% 3.44/3.73 tff(22498,plain,
% 3.44/3.73 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22497, 22496])).
% 3.44/3.73 tff(22499,plain,
% 3.44/3.73 (~r(s(s(s(s(z)))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22498, 333, 11546, 224, 3559])).
% 3.44/3.73 tff(22500,plain,
% 3.44/3.73 (~r(s(elem!1), s(z))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22499, 22492])).
% 3.44/3.73 tff(22501,plain,
% 3.44/3.73 (b(s(elem!1), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[486, 22500, 1])).
% 3.44/3.73 tff(22502,plain,
% 3.44/3.73 (((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22503,plain,
% 3.44/3.73 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22504,plain,
% 3.44/3.73 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22503])).
% 3.44/3.73 tff(22505,plain,
% 3.44/3.73 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.73 inference(transitivity,[status(thm)],[22504, 22502])).
% 3.44/3.73 tff(22506,plain,
% 3.44/3.73 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.44/3.73 inference(quant_inst,[status(thm)],[])).
% 3.44/3.73 tff(22507,plain,
% 3.44/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22506, 22505])).
% 3.44/3.73 tff(22508,plain,
% 3.44/3.73 (~r(s(z), s(s(s(s(z)))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22507, 333, 11546, 224, 3559])).
% 3.44/3.73 tff(22509,plain,
% 3.44/3.73 (~r(s(z), s(elem!1))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22508, 19696])).
% 3.44/3.73 tff(22510,plain,
% 3.44/3.73 (b(s(z), s(elem!1))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1244, 22509, 1229])).
% 3.44/3.73 tff(22511,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1853, 22510, 22501, 490, 585])).
% 3.44/3.73 tff(22512,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22513,plain,
% 3.44/3.73 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22512, 22488, 22476, 1, 3238, 11546, 22490])).
% 3.44/3.73 tff(22514,plain,
% 3.44/3.73 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[9759, 19807])).
% 3.44/3.73 tff(22515,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[525, 22514])).
% 3.44/3.73 tff(22516,plain,(r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22517,plain,
% 3.44/3.73 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22516, 22513, 3238])).
% 3.44/3.73 tff(22518,plain,
% 3.44/3.73 (~r(s(elem!1), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[15098, 22517, 2484, 624, 1722, 22488, 132, 259, 22467, 22466])).
% 3.44/3.73 tff(22519,plain,
% 3.44/3.73 (b(s(elem!1), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[448, 22518, 433])).
% 3.44/3.73 tff(22520,plain,
% 3.44/3.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22519, 20397])).
% 3.44/3.73 tff(22521,plain,
% 3.44/3.73 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[19607])).
% 3.44/3.73 tff(22522,plain,
% 3.44/3.73 (b(z, s(s(s(s(z)))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22488, 22521])).
% 3.44/3.73 tff(22523,plain,
% 3.44/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22524,plain,
% 3.44/3.73 (((~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(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), 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))))))),
% 3.44/3.73 inference(rewrite,[status(thm)],[])).
% 3.44/3.73 tff(22525,plain,
% 3.44/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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)))))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22524])).
% 3.44/3.73 tff(22526,plain,
% 3.44/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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))))))),
% 3.44/3.73 inference(transitivity,[status(thm)],[22525, 22523])).
% 3.44/3.73 tff(22527,plain,
% 3.44/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(z)))))))),
% 3.44/3.73 inference(quant_inst,[status(thm)],[])).
% 3.44/3.73 tff(22528,plain,
% 3.44/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[22527, 22526])).
% 3.44/3.73 tff(22529,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22528, 144, 22476, 284, 56, 22522, 22520])).
% 3.44/3.73 tff(22530,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~(elem!1 = s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22531,plain,
% 3.44/3.73 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22530, 22464, 284, 22454, 22458, 2484, 624, 132, 1, 11546, 323, 2254])).
% 3.44/3.73 tff(22532,plain,
% 3.44/3.73 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[279, 22531])).
% 3.44/3.73 tff(22533,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19046, 333, 323, 11546, 22462, 22532])).
% 3.44/3.73 tff(22534,plain,((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22535,plain,
% 3.44/3.73 (~r(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22534, 323, 11546, 284, 2484, 624, 132, 1, 2254, 863])).
% 3.44/3.73 tff(22536,plain,
% 3.44/3.73 (b(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[406, 22535, 706])).
% 3.44/3.73 tff(22537,plain,
% 3.44/3.73 (~b(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19089, 22536, 11546, 132, 2484, 624])).
% 3.44/3.73 tff(22538,plain,
% 3.44/3.73 (r(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[658, 22537, 71])).
% 3.44/3.73 tff(22539,plain,
% 3.44/3.73 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[21949, 22538, 323, 11546])).
% 3.44/3.73 tff(22540,plain,
% 3.44/3.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[302, 22539])).
% 3.44/3.73 tff(22541,plain,
% 3.44/3.73 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[14405, 22540, 132, 624])).
% 3.44/3.73 tff(22542,plain,
% 3.44/3.73 (~(s(s(s(z))) = elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[609, 22537, 284])).
% 3.44/3.73 tff(22543,plain,
% 3.44/3.73 (~(elem!1 = s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[10997, 22542])).
% 3.44/3.73 tff(22544,plain,
% 3.44/3.73 (r(elem!1, s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1538, 22543, 22452])).
% 3.44/3.73 tff(22545,plain,
% 3.44/3.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[21978, 22544, 2484, 22538])).
% 3.44/3.73 tff(22546,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[279, 22545, 22541])).
% 3.44/3.73 tff(22547,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22548,plain,
% 3.44/3.73 (~r(s(z), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22547, 624, 17789, 22451, 15126, 21154, 15133, 1, 21806])).
% 3.44/3.73 tff(22549,plain,
% 3.44/3.73 (b(s(z), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[348, 22548])).
% 3.44/3.73 tff(22550,plain,
% 3.44/3.73 (~r(z, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19017, 333, 11546, 2484, 51])).
% 3.44/3.73 tff(22551,plain,
% 3.44/3.73 (b(z, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[372, 22550])).
% 3.44/3.73 tff(22552,plain,
% 3.44/3.73 (~b(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[387, 144, 624, 22551, 489])).
% 3.44/3.73 tff(22553,plain,
% 3.44/3.73 (r(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[720, 22552, 713])).
% 3.44/3.73 tff(22554,plain,
% 3.44/3.73 (elem!1 = s(s(s(z)))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1538, 22453, 12397])).
% 3.44/3.73 tff(22555,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22554])).
% 3.44/3.73 tff(22556,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[2484, 22555])).
% 3.44/3.73 tff(22557,plain,
% 3.44/3.73 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22554])).
% 3.44/3.73 tff(22558,plain,
% 3.44/3.73 (r(s(z), s(s(s(z))))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[409, 22557])).
% 3.44/3.73 tff(22559,plain,
% 3.44/3.73 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 3.44/3.73 inference(monotonicity,[status(thm)],[22554])).
% 3.44/3.73 tff(22560,plain,
% 3.44/3.73 (r(s(s(s(z))), s(z))),
% 3.44/3.73 inference(modus_ponens,[status(thm)],[722, 22559])).
% 3.44/3.73 tff(22561,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[15517, 333, 22560, 22558, 11546, 22556])).
% 3.44/3.73 tff(22562,plain,((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22563,plain,
% 3.44/3.73 (~r(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22562, 22553, 2484, 11546, 12397])).
% 3.44/3.73 tff(22564,plain,
% 3.44/3.73 (b(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[406, 22563, 706])).
% 3.44/3.73 tff(22565,plain,
% 3.44/3.73 (~b(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19089, 22564, 11546, 132, 2484, 624])).
% 3.44/3.73 tff(22566,plain,
% 3.44/3.73 (r(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[658, 22565, 74])).
% 3.44/3.73 tff(22567,plain,
% 3.44/3.73 (~r(elem!1, s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[21978, 22566, 2484, 51])).
% 3.44/3.73 tff(22568,plain,
% 3.44/3.73 (~(s(s(s(z))) = elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[609, 22565, 284])).
% 3.44/3.73 tff(22569,plain,
% 3.44/3.73 (~(elem!1 = s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[10997, 22568])).
% 3.44/3.73 tff(22570,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1538, 22569, 22567, 12397])).
% 3.44/3.73 tff(22571,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(z))))) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22572,plain,
% 3.44/3.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22571, 21815, 22451, 21154, 71, 15126, 17789, 624, 15133, 22549])).
% 3.44/3.73 tff(22573,plain,
% 3.44/3.73 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[279, 22572])).
% 3.44/3.73 tff(22574,plain,
% 3.44/3.73 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[16228, 22573, 21154, 21806])).
% 3.44/3.73 tff(22575,plain,
% 3.44/3.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[249, 22574])).
% 3.44/3.73 tff(22576,plain,
% 3.44/3.73 (~b(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19178, 22573, 624, 22549, 17789])).
% 3.44/3.73 tff(22577,plain,
% 3.44/3.73 (r(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[720, 22576, 15134])).
% 3.44/3.73 tff(22578,plain,
% 3.44/3.73 (~r(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22562, 22577, 22451, 15126, 21815])).
% 3.44/3.73 tff(22579,plain,
% 3.44/3.73 (b(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[406, 22578, 15133])).
% 3.44/3.73 tff(22580,plain,
% 3.44/3.73 (~b(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19089, 22579, 15126, 17789, 22451, 624])).
% 3.44/3.73 tff(22581,plain,
% 3.44/3.73 (r(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[658, 22580, 71])).
% 3.44/3.73 tff(22582,plain,
% 3.44/3.73 (~r(z, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[19182, 22581, 15126, 22451, 624, 17789, 15134, 22549])).
% 3.44/3.73 tff(22583,plain,
% 3.44/3.73 (b(z, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[372, 22582])).
% 3.44/3.73 tff(22584,plain,
% 3.44/3.73 (~(s(s(s(z))) = elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[609, 22580, 21154])).
% 3.44/3.73 tff(22585,plain,
% 3.44/3.73 (~r(s(s(s(z))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22447, 22581, 15126, 15133, 17789, 21806, 21154, 77, 17787, 22573, 22584, 3])).
% 3.44/3.73 tff(22586,plain,
% 3.44/3.73 (b(s(s(s(z))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[2794, 22585])).
% 3.44/3.73 tff(22587,plain,
% 3.44/3.73 (~b(s(s(s(z))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[2273, 22586, 22549, 22583])).
% 3.44/3.73 tff(22588,plain,
% 3.44/3.73 (r(s(s(s(z))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[396, 22587])).
% 3.44/3.73 tff(22589,plain,
% 3.44/3.73 (~(elem!1 = s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[10997, 22584])).
% 3.44/3.73 tff(22590,plain,
% 3.44/3.73 (r(elem!1, s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[1538, 22589, 21815])).
% 3.44/3.73 tff(22591,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[21803, 333, 22590, 22588, 22451, 22575])).
% 3.44/3.73 tff(22592,plain,((~b(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22593,plain,
% 3.44/3.73 (~b(elem!1, z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22592, 1, 3])).
% 3.44/3.73 tff(22594,plain,
% 3.44/3.73 (r(elem!1, z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[653, 22593, 77])).
% 3.44/3.73 tff(22595,plain,
% 3.44/3.73 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[14348, 354, 22451, 22594])).
% 3.44/3.73 tff(22596,plain,
% 3.44/3.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[302, 22595])).
% 3.44/3.73 tff(22597,plain,
% 3.44/3.73 (~r(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[20609, 354, 22594, 15126])).
% 3.44/3.73 tff(22598,plain,
% 3.44/3.73 (b(elem!1, s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[720, 22597, 15134])).
% 3.44/3.73 tff(22599,plain,
% 3.44/3.73 (~r(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[20599, 22594, 15126, 22451])).
% 3.44/3.73 tff(22600,plain,
% 3.44/3.73 (b(s(z), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[406, 22599, 15133])).
% 3.44/3.73 tff(22601,plain,
% 3.44/3.73 (~b(s(s(s(z))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[14036, 144, 21806, 22596, 259])).
% 3.44/3.73 tff(22602,plain,
% 3.44/3.73 (r(s(s(s(z))), z)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[396, 22601])).
% 3.44/3.73 tff(22603,plain,
% 3.44/3.73 (~r(elem!1, s(s(s(z))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[20649, 333, 354, 22594, 22602])).
% 3.44/3.73 tff(22604,plain,
% 3.44/3.73 (~r(s(s(s(z))), elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[2122, 22602, 22594, 354])).
% 3.44/3.73 tff(22605,plain,
% 3.44/3.73 (~r(s(s(s(z))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22447, 8715, 11546, 17796, 132, 2254, 284, 730, 114, 259, 21754, 3])).
% 3.44/3.73 tff(22606,plain,
% 3.44/3.73 (b(s(s(s(z))), s(z))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[2794, 22605])).
% 3.44/3.73 tff(22607,plain,
% 3.44/3.73 ($false),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[4375, 22606, 21755, 305, 134])).
% 3.44/3.73 tff(22608,plain,(b(z, elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | r(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.73 tff(22609,plain,
% 3.44/3.73 (b(z, elem!1)),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[22608, 22604, 22600, 22598, 15126, 17789, 21806, 21154, 17787, 259, 3, 71])).
% 3.44/3.73 tff(22610,plain,
% 3.44/3.73 (s(s(s(z))) = elem!1),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[21799, 22609, 21154, 22604, 22603])).
% 3.44/3.73 tff(22611,plain,
% 3.44/3.73 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.73 inference(unit_resolution,[status(thm)],[12214, 22610])).
% 3.44/3.74 tff(22612,plain,
% 3.44/3.74 (~b(s(elem!1), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[20903, 22611, 22451, 22600, 22598, 1, 15126, 22593, 22596, 259])).
% 3.44/3.74 tff(22613,plain,
% 3.44/3.74 (r(s(elem!1), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[507, 22612])).
% 3.44/3.74 tff(22614,plain,
% 3.44/3.74 (~(s(s(elem!1)) = elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[7595, 22610, 19208])).
% 3.44/3.74 tff(22615,plain,
% 3.44/3.74 (~(elem!1 = s(s(elem!1)))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[5603, 22614])).
% 3.44/3.74 tff(22616,plain,
% 3.44/3.74 (~(s(elem!1) = elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[5813, 22615])).
% 3.44/3.74 tff(22617,plain,
% 3.44/3.74 (~r(s(elem!1), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[1610, 333, 354, 22594, 22613])).
% 3.44/3.74 tff(22618,plain,
% 3.44/3.74 (b(s(elem!1), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[448, 22617, 22616])).
% 3.44/3.74 tff(22619,plain,
% 3.44/3.74 (~b(s(elem!1), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[4344, 144, 22618, 22600, 22598])).
% 3.44/3.74 tff(22620,plain,
% 3.44/3.74 (r(s(elem!1), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[486, 22619, 1])).
% 3.44/3.74 tff(22621,plain,
% 3.44/3.74 (((~![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(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), 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(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.74 inference(rewrite,[status(thm)],[])).
% 3.44/3.74 tff(22622,plain,
% 3.44/3.74 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.74 inference(rewrite,[status(thm)],[])).
% 3.44/3.74 tff(22623,plain,
% 3.44/3.74 (((~![X0: $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(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), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22622])).
% 3.44/3.74 tff(22624,plain,
% 3.44/3.74 (((~![X0: $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(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), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.74 inference(transitivity,[status(thm)],[22623, 22621])).
% 3.44/3.74 tff(22625,plain,
% 3.44/3.74 ((~![X0: $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(z))))))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 3.44/3.74 inference(quant_inst,[status(thm)],[])).
% 3.44/3.74 tff(22626,plain,
% 3.44/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[22625, 22624])).
% 3.44/3.74 tff(22627,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22626, 333, 354, 22620, 22613, 15126])).
% 3.44/3.74 tff(22628,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22629,plain,
% 3.44/3.74 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22628, 354, 1, 3])).
% 3.44/3.74 tff(22630,plain,
% 3.44/3.74 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[279, 22629])).
% 3.44/3.74 tff(22631,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[19017, 333, 354, 15126, 22451, 22630])).
% 3.44/3.74 tff(22632,plain,((~r(z, s(z))) | (s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22633,plain,
% 3.44/3.74 (~r(z, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22632, 1, 3])).
% 3.44/3.74 tff(22634,plain,
% 3.44/3.74 (b(z, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[372, 22633])).
% 3.44/3.74 tff(22635,plain,
% 3.44/3.74 (~r(z, elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2938, 51, 2484, 408])).
% 3.44/3.74 tff(22636,plain,
% 3.44/3.74 (b(z, elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[658, 22635, 71])).
% 3.44/3.74 tff(22637,plain,
% 3.44/3.74 (~b(elem!1, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[7079, 22636, 134, 490])).
% 3.44/3.74 tff(22638,plain,
% 3.44/3.74 (r(elem!1, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[720, 22637, 714])).
% 3.44/3.74 tff(22639,plain,
% 3.44/3.74 (~r(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[19075, 333, 11546, 2484, 51])).
% 3.44/3.74 tff(22640,plain,
% 3.44/3.74 (b(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[348, 22639])).
% 3.44/3.74 tff(22641,plain,
% 3.44/3.74 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[20761, 22640, 2484, 408, 132, 134, 11546, 490, 1, 22636])).
% 3.44/3.74 tff(22642,plain,
% 3.44/3.74 (~(s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[12214, 22641])).
% 3.44/3.74 tff(22643,plain,
% 3.44/3.74 (~(elem!1 = s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[10997, 22642])).
% 3.44/3.74 tff(22644,plain,
% 3.44/3.74 (~b(elem!1, s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2090, 22636, 284, 490, 134])).
% 3.44/3.74 tff(22645,plain,
% 3.44/3.74 (b(s(s(s(z))), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22309, 22642, 408, 284, 51, 22638, 22640, 22644])).
% 3.44/3.74 tff(22646,plain,
% 3.44/3.74 (~r(s(s(s(z))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[10812, 22645, 284, 22640, 134, 22636, 490, 22643, 22638])).
% 3.44/3.74 tff(22647,plain,
% 3.44/3.74 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[20641, 144, 22636, 132, 2254])).
% 3.44/3.74 tff(22648,plain,
% 3.44/3.74 (~b(s(s(s(z))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22647, 22645])).
% 3.44/3.74 tff(22649,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[396, 22648, 22646])).
% 3.44/3.74 tff(22650,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22651,plain,
% 3.44/3.74 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22650, 17789, 21806, 21154, 22600, 22634, 22594, 22451, 15126, 1, 15134])).
% 3.44/3.74 tff(22652,plain,
% 3.44/3.74 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[279, 22651])).
% 3.44/3.74 tff(22653,plain,
% 3.44/3.74 (~b(z, elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[14578, 22652, 17789, 22600, 22634])).
% 3.44/3.74 tff(22654,plain,
% 3.44/3.74 (r(z, elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[658, 22653, 71])).
% 3.44/3.74 tff(22655,plain,
% 3.44/3.74 (~(s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[609, 22653, 21154])).
% 3.44/3.74 tff(22656,plain,
% 3.44/3.74 (~r(s(s(s(z))), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22447, 22654, 15126, 15133, 17789, 21806, 21154, 77, 17787, 22652, 22655, 3])).
% 3.44/3.74 tff(22657,plain,
% 3.44/3.74 (b(s(s(s(z))), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2794, 22656])).
% 3.44/3.74 tff(22658,plain,
% 3.44/3.74 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[17864, 144, 22600, 17789, 21806])).
% 3.44/3.74 tff(22659,plain,
% 3.44/3.74 (~b(s(s(s(z))), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22658, 22657])).
% 3.44/3.74 tff(22660,plain,
% 3.44/3.74 (r(s(s(s(z))), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[704, 22659, 22655])).
% 3.44/3.74 tff(22661,plain,
% 3.44/3.74 (~r(s(s(s(z))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2079, 22660, 22594, 22654])).
% 3.44/3.74 tff(22662,plain,
% 3.44/3.74 (b(s(s(s(z))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[396, 22661])).
% 3.44/3.74 tff(22663,plain,
% 3.44/3.74 (~b(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2273, 22662, 22657, 22634])).
% 3.44/3.74 tff(22664,plain,
% 3.44/3.74 (r(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[348, 22663])).
% 3.44/3.74 tff(22665,plain,
% 3.44/3.74 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[21949, 22664, 22654, 15126])).
% 3.44/3.74 tff(22666,plain,
% 3.44/3.74 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[302, 22665])).
% 3.44/3.74 tff(22667,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[14138, 144, 22662, 21806, 22666, 22652])).
% 3.44/3.74 tff(22668,plain,((s(elem!1) = s(z)) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22669,plain,
% 3.44/3.74 (s(elem!1) = s(z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22668, 3])).
% 3.44/3.74 tff(22670,plain,
% 3.44/3.74 (z = elem!1),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[8683, 22669])).
% 3.44/3.74 tff(22671,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22670])).
% 3.44/3.74 tff(22672,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.44/3.74 inference(transitivity,[status(thm)],[22671, 2])).
% 3.44/3.74 tff(22673,plain,
% 3.44/3.74 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22672])).
% 3.44/3.74 tff(22674,plain,
% 3.44/3.74 (~(elem!1 = s(s(s(z))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[392, 22673])).
% 3.44/3.74 tff(22675,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(transitivity,[status(thm)],[22672, 4795])).
% 3.44/3.74 tff(22676,plain,
% 3.44/3.74 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22675])).
% 3.44/3.74 tff(22677,plain,
% 3.44/3.74 (~(s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[392, 22676])).
% 3.44/3.74 tff(22678,plain,
% 3.44/3.74 (b(s(s(s(z))), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2794, 2788])).
% 3.44/3.74 tff(22679,plain,
% 3.44/3.74 (elem!1 = z),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[18287, 22670])).
% 3.44/3.74 tff(22680,plain,
% 3.44/3.74 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[14770, 22679, 2545])).
% 3.44/3.74 tff(22681,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[302, 22680])).
% 3.44/3.74 tff(22682,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[66])).
% 3.44/3.74 tff(22683,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(symmetry,[status(thm)],[22682])).
% 3.44/3.74 tff(22684,plain,
% 3.44/3.74 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22683])).
% 3.44/3.74 tff(22685,plain,
% 3.44/3.74 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[54, 22684])).
% 3.44/3.74 tff(22686,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[321, 22685])).
% 3.44/3.74 tff(22687,plain,((~(z = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22688,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22687, 22681, 22670])).
% 3.44/3.74 tff(22689,plain,
% 3.44/3.74 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22669])).
% 3.44/3.74 tff(22690,plain,
% 3.44/3.74 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22669])).
% 3.44/3.74 tff(22691,plain,
% 3.44/3.74 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 3.44/3.74 inference(transitivity,[status(thm)],[22690, 52])).
% 3.44/3.74 tff(22692,plain,
% 3.44/3.74 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22691])).
% 3.44/3.74 tff(22693,plain,
% 3.44/3.74 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22692])).
% 3.44/3.74 tff(22694,plain,
% 3.44/3.74 (~(s(z) = elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[15132, 3, 11546])).
% 3.44/3.74 tff(22695,plain,
% 3.44/3.74 (~(elem!1 = s(elem!1))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[22694, 22693])).
% 3.44/3.74 tff(22696,plain,
% 3.44/3.74 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22669])).
% 3.44/3.74 tff(22697,plain,
% 3.44/3.74 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22696])).
% 3.44/3.74 tff(22698,plain,
% 3.44/3.74 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[11546, 22697])).
% 3.44/3.74 tff(22699,plain,
% 3.44/3.74 (~(elem!1 = s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[712, 22694])).
% 3.44/3.74 tff(22700,plain,
% 3.44/3.74 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[12011, 22688])).
% 3.44/3.74 tff(22701,plain,
% 3.44/3.74 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[121, 22700, 3])).
% 3.44/3.74 tff(22702,plain,
% 3.44/3.74 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.74 tff(22703,plain,
% 3.44/3.74 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.44/3.74 inference(transitivity,[status(thm)],[22702, 1218])).
% 3.44/3.74 tff(22704,plain,
% 3.44/3.74 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22703])).
% 3.44/3.74 tff(22705,plain,
% 3.44/3.74 (~(elem!1 = s(s(elem!1)))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[1094, 22704])).
% 3.44/3.74 tff(22706,plain,
% 3.44/3.74 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18019, 18125])).
% 3.44/3.74 tff(22707,plain,
% 3.44/3.74 (elem!1 = z),
% 3.44/3.74 inference(symmetry,[status(thm)],[18019])).
% 3.44/3.74 tff(22708,plain,
% 3.44/3.74 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22707])).
% 3.44/3.74 tff(22709,plain,
% 3.44/3.74 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.44/3.74 inference(transitivity,[status(thm)],[22708, 22706])).
% 3.44/3.74 tff(22710,plain,
% 3.44/3.74 ((~r(elem!1, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22709])).
% 3.44/3.74 tff(22711,plain,
% 3.44/3.74 (elem!1 = z),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[18287, 18019])).
% 3.44/3.74 tff(22712,plain,
% 3.44/3.74 (b(s(z), elem!1) <=> b(s(z), z)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[72])).
% 3.44/3.74 tff(22713,plain,
% 3.44/3.74 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.44/3.74 inference(symmetry,[status(thm)],[22712])).
% 3.44/3.74 tff(22714,plain,
% 3.44/3.74 (b(s(z), elem!1)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[489, 22713])).
% 3.44/3.74 tff(22715,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[350, 22714])).
% 3.44/3.74 tff(22716,plain,((~(elem!1 = z)) | b(s(z), elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22717,plain,
% 3.44/3.74 (~b(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22716, 350, 22711])).
% 3.44/3.74 tff(22718,plain,
% 3.44/3.74 (r(s(z), z)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[348, 22717])).
% 3.44/3.74 tff(22719,plain,
% 3.44/3.74 (~r(z, s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[19065, 22718, 11546, 321])).
% 3.44/3.74 tff(22720,plain,
% 3.44/3.74 (b(z, s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[619, 22719])).
% 3.44/3.74 tff(22721,plain,
% 3.44/3.74 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[21591, 22720, 11546, 321])).
% 3.44/3.74 tff(22722,plain,
% 3.44/3.74 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[1137, 22721])).
% 3.44/3.74 tff(22723,plain,
% 3.44/3.74 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.74 tff(22724,plain,
% 3.44/3.74 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22723])).
% 3.44/3.74 tff(22725,plain,
% 3.44/3.74 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[132, 22724])).
% 3.44/3.74 tff(22726,plain,
% 3.44/3.74 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.74 tff(22727,plain,
% 3.44/3.74 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22726])).
% 3.44/3.74 tff(22728,plain,
% 3.44/3.74 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[11546, 22727])).
% 3.44/3.74 tff(22729,plain,
% 3.44/3.74 (r(s(elem!1), z) <=> r(s(z), z)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.74 tff(22730,plain,
% 3.44/3.74 (r(s(z), z) <=> r(s(elem!1), z)),
% 3.44/3.74 inference(symmetry,[status(thm)],[22729])).
% 3.44/3.74 tff(22731,plain,
% 3.44/3.74 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.74 tff(22732,plain,
% 3.44/3.74 (r(s(z), elem!1) <=> r(s(z), z)),
% 3.44/3.74 inference(symmetry,[status(thm)],[22731])).
% 3.44/3.74 tff(22733,plain,
% 3.44/3.74 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 3.44/3.74 inference(transitivity,[status(thm)],[22732, 22730])).
% 3.44/3.74 tff(22734,plain,
% 3.44/3.74 (r(s(elem!1), z)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[2169, 22733])).
% 3.44/3.74 tff(22735,plain,
% 3.44/3.74 (~r(z, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[14540, 22734, 321, 22728])).
% 3.44/3.74 tff(22736,plain,
% 3.44/3.74 (b(z, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[372, 22735])).
% 3.44/3.74 tff(22737,plain,
% 3.44/3.74 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22484, 22736, 22725, 22722, 22720])).
% 3.44/3.74 tff(22738,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[319, 22737])).
% 3.44/3.74 tff(22739,plain,
% 3.44/3.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22687, 321, 18019])).
% 3.44/3.74 tff(22740,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 3.44/3.74 tff(22741,plain,
% 3.44/3.74 ($false),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[18930, 333, 409, 2484, 322, 22740])).
% 3.44/3.74 tff(22742,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.74 tff(22743,plain,
% 3.44/3.74 (~r(elem!1, s(s(z)))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[22742, 2169, 22739, 22738])).
% 3.44/3.74 tff(22744,plain,
% 3.44/3.74 (~r(elem!1, s(s(elem!1)))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[22743, 22710])).
% 3.44/3.74 tff(22745,plain,
% 3.44/3.74 (b(elem!1, s(s(elem!1)))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[2522, 22744, 22705])).
% 3.44/3.74 tff(22746,plain,
% 3.44/3.74 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.74 tff(22747,plain,
% 3.44/3.74 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 3.44/3.74 inference(transitivity,[status(thm)],[22746, 52])).
% 3.44/3.74 tff(22748,plain,
% 3.44/3.74 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22747])).
% 3.44/3.74 tff(22749,plain,
% 3.44/3.74 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22748])).
% 3.44/3.74 tff(22750,plain,
% 3.44/3.74 (~(elem!1 = s(elem!1))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[706, 22749])).
% 3.44/3.74 tff(22751,plain,
% 3.44/3.74 (r(s(elem!1), elem!1)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[2169, 18035])).
% 3.44/3.74 tff(22752,plain,
% 3.44/3.74 (~r(elem!1, s(elem!1))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[12698, 22751, 22739, 22728])).
% 3.44/3.74 tff(22753,plain,
% 3.44/3.74 (b(elem!1, s(elem!1))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[560, 22752, 22750])).
% 3.44/3.74 tff(22754,plain,
% 3.44/3.74 (~r(elem!1, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[12172, 22738, 22739, 2169])).
% 3.44/3.74 tff(22755,plain,
% 3.44/3.74 (b(elem!1, s(z))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[720, 22754, 713])).
% 3.44/3.74 tff(22756,plain,
% 3.44/3.74 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.74 tff(22757,plain,
% 3.44/3.74 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.44/3.74 inference(symmetry,[status(thm)],[22756])).
% 3.44/3.74 tff(22758,plain,
% 3.44/3.74 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22757])).
% 3.44/3.74 tff(22759,plain,
% 3.44/3.74 (~(s(s(elem!1)) = s(elem!1))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[107, 22758])).
% 3.44/3.74 tff(22760,plain,
% 3.44/3.74 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18101])).
% 3.44/3.74 tff(22761,plain,
% 3.44/3.74 (b(elem!1, s(s(z)))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[22745, 22760])).
% 3.44/3.74 tff(22762,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.74 tff(22763,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.44/3.74 inference(transitivity,[status(thm)],[22762, 2])).
% 3.44/3.74 tff(22764,plain,
% 3.44/3.74 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(transitivity,[status(thm)],[22763, 4795])).
% 3.44/3.74 tff(22765,plain,
% 3.44/3.74 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22764])).
% 3.44/3.74 tff(22766,plain,
% 3.44/3.74 (~(s(s(s(z))) = elem!1)),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[392, 22765])).
% 3.44/3.74 tff(22767,plain,
% 3.44/3.74 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.44/3.74 inference(monotonicity,[status(thm)],[22763])).
% 3.44/3.74 tff(22768,plain,
% 3.44/3.74 (~(elem!1 = s(s(s(z))))),
% 3.44/3.74 inference(modus_ponens,[status(thm)],[392, 22767])).
% 3.44/3.74 tff(22769,plain,
% 3.44/3.74 (~r(elem!1, s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[17853, 2169, 22739, 11546])).
% 3.44/3.74 tff(22770,plain,
% 3.44/3.74 (b(elem!1, s(s(s(z))))),
% 3.44/3.74 inference(unit_resolution,[status(thm)],[1538, 22769, 22768])).
% 3.44/3.75 tff(22771,plain,
% 3.44/3.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[18960, 22722, 132, 22770])).
% 3.44/3.75 tff(22772,plain,
% 3.44/3.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[249, 22771])).
% 3.44/3.75 tff(22773,plain,
% 3.44/3.75 (~r(s(s(s(z))), s(z))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[20837, 22738, 22772, 22718])).
% 3.44/3.75 tff(22774,plain,
% 3.44/3.75 (b(s(s(s(z))), s(z))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[2794, 22773])).
% 3.44/3.75 tff(22775,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[18973, 144, 2082, 305, 56, 838])).
% 3.44/3.75 tff(22776,plain,((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22777,plain,
% 3.44/3.75 (~b(s(z), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22776, 22774, 22770, 22755])).
% 3.44/3.75 tff(22778,plain,
% 3.44/3.75 (r(s(z), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[172, 22777])).
% 3.44/3.75 tff(22779,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22388, 333, 707, 353, 224, 322])).
% 3.44/3.75 tff(22780,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22781,plain,
% 3.44/3.75 (~r(s(s(s(z))), elem!1)),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22780, 22778, 22772, 22738])).
% 3.44/3.75 tff(22782,plain,
% 3.44/3.75 (b(s(s(s(z))), elem!1)),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[704, 22781, 22766])).
% 3.44/3.75 tff(22783,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 3.44/3.75 tff(22784,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 3.44/3.75 tff(22785,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22786,plain,
% 3.44/3.75 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22787,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22786])).
% 3.44/3.75 tff(22788,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(transitivity,[status(thm)],[22787, 22785])).
% 3.44/3.75 tff(22789,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 3.44/3.75 inference(quant_inst,[status(thm)],[])).
% 3.44/3.75 tff(22790,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22789, 22788])).
% 3.44/3.75 tff(22791,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22790, 144, 305, 1398, 132, 22783, 22784])).
% 3.44/3.75 tff(22792,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22793,plain,
% 3.44/3.75 (~b(s(z), s(s(z)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22792, 1398, 305, 132, 22783])).
% 3.44/3.75 tff(22794,plain,
% 3.44/3.75 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[18125])).
% 3.44/3.75 tff(22795,plain,
% 3.44/3.75 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.44/3.75 inference(symmetry,[status(thm)],[22794])).
% 3.44/3.75 tff(22796,plain,
% 3.44/3.75 (b(s(z), s(s(z)))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[5486, 22795])).
% 3.44/3.75 tff(22797,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 3.44/3.75 tff(22798,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22797, 22796])).
% 3.44/3.75 tff(22799,plain,(b(s(z), s(s(z))) | (~b(s(z), s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22800,plain,
% 3.44/3.75 (~b(s(z), s(s(elem!1)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22799, 22793, 8677])).
% 3.44/3.75 tff(22801,plain,
% 3.44/3.75 (r(s(z), s(s(elem!1)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[5484, 22800])).
% 3.44/3.75 tff(22802,plain,
% 3.44/3.75 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[18125])).
% 3.44/3.75 tff(22803,plain,
% 3.44/3.75 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 3.44/3.75 inference(symmetry,[status(thm)],[22802])).
% 3.44/3.75 tff(22804,plain,
% 3.44/3.75 (r(s(z), s(s(z)))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[5724, 22803])).
% 3.44/3.75 tff(22805,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 3.44/3.75 tff(22806,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22805, 22804])).
% 3.44/3.75 tff(22807,plain,(r(s(z), s(s(z))) | (~r(s(z), s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22808,plain,
% 3.44/3.75 (r(s(z), s(s(z)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22807, 22801, 8677])).
% 3.44/3.75 tff(22809,plain,
% 3.44/3.75 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[18101])).
% 3.44/3.75 tff(22810,plain,
% 3.44/3.75 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[18101])).
% 3.44/3.75 tff(22811,plain,
% 3.44/3.75 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.44/3.75 inference(symmetry,[status(thm)],[22810])).
% 3.44/3.75 tff(22812,plain,
% 3.44/3.75 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22811])).
% 3.44/3.75 tff(22813,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22814,plain,
% 3.44/3.75 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22815,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22814])).
% 3.44/3.75 tff(22816,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(transitivity,[status(thm)],[22815, 22813])).
% 3.44/3.75 tff(22817,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 3.44/3.75 inference(quant_inst,[status(thm)],[])).
% 3.44/3.75 tff(22818,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22817, 22816])).
% 3.44/3.75 tff(22819,plain,
% 3.44/3.75 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22818, 144, 1398, 2254, 4367, 22783])).
% 3.44/3.75 tff(22820,plain,
% 3.44/3.75 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22819, 22812])).
% 3.44/3.75 tff(22821,plain,
% 3.44/3.75 (r(s(s(s(z))), s(s(elem!1)))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[1301, 22820, 1184])).
% 3.44/3.75 tff(22822,plain,
% 3.44/3.75 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22821, 22809])).
% 3.44/3.75 tff(22823,plain,
% 3.44/3.75 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[18101, 18102])).
% 3.44/3.75 tff(22824,plain,
% 3.44/3.75 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.44/3.75 inference(symmetry,[status(thm)],[22823])).
% 3.44/3.75 tff(22825,plain,
% 3.44/3.75 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22824])).
% 3.44/3.75 tff(22826,plain,
% 3.44/3.75 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[217, 22825])).
% 3.44/3.75 tff(22827,plain,
% 3.44/3.75 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22707])).
% 3.44/3.75 tff(22828,plain,
% 3.44/3.75 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.44/3.75 inference(symmetry,[status(thm)],[22827])).
% 3.44/3.75 tff(22829,plain,
% 3.44/3.75 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22828])).
% 3.44/3.75 tff(22830,plain,
% 3.44/3.75 (~(s(s(z)) = elem!1)),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[164, 22829])).
% 3.44/3.75 tff(22831,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 3.44/3.75 tff(22832,plain,
% 3.44/3.75 (((~![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(s(s(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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22833,plain,
% 3.44/3.75 (((~r(s(s(z)), elem!1)) | (~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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22834,plain,
% 3.44/3.75 (((~![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))), 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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22833])).
% 3.44/3.75 tff(22835,plain,
% 3.44/3.75 (((~![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))), 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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.44/3.75 inference(transitivity,[status(thm)],[22834, 22832])).
% 3.44/3.75 tff(22836,plain,
% 3.44/3.75 ((~![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))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.44/3.75 inference(quant_inst,[status(thm)],[])).
% 3.44/3.75 tff(22837,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22836, 22835])).
% 3.44/3.75 tff(22838,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22837, 333, 353, 7155, 19432, 22831])).
% 3.44/3.75 tff(22839,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.75 tff(22840,plain,
% 3.44/3.75 (~r(s(s(z)), elem!1)),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22839, 22808, 353, 22822])).
% 3.44/3.75 tff(22841,plain,
% 3.44/3.75 (b(s(s(z)), elem!1)),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[7970, 22840, 22830])).
% 3.44/3.75 tff(22842,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22843,plain,
% 3.44/3.75 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22844,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22843])).
% 3.44/3.75 tff(22845,plain,
% 3.44/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.75 inference(transitivity,[status(thm)],[22844, 22842])).
% 3.44/3.75 tff(22846,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.44/3.75 inference(quant_inst,[status(thm)],[])).
% 3.44/3.75 tff(22847,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22846, 22845])).
% 3.44/3.75 tff(22848,plain,
% 3.44/3.75 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22847, 144, 1398, 132, 4367])).
% 3.44/3.75 tff(22849,plain,
% 3.44/3.75 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22848, 22841])).
% 3.44/3.75 tff(22850,plain,
% 3.44/3.75 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[18122, 22849, 8677])).
% 3.44/3.75 tff(22851,plain,
% 3.44/3.75 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[4311, 22850, 22826])).
% 3.44/3.75 tff(22852,plain,
% 3.44/3.75 (r(s(s(z)), s(s(s(z))))),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[18132, 22851, 8677])).
% 3.44/3.75 tff(22853,plain,
% 3.44/3.75 (((~![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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22854,plain,
% 3.44/3.75 (((~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(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.75 inference(rewrite,[status(thm)],[])).
% 3.44/3.75 tff(22855,plain,
% 3.44/3.75 (((~![X0: $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(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.44/3.75 inference(monotonicity,[status(thm)],[22854])).
% 3.44/3.75 tff(22856,plain,
% 3.44/3.75 (((~![X0: $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(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.75 inference(transitivity,[status(thm)],[22855, 22853])).
% 3.44/3.75 tff(22857,plain,
% 3.44/3.75 ((~![X0: $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))))))),
% 3.44/3.75 inference(quant_inst,[status(thm)],[])).
% 3.44/3.75 tff(22858,plain,
% 3.44/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.44/3.75 inference(modus_ponens,[status(thm)],[22857, 22856])).
% 3.44/3.75 tff(22859,plain,
% 3.44/3.75 ($false),
% 3.44/3.75 inference(unit_resolution,[status(thm)],[22858, 333, 353, 22852, 22822, 22808])).
% 3.44/3.75 tff(22860,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22861,plain,
% 3.44/3.76 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22860, 22778, 8677, 132, 22782, 22755, 22761, 863, 22722])).
% 3.44/3.76 tff(22862,plain,
% 3.44/3.76 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[1451, 22861])).
% 3.44/3.76 tff(22863,plain,
% 3.44/3.76 (~r(s(s(z)), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[21056, 22862, 22739, 11546])).
% 3.44/3.76 tff(22864,plain,
% 3.44/3.76 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[18125])).
% 3.44/3.76 tff(22865,plain,
% 3.44/3.76 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 3.44/3.76 inference(symmetry,[status(thm)],[22864])).
% 3.44/3.76 tff(22866,plain,
% 3.44/3.76 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.76 tff(22867,plain,
% 3.44/3.76 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 3.44/3.76 inference(transitivity,[status(thm)],[22866, 22865])).
% 3.44/3.76 tff(22868,plain,
% 3.44/3.76 (r(s(s(z)), s(z))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[2737, 22867])).
% 3.44/3.76 tff(22869,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 3.44/3.76 tff(22870,plain,
% 3.44/3.76 ($false),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22869, 22868])).
% 3.44/3.76 tff(22871,plain,((~r(s(s(elem!1)), s(elem!1))) | r(s(s(z)), s(z)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22872,plain,
% 3.44/3.76 (~r(s(s(elem!1)), s(elem!1))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22871, 22863, 8677])).
% 3.44/3.76 tff(22873,plain,
% 3.44/3.76 (b(s(s(elem!1)), s(elem!1))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[1283, 22872, 22759])).
% 3.44/3.76 tff(22874,plain,
% 3.44/3.76 (~b(s(z), s(s(elem!1)))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[5494, 22873, 22755, 22753, 22745])).
% 3.44/3.76 tff(22875,plain,
% 3.44/3.76 (r(s(z), s(s(elem!1)))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[5484, 22874])).
% 3.44/3.76 tff(22876,plain,
% 3.44/3.76 (r(s(z), s(s(z)))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22807, 22875, 8677])).
% 3.44/3.76 tff(22877,plain,
% 3.44/3.76 (((~![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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22878,plain,
% 3.44/3.76 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22879,plain,
% 3.44/3.76 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[22878])).
% 3.44/3.76 tff(22880,plain,
% 3.44/3.76 (((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(transitivity,[status(thm)],[22879, 22877])).
% 3.44/3.76 tff(22881,plain,
% 3.44/3.76 ((~![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(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 3.44/3.76 inference(quant_inst,[status(thm)],[])).
% 3.44/3.76 tff(22882,plain,
% 3.44/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[22881, 22880])).
% 3.44/3.76 tff(22883,plain,
% 3.44/3.76 ($false),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22882, 333, 22862, 11546, 22739, 22876])).
% 3.44/3.76 tff(22884,plain,(b(s(z), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22885,plain,
% 3.44/3.76 (b(s(z), elem!1)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22884, 22669, 11546, 22701, 22681, 22694])).
% 3.44/3.76 tff(22886,plain,
% 3.44/3.76 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22687, 321, 66])).
% 3.44/3.76 tff(22887,plain,
% 3.44/3.76 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.76 inference(monotonicity,[status(thm)],[66])).
% 3.44/3.76 tff(22888,plain,
% 3.44/3.76 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.44/3.76 inference(transitivity,[status(thm)],[22887, 2])).
% 3.44/3.76 tff(22889,plain,
% 3.44/3.76 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.44/3.76 inference(transitivity,[status(thm)],[22888, 4795])).
% 3.44/3.76 tff(22890,plain,
% 3.44/3.76 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[22889])).
% 3.44/3.76 tff(22891,plain,
% 3.44/3.76 (~(s(s(s(z))) = elem!1)),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[392, 22890])).
% 3.44/3.76 tff(22892,plain,
% 3.44/3.76 (~b(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[846, 12179, 304, 838])).
% 3.44/3.76 tff(22893,plain,
% 3.44/3.76 (r(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[2794, 22892])).
% 3.44/3.76 tff(22894,plain,
% 3.44/3.76 (((~![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(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22895,plain,
% 3.44/3.76 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22896,plain,
% 3.44/3.76 (((~![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(s(s(s(s(s(z))))))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[22895])).
% 3.44/3.76 tff(22897,plain,
% 3.44/3.76 (((~![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(s(s(s(s(s(z))))))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(transitivity,[status(thm)],[22896, 22894])).
% 3.44/3.76 tff(22898,plain,
% 3.44/3.76 ((~![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(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 3.44/3.76 inference(quant_inst,[status(thm)],[])).
% 3.44/3.76 tff(22899,plain,
% 3.44/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[22898, 22897])).
% 3.44/3.76 tff(22900,plain,
% 3.44/3.76 ($false),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22899, 333, 722, 22893, 707, 11546])).
% 3.44/3.76 tff(22901,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22902,plain,
% 3.44/3.76 (~r(s(s(s(z))), elem!1)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22901, 838, 11546, 304, 722, 2484])).
% 3.44/3.76 tff(22903,plain,
% 3.44/3.76 (b(s(s(s(z))), elem!1)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[704, 22902, 22891])).
% 3.44/3.76 tff(22904,plain,
% 3.44/3.76 (~b(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[21016, 22903])).
% 3.44/3.76 tff(22905,plain,
% 3.44/3.76 (r(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[2794, 22904])).
% 3.44/3.76 tff(22906,plain,
% 3.44/3.76 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[66])).
% 3.44/3.76 tff(22907,plain,
% 3.44/3.76 (b(s(z), elem!1) <=> b(s(z), z)),
% 3.44/3.76 inference(symmetry,[status(thm)],[18057])).
% 3.44/3.76 tff(22908,plain,
% 3.44/3.76 (b(s(z), z)),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[134, 22907])).
% 3.44/3.76 tff(22909,plain,
% 3.44/3.76 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 3.44/3.76 inference(monotonicity,[status(thm)],[66])).
% 3.44/3.76 tff(22910,plain,
% 3.44/3.76 (r(s(s(s(z))), elem!1)),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[1699, 22909])).
% 3.44/3.76 tff(22911,plain,
% 3.44/3.76 ($false),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[699, 22910])).
% 3.44/3.76 tff(22912,plain,((~r(s(s(s(z))), z)) | r(s(s(s(z))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22913,plain,
% 3.44/3.76 (~r(s(s(s(z))), z)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22912, 22902, 66])).
% 3.44/3.76 tff(22914,plain,
% 3.44/3.76 (b(s(s(s(z))), z)),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[396, 22913])).
% 3.44/3.76 tff(22915,plain,
% 3.44/3.76 (~b(z, s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[2156, 22914, 22908, 838])).
% 3.44/3.76 tff(22916,plain,
% 3.44/3.76 (r(z, s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[619, 22915])).
% 3.44/3.76 tff(22917,plain,
% 3.44/3.76 (r(elem!1, s(s(s(z))))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[22916, 22906])).
% 3.44/3.76 tff(22918,plain,
% 3.44/3.76 (((~![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(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22919,plain,
% 3.44/3.76 (((~r(s(z), s(s(s(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22920,plain,
% 3.44/3.76 (((~![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(s(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[22919])).
% 3.44/3.76 tff(22921,plain,
% 3.44/3.76 (((~![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(s(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.76 inference(transitivity,[status(thm)],[22920, 22918])).
% 3.44/3.76 tff(22922,plain,
% 3.44/3.76 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 3.44/3.76 inference(quant_inst,[status(thm)],[])).
% 3.44/3.76 tff(22923,plain,
% 3.44/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[22922, 22921])).
% 3.44/3.76 tff(22924,plain,
% 3.44/3.76 ($false),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22923, 333, 22917, 722, 22905, 11546])).
% 3.44/3.76 tff(22925,plain,((~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.76 tff(22926,plain,
% 3.44/3.76 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[22925, 838, 11546, 66, 134, 132, 722, 304, 22886])).
% 3.44/3.76 tff(22927,plain,
% 3.44/3.76 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[1137, 22926])).
% 3.44/3.76 tff(22928,plain,
% 3.44/3.76 (~r(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[17809, 22927, 22886, 11546])).
% 3.44/3.76 tff(22929,plain,
% 3.44/3.76 (b(s(s(s(z))), s(z))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[2794, 22928])).
% 3.44/3.76 tff(22930,plain,
% 3.44/3.76 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[846, 22929, 304, 838])).
% 3.44/3.76 tff(22931,plain,
% 3.44/3.76 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[249, 22930])).
% 3.44/3.76 tff(22932,plain,
% 3.44/3.76 (~b(z, s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[21591, 22927, 11546, 321])).
% 3.44/3.76 tff(22933,plain,
% 3.44/3.76 (r(z, s(s(s(z))))),
% 3.44/3.76 inference(unit_resolution,[status(thm)],[619, 22932])).
% 3.44/3.76 tff(22934,plain,
% 3.44/3.76 (r(elem!1, s(s(s(z))))),
% 3.44/3.76 inference(modus_ponens,[status(thm)],[22933, 22906])).
% 3.44/3.76 tff(22935,plain,
% 3.44/3.76 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22936,plain,
% 3.44/3.76 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.76 inference(rewrite,[status(thm)],[])).
% 3.44/3.76 tff(22937,plain,
% 3.44/3.76 (((~![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(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.44/3.76 inference(monotonicity,[status(thm)],[22936])).
% 3.44/3.76 tff(22938,plain,
% 3.44/3.76 (((~![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(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.77 inference(transitivity,[status(thm)],[22937, 22935])).
% 3.44/3.77 tff(22939,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.77 inference(quant_inst,[status(thm)],[])).
% 3.44/3.77 tff(22940,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22939, 22938])).
% 3.44/3.77 tff(22941,plain,
% 3.44/3.77 ($false),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22940, 333, 22934, 22886, 22931, 22927])).
% 3.44/3.77 tff(22942,plain,((~b(s(z), s(s(s(z))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.77 tff(22943,plain,
% 3.44/3.77 (~b(s(z), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22942, 722, 304, 11546, 321, 134, 132, 18019])).
% 3.44/3.77 tff(22944,plain,
% 3.44/3.77 (r(s(z), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[172, 22943])).
% 3.44/3.77 tff(22945,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[21397, 22944, 11546, 321])).
% 3.44/3.77 tff(22946,plain,
% 3.44/3.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[1137, 22945])).
% 3.44/3.77 tff(22947,plain,
% 3.44/3.77 (r(z, s(z)) <=> r(elem!1, s(z))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.77 tff(22948,plain,
% 3.44/3.77 (r(elem!1, s(z)) <=> r(z, s(z))),
% 3.44/3.77 inference(symmetry,[status(thm)],[22947])).
% 3.44/3.77 tff(22949,plain,
% 3.44/3.77 (r(z, s(z))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[722, 22948])).
% 3.44/3.77 tff(22950,plain,
% 3.44/3.77 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.77 tff(22951,plain,
% 3.44/3.77 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[22950])).
% 3.44/3.77 tff(22952,plain,
% 3.44/3.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[15519, 3193, 11546, 353])).
% 3.44/3.77 tff(22953,plain,
% 3.44/3.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[249, 22952])).
% 3.44/3.77 tff(22954,plain,
% 3.44/3.77 (~b(z, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[16228, 22953, 2254, 259])).
% 3.44/3.77 tff(22955,plain,
% 3.44/3.77 (r(z, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[619, 22954])).
% 3.44/3.77 tff(22956,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(elem!1))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[3011, 22955, 353, 354])).
% 3.44/3.77 tff(22957,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(z))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22956, 22951])).
% 3.44/3.77 tff(22958,plain,
% 3.44/3.77 ($false),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[3193, 22957])).
% 3.44/3.77 tff(22959,plain,((~r(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.77 tff(22960,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22959, 22944, 8677, 22949, 22946, 22725, 11546])).
% 3.44/3.77 tff(22961,plain,
% 3.44/3.77 (b(s(s(s(z))), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[2794, 22960])).
% 3.44/3.77 tff(22962,plain,
% 3.44/3.77 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[17864, 144, 134, 132, 22946])).
% 3.44/3.77 tff(22963,plain,
% 3.44/3.77 (~b(s(s(s(z))), elem!1)),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22962, 22961])).
% 3.44/3.77 tff(22964,plain,
% 3.44/3.77 (b(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[12402, 22963, 22766, 722, 22944])).
% 3.44/3.77 tff(22965,plain,
% 3.44/3.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[18960, 22964, 132, 22946])).
% 3.44/3.77 tff(22966,plain,
% 3.44/3.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[249, 22965])).
% 3.44/3.77 tff(22967,plain,
% 3.44/3.77 (r(s(s(s(z))), elem!1)),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[704, 22963, 22766])).
% 3.44/3.77 tff(22968,plain,
% 3.44/3.77 ($false),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[12177, 333, 722, 22967, 22739, 22966])).
% 3.44/3.77 tff(22969,plain,((~r(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.77 tff(22970,plain,
% 3.44/3.77 (~r(elem!1, s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22969, 304, 134, 8677, 11546, 321, 132])).
% 3.44/3.77 tff(22971,plain,
% 3.44/3.77 (b(elem!1, s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[720, 22970, 714])).
% 3.44/3.77 tff(22972,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[17809, 6107, 2484, 11546])).
% 3.44/3.77 tff(22973,plain,
% 3.44/3.77 (b(s(s(s(z))), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[2794, 22972])).
% 3.44/3.77 tff(22974,plain,
% 3.44/3.77 (~r(s(z), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[21397, 6107, 11546, 321])).
% 3.44/3.77 tff(22975,plain,
% 3.44/3.77 (b(s(z), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[172, 22974])).
% 3.44/3.77 tff(22976,plain,
% 3.44/3.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[846, 22975, 304, 22973])).
% 3.44/3.77 tff(22977,plain,
% 3.44/3.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[249, 22976])).
% 3.44/3.77 tff(22978,plain,
% 3.44/3.77 (~b(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22776, 22975, 305, 22973])).
% 3.44/3.77 tff(22979,plain,
% 3.44/3.77 (r(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[1538, 22978, 1524])).
% 3.44/3.77 tff(22980,plain,
% 3.44/3.77 ($false),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22940, 333, 22979, 2484, 22977, 6107])).
% 3.44/3.77 tff(22981,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.77 tff(22982,plain,
% 3.44/3.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22981, 22971, 22768, 22739, 304, 11546, 321])).
% 3.44/3.77 tff(22983,plain,
% 3.44/3.77 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[18019])).
% 3.44/3.77 tff(22984,plain,
% 3.44/3.77 ((~r(elem!1, s(z))) <=> (~r(z, s(z)))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[22948])).
% 3.44/3.77 tff(22985,plain,
% 3.44/3.77 (~r(z, s(z))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22970, 22984])).
% 3.44/3.77 tff(22986,plain,
% 3.44/3.77 (b(z, s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[372, 22985])).
% 3.44/3.77 tff(22987,plain,
% 3.44/3.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[1137, 22982])).
% 3.44/3.77 tff(22988,plain,
% 3.44/3.77 (~b(z, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22484, 22987, 22725, 304, 22986])).
% 3.44/3.77 tff(22989,plain,
% 3.44/3.77 (r(z, s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[619, 22988])).
% 3.44/3.77 tff(22990,plain,
% 3.44/3.77 (r(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22989, 22983])).
% 3.44/3.77 tff(22991,plain,
% 3.44/3.77 (~r(s(s(z)), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[21056, 2671, 2484, 11546])).
% 3.44/3.77 tff(22992,plain,
% 3.44/3.77 (~r(s(s(elem!1)), s(elem!1))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[22871, 22991, 8677])).
% 3.44/3.77 tff(22993,plain,
% 3.44/3.77 (b(s(s(elem!1)), s(elem!1))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[1283, 22992, 22759])).
% 3.44/3.77 tff(22994,plain,
% 3.44/3.77 (b(s(s(z)), s(z))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[18895, 22993, 8677])).
% 3.44/3.77 tff(22995,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(22996,plain,
% 3.44/3.77 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(22997,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[22996])).
% 3.44/3.77 tff(22998,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 3.44/3.77 inference(transitivity,[status(thm)],[22997, 22995])).
% 3.44/3.77 tff(22999,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 3.44/3.77 inference(quant_inst,[status(thm)],[])).
% 3.44/3.77 tff(23000,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22999, 22998])).
% 3.44/3.77 tff(23001,plain,
% 3.44/3.77 (~b(s(s(z)), elem!1)),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[23000, 144, 134, 305, 22994])).
% 3.44/3.77 tff(23002,plain,
% 3.44/3.77 (r(s(s(z)), elem!1)),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[7970, 23001, 22830])).
% 3.44/3.77 tff(23003,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(23004,plain,
% 3.44/3.77 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(23005,plain,
% 3.44/3.77 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[23004])).
% 3.44/3.77 tff(23006,plain,
% 3.44/3.77 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.77 inference(transitivity,[status(thm)],[23005, 23003])).
% 3.44/3.77 tff(23007,plain,
% 3.44/3.77 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.77 inference(quant_inst,[status(thm)],[])).
% 3.44/3.77 tff(23008,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[23007, 23006])).
% 3.44/3.77 tff(23009,plain,
% 3.44/3.77 ($false),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[23008, 333, 1525, 2671, 2484, 23002])).
% 3.44/3.77 tff(23010,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.77 tff(23011,plain,
% 3.44/3.77 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[23010, 22990, 22739, 134, 22971, 8677, 11546])).
% 3.44/3.77 tff(23012,plain,
% 3.44/3.77 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[1451, 23011])).
% 3.44/3.77 tff(23013,plain,
% 3.44/3.77 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[18102])).
% 3.44/3.77 tff(23014,plain,
% 3.44/3.77 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.44/3.77 inference(symmetry,[status(thm)],[23013])).
% 3.44/3.77 tff(23015,plain,
% 3.44/3.77 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.44/3.77 inference(transitivity,[status(thm)],[22983, 23014])).
% 3.44/3.77 tff(23016,plain,
% 3.44/3.77 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[22989, 23015])).
% 3.44/3.77 tff(23017,plain,
% 3.44/3.77 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.44/3.77 inference(symmetry,[status(thm)],[22708])).
% 3.44/3.77 tff(23018,plain,
% 3.44/3.77 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 3.44/3.77 inference(symmetry,[status(thm)],[22706])).
% 3.44/3.77 tff(23019,plain,
% 3.44/3.77 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 3.44/3.77 inference(transitivity,[status(thm)],[23018, 23017])).
% 3.44/3.77 tff(23020,plain,
% 3.44/3.77 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.44/3.77 inference(symmetry,[status(thm)],[22760])).
% 3.44/3.77 tff(23021,plain,
% 3.44/3.77 ((~b(elem!1, s(s(z)))) <=> (~b(elem!1, s(s(elem!1))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[23020])).
% 3.44/3.77 tff(23022,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(23023,plain,
% 3.44/3.77 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(23024,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[23023])).
% 3.44/3.77 tff(23025,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.77 inference(transitivity,[status(thm)],[23024, 23022])).
% 3.44/3.77 tff(23026,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))),
% 3.44/3.77 inference(quant_inst,[status(thm)],[])).
% 3.44/3.77 tff(23027,plain,
% 3.44/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[23026, 23025])).
% 3.44/3.77 tff(23028,plain,
% 3.44/3.77 (~b(elem!1, s(s(z)))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[23027, 144, 305, 1398, 132, 304])).
% 3.44/3.77 tff(23029,plain,
% 3.44/3.77 (~b(elem!1, s(s(elem!1)))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[23028, 23021])).
% 3.44/3.77 tff(23030,plain,
% 3.44/3.77 (r(elem!1, s(s(elem!1)))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[2522, 23029, 22705])).
% 3.44/3.77 tff(23031,plain,
% 3.44/3.77 (r(elem!1, s(s(z)))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[23030, 23019])).
% 3.44/3.77 tff(23032,plain,
% 3.44/3.77 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[7952, 7926, 1398, 7927])).
% 3.44/3.77 tff(23033,plain,
% 3.44/3.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[18122, 23032, 8677])).
% 3.44/3.77 tff(23034,plain,
% 3.44/3.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[4311, 23033, 22826])).
% 3.44/3.77 tff(23035,plain,
% 3.44/3.77 (r(s(s(z)), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[18132, 23034, 8677])).
% 3.44/3.77 tff(23036,plain,
% 3.44/3.77 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.77 tff(23037,plain,
% 3.44/3.77 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 3.44/3.77 inference(transitivity,[status(thm)],[23036, 3061])).
% 3.44/3.77 tff(23038,plain,
% 3.44/3.77 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.44/3.77 inference(symmetry,[status(thm)],[23037])).
% 3.44/3.77 tff(23039,plain,
% 3.44/3.77 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.77 inference(transitivity,[status(thm)],[23038, 3251])).
% 3.44/3.77 tff(23040,plain,
% 3.44/3.77 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.44/3.77 inference(monotonicity,[status(thm)],[23039])).
% 3.44/3.77 tff(23041,plain,
% 3.44/3.77 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.77 inference(modus_ponens,[status(thm)],[1096, 23040])).
% 3.44/3.77 tff(23042,plain,
% 3.44/3.77 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[7952, 1398, 7926, 7927])).
% 3.44/3.77 tff(23043,plain,
% 3.44/3.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[18122, 23042, 8677])).
% 3.44/3.77 tff(23044,plain,
% 3.44/3.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.77 inference(unit_resolution,[status(thm)],[4311, 23043, 22826])).
% 3.44/3.77 tff(23045,plain,
% 3.44/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.44/3.77 inference(rewrite,[status(thm)],[])).
% 3.44/3.77 tff(23046,plain,
% 3.44/3.77 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.44/3.78 inference(rewrite,[status(thm)],[])).
% 3.44/3.78 tff(23047,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23046])).
% 3.44/3.78 tff(23048,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.44/3.78 inference(transitivity,[status(thm)],[23047, 23045])).
% 3.44/3.78 tff(23049,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 3.44/3.78 inference(quant_inst,[status(thm)],[])).
% 3.44/3.78 tff(23050,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23049, 23048])).
% 3.44/3.78 tff(23051,plain,
% 3.44/3.78 ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23050, 333])).
% 3.44/3.78 tff(23052,plain,
% 3.44/3.78 (~r(elem!1, s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23051, 23044, 13059, 1024])).
% 3.44/3.78 tff(23053,plain,
% 3.44/3.78 (b(elem!1, s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2522, 23052, 22705])).
% 3.44/3.78 tff(23054,plain,
% 3.44/3.78 (b(elem!1, s(s(z)))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23053, 22760])).
% 3.44/3.78 tff(23055,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23027, 144, 305, 1398, 132, 304, 23054])).
% 3.44/3.78 tff(23056,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23057,plain,
% 3.44/3.78 (~r(s(s(s(elem!1))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23056, 7926, 132, 304, 8677, 13059, 305, 1398, 7927])).
% 3.44/3.78 tff(23058,plain,
% 3.44/3.78 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.78 tff(23059,plain,
% 3.44/3.78 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(symmetry,[status(thm)],[23058])).
% 3.44/3.78 tff(23060,plain,
% 3.44/3.78 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23059])).
% 3.44/3.78 tff(23061,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 3.44/3.78 tff(23062,plain,
% 3.44/3.78 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23061, 23060])).
% 3.44/3.78 tff(23063,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[9749, 23062])).
% 3.44/3.78 tff(23064,plain,((~(s(elem!1) = s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23065,plain,
% 3.44/3.78 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23064, 23057, 8677])).
% 3.44/3.78 tff(23066,plain,
% 3.44/3.78 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4697, 23065, 23041])).
% 3.44/3.78 tff(23067,plain,
% 3.44/3.78 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.78 tff(23068,plain,
% 3.44/3.78 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(symmetry,[status(thm)],[23067])).
% 3.44/3.78 tff(23069,plain,
% 3.44/3.78 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[18102])).
% 3.44/3.78 tff(23070,plain,
% 3.44/3.78 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.44/3.78 inference(symmetry,[status(thm)],[23069])).
% 3.44/3.78 tff(23071,plain,
% 3.44/3.78 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(transitivity,[status(thm)],[23070, 23068])).
% 3.44/3.78 tff(23072,plain,
% 3.44/3.78 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23071])).
% 3.44/3.78 tff(23073,plain,
% 3.44/3.78 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[2789, 23072])).
% 3.44/3.78 tff(23074,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4684, 23073])).
% 3.44/3.78 tff(23075,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23076,plain,
% 3.44/3.78 (b(s(s(s(z))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23075, 23066, 8677])).
% 3.44/3.78 tff(23077,plain,
% 3.44/3.78 (~b(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4375, 23076, 134, 305])).
% 3.44/3.78 tff(23078,plain,
% 3.44/3.78 (r(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[704, 23077, 22766])).
% 3.44/3.78 tff(23079,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.44/3.78 inference(rewrite,[status(thm)],[])).
% 3.44/3.78 tff(23080,plain,
% 3.44/3.78 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.44/3.78 inference(rewrite,[status(thm)],[])).
% 3.44/3.78 tff(23081,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)), s(s(s(z))))) | (~r(elem!1, s(s(z))))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23080])).
% 3.44/3.78 tff(23082,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.44/3.78 inference(transitivity,[status(thm)],[23081, 23079])).
% 3.44/3.78 tff(23083,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.44/3.78 inference(quant_inst,[status(thm)],[])).
% 3.44/3.78 tff(23084,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z))))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23083, 23082])).
% 3.44/3.78 tff(23085,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23084, 333, 1525, 23078, 23035, 23031])).
% 3.44/3.78 tff(23086,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23087,plain,
% 3.44/3.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23086, 22990, 134, 22971, 8677, 132, 304, 23016, 23012, 22982])).
% 3.44/3.78 tff(23088,plain,
% 3.44/3.78 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 3.44/3.78 inference(symmetry,[status(thm)],[18023])).
% 3.44/3.78 tff(23089,plain,
% 3.44/3.78 ((~r(elem!1, s(z))) <=> (~r(elem!1, s(elem!1)))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23088])).
% 3.44/3.78 tff(23090,plain,
% 3.44/3.78 (~r(elem!1, s(elem!1))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[22970, 23089])).
% 3.44/3.78 tff(23091,plain,
% 3.44/3.78 (b(elem!1, s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[560, 23090, 902])).
% 3.44/3.78 tff(23092,plain,
% 3.44/3.78 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 3.44/3.78 inference(monotonicity,[status(thm)],[18101])).
% 3.44/3.78 tff(23093,plain,
% 3.44/3.78 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.44/3.78 inference(symmetry,[status(thm)],[23092])).
% 3.44/3.78 tff(23094,plain,
% 3.44/3.78 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22981, 305, 22768, 22739, 304, 11546, 321])).
% 3.44/3.78 tff(23095,plain,
% 3.44/3.78 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[1137, 23094])).
% 3.44/3.78 tff(23096,plain,
% 3.44/3.78 (~b(z, s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22484, 23095, 22725, 304, 22986])).
% 3.44/3.78 tff(23097,plain,
% 3.44/3.78 (r(z, s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[619, 23096])).
% 3.44/3.78 tff(23098,plain,
% 3.44/3.78 (r(elem!1, s(s(s(z))))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23097, 22983])).
% 3.44/3.78 tff(23099,plain,
% 3.44/3.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[846, 56, 304, 838])).
% 3.44/3.78 tff(23100,plain,
% 3.44/3.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[249, 23099])).
% 3.44/3.78 tff(23101,plain,
% 3.44/3.78 (~b(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4375, 56, 134, 305])).
% 3.44/3.78 tff(23102,plain,
% 3.44/3.78 (r(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[704, 23101, 698])).
% 3.44/3.78 tff(23103,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[14901, 333, 1525, 23102, 2484, 23100])).
% 3.44/3.78 tff(23104,plain,((~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23105,plain,
% 3.44/3.78 (~b(s(s(s(z))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23104, 838, 22739, 22766, 304, 23098, 134, 305])).
% 3.44/3.78 tff(23106,plain,
% 3.44/3.78 (r(s(s(s(z))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2794, 23105])).
% 3.44/3.78 tff(23107,plain,
% 3.44/3.78 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22410, 23106, 22739, 23098])).
% 3.44/3.78 tff(23108,plain,
% 3.44/3.78 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23097, 23015])).
% 3.44/3.78 tff(23109,plain,
% 3.44/3.78 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23075, 23105, 8677])).
% 3.44/3.78 tff(23110,plain,
% 3.44/3.78 (r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4697, 23109, 23041])).
% 3.44/3.78 tff(23111,plain,
% 3.44/3.78 (r(s(s(s(elem!1))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23064, 23110, 8677])).
% 3.44/3.78 tff(23112,plain,
% 3.44/3.78 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23056, 23111, 132, 304, 8677, 23108, 305, 23107, 23094])).
% 3.44/3.78 tff(23113,plain,
% 3.44/3.78 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[1451, 23112])).
% 3.44/3.78 tff(23114,plain,
% 3.44/3.78 (~r(s(s(z)), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[21056, 23113, 22739, 11546])).
% 3.44/3.78 tff(23115,plain,
% 3.44/3.78 (~r(s(s(elem!1)), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22871, 23114, 8677])).
% 3.44/3.78 tff(23116,plain,
% 3.44/3.78 (b(s(s(elem!1)), s(elem!1))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[1283, 23115, 22759])).
% 3.44/3.78 tff(23117,plain,
% 3.44/3.78 (b(s(s(z)), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[18895, 23116, 8677])).
% 3.44/3.78 tff(23118,plain,
% 3.44/3.78 (~b(s(s(z)), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23000, 144, 134, 305, 23117])).
% 3.44/3.78 tff(23119,plain,
% 3.44/3.78 (r(s(s(z)), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[7970, 23118, 22830])).
% 3.44/3.78 tff(23120,plain,
% 3.44/3.78 (r(s(s(elem!1)), elem!1)),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23119, 23093])).
% 3.44/3.78 tff(23121,plain,
% 3.44/3.78 (~r(s(z), s(s(z)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22882, 333, 23113, 11546, 22739])).
% 3.44/3.78 tff(23122,plain,
% 3.44/3.78 (~r(s(z), s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[22807, 23121, 8677])).
% 3.44/3.78 tff(23123,plain,
% 3.44/3.78 (b(s(z), s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[5484, 23122])).
% 3.44/3.78 tff(23124,plain,
% 3.44/3.78 (~b(elem!1, s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[5494, 23123, 305, 547, 23116])).
% 3.44/3.78 tff(23125,plain,
% 3.44/3.78 (r(elem!1, s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2522, 23124, 22705])).
% 3.44/3.78 tff(23126,plain,
% 3.44/3.78 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[66])).
% 3.44/3.78 tff(23127,plain,
% 3.44/3.78 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 3.44/3.78 inference(symmetry,[status(thm)],[23126])).
% 3.44/3.78 tff(23128,plain,
% 3.44/3.78 (r(z, s(s(elem!1)))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[2736, 23127])).
% 3.44/3.78 tff(23129,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2834, 23128])).
% 3.44/3.78 tff(23130,plain,((~r(elem!1, s(s(elem!1)))) | r(z, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23131,plain,
% 3.44/3.78 (r(z, s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23130, 23125, 18019])).
% 3.44/3.78 tff(23132,plain,
% 3.44/3.78 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[18125])).
% 3.44/3.78 tff(23133,plain,
% 3.44/3.78 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.44/3.78 inference(transitivity,[status(thm)],[23132, 13328])).
% 3.44/3.78 tff(23134,plain,
% 3.44/3.78 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23133])).
% 3.44/3.78 tff(23135,plain,
% 3.44/3.78 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[1446, 23134])).
% 3.44/3.78 tff(23136,plain,
% 3.44/3.78 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[18101])).
% 3.44/3.78 tff(23137,plain,
% 3.44/3.78 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.78 inference(symmetry,[status(thm)],[23136])).
% 3.44/3.78 tff(23138,plain,
% 3.44/3.78 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23137])).
% 3.44/3.78 tff(23139,plain,
% 3.44/3.78 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[249, 23107])).
% 3.44/3.78 tff(23140,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.44/3.78 inference(rewrite,[status(thm)],[])).
% 3.44/3.78 tff(23141,plain,
% 3.44/3.78 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.44/3.78 inference(rewrite,[status(thm)],[])).
% 3.44/3.78 tff(23142,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.44/3.78 inference(monotonicity,[status(thm)],[23141])).
% 3.44/3.78 tff(23143,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.44/3.78 inference(transitivity,[status(thm)],[23142, 23140])).
% 3.44/3.78 tff(23144,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.44/3.78 inference(quant_inst,[status(thm)],[])).
% 3.44/3.78 tff(23145,plain,
% 3.44/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23144, 23143])).
% 3.44/3.78 tff(23146,plain,
% 3.44/3.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23145, 144, 23117, 838, 23139, 304])).
% 3.44/3.78 tff(23147,plain,
% 3.44/3.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.78 inference(modus_ponens,[status(thm)],[23146, 23138])).
% 3.44/3.78 tff(23148,plain,
% 3.44/3.78 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2758, 23147, 23135])).
% 3.44/3.78 tff(23149,plain,
% 3.44/3.78 (~r(s(s(elem!1)), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[9411, 23148, 321, 23131])).
% 3.44/3.78 tff(23150,plain,
% 3.44/3.78 ($false),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23149, 23120])).
% 3.44/3.78 tff(23151,plain,((~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.78 tff(23152,plain,
% 3.44/3.78 (~b(s(z), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[23151, 22971, 321, 8677, 23091, 11546, 134, 304, 132])).
% 3.44/3.78 tff(23153,plain,
% 3.44/3.78 (r(s(z), s(s(s(z))))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[172, 23152])).
% 3.44/3.78 tff(23154,plain,
% 3.44/3.78 (~r(s(s(s(z))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[15519, 23087, 11546, 23153])).
% 3.44/3.78 tff(23155,plain,
% 3.44/3.78 (b(s(s(s(z))), s(z))),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[2794, 23154])).
% 3.44/3.78 tff(23156,plain,
% 3.44/3.78 (~b(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[4375, 23155, 134, 22971])).
% 3.44/3.78 tff(23157,plain,
% 3.44/3.78 (r(s(s(s(z))), elem!1)),
% 3.44/3.78 inference(unit_resolution,[status(thm)],[704, 23156, 22766])).
% 3.44/3.78 tff(23158,plain,
% 3.44/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23159,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23160,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23159, 23158])).
% 3.44/3.79 tff(23161,plain,
% 3.44/3.79 ($false),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23160, 333, 22990, 23157, 22739, 23087])).
% 3.44/3.79 tff(23162,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.79 tff(23163,plain,
% 3.44/3.79 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23162, 22885, 11546, 22669, 22701, 22681, 22695, 22699])).
% 3.44/3.79 tff(23164,plain,
% 3.44/3.79 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[319, 23163])).
% 3.44/3.79 tff(23165,plain,
% 3.44/3.79 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[8677])).
% 3.44/3.79 tff(23166,plain,
% 3.44/3.79 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.79 inference(symmetry,[status(thm)],[23165])).
% 3.44/3.79 tff(23167,plain,
% 3.44/3.79 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[322, 23166])).
% 3.44/3.79 tff(23168,plain,
% 3.44/3.79 ($false),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[535, 23167])).
% 3.44/3.79 tff(23169,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.79 tff(23170,plain,
% 3.44/3.79 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23169, 23164, 22669])).
% 3.44/3.79 tff(23171,plain,
% 3.44/3.79 (~r(elem!1, s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[12088, 23170, 22688, 22698])).
% 3.44/3.79 tff(23172,plain,
% 3.44/3.79 (b(elem!1, s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[560, 23171, 22695])).
% 3.44/3.79 tff(23173,plain,
% 3.44/3.79 (b(elem!1, s(z))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23172, 22689])).
% 3.44/3.79 tff(23174,plain,
% 3.44/3.79 (~b(s(s(s(z))), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[4375, 22973, 134, 305])).
% 3.44/3.79 tff(23175,plain,
% 3.44/3.79 (r(s(s(s(z))), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[704, 23174, 698])).
% 3.44/3.79 tff(23176,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23177,plain,
% 3.44/3.79 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23178,plain,
% 3.44/3.79 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), 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(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[23177])).
% 3.44/3.79 tff(23179,plain,
% 3.44/3.79 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), 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(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.44/3.79 inference(transitivity,[status(thm)],[23178, 23176])).
% 3.44/3.79 tff(23180,plain,
% 3.44/3.79 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23181,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23180, 23179])).
% 3.44/3.79 tff(23182,plain,
% 3.44/3.79 ($false),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23181, 333, 22979, 23175, 2484, 6107])).
% 3.44/3.79 tff(23183,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.79 tff(23184,plain,
% 3.44/3.79 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23183, 22688, 22677, 22674, 22885, 23173, 11546, 22681])).
% 3.44/3.79 tff(23185,plain,
% 3.44/3.79 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[1137, 7927])).
% 3.44/3.79 tff(23186,plain,
% 3.44/3.79 (~b(elem!1, s(s(s(z))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[18960, 23185, 132, 17795])).
% 3.44/3.79 tff(23187,plain,
% 3.44/3.79 (r(elem!1, s(s(s(z))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[1538, 23186, 22768])).
% 3.44/3.79 tff(23188,plain,
% 3.44/3.79 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23010, 23187, 2484, 134, 305, 8677, 11546])).
% 3.44/3.79 tff(23189,plain,
% 3.44/3.79 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[1451, 23188])).
% 3.44/3.79 tff(23190,plain,
% 3.44/3.79 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[7952, 23189, 7926, 7927])).
% 3.44/3.79 tff(23191,plain,
% 3.44/3.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[18122, 23190, 8677])).
% 3.44/3.79 tff(23192,plain,
% 3.44/3.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[4311, 23191, 22826])).
% 3.44/3.79 tff(23193,plain,
% 3.44/3.79 (r(s(s(z)), s(s(s(z))))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[18132, 23192, 8677])).
% 3.44/3.79 tff(23194,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23195,plain,
% 3.44/3.79 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23196,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[23195])).
% 3.44/3.79 tff(23197,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.79 inference(transitivity,[status(thm)],[23196, 23194])).
% 3.44/3.79 tff(23198,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23199,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23198, 23197])).
% 3.44/3.79 tff(23200,plain,
% 3.44/3.79 ($false),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23199, 333, 1525, 3193, 7155, 6330])).
% 3.44/3.79 tff(23201,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.79 tff(23202,plain,
% 3.44/3.79 (~r(s(s(z)), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23201, 3193, 6330, 1525])).
% 3.44/3.79 tff(23203,plain,
% 3.44/3.79 (b(s(s(z)), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[7970, 23202, 22830])).
% 3.44/3.79 tff(23204,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23205,plain,
% 3.44/3.79 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23206,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[23205])).
% 3.44/3.79 tff(23207,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(transitivity,[status(thm)],[23206, 23204])).
% 3.44/3.79 tff(23208,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23209,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23208, 23207])).
% 3.44/3.79 tff(23210,plain,
% 3.44/3.79 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23209, 144, 134, 1398, 132])).
% 3.44/3.79 tff(23211,plain,
% 3.44/3.79 (~b(s(s(z)), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23210, 23203])).
% 3.44/3.79 tff(23212,plain,
% 3.44/3.79 (~b(s(s(elem!1)), s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[18895, 23211, 8677])).
% 3.44/3.79 tff(23213,plain,
% 3.44/3.79 (r(s(s(elem!1)), s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[1283, 23212, 22759])).
% 3.44/3.79 tff(23214,plain,
% 3.44/3.79 (r(s(s(z)), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[22871, 23213, 8677])).
% 3.44/3.79 tff(23215,plain,
% 3.44/3.79 ($false),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[20223, 333, 3193, 11546, 6330, 23214])).
% 3.44/3.79 tff(23216,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.79 tff(23217,plain,
% 3.44/3.79 (~r(s(s(s(z))), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23216, 23193, 11546, 8677, 134, 23189, 132, 23187])).
% 3.44/3.79 tff(23218,plain,
% 3.44/3.79 (b(s(s(s(z))), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[2794, 23217])).
% 3.44/3.79 tff(23219,plain,
% 3.44/3.79 (~b(s(s(s(z))), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[4375, 23218, 134, 305])).
% 3.44/3.79 tff(23220,plain,
% 3.44/3.79 (r(s(s(s(z))), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[704, 23219, 22766])).
% 3.44/3.79 tff(23221,plain,
% 3.44/3.79 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23222,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[23221])).
% 3.44/3.79 tff(23223,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.79 inference(transitivity,[status(thm)],[23222, 7440])).
% 3.44/3.79 tff(23224,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23225,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23224, 23223])).
% 3.44/3.79 tff(23226,plain,
% 3.44/3.79 (~r(s(s(z)), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23225, 333, 23187, 23220, 23193])).
% 3.44/3.79 tff(23227,plain,
% 3.44/3.79 (b(s(s(z)), elem!1)),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[7970, 23226, 22830])).
% 3.44/3.79 tff(23228,plain,
% 3.44/3.79 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23209, 144, 134, 23189, 132])).
% 3.44/3.79 tff(23229,plain,
% 3.44/3.79 (~b(s(s(z)), s(z))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23228, 23227])).
% 3.44/3.79 tff(23230,plain,
% 3.44/3.79 (~b(s(s(elem!1)), s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[18895, 23229, 8677])).
% 3.44/3.79 tff(23231,plain,
% 3.44/3.79 (r(s(s(elem!1)), s(elem!1))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[1283, 23230, 22759])).
% 3.44/3.79 tff(23232,plain,
% 3.44/3.79 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[3662, 23231, 22728, 524])).
% 3.44/3.79 tff(23233,plain,
% 3.44/3.79 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[2758, 23232, 23135])).
% 3.44/3.79 tff(23234,plain,
% 3.44/3.79 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23233, 23136])).
% 3.44/3.79 tff(23235,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23236,plain,
% 3.44/3.79 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(rewrite,[status(thm)],[])).
% 3.44/3.79 tff(23237,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.79 inference(monotonicity,[status(thm)],[23236])).
% 3.44/3.79 tff(23238,plain,
% 3.44/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(transitivity,[status(thm)],[23237, 23235])).
% 3.44/3.79 tff(23239,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.79 inference(quant_inst,[status(thm)],[])).
% 3.44/3.79 tff(23240,plain,
% 3.44/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23239, 23238])).
% 3.44/3.79 tff(23241,plain,
% 3.44/3.79 (~b(elem!1, s(s(z)))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23240, 144, 23189, 132, 23234])).
% 3.44/3.79 tff(23242,plain,
% 3.44/3.79 (~b(elem!1, s(s(elem!1)))),
% 3.44/3.79 inference(modus_ponens,[status(thm)],[23241, 23021])).
% 3.44/3.79 tff(23243,plain,
% 3.44/3.79 (~r(elem!1, s(s(z)))),
% 3.44/3.79 inference(unit_resolution,[status(thm)],[23084, 333, 23187, 23220, 23193])).
% 3.53/3.80 tff(23244,plain,
% 3.53/3.80 (~r(elem!1, s(s(elem!1)))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[23243, 22710])).
% 3.53/3.80 tff(23245,plain,
% 3.53/3.80 (b(elem!1, s(s(elem!1)))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[2522, 23244, 22705])).
% 3.53/3.80 tff(23246,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23245, 23242])).
% 3.53/3.80 tff(23247,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23248,plain,
% 3.53/3.80 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23247, 23184, 22701, 23170, 22885, 23173, 11546, 22669, 22688])).
% 3.53/3.80 tff(23249,plain,
% 3.53/3.80 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[1137, 23184])).
% 3.53/3.80 tff(23250,plain,
% 3.53/3.80 (~r(s(z), s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[15519, 3193, 11546, 224])).
% 3.53/3.80 tff(23251,plain,
% 3.53/3.80 (b(s(z), s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[172, 23250])).
% 3.53/3.80 tff(23252,plain,
% 3.53/3.80 (~r(elem!1, s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[22410, 3193, 2484, 224])).
% 3.53/3.80 tff(23253,plain,
% 3.53/3.80 (b(elem!1, s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[1538, 23252, 1524])).
% 3.53/3.80 tff(23254,plain,
% 3.53/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(rewrite,[status(thm)],[])).
% 3.53/3.80 tff(23255,plain,
% 3.53/3.80 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(rewrite,[status(thm)],[])).
% 3.53/3.80 tff(23256,plain,
% 3.53/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23255])).
% 3.53/3.80 tff(23257,plain,
% 3.53/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(transitivity,[status(thm)],[23256, 23254])).
% 3.53/3.80 tff(23258,plain,
% 3.53/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 3.53/3.80 inference(quant_inst,[status(thm)],[])).
% 3.53/3.80 tff(23259,plain,
% 3.53/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[23258, 23257])).
% 3.53/3.80 tff(23260,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23259, 144, 23253, 305, 23251, 132, 2254])).
% 3.53/3.80 tff(23261,plain,((~r(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23262,plain,
% 3.53/3.80 (~r(s(s(s(z))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23261, 23173, 22701, 23249, 22674, 11546, 23248, 22688])).
% 3.53/3.80 tff(23263,plain,
% 3.53/3.80 (b(s(s(s(z))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[2794, 23262])).
% 3.53/3.80 tff(23264,plain,
% 3.53/3.80 (~b(s(s(s(z))), elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[4375, 23263, 22885, 23173])).
% 3.53/3.80 tff(23265,plain,
% 3.53/3.80 (r(s(s(s(z))), elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[704, 23264, 22677])).
% 3.53/3.80 tff(23266,plain,
% 3.53/3.80 (~r(s(z), s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[22780, 23265, 23164, 23248])).
% 3.53/3.80 tff(23267,plain,
% 3.53/3.80 (b(s(z), s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[172, 23266])).
% 3.53/3.80 tff(23268,plain,
% 3.53/3.80 (~b(elem!1, s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[22776, 23267, 23173, 23263])).
% 3.53/3.80 tff(23269,plain,
% 3.53/3.80 (r(elem!1, s(s(s(z))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[1538, 23268, 22674])).
% 3.53/3.80 tff(23270,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[14901, 333, 23269, 23265, 22688, 23248])).
% 3.53/3.80 tff(23271,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23272,plain,
% 3.53/3.80 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23271, 11546, 2545])).
% 3.53/3.80 tff(23273,plain,
% 3.53/3.80 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, elem!1)),
% 3.53/3.80 inference(monotonicity,[status(thm)],[81])).
% 3.53/3.80 tff(23274,plain,
% 3.53/3.80 (r(elem!1, elem!1) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(symmetry,[status(thm)],[23273])).
% 3.53/3.80 tff(23275,plain,
% 3.53/3.80 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23274])).
% 3.53/3.80 tff(23276,plain,
% 3.53/3.80 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[9917, 23275])).
% 3.53/3.80 tff(23277,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[2323, 23276])).
% 3.53/3.80 tff(23278,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23279,plain,
% 3.53/3.80 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23278, 23272])).
% 3.53/3.80 tff(23280,plain,
% 3.53/3.80 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[130, 23279, 2545])).
% 3.53/3.80 tff(23281,plain,
% 3.53/3.80 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(rewrite,[status(thm)],[])).
% 3.53/3.80 tff(23282,plain,
% 3.53/3.80 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(rewrite,[status(thm)],[])).
% 3.53/3.80 tff(23283,plain,
% 3.53/3.80 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23282])).
% 3.53/3.80 tff(23284,plain,
% 3.53/3.80 (((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(transitivity,[status(thm)],[23283, 23281])).
% 3.53/3.80 tff(23285,plain,
% 3.53/3.80 ((~![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(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 3.53/3.80 inference(quant_inst,[status(thm)],[])).
% 3.53/3.80 tff(23286,plain,
% 3.53/3.80 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[23285, 23284])).
% 3.53/3.80 tff(23287,plain,
% 3.53/3.80 (~r(elem!1, s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23286, 333, 11546, 23280, 23272])).
% 3.53/3.80 tff(23288,plain,
% 3.53/3.80 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 3.53/3.80 inference(monotonicity,[status(thm)],[57])).
% 3.53/3.80 tff(23289,plain,
% 3.53/3.80 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 3.53/3.80 inference(transitivity,[status(thm)],[23288, 198])).
% 3.53/3.80 tff(23290,plain,
% 3.53/3.80 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 3.53/3.80 inference(symmetry,[status(thm)],[23289])).
% 3.53/3.80 tff(23291,plain,
% 3.53/3.80 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23290])).
% 3.53/3.80 tff(23292,plain,
% 3.53/3.80 (~(s(elem!1) = s(z))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[2483, 23291])).
% 3.53/3.80 tff(23293,plain,
% 3.53/3.80 ((s(z) = z) <=> (elem!1 = z)),
% 3.53/3.80 inference(monotonicity,[status(thm)],[57])).
% 3.53/3.80 tff(23294,plain,
% 3.53/3.80 ((s(z) = z) <=> (z = elem!1)),
% 3.53/3.80 inference(transitivity,[status(thm)],[23293, 18283])).
% 3.53/3.80 tff(23295,plain,
% 3.53/3.80 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23294])).
% 3.53/3.80 tff(23296,plain,
% 3.53/3.80 (~(z = elem!1)),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[344, 23295])).
% 3.53/3.80 tff(23297,plain,
% 3.53/3.80 (r(z, elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[658, 606, 23296])).
% 3.53/3.80 tff(23298,plain,
% 3.53/3.80 (~b(z, s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[8102, 606, 57])).
% 3.53/3.80 tff(23299,plain,
% 3.53/3.80 (r(z, s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[372, 23298])).
% 3.53/3.80 tff(23300,plain,
% 3.53/3.80 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[5278])).
% 3.53/3.80 tff(23301,plain,
% 3.53/3.80 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[2545, 23300])).
% 3.53/3.80 tff(23302,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[304, 23301])).
% 3.53/3.80 tff(23303,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23304,plain,
% 3.53/3.80 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23303, 57, 2545])).
% 3.53/3.80 tff(23305,plain,
% 3.53/3.80 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[319, 23304])).
% 3.53/3.80 tff(23306,plain,
% 3.53/3.80 (~b(s(s(s(z))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[63, 55, 57])).
% 3.53/3.80 tff(23307,plain,
% 3.53/3.80 (r(s(s(s(z))), s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[2794, 23306])).
% 3.53/3.80 tff(23308,plain,
% 3.53/3.80 (r(s(s(s(z))), elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[704, 55, 4798])).
% 3.53/3.80 tff(23309,plain,
% 3.53/3.80 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(rewrite,[status(thm)],[])).
% 3.53/3.80 tff(23310,plain,
% 3.53/3.80 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23309])).
% 3.53/3.80 tff(23311,plain,
% 3.53/3.80 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.80 inference(transitivity,[status(thm)],[23310, 18725])).
% 3.53/3.80 tff(23312,plain,
% 3.53/3.80 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 3.53/3.80 inference(quant_inst,[status(thm)],[])).
% 3.53/3.80 tff(23313,plain,
% 3.53/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[23312, 23311])).
% 3.53/3.80 tff(23314,plain,
% 3.53/3.80 ($false),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23313, 333, 707, 2484, 2323, 6107])).
% 3.53/3.80 tff(23315,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.80 tff(23316,plain,
% 3.53/3.80 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[23315, 707, 23272, 23280])).
% 3.53/3.80 tff(23317,plain,
% 3.53/3.80 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[1137, 23316])).
% 3.53/3.80 tff(23318,plain,
% 3.53/3.80 ((s(z) = z) <=> (elem!1 = z)),
% 3.53/3.80 inference(transitivity,[status(thm)],[23294, 18284])).
% 3.53/3.80 tff(23319,plain,
% 3.53/3.80 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[23318])).
% 3.53/3.80 tff(23320,plain,
% 3.53/3.80 (~(elem!1 = z)),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[344, 23319])).
% 3.53/3.80 tff(23321,plain,
% 3.53/3.80 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[23317, 4584])).
% 3.53/3.80 tff(23322,plain,
% 3.53/3.80 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.80 inference(modus_ponens,[status(thm)],[283, 4018])).
% 3.53/3.80 tff(23323,plain,
% 3.53/3.80 (~r(z, elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[2541, 51, 23272, 23305])).
% 3.53/3.80 tff(23324,plain,
% 3.53/3.80 (b(z, elem!1)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[658, 23323, 23296])).
% 3.53/3.80 tff(23325,plain,
% 3.53/3.80 (b(z, s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[9366, 23324, 57])).
% 3.53/3.80 tff(23326,plain,
% 3.53/3.80 (~b(elem!1, s(z))),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[6528, 57])).
% 3.53/3.80 tff(23327,plain,
% 3.53/3.80 (elem!1 = s(z)),
% 3.53/3.80 inference(unit_resolution,[status(thm)],[720, 23326, 23287])).
% 3.53/3.80 tff(23328,plain,
% 3.53/3.80 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[9386])).
% 3.53/3.80 tff(23329,plain,
% 3.53/3.80 ((z = elem!1) <=> (z = s(z))),
% 3.53/3.80 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.80 tff(23330,plain,
% 3.53/3.80 ((z = elem!1) <=> (s(z) = z)),
% 3.53/3.81 inference(transitivity,[status(thm)],[23329, 364])).
% 3.53/3.81 tff(23331,plain,
% 3.53/3.81 ((s(z) = z) <=> (z = elem!1)),
% 3.53/3.81 inference(symmetry,[status(thm)],[23330])).
% 3.53/3.81 tff(23332,plain,
% 3.53/3.81 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23331])).
% 3.53/3.81 tff(23333,plain,
% 3.53/3.81 (~(z = elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[344, 23332])).
% 3.53/3.81 tff(23334,plain,
% 3.53/3.81 (b(z, elem!1)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[658, 23333, 1575])).
% 3.53/3.81 tff(23335,plain,
% 3.53/3.81 (r(z, elem!1) <=> r(z, s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23336,plain,
% 3.53/3.81 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23335])).
% 3.53/3.81 tff(23337,plain,
% 3.53/3.81 (~r(z, s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[1575, 23336])).
% 3.53/3.81 tff(23338,plain,
% 3.53/3.81 (b(z, s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[372, 23337])).
% 3.53/3.81 tff(23339,plain,
% 3.53/3.81 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.81 tff(23340,plain,
% 3.53/3.81 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23339])).
% 3.53/3.81 tff(23341,plain,
% 3.53/3.81 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9445])).
% 3.53/3.81 tff(23342,plain,
% 3.53/3.81 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23341])).
% 3.53/3.81 tff(23343,plain,
% 3.53/3.81 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.81 tff(23344,plain,
% 3.53/3.81 ((elem!1 = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23345,plain,
% 3.53/3.81 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 3.53/3.81 inference(transitivity,[status(thm)],[23344, 157])).
% 3.53/3.81 tff(23346,plain,
% 3.53/3.81 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23345])).
% 3.53/3.81 tff(23347,plain,
% 3.53/3.81 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 3.53/3.81 inference(transitivity,[status(thm)],[23346, 4795])).
% 3.53/3.81 tff(23348,plain,
% 3.53/3.81 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23347])).
% 3.53/3.81 tff(23349,plain,
% 3.53/3.81 (~(s(s(s(z))) = elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[166, 23348])).
% 3.53/3.81 tff(23350,plain,
% 3.53/3.81 (r(s(elem!1), elem!1)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[448, 3616, 9469])).
% 3.53/3.81 tff(23351,plain,
% 3.53/3.81 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 3.53/3.81 inference(monotonicity,[status(thm)],[710])).
% 3.53/3.81 tff(23352,plain,
% 3.53/3.81 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23351])).
% 3.53/3.81 tff(23353,plain,
% 3.53/3.81 (r(s(s(z)), elem!1) <=> r(s(elem!1), s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9445, 709])).
% 3.53/3.81 tff(23354,plain,
% 3.53/3.81 (r(s(elem!1), s(z)) <=> r(s(s(z)), elem!1)),
% 3.53/3.81 inference(symmetry,[status(thm)],[23353])).
% 3.53/3.81 tff(23355,plain,
% 3.53/3.81 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23356,plain,
% 3.53/3.81 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 3.53/3.81 inference(transitivity,[status(thm)],[23355, 1577])).
% 3.53/3.81 tff(23357,plain,
% 3.53/3.81 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23356])).
% 3.53/3.81 tff(23358,plain,
% 3.53/3.81 (~(s(elem!1) = s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[9430, 23357])).
% 3.53/3.81 tff(23359,plain,
% 3.53/3.81 (~b(s(elem!1), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[3619, 3616, 9383])).
% 3.53/3.81 tff(23360,plain,
% 3.53/3.81 (r(s(elem!1), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[486, 23359, 23358])).
% 3.53/3.81 tff(23361,plain,
% 3.53/3.81 (r(s(s(z)), elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23360, 23354])).
% 3.53/3.81 tff(23362,plain,
% 3.53/3.81 (r(s(s(z)), s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23361, 23352])).
% 3.53/3.81 tff(23363,plain,
% 3.53/3.81 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23364,plain,
% 3.53/3.81 (r(s(s(s(z))), s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[707, 23363])).
% 3.53/3.81 tff(23365,plain,
% 3.53/3.81 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.81 tff(23366,plain,
% 3.53/3.81 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23365])).
% 3.53/3.81 tff(23367,plain,
% 3.53/3.81 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23315, 707, 2484, 2323])).
% 3.53/3.81 tff(23368,plain,
% 3.53/3.81 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[1137, 23367])).
% 3.53/3.81 tff(23369,plain,
% 3.53/3.81 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23368, 23366])).
% 3.53/3.81 tff(23370,plain,
% 3.53/3.81 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[15019, 23369, 2323, 2484, 9383, 435])).
% 3.53/3.81 tff(23371,plain,
% 3.53/3.81 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[1283, 23370, 9481])).
% 3.53/3.81 tff(23372,plain,
% 3.53/3.81 (r(s(s(s(z))), s(elem!1))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23371, 13440])).
% 3.53/3.81 tff(23373,plain,
% 3.53/3.81 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[13447, 23372, 709])).
% 3.53/3.81 tff(23374,plain,
% 3.53/3.81 (~r(s(s(s(z))), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[19440, 23373, 9770, 11546])).
% 3.53/3.81 tff(23375,plain,
% 3.53/3.81 ($false),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23374, 23364])).
% 3.53/3.81 tff(23376,plain,((~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.81 tff(23377,plain,
% 3.53/3.81 (~r(s(s(s(z))), elem!1)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23376, 23362, 709, 11546, 2323, 2484, 23350])).
% 3.53/3.81 tff(23378,plain,
% 3.53/3.81 (b(s(s(s(z))), elem!1)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[704, 23377, 23349])).
% 3.53/3.81 tff(23379,plain,
% 3.53/3.81 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23380,plain,
% 3.53/3.81 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[2484, 23379])).
% 3.53/3.81 tff(23381,plain,
% 3.53/3.81 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23382,plain,
% 3.53/3.81 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23381])).
% 3.53/3.81 tff(23383,plain,
% 3.53/3.81 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(transitivity,[status(thm)],[23382, 17905])).
% 3.53/3.81 tff(23384,plain,
% 3.53/3.81 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(quant_inst,[status(thm)],[])).
% 3.53/3.81 tff(23385,plain,
% 3.53/3.81 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23384, 23383])).
% 3.53/3.81 tff(23386,plain,
% 3.53/3.81 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23385, 333, 11546, 23380])).
% 3.53/3.81 tff(23387,plain,
% 3.53/3.81 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23386, 23362])).
% 3.53/3.81 tff(23388,plain,
% 3.53/3.81 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23387, 9630])).
% 3.53/3.81 tff(23389,plain,
% 3.53/3.81 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23390,plain,
% 3.53/3.81 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23391,plain,
% 3.53/3.81 (((~![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(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $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(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23390])).
% 3.53/3.81 tff(23392,plain,
% 3.53/3.81 (((~![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(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $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(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.81 inference(transitivity,[status(thm)],[23391, 23389])).
% 3.53/3.81 tff(23393,plain,
% 3.53/3.81 ((~![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(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.53/3.81 inference(quant_inst,[status(thm)],[])).
% 3.53/3.81 tff(23394,plain,
% 3.53/3.81 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23393, 23392])).
% 3.53/3.81 tff(23395,plain,
% 3.53/3.81 ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23394, 333, 11546, 23380])).
% 3.53/3.81 tff(23396,plain,
% 3.53/3.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23395, 23362])).
% 3.53/3.81 tff(23397,plain,
% 3.53/3.81 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23396, 9633])).
% 3.53/3.81 tff(23398,plain,
% 3.53/3.81 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23399,plain,
% 3.53/3.81 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 3.53/3.81 inference(symmetry,[status(thm)],[23398])).
% 3.53/3.81 tff(23400,plain,
% 3.53/3.81 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.81 tff(23401,plain,
% 3.53/3.81 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.53/3.81 inference(symmetry,[status(thm)],[23400])).
% 3.53/3.81 tff(23402,plain,
% 3.53/3.81 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 3.53/3.81 inference(transitivity,[status(thm)],[23401, 23399])).
% 3.53/3.81 tff(23403,plain,
% 3.53/3.81 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23363])).
% 3.53/3.81 tff(23404,plain,
% 3.53/3.81 (~r(s(s(s(z))), s(z))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23377, 23403])).
% 3.53/3.81 tff(23405,plain,
% 3.53/3.81 (b(s(s(s(z))), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[2792, 44, 166, 23404])).
% 3.53/3.81 tff(23406,plain,
% 3.53/3.81 (b(s(s(elem!1)), elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23405, 23402])).
% 3.53/3.81 tff(23407,plain,
% 3.53/3.81 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.53/3.81 inference(transitivity,[status(thm)],[23363, 9389, 9385])).
% 3.53/3.81 tff(23408,plain,
% 3.53/3.81 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23407])).
% 3.53/3.81 tff(23409,plain,
% 3.53/3.81 (~r(s(s(elem!1)), elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23377, 23408])).
% 3.53/3.81 tff(23410,plain,
% 3.53/3.81 ((s(z) = z) <=> (elem!1 = z)),
% 3.53/3.81 inference(transitivity,[status(thm)],[23331, 18284])).
% 3.53/3.81 tff(23411,plain,
% 3.53/3.81 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23410])).
% 3.53/3.81 tff(23412,plain,
% 3.53/3.81 (~(elem!1 = z)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[344, 23411])).
% 3.53/3.81 tff(23413,plain,
% 3.53/3.81 (r(elem!1, z) <=> r(s(z), z)),
% 3.53/3.81 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.81 tff(23414,plain,
% 3.53/3.81 (r(s(z), z)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[408, 23413])).
% 3.53/3.81 tff(23415,plain,
% 3.53/3.81 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[2331, 408, 322, 2323])).
% 3.53/3.81 tff(23416,plain,
% 3.53/3.81 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[279, 23415])).
% 3.53/3.81 tff(23417,plain,
% 3.53/3.81 (~b(z, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[8386, 23416, 535, 9578, 466])).
% 3.53/3.81 tff(23418,plain,
% 3.53/3.81 (r(z, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[583, 23417])).
% 3.53/3.81 tff(23419,plain,
% 3.53/3.81 (~r(s(z), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[8274, 23418, 321, 322])).
% 3.53/3.81 tff(23420,plain,
% 3.53/3.81 ($false),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23419, 23414])).
% 3.53/3.81 tff(23421,plain,((~r(elem!1, z)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.81 tff(23422,plain,
% 3.53/3.81 (~r(elem!1, z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23421, 23397, 321, 23380, 709, 23388, 2323])).
% 3.53/3.81 tff(23423,plain,
% 3.53/3.81 (b(elem!1, z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[1380, 23422, 23412])).
% 3.53/3.81 tff(23424,plain,
% 3.53/3.81 (~b(s(s(s(z))), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[10565, 624, 251, 4367])).
% 3.53/3.81 tff(23425,plain,
% 3.53/3.81 (r(s(s(s(z))), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[396, 23424])).
% 3.53/3.81 tff(23426,plain,
% 3.53/3.81 (r(s(s(elem!1)), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[6447, 23425, 9383])).
% 3.53/3.81 tff(23427,plain,
% 3.53/3.81 (~r(z, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[5505, 23426, 435, 2737])).
% 3.53/3.81 tff(23428,plain,
% 3.53/3.81 (b(z, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[583, 23427])).
% 3.53/3.81 tff(23429,plain,
% 3.53/3.81 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[8386, 23428, 535, 9578, 466])).
% 3.53/3.81 tff(23430,plain,
% 3.53/3.81 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[279, 23429])).
% 3.53/3.81 tff(23431,plain,
% 3.53/3.81 (~b(elem!1, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[13461, 23430, 709, 624, 23425, 435, 2737])).
% 3.53/3.81 tff(23432,plain,
% 3.53/3.81 (r(elem!1, s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[560, 23431, 9430])).
% 3.53/3.81 tff(23433,plain,
% 3.53/3.81 (~r(elem!1, s(s(elem!1)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[2745, 2737, 434, 563])).
% 3.53/3.81 tff(23434,plain,
% 3.53/3.81 (b(elem!1, s(s(elem!1)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[2522, 23433, 2462])).
% 3.53/3.81 tff(23435,plain,
% 3.53/3.81 (~b(s(s(s(s(z)))), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[12662, 144, 251, 624, 3529])).
% 3.53/3.81 tff(23436,plain,
% 3.53/3.81 (r(s(s(s(s(z)))), z)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[4243, 44, 242, 23435])).
% 3.53/3.81 tff(23437,plain,
% 3.53/3.81 (~b(z, s(s(elem!1)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[11841, 2812, 4972, 251])).
% 3.53/3.81 tff(23438,plain,
% 3.53/3.81 (~b(z, s(s(s(z))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[2828, 23437, 57])).
% 3.53/3.81 tff(23439,plain,
% 3.53/3.81 (r(z, s(s(s(z))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[619, 23438])).
% 3.53/3.81 tff(23440,plain,
% 3.53/3.81 (r(z, s(s(elem!1)))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23439, 2832])).
% 3.53/3.81 tff(23441,plain,
% 3.53/3.81 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[6730, 144, 2812, 3529, 4972])).
% 3.53/3.81 tff(23442,plain,
% 3.53/3.81 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23441, 4285])).
% 3.53/3.81 tff(23443,plain,
% 3.53/3.81 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[1116, 23442, 4283])).
% 3.53/3.81 tff(23444,plain,
% 3.53/3.81 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23443, 4272])).
% 3.53/3.81 tff(23445,plain,
% 3.53/3.81 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23446,plain,
% 3.53/3.81 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23447,plain,
% 3.53/3.81 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23446])).
% 3.53/3.81 tff(23448,plain,
% 3.53/3.81 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.53/3.81 inference(transitivity,[status(thm)],[23447, 23445])).
% 3.53/3.81 tff(23449,plain,
% 3.53/3.81 ((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 3.53/3.81 inference(quant_inst,[status(thm)],[])).
% 3.53/3.81 tff(23450,plain,
% 3.53/3.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23449, 23448])).
% 3.53/3.81 tff(23451,plain,
% 3.53/3.81 ($false),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23450, 333, 2737, 23444, 23440, 23436])).
% 3.53/3.81 tff(23452,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.81 tff(23453,plain,
% 3.53/3.81 (~b(s(s(s(s(z)))), elem!1)),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[23452, 2737, 57, 23434, 4972, 251, 624])).
% 3.53/3.81 tff(23454,plain,
% 3.53/3.81 (~b(s(s(s(elem!1))), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[3588, 23453, 57])).
% 3.53/3.81 tff(23455,plain,
% 3.53/3.81 (r(s(s(s(elem!1))), s(z))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[1101, 23454])).
% 3.53/3.81 tff(23456,plain,
% 3.53/3.81 (r(s(s(s(s(z)))), elem!1)),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23455, 4625])).
% 3.53/3.81 tff(23457,plain,
% 3.53/3.81 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[9510, 333, 563, 435, 23456])).
% 3.53/3.81 tff(23458,plain,
% 3.53/3.81 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23457, 9506])).
% 3.53/3.81 tff(23459,plain,
% 3.53/3.81 (b(s(s(s(elem!1))), s(elem!1))),
% 3.53/3.81 inference(unit_resolution,[status(thm)],[4697, 23458, 3523])).
% 3.53/3.81 tff(23460,plain,
% 3.53/3.81 (b(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.81 inference(modus_ponens,[status(thm)],[23459, 9504])).
% 3.53/3.81 tff(23461,plain,
% 3.53/3.81 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.81 inference(rewrite,[status(thm)],[])).
% 3.53/3.81 tff(23462,plain,
% 3.53/3.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.53/3.81 inference(monotonicity,[status(thm)],[23461])).
% 3.53/3.81 tff(23463,plain,
% 3.53/3.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23462, 4723])).
% 3.53/3.82 tff(23464,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(quant_inst,[status(thm)],[])).
% 3.53/3.82 tff(23465,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23464, 23463])).
% 3.53/3.82 tff(23466,plain,
% 3.53/3.82 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23465, 144, 23434, 5659, 4972])).
% 3.53/3.82 tff(23467,plain,
% 3.53/3.82 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[130, 23466, 4182])).
% 3.53/3.82 tff(23468,plain,
% 3.53/3.82 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[12633, 333, 563, 23456, 23467])).
% 3.53/3.82 tff(23469,plain,
% 3.53/3.82 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[3556, 44, 12644, 23468])).
% 3.53/3.82 tff(23470,plain,
% 3.53/3.82 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[12787, 23467, 12779, 563])).
% 3.53/3.82 tff(23471,plain,
% 3.53/3.82 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1451, 23470])).
% 3.53/3.82 tff(23472,plain,
% 3.53/3.82 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23471, 2686])).
% 3.53/3.82 tff(23473,plain,
% 3.53/3.82 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[12793, 333, 563, 435, 23467])).
% 3.53/3.82 tff(23474,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[540, 44, 2698, 23473])).
% 3.53/3.82 tff(23475,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[12651, 144, 23474, 23472, 23469, 23460])).
% 3.53/3.82 tff(23476,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23477,plain,
% 3.53/3.82 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23476, 23432, 251, 435, 434, 4972, 2737, 624, 9383])).
% 3.53/3.82 tff(23478,plain,
% 3.53/3.82 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[2758, 23477, 9402])).
% 3.53/3.82 tff(23479,plain,
% 3.53/3.82 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[2771])).
% 3.53/3.82 tff(23480,plain,
% 3.53/3.82 (~r(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[14204, 23479])).
% 3.53/3.82 tff(23481,plain,
% 3.53/3.82 (b(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[704, 23480, 4798])).
% 3.53/3.82 tff(23482,plain,
% 3.53/3.82 (~b(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[10565, 23481, 251, 624])).
% 3.53/3.82 tff(23483,plain,
% 3.53/3.82 (r(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[396, 23482])).
% 3.53/3.82 tff(23484,plain,
% 3.53/3.82 (r(s(s(elem!1)), z)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23483, 6423])).
% 3.53/3.82 tff(23485,plain,
% 3.53/3.82 (b(s(s(elem!1)), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1260, 44, 14204, 4575])).
% 3.53/3.82 tff(23486,plain,
% 3.53/3.82 (~b(elem!1, s(s(elem!1)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[11841, 23485, 2811, 251])).
% 3.53/3.82 tff(23487,plain,
% 3.53/3.82 (r(elem!1, s(s(elem!1)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[2522, 23486, 2462])).
% 3.53/3.82 tff(23488,plain,
% 3.53/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, 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)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(rewrite,[status(thm)],[])).
% 3.53/3.82 tff(23489,plain,
% 3.53/3.82 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(rewrite,[status(thm)],[])).
% 3.53/3.82 tff(23490,plain,
% 3.53/3.82 (((~![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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[23489])).
% 3.53/3.82 tff(23491,plain,
% 3.53/3.82 (((~![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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23490, 23488])).
% 3.53/3.82 tff(23492,plain,
% 3.53/3.82 ((~![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)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.82 inference(quant_inst,[status(thm)],[])).
% 3.53/3.82 tff(23493,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23492, 23491])).
% 3.53/3.82 tff(23494,plain,
% 3.53/3.82 (~r(s(s(elem!1)), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23493, 333, 23487, 3654, 2323])).
% 3.53/3.82 tff(23495,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23494, 23484])).
% 3.53/3.82 tff(23496,plain,(r(s(s(elem!1)), elem!1) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23497,plain,
% 3.53/3.82 (~b(z, s(s(elem!1)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23496, 23478, 2323, 9383, 251, 14204, 624])).
% 3.53/3.82 tff(23498,plain,
% 3.53/3.82 (~r(s(s(elem!1)), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[13396, 2484, 3654, 563])).
% 3.53/3.82 tff(23499,plain,
% 3.53/3.82 (~r(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23498, 23479])).
% 3.53/3.82 tff(23500,plain,
% 3.53/3.82 (b(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[704, 23499, 4798])).
% 3.53/3.82 tff(23501,plain,
% 3.53/3.82 (~b(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[10565, 23500, 251, 624])).
% 3.53/3.82 tff(23502,plain,
% 3.53/3.82 (r(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[396, 23501])).
% 3.53/3.82 tff(23503,plain,
% 3.53/3.82 (r(s(s(elem!1)), z)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23502, 6423])).
% 3.53/3.82 tff(23504,plain,
% 3.53/3.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[6791, 23503, 2833])).
% 3.53/3.82 tff(23505,plain,
% 3.53/3.82 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[277, 44, 23504])).
% 3.53/3.82 tff(23506,plain,
% 3.53/3.82 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23505, 274])).
% 3.53/3.82 tff(23507,plain,
% 3.53/3.82 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[12789, 2686])).
% 3.53/3.82 tff(23508,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[8384, 144, 585, 12795, 23507, 23506])).
% 3.53/3.82 tff(23509,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23510,plain,
% 3.53/3.82 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23509, 623, 57, 3654, 585, 251, 624, 563, 435])).
% 3.53/3.82 tff(23511,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[130, 23510, 4182])).
% 3.53/3.82 tff(23512,plain,
% 3.53/3.82 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[880, 23511, 624, 251])).
% 3.53/3.82 tff(23513,plain,
% 3.53/3.82 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[302, 23512])).
% 3.53/3.82 tff(23514,plain,
% 3.53/3.82 (~r(s(s(elem!1)), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[9411, 23513, 3654, 2833])).
% 3.53/3.82 tff(23515,plain,
% 3.53/3.82 (~r(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23514, 23479])).
% 3.53/3.82 tff(23516,plain,
% 3.53/3.82 (b(s(s(s(z))), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[704, 23515, 4798])).
% 3.53/3.82 tff(23517,plain,
% 3.53/3.82 (~b(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[10565, 23516, 251, 624])).
% 3.53/3.82 tff(23518,plain,
% 3.53/3.82 (r(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[396, 23517])).
% 3.53/3.82 tff(23519,plain,
% 3.53/3.82 (r(s(s(elem!1)), z)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23518, 6423])).
% 3.53/3.82 tff(23520,plain,
% 3.53/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(rewrite,[status(thm)],[])).
% 3.53/3.82 tff(23521,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.82 inference(quant_inst,[status(thm)],[])).
% 3.53/3.82 tff(23522,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23521, 23520])).
% 3.53/3.82 tff(23523,plain,
% 3.53/3.82 (~r(s(s(elem!1)), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23522, 333, 3654, 23513, 2833])).
% 3.53/3.82 tff(23524,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23523, 23519])).
% 3.53/3.82 tff(23525,plain,((~r(z, s(s(s(z))))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23526,plain,
% 3.53/3.82 (~r(z, s(s(s(z))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23525, 23478, 9383, 251, 624, 23428, 23432, 435])).
% 3.53/3.82 tff(23527,plain,
% 3.53/3.82 (b(z, s(s(s(z))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[619, 23526])).
% 3.53/3.82 tff(23528,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[2828, 23527, 23497, 9383])).
% 3.53/3.82 tff(23529,plain,((~b(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~(elem!1 = s(z))) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23530,plain,
% 3.53/3.82 (~r(s(s(elem!1)), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23529, 23423, 251, 23409, 23350, 23360, 23406, 2323, 709, 23397, 23388, 23378])).
% 3.53/3.82 tff(23531,plain,
% 3.53/3.82 (b(s(s(elem!1)), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1283, 23530, 9481])).
% 3.53/3.82 tff(23532,plain,
% 3.53/3.82 (b(s(s(s(z))), s(elem!1))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23531, 23343])).
% 3.53/3.82 tff(23533,plain,
% 3.53/3.82 (b(s(s(s(z))), s(s(z)))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23532, 23342])).
% 3.53/3.82 tff(23534,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9445])).
% 3.53/3.82 tff(23535,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.82 inference(symmetry,[status(thm)],[23534])).
% 3.53/3.82 tff(23536,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[542, 23397, 9578])).
% 3.53/3.82 tff(23537,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23536, 23535])).
% 3.53/3.82 tff(23538,plain,
% 3.53/3.82 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1451, 23387])).
% 3.53/3.82 tff(23539,plain,
% 3.53/3.82 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[9783, 144, 23538, 23537])).
% 3.53/3.82 tff(23540,plain,
% 3.53/3.82 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23539, 23533])).
% 3.53/3.82 tff(23541,plain,
% 3.53/3.82 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1137, 23540])).
% 3.53/3.82 tff(23542,plain,
% 3.53/3.82 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23541, 23340])).
% 3.53/3.82 tff(23543,plain,
% 3.53/3.82 (~b(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[10565, 23423, 251, 23378])).
% 3.53/3.82 tff(23544,plain,
% 3.53/3.82 (r(s(s(s(z))), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[396, 23543])).
% 3.53/3.82 tff(23545,plain,
% 3.53/3.82 (r(s(s(elem!1)), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[6447, 23544, 9383])).
% 3.53/3.82 tff(23546,plain,
% 3.53/3.82 (~r(z, s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[6460, 23541, 9383, 23545, 321])).
% 3.53/3.82 tff(23547,plain,
% 3.53/3.82 (b(z, s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[583, 23546])).
% 3.53/3.82 tff(23548,plain,
% 3.53/3.82 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[8386, 23547, 23397, 9578, 23388])).
% 3.53/3.82 tff(23549,plain,
% 3.53/3.82 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[279, 23548])).
% 3.53/3.82 tff(23550,plain,
% 3.53/3.82 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[18624, 23549, 11546, 23380, 490])).
% 3.53/3.82 tff(23551,plain,
% 3.53/3.82 ($false),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23550, 23542])).
% 3.53/3.82 tff(23552,plain,(b(s(elem!1), elem!1) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.82 tff(23553,plain,
% 3.53/3.82 (b(s(elem!1), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23552, 709, 11546, 23338, 321, 23334, 2323, 2484])).
% 3.53/3.82 tff(23554,plain,
% 3.53/3.82 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 3.53/3.82 inference(transitivity,[status(thm)],[13440, 13443])).
% 3.53/3.82 tff(23555,plain,
% 3.53/3.82 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.53/3.82 inference(symmetry,[status(thm)],[23343])).
% 3.53/3.82 tff(23556,plain,
% 3.53/3.82 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23341, 23555])).
% 3.53/3.82 tff(23557,plain,
% 3.53/3.82 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[23556])).
% 3.53/3.82 tff(23558,plain,
% 3.53/3.82 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9386])).
% 3.53/3.82 tff(23559,plain,
% 3.53/3.82 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.82 tff(23560,plain,
% 3.53/3.82 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23559, 23558])).
% 3.53/3.82 tff(23561,plain,
% 3.53/3.82 (b(s(elem!1), elem!1)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23552, 709, 11546, 490, 321, 251, 2323, 2484])).
% 3.53/3.82 tff(23562,plain,
% 3.53/3.82 (b(s(s(z)), s(z))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23561, 23560])).
% 3.53/3.82 tff(23563,plain,
% 3.53/3.82 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[2674, 466, 9383])).
% 3.53/3.82 tff(23564,plain,
% 3.53/3.82 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[1451, 23563])).
% 3.53/3.82 tff(23565,plain,
% 3.53/3.82 (r(z, s(s(z)))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[562, 23328])).
% 3.53/3.82 tff(23566,plain,
% 3.53/3.82 (b(s(elem!1), s(z))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[451, 23559])).
% 3.53/3.82 tff(23567,plain,
% 3.53/3.82 (~r(s(z), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[8274, 562, 321, 23380])).
% 3.53/3.82 tff(23568,plain,
% 3.53/3.82 (b(s(z), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[348, 23567])).
% 3.53/3.82 tff(23569,plain,
% 3.53/3.82 (~b(s(elem!1), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[499, 23568, 490, 23566])).
% 3.53/3.82 tff(23570,plain,
% 3.53/3.82 (r(s(elem!1), z)),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[507, 23569])).
% 3.53/3.82 tff(23571,plain,
% 3.53/3.82 (r(s(s(z)), z)),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23570, 9393])).
% 3.53/3.82 tff(23572,plain,
% 3.53/3.82 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.53/3.82 inference(rewrite,[status(thm)],[])).
% 3.53/3.82 tff(23573,plain,
% 3.53/3.82 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.53/3.82 inference(quant_inst,[status(thm)],[])).
% 3.53/3.82 tff(23574,plain,
% 3.53/3.82 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23573, 23572])).
% 3.53/3.82 tff(23575,plain,
% 3.53/3.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[23574, 333, 321, 23571, 23565])).
% 3.53/3.82 tff(23576,plain,
% 3.53/3.82 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23575, 9633])).
% 3.53/3.82 tff(23577,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[542, 23576, 9578])).
% 3.53/3.82 tff(23578,plain,
% 3.53/3.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23577, 23535])).
% 3.53/3.82 tff(23579,plain,
% 3.53/3.82 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9693])).
% 3.53/3.82 tff(23580,plain,
% 3.53/3.82 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.82 inference(symmetry,[status(thm)],[23579])).
% 3.53/3.82 tff(23581,plain,
% 3.53/3.82 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.82 tff(23582,plain,
% 3.53/3.82 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23581, 972])).
% 3.53/3.82 tff(23583,plain,
% 3.53/3.82 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[23582])).
% 3.53/3.82 tff(23584,plain,
% 3.53/3.82 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.82 inference(unit_resolution,[status(thm)],[4281, 9481])).
% 3.53/3.82 tff(23585,plain,
% 3.53/3.82 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.53/3.82 inference(modus_ponens,[status(thm)],[23584, 23583])).
% 3.53/3.82 tff(23586,plain,
% 3.53/3.82 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9417, 9690])).
% 3.53/3.82 tff(23587,plain,
% 3.53/3.82 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.82 inference(symmetry,[status(thm)],[23586])).
% 3.53/3.82 tff(23588,plain,
% 3.53/3.82 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[9690])).
% 3.53/3.82 tff(23589,plain,
% 3.53/3.82 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23588, 23587])).
% 3.53/3.82 tff(23590,plain,
% 3.53/3.82 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[23589])).
% 3.53/3.82 tff(23591,plain,
% 3.53/3.82 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.82 inference(rewrite,[status(thm)],[])).
% 3.53/3.82 tff(23592,plain,
% 3.53/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.82 inference(monotonicity,[status(thm)],[23591])).
% 3.53/3.82 tff(23593,plain,
% 3.53/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.82 inference(transitivity,[status(thm)],[23592, 9778])).
% 3.53/3.82 tff(23594,plain,
% 3.53/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23595,plain,
% 3.53/3.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23594, 23593])).
% 3.53/3.83 tff(23596,plain,
% 3.53/3.83 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23595, 144, 1398, 2254, 9739])).
% 3.53/3.83 tff(23597,plain,
% 3.53/3.83 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23596, 23557])).
% 3.53/3.83 tff(23598,plain,
% 3.53/3.83 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[1283, 23597, 9481])).
% 3.53/3.83 tff(23599,plain,
% 3.53/3.83 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23598, 23554])).
% 3.53/3.83 tff(23600,plain,
% 3.53/3.83 (~b(s(elem!1), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[499, 489, 490, 23566])).
% 3.53/3.83 tff(23601,plain,
% 3.53/3.83 (r(s(elem!1), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[507, 23600])).
% 3.53/3.83 tff(23602,plain,
% 3.53/3.83 (r(s(s(z)), z)),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23601, 9393])).
% 3.53/3.83 tff(23603,plain,
% 3.53/3.83 (((~![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(z))), s(s(z)))) | (~r(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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23604,plain,
% 3.53/3.83 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23605,plain,
% 3.53/3.83 (((~![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(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23604])).
% 3.53/3.83 tff(23606,plain,
% 3.53/3.83 (((~![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(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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(transitivity,[status(thm)],[23605, 23603])).
% 3.53/3.83 tff(23607,plain,
% 3.53/3.83 ((~![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(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23608,plain,
% 3.53/3.83 ((~![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(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23607, 23606])).
% 3.53/3.83 tff(23609,plain,
% 3.53/3.83 (~r(s(s(s(z))), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23608, 333, 23602, 23565, 23599])).
% 3.53/3.83 tff(23610,plain,
% 3.53/3.83 (b(s(s(s(z))), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[396, 23609])).
% 3.53/3.83 tff(23611,plain,
% 3.53/3.83 (((~![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))), s(s(z)))) | (~r(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(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23612,plain,
% 3.53/3.83 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23613,plain,
% 3.53/3.83 (((~![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(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(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23612])).
% 3.53/3.83 tff(23614,plain,
% 3.53/3.83 (((~![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(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(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.83 inference(transitivity,[status(thm)],[23613, 23611])).
% 3.53/3.83 tff(23615,plain,
% 3.53/3.83 ((~![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(z)))) | (~r(z, s(s(s(z))))))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23616,plain,
% 3.53/3.83 ((~![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))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23615, 23614])).
% 3.53/3.83 tff(23617,plain,
% 3.53/3.83 (~r(z, s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23616, 333, 23602, 23565, 23599])).
% 3.53/3.83 tff(23618,plain,
% 3.53/3.83 (b(z, s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[619, 23617])).
% 3.53/3.83 tff(23619,plain,
% 3.53/3.83 (~b(s(z), s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2156, 23618, 489, 23610])).
% 3.53/3.83 tff(23620,plain,
% 3.53/3.83 (r(s(z), s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[172, 23619])).
% 3.53/3.83 tff(23621,plain,
% 3.53/3.83 (b(elem!1, z) <=> b(s(z), z)),
% 3.53/3.83 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.83 tff(23622,plain,
% 3.53/3.83 (b(s(z), z) <=> b(elem!1, z)),
% 3.53/3.83 inference(symmetry,[status(thm)],[23621])).
% 3.53/3.83 tff(23623,plain,
% 3.53/3.83 (b(elem!1, z)),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[489, 23622])).
% 3.53/3.83 tff(23624,plain,
% 3.53/3.83 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.53/3.83 inference(symmetry,[status(thm)],[9717])).
% 3.53/3.83 tff(23625,plain,
% 3.53/3.83 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 3.53/3.83 inference(transitivity,[status(thm)],[9766, 23624])).
% 3.53/3.83 tff(23626,plain,
% 3.53/3.83 ((~r(s(z), s(s(z)))) <=> (~r(elem!1, s(elem!1)))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23625])).
% 3.53/3.83 tff(23627,plain,
% 3.53/3.83 (b(z, s(s(elem!1)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2828, 23618, 9383])).
% 3.53/3.83 tff(23628,plain,
% 3.53/3.83 (~b(elem!1, s(s(elem!1)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2821, 23627, 9383, 23623, 23610])).
% 3.53/3.83 tff(23629,plain,
% 3.53/3.83 (r(elem!1, s(s(elem!1)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2522, 23628, 9488])).
% 3.53/3.83 tff(23630,plain,
% 3.53/3.83 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[6233, 23629, 2323, 23598])).
% 3.53/3.83 tff(23631,plain,
% 3.53/3.83 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2758, 23630, 9402])).
% 3.53/3.83 tff(23632,plain,
% 3.53/3.83 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23631, 9398])).
% 3.53/3.83 tff(23633,plain,
% 3.53/3.83 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23634,plain,
% 3.53/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23633])).
% 3.53/3.83 tff(23635,plain,
% 3.53/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.83 inference(transitivity,[status(thm)],[23634, 7944])).
% 3.53/3.83 tff(23636,plain,
% 3.53/3.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23637,plain,
% 3.53/3.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23636, 23635])).
% 3.53/3.83 tff(23638,plain,
% 3.53/3.83 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23637, 144, 1398, 23632, 2254])).
% 3.53/3.83 tff(23639,plain,
% 3.53/3.83 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[1473, 44, 23638, 217])).
% 3.53/3.83 tff(23640,plain,
% 3.53/3.83 (~b(s(s(s(z))), s(z))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2271, 144, 490, 489, 23610])).
% 3.53/3.83 tff(23641,plain,
% 3.53/3.83 (r(s(s(s(z))), s(z))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[2794, 23640])).
% 3.53/3.83 tff(23642,plain,
% 3.53/3.83 (((~![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(s(s(s(z))), s(z))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23643,plain,
% 3.53/3.83 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23644,plain,
% 3.53/3.83 (((~![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(z)), s(s(s(z))))) | (~r(s(z), 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(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23643])).
% 3.53/3.83 tff(23645,plain,
% 3.53/3.83 (((~![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(z)), s(s(s(z))))) | (~r(s(z), 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(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.53/3.83 inference(transitivity,[status(thm)],[23644, 23642])).
% 3.53/3.83 tff(23646,plain,
% 3.53/3.83 ((~![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(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23647,plain,
% 3.53/3.83 ((~![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(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23646, 23645])).
% 3.53/3.83 tff(23648,plain,
% 3.53/3.83 (~r(s(z), s(s(z)))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23647, 333, 23641, 23620, 23639])).
% 3.53/3.83 tff(23649,plain,
% 3.53/3.83 (~r(elem!1, s(elem!1))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23648, 23626])).
% 3.53/3.83 tff(23650,plain,
% 3.53/3.83 (b(elem!1, s(elem!1))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[560, 23649, 9430])).
% 3.53/3.83 tff(23651,plain,
% 3.53/3.83 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[3526])).
% 3.53/3.83 tff(23652,plain,
% 3.53/3.83 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.53/3.83 inference(transitivity,[status(thm)],[23651, 2476])).
% 3.53/3.83 tff(23653,plain,
% 3.53/3.83 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.53/3.83 inference(symmetry,[status(thm)],[23652])).
% 3.53/3.83 tff(23654,plain,
% 3.53/3.83 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.53/3.83 inference(monotonicity,[status(thm)],[23653])).
% 3.53/3.83 tff(23655,plain,
% 3.53/3.83 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[3524, 23654])).
% 3.53/3.83 tff(23656,plain,
% 3.53/3.83 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[12662, 144, 251, 624])).
% 3.53/3.83 tff(23657,plain,
% 3.53/3.83 (~b(s(s(s(s(z)))), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23656, 3529])).
% 3.53/3.83 tff(23658,plain,
% 3.53/3.83 (r(s(s(s(s(z)))), z)),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[4243, 44, 242, 23657])).
% 3.53/3.83 tff(23659,plain,
% 3.53/3.83 (((~![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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(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(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23660,plain,
% 3.53/3.83 ((~![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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.53/3.83 inference(quant_inst,[status(thm)],[])).
% 3.53/3.83 tff(23661,plain,
% 3.53/3.83 ((~![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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.53/3.83 inference(modus_ponens,[status(thm)],[23660, 23659])).
% 3.53/3.83 tff(23662,plain,
% 3.53/3.83 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.83 inference(unit_resolution,[status(thm)],[23661, 333, 509, 562, 23658])).
% 3.53/3.83 tff(23663,plain,
% 3.53/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23664,plain,
% 3.53/3.83 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.53/3.83 inference(rewrite,[status(thm)],[])).
% 3.53/3.83 tff(23665,plain,
% 3.53/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23664])).
% 3.53/3.84 tff(23666,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.53/3.84 inference(transitivity,[status(thm)],[23665, 23663])).
% 3.53/3.84 tff(23667,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23668,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23667, 23666])).
% 3.53/3.84 tff(23669,plain,
% 3.53/3.84 ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23668, 144, 547, 451])).
% 3.53/3.84 tff(23670,plain,
% 3.53/3.84 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23669, 3529])).
% 3.53/3.84 tff(23671,plain,
% 3.53/3.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23672,plain,
% 3.53/3.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23673,plain,
% 3.53/3.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23672, 23671])).
% 3.53/3.84 tff(23674,plain,
% 3.53/3.84 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23673, 44, 23670])).
% 3.53/3.84 tff(23675,plain,
% 3.53/3.84 ($false),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23674, 23662, 23655])).
% 3.53/3.84 tff(23676,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.84 tff(23677,plain,
% 3.53/3.84 (~b(s(s(s(s(z)))), elem!1)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23676, 23650, 9383, 251, 451, 562, 23623, 23601])).
% 3.53/3.84 tff(23678,plain,
% 3.53/3.84 (~b(s(s(s(elem!1))), s(z))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[3588, 23677, 9383])).
% 3.53/3.84 tff(23679,plain,
% 3.53/3.84 (r(s(s(s(elem!1))), s(z))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1101, 23678])).
% 3.53/3.84 tff(23680,plain,
% 3.53/3.84 (r(s(s(s(s(z)))), s(z))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23679, 9424])).
% 3.53/3.84 tff(23681,plain,
% 3.53/3.84 (((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), 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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23682,plain,
% 3.53/3.84 ((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23683,plain,
% 3.53/3.84 ((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23682, 23681])).
% 3.53/3.84 tff(23684,plain,
% 3.53/3.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23683, 333, 23641, 23680, 23620])).
% 3.53/3.84 tff(23685,plain,
% 3.53/3.84 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23684, 23590])).
% 3.53/3.84 tff(23686,plain,
% 3.53/3.84 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1116, 23685, 23585])).
% 3.53/3.84 tff(23687,plain,
% 3.53/3.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23686, 23580])).
% 3.53/3.84 tff(23688,plain,
% 3.53/3.84 (((~![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(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23689,plain,
% 3.53/3.84 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23690,plain,
% 3.53/3.84 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23689])).
% 3.53/3.84 tff(23691,plain,
% 3.53/3.84 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.84 inference(transitivity,[status(thm)],[23690, 23688])).
% 3.53/3.84 tff(23692,plain,
% 3.53/3.84 ((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23693,plain,
% 3.53/3.84 ((~![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(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23692, 23691])).
% 3.53/3.84 tff(23694,plain,
% 3.53/3.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23693, 333, 23680, 23620, 322])).
% 3.53/3.84 tff(23695,plain,
% 3.53/3.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[3556, 44, 196, 23694])).
% 3.53/3.84 tff(23696,plain,
% 3.53/3.84 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23697,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23696])).
% 3.53/3.84 tff(23698,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.84 inference(transitivity,[status(thm)],[23697, 18459])).
% 3.53/3.84 tff(23699,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23700,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23699, 23698])).
% 3.53/3.84 tff(23701,plain,
% 3.53/3.84 ($false),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23700, 144, 23632, 2254, 23695, 23687])).
% 3.53/3.84 tff(23702,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.84 tff(23703,plain,
% 3.53/3.84 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23702, 562, 23380, 251, 451, 709, 1398, 490, 23568, 2323, 23578])).
% 3.53/3.84 tff(23704,plain,
% 3.53/3.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1137, 23703])).
% 3.53/3.84 tff(23705,plain,
% 3.53/3.84 (~r(s(s(elem!1)), z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[6460, 23704, 9383, 562, 321])).
% 3.53/3.84 tff(23706,plain,
% 3.53/3.84 (~r(s(s(s(z))), z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[6447, 23705, 9383])).
% 3.53/3.84 tff(23707,plain,
% 3.53/3.84 (b(elem!1, z)),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23568, 23622])).
% 3.53/3.84 tff(23708,plain,
% 3.53/3.84 (~r(s(s(s(z))), elem!1)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23315, 23704, 2484, 2323])).
% 3.53/3.84 tff(23709,plain,
% 3.53/3.84 (b(s(s(s(z))), elem!1)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[704, 23708, 23349])).
% 3.53/3.84 tff(23710,plain,
% 3.53/3.84 (~b(s(s(s(z))), z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[10565, 23709, 251, 23707])).
% 3.53/3.84 tff(23711,plain,
% 3.53/3.84 ($false),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[396, 23710, 23706])).
% 3.53/3.84 tff(23712,plain,((~r(z, s(elem!1))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.84 tff(23713,plain,
% 3.53/3.84 (~r(z, s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23712, 23564, 321, 2484, 2323, 23561, 709, 251, 490])).
% 3.53/3.84 tff(23714,plain,
% 3.53/3.84 (b(z, s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[583, 23713])).
% 3.53/3.84 tff(23715,plain,
% 3.53/3.84 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(transitivity,[status(thm)],[9576, 175])).
% 3.53/3.84 tff(23716,plain,
% 3.53/3.84 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23715])).
% 3.53/3.84 tff(23717,plain,
% 3.53/3.84 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[1446, 23716])).
% 3.53/3.84 tff(23718,plain,
% 3.53/3.84 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[472, 466, 23717])).
% 3.53/3.84 tff(23719,plain,
% 3.53/3.84 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.84 tff(23720,plain,
% 3.53/3.84 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23346])).
% 3.53/3.84 tff(23721,plain,
% 3.53/3.84 (~(elem!1 = s(s(s(z))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[166, 23720])).
% 3.53/3.84 tff(23722,plain,
% 3.53/3.84 (~r(z, s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[642, 23414, 321, 322])).
% 3.53/3.84 tff(23723,plain,
% 3.53/3.84 (b(z, s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[619, 23722])).
% 3.53/3.84 tff(23724,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23725,plain,
% 3.53/3.84 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.53/3.84 inference(rewrite,[status(thm)],[])).
% 3.53/3.84 tff(23726,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[23725])).
% 3.53/3.84 tff(23727,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.53/3.84 inference(transitivity,[status(thm)],[23726, 23724])).
% 3.53/3.84 tff(23728,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 3.53/3.84 inference(quant_inst,[status(thm)],[])).
% 3.53/3.84 tff(23729,plain,
% 3.53/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23728, 23727])).
% 3.53/3.84 tff(23730,plain,
% 3.53/3.84 ($false),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23729, 144, 451, 251, 585, 2082, 284])).
% 3.53/3.84 tff(23731,plain,((~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.84 tff(23732,plain,
% 3.53/3.84 (~b(elem!1, s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23731, 23723, 251, 451, 585])).
% 3.53/3.84 tff(23733,plain,
% 3.53/3.84 (r(elem!1, s(s(s(z))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1538, 23732, 23721])).
% 3.53/3.84 tff(23734,plain,
% 3.53/3.84 (r(s(z), s(s(s(z))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23733, 23719])).
% 3.53/3.84 tff(23735,plain,
% 3.53/3.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[16388, 23734, 11546, 322])).
% 3.53/3.84 tff(23736,plain,
% 3.53/3.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1137, 23735])).
% 3.53/3.84 tff(23737,plain,
% 3.53/3.84 (b(z, s(s(elem!1)))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[2828, 23723, 9383])).
% 3.53/3.84 tff(23738,plain,
% 3.53/3.84 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[8401, 23737, 450, 585, 23416])).
% 3.53/3.84 tff(23739,plain,
% 3.53/3.84 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1283, 23738, 9481])).
% 3.53/3.84 tff(23740,plain,
% 3.53/3.84 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.84 tff(23741,plain,
% 3.53/3.84 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.53/3.84 inference(symmetry,[status(thm)],[23740])).
% 3.53/3.84 tff(23742,plain,
% 3.53/3.84 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[9387])).
% 3.53/3.84 tff(23743,plain,
% 3.53/3.84 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 3.53/3.84 inference(symmetry,[status(thm)],[23742])).
% 3.53/3.84 tff(23744,plain,
% 3.53/3.84 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.53/3.84 inference(transitivity,[status(thm)],[23719, 23743, 23741])).
% 3.53/3.84 tff(23745,plain,
% 3.53/3.84 (r(elem!1, s(s(elem!1)))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23733, 23744])).
% 3.53/3.84 tff(23746,plain,
% 3.53/3.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[6233, 23745, 2323, 23739])).
% 3.53/3.84 tff(23747,plain,
% 3.53/3.84 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[2758, 23746, 9402])).
% 3.53/3.84 tff(23748,plain,
% 3.53/3.84 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23747, 9398])).
% 3.53/3.84 tff(23749,plain,
% 3.53/3.84 ($false),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[16226, 144, 23723, 23748, 23736, 23416])).
% 3.53/3.84 tff(23750,plain,((~r(elem!1, z)) | (~(elem!1 = s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.84 tff(23751,plain,
% 3.53/3.84 (~r(elem!1, z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[23750, 23718, 2323, 11546, 23380, 709, 23714, 251, 23561, 321])).
% 3.53/3.84 tff(23752,plain,
% 3.53/3.84 (b(elem!1, z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[1380, 23751, 23412])).
% 3.53/3.84 tff(23753,plain,
% 3.53/3.84 (~b(s(elem!1), z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[916, 23752, 251, 23561])).
% 3.53/3.84 tff(23754,plain,
% 3.53/3.84 (r(s(elem!1), z)),
% 3.53/3.84 inference(unit_resolution,[status(thm)],[507, 23753])).
% 3.53/3.84 tff(23755,plain,
% 3.53/3.84 (r(s(s(z)), z)),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[23754, 9393])).
% 3.53/3.84 tff(23756,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 3.53/3.84 tff(23757,plain,
% 3.53/3.84 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 3.53/3.84 inference(monotonicity,[status(thm)],[9386])).
% 3.53/3.84 tff(23758,plain,
% 3.53/3.84 (b(z, s(s(z)))),
% 3.53/3.84 inference(modus_ponens,[status(thm)],[585, 23757])).
% 3.53/3.84 tff(23759,plain,
% 3.53/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23760,plain,
% 3.53/3.85 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23761,plain,
% 3.53/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23760])).
% 3.53/3.85 tff(23762,plain,
% 3.53/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 3.53/3.85 inference(transitivity,[status(thm)],[23761, 23759])).
% 3.53/3.85 tff(23763,plain,
% 3.53/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 3.53/3.85 inference(quant_inst,[status(thm)],[])).
% 3.53/3.85 tff(23764,plain,
% 3.53/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23763, 23762])).
% 3.53/3.85 tff(23765,plain,
% 3.53/3.85 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23764, 144, 490, 1417, 23758])).
% 3.53/3.85 tff(23766,plain,
% 3.53/3.85 (~b(z, s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23765, 23756])).
% 3.53/3.85 tff(23767,plain,
% 3.53/3.85 (r(z, s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[619, 23766])).
% 3.53/3.85 tff(23768,plain,
% 3.53/3.85 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[9639, 333, 23767, 321, 9615])).
% 3.53/3.85 tff(23769,plain,
% 3.53/3.85 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[9653, 44, 23768])).
% 3.53/3.85 tff(23770,plain,
% 3.53/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23769, 9614])).
% 3.53/3.85 tff(23771,plain,
% 3.53/3.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[9783, 144, 23564, 23770, 23756])).
% 3.53/3.85 tff(23772,plain,
% 3.53/3.85 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1137, 23771])).
% 3.53/3.85 tff(23773,plain,
% 3.53/3.85 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23772, 23340])).
% 3.53/3.85 tff(23774,plain,
% 3.53/3.85 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23768, 9633])).
% 3.53/3.85 tff(23775,plain,
% 3.53/3.85 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[8386, 23774, 585, 9578, 466])).
% 3.53/3.85 tff(23776,plain,
% 3.53/3.85 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[279, 23775])).
% 3.53/3.85 tff(23777,plain,
% 3.53/3.85 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[18624, 23776, 11546, 322, 490])).
% 3.53/3.85 tff(23778,plain,
% 3.53/3.85 ($false),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23777, 23773])).
% 3.53/3.85 tff(23779,plain,((~b(s(s(s(z))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.85 tff(23780,plain,
% 3.53/3.85 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23779, 23714, 11546, 23380, 490, 709, 466, 321, 23755, 23562])).
% 3.53/3.85 tff(23781,plain,
% 3.53/3.85 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23780, 23557])).
% 3.53/3.85 tff(23782,plain,
% 3.53/3.85 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1283, 23781, 9481])).
% 3.53/3.85 tff(23783,plain,
% 3.53/3.85 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23782, 23554])).
% 3.53/3.85 tff(23784,plain,
% 3.53/3.85 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[709])).
% 3.53/3.85 tff(23785,plain,
% 3.53/3.85 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.53/3.85 inference(symmetry,[status(thm)],[23784])).
% 3.53/3.85 tff(23786,plain,
% 3.53/3.85 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 3.53/3.85 inference(transitivity,[status(thm)],[23356, 1578])).
% 3.53/3.85 tff(23787,plain,
% 3.53/3.85 ((~(elem!1 = s(elem!1))) <=> (~(s(z) = s(elem!1)))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23786])).
% 3.53/3.85 tff(23788,plain,
% 3.53/3.85 (~(s(z) = s(elem!1))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[9430, 23787])).
% 3.53/3.85 tff(23789,plain,
% 3.53/3.85 (b(s(elem!1), s(z))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23561, 23559])).
% 3.53/3.85 tff(23790,plain,
% 3.53/3.85 (~b(s(z), s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1853, 23714, 490, 23789])).
% 3.53/3.85 tff(23791,plain,
% 3.53/3.85 (r(s(z), s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1244, 23790, 23788])).
% 3.53/3.85 tff(23792,plain,
% 3.53/3.85 (r(s(z), s(s(z)))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23791, 9767])).
% 3.53/3.85 tff(23793,plain,
% 3.53/3.85 (((~![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(s(s(z))), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23794,plain,
% 3.53/3.85 (((~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(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23795,plain,
% 3.53/3.85 (((~![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(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23794])).
% 3.53/3.85 tff(23796,plain,
% 3.53/3.85 (((~![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(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(transitivity,[status(thm)],[23795, 23793])).
% 3.53/3.85 tff(23797,plain,
% 3.53/3.85 ((~![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))))))),
% 3.53/3.85 inference(quant_inst,[status(thm)],[])).
% 3.53/3.85 tff(23798,plain,
% 3.53/3.85 ((~![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(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23797, 23796])).
% 3.53/3.85 tff(23799,plain,
% 3.53/3.85 ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23798, 333, 23755, 23783])).
% 3.53/3.85 tff(23800,plain,
% 3.53/3.85 (~r(s(z), s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23799, 23792])).
% 3.53/3.85 tff(23801,plain,
% 3.53/3.85 (b(s(z), s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[172, 23800])).
% 3.53/3.85 tff(23802,plain,
% 3.53/3.85 (b(elem!1, s(s(s(z))))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23801, 23785])).
% 3.53/3.85 tff(23803,plain,
% 3.53/3.85 (~b(z, s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23731, 23802, 251, 23561, 23714])).
% 3.53/3.85 tff(23804,plain,
% 3.53/3.85 (r(z, s(s(s(z))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[619, 23803])).
% 3.53/3.85 tff(23805,plain,
% 3.53/3.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 3.53/3.85 inference(symmetry,[status(thm)],[23363])).
% 3.53/3.85 tff(23806,plain,
% 3.53/3.85 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23805])).
% 3.53/3.85 tff(23807,plain,
% 3.53/3.85 (((~![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(s(s(z))), s(z))) | (~r(s(s(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), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23808,plain,
% 3.53/3.85 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23809,plain,
% 3.53/3.85 (((~![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(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23808])).
% 3.53/3.85 tff(23810,plain,
% 3.53/3.85 (((~![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(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(transitivity,[status(thm)],[23809, 23807])).
% 3.53/3.85 tff(23811,plain,
% 3.53/3.85 ((~![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(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.53/3.85 inference(quant_inst,[status(thm)],[])).
% 3.53/3.85 tff(23812,plain,
% 3.53/3.85 ((~![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(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23811, 23810])).
% 3.53/3.85 tff(23813,plain,
% 3.53/3.85 ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23812, 333, 23755, 23783])).
% 3.53/3.85 tff(23814,plain,
% 3.53/3.85 (~r(s(s(s(z))), s(z))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23813, 23792])).
% 3.53/3.85 tff(23815,plain,
% 3.53/3.85 (~r(s(s(s(z))), elem!1)),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23814, 23806])).
% 3.53/3.85 tff(23816,plain,
% 3.53/3.85 (b(s(s(s(z))), elem!1)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[704, 23815, 23349])).
% 3.53/3.85 tff(23817,plain,
% 3.53/3.85 (~b(s(s(s(z))), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[10565, 23816, 251, 23752])).
% 3.53/3.85 tff(23818,plain,
% 3.53/3.85 (r(s(s(s(z))), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[396, 23817])).
% 3.53/3.85 tff(23819,plain,
% 3.53/3.85 (((~![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(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(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23820,plain,
% 3.53/3.85 (((~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(rewrite,[status(thm)],[])).
% 3.53/3.85 tff(23821,plain,
% 3.53/3.85 (((~![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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.53/3.85 inference(monotonicity,[status(thm)],[23820])).
% 3.53/3.85 tff(23822,plain,
% 3.53/3.85 (((~![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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.53/3.85 inference(transitivity,[status(thm)],[23821, 23819])).
% 3.53/3.85 tff(23823,plain,
% 3.53/3.85 ((~![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)))))),
% 3.53/3.85 inference(quant_inst,[status(thm)],[])).
% 3.53/3.85 tff(23824,plain,
% 3.53/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23823, 23822])).
% 3.53/3.85 tff(23825,plain,
% 3.53/3.85 ($false),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23824, 333, 23818, 23804, 23755, 23783])).
% 3.53/3.85 tff(23826,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.85 tff(23827,plain,
% 3.53/3.85 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23826, 23334, 709, 11546, 23338, 321, 2323, 2484])).
% 3.53/3.85 tff(23828,plain,
% 3.53/3.85 (~r(elem!1, s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[4103, 23827, 321, 2323])).
% 3.53/3.85 tff(23829,plain,
% 3.53/3.85 (b(elem!1, s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[560, 23828, 9430])).
% 3.53/3.85 tff(23830,plain,
% 3.53/3.85 (~b(z, s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1642, 23829, 23334, 23553])).
% 3.53/3.85 tff(23831,plain,
% 3.53/3.85 (r(z, s(elem!1))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[583, 23830])).
% 3.53/3.85 tff(23832,plain,
% 3.53/3.85 (r(z, s(s(z)))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23831, 23328])).
% 3.53/3.85 tff(23833,plain,
% 3.53/3.85 (b(s(elem!1), s(z))),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23553, 23559])).
% 3.53/3.85 tff(23834,plain,
% 3.53/3.85 (~r(s(z), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[8300, 23831, 321, 23827, 23553, 9383, 23829])).
% 3.53/3.85 tff(23835,plain,
% 3.53/3.85 (b(s(z), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[348, 23834])).
% 3.53/3.85 tff(23836,plain,
% 3.53/3.85 (~b(s(elem!1), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[499, 23835, 23338, 23833])).
% 3.53/3.85 tff(23837,plain,
% 3.53/3.85 (r(s(elem!1), z)),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[507, 23836])).
% 3.53/3.85 tff(23838,plain,
% 3.53/3.85 (r(s(s(z)), z)),
% 3.53/3.85 inference(modus_ponens,[status(thm)],[23837, 9393])).
% 3.53/3.85 tff(23839,plain,
% 3.53/3.85 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[23712, 23831, 321, 2484, 2323, 23553, 709, 23334, 23338])).
% 3.53/3.85 tff(23840,plain,
% 3.53/3.85 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.85 inference(unit_resolution,[status(thm)],[1451, 23839])).
% 3.53/3.85 tff(23841,plain,
% 3.53/3.85 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23842,plain,
% 3.53/3.86 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23843,plain,
% 3.53/3.86 (((~![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(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), 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(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23842])).
% 3.53/3.86 tff(23844,plain,
% 3.53/3.86 (((~![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(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), 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(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23843, 23841])).
% 3.53/3.86 tff(23845,plain,
% 3.53/3.86 ((~![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(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.86 inference(quant_inst,[status(thm)],[])).
% 3.53/3.86 tff(23846,plain,
% 3.53/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23845, 23844])).
% 3.53/3.86 tff(23847,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23846, 333, 23840, 321, 23838, 23832])).
% 3.53/3.86 tff(23848,plain,((~(elem!1 = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23849,plain,
% 3.53/3.86 (r(z, elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23848, 321, 2484, 2323, 11546, 709])).
% 3.53/3.86 tff(23850,plain,
% 3.53/3.86 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23851,plain,
% 3.53/3.86 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23852,plain,
% 3.53/3.86 (((~![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(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23851])).
% 3.53/3.86 tff(23853,plain,
% 3.53/3.86 (((~![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(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23852, 23850])).
% 3.53/3.86 tff(23854,plain,
% 3.53/3.86 ((~![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(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.86 inference(quant_inst,[status(thm)],[])).
% 3.53/3.86 tff(23855,plain,
% 3.53/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23854, 23853])).
% 3.53/3.86 tff(23856,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23855, 333, 23849, 2484, 2323, 321])).
% 3.53/3.86 tff(23857,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23858,plain,
% 3.53/3.86 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23857, 23327, 23272, 11546, 23280])).
% 3.53/3.86 tff(23859,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[302, 23858])).
% 3.53/3.86 tff(23860,plain,
% 3.53/3.86 (~r(s(z), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[15633, 51, 11546, 23305])).
% 3.53/3.86 tff(23861,plain,
% 3.53/3.86 (b(s(z), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[348, 23860])).
% 3.53/3.86 tff(23862,plain,
% 3.53/3.86 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[17920, 23325, 11546, 23305, 51, 23861])).
% 3.53/3.86 tff(23863,plain,
% 3.53/3.86 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1451, 23862])).
% 3.53/3.86 tff(23864,plain,
% 3.53/3.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2689, 23863, 57])).
% 3.53/3.86 tff(23865,plain,
% 3.53/3.86 (~b(s(elem!1), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[15113, 144, 5659, 6147, 23864])).
% 3.53/3.86 tff(23866,plain,
% 3.53/3.86 (r(s(elem!1), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2860, 44, 23865, 2857])).
% 3.53/3.86 tff(23867,plain,
% 3.53/3.86 (~r(z, elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2541, 51, 2323, 322])).
% 3.53/3.86 tff(23868,plain,
% 3.53/3.86 (b(z, elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[658, 23867, 23296])).
% 3.53/3.86 tff(23869,plain,
% 3.53/3.86 (b(z, s(z))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[9366, 23868, 57])).
% 3.53/3.86 tff(23870,plain,
% 3.53/3.86 (~r(elem!1, s(z))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23286, 333, 11546, 2484, 2323])).
% 3.53/3.86 tff(23871,plain,
% 3.53/3.86 (elem!1 = s(z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[720, 23326, 23870])).
% 3.53/3.86 tff(23872,plain,
% 3.53/3.86 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23857, 23871, 2323, 11546, 2484])).
% 3.53/3.86 tff(23873,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[302, 23872])).
% 3.53/3.86 tff(23874,plain,
% 3.53/3.86 (s(z) = elem!1),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[18838, 490, 2323, 11546, 322, 251])).
% 3.53/3.86 tff(23875,plain,
% 3.53/3.86 (~(s(s(s(elem!1))) = elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2468, 23874])).
% 3.53/3.86 tff(23876,plain,
% 3.53/3.86 (~(elem!1 = s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2482, 23875])).
% 3.53/3.86 tff(23877,plain,
% 3.53/3.86 (~(s(s(elem!1)) = s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1196, 23876])).
% 3.53/3.86 tff(23878,plain,
% 3.53/3.86 (s(s(z)) = s(elem!1)),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23874])).
% 3.53/3.86 tff(23879,plain,
% 3.53/3.86 (s(s(s(z))) = s(s(elem!1))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23878])).
% 3.53/3.86 tff(23880,plain,
% 3.53/3.86 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23879])).
% 3.53/3.86 tff(23881,plain,
% 3.53/3.86 (b(s(s(elem!1)), z)),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[285, 23880])).
% 3.53/3.86 tff(23882,plain,
% 3.53/3.86 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23878])).
% 3.53/3.86 tff(23883,plain,
% 3.53/3.86 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23882, 174])).
% 3.53/3.86 tff(23884,plain,
% 3.53/3.86 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23883, 175])).
% 3.53/3.86 tff(23885,plain,
% 3.53/3.86 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23884])).
% 3.53/3.86 tff(23886,plain,
% 3.53/3.86 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[1446, 23885])).
% 3.53/3.86 tff(23887,plain,
% 3.53/3.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[13493, 51, 2484, 509])).
% 3.53/3.86 tff(23888,plain,
% 3.53/3.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[472, 23887, 23886])).
% 3.53/3.86 tff(23889,plain,
% 3.53/3.86 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23879])).
% 3.53/3.86 tff(23890,plain,
% 3.53/3.86 (~r(s(z), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[15633, 51, 11546, 322])).
% 3.53/3.86 tff(23891,plain,
% 3.53/3.86 (b(s(z), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[348, 23890])).
% 3.53/3.86 tff(23892,plain,
% 3.53/3.86 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[19392, 23891, 11546, 322, 490, 51])).
% 3.53/3.86 tff(23893,plain,
% 3.53/3.86 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1137, 23892])).
% 3.53/3.86 tff(23894,plain,
% 3.53/3.86 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23893, 23889])).
% 3.53/3.86 tff(23895,plain,
% 3.53/3.86 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[13623, 144, 286, 23894, 23888, 23881])).
% 3.53/3.86 tff(23896,plain,
% 3.53/3.86 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1283, 23895, 23877])).
% 3.53/3.86 tff(23897,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23879])).
% 3.53/3.86 tff(23898,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.86 inference(symmetry,[status(thm)],[23897])).
% 3.53/3.86 tff(23899,plain,
% 3.53/3.86 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23879])).
% 3.53/3.86 tff(23900,plain,
% 3.53/3.86 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23899])).
% 3.53/3.86 tff(23901,plain,
% 3.53/3.86 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[244, 23900])).
% 3.53/3.86 tff(23902,plain,
% 3.53/3.86 (~r(elem!1, z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2331, 51, 2323, 322])).
% 3.53/3.86 tff(23903,plain,
% 3.53/3.86 (b(elem!1, z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1380, 23902, 1368])).
% 3.53/3.86 tff(23904,plain,
% 3.53/3.86 (~b(s(s(elem!1)), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[13370, 144, 251, 23903, 23881])).
% 3.53/3.86 tff(23905,plain,
% 3.53/3.86 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23874])).
% 3.53/3.86 tff(23906,plain,
% 3.53/3.86 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23905, 1218])).
% 3.53/3.86 tff(23907,plain,
% 3.53/3.86 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 3.53/3.86 inference(transitivity,[status(thm)],[23906, 4572])).
% 3.53/3.86 tff(23908,plain,
% 3.53/3.86 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23907])).
% 3.53/3.86 tff(23909,plain,
% 3.53/3.86 (~(s(s(elem!1)) = elem!1)),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[107, 23908])).
% 3.53/3.86 tff(23910,plain,
% 3.53/3.86 (r(s(s(elem!1)), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1260, 44, 23909, 23904])).
% 3.53/3.86 tff(23911,plain,
% 3.53/3.86 (((~![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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23912,plain,
% 3.53/3.86 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23913,plain,
% 3.53/3.86 (((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23912])).
% 3.53/3.86 tff(23914,plain,
% 3.53/3.86 (((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23913, 23911])).
% 3.53/3.86 tff(23915,plain,
% 3.53/3.86 ((~![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(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.53/3.86 inference(quant_inst,[status(thm)],[])).
% 3.53/3.86 tff(23916,plain,
% 3.53/3.86 ((~![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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23915, 23914])).
% 3.53/3.86 tff(23917,plain,
% 3.53/3.86 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23916, 333, 23910, 2484, 2323])).
% 3.53/3.86 tff(23918,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2758, 23917, 23901])).
% 3.53/3.86 tff(23919,plain,
% 3.53/3.86 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23918, 23898])).
% 3.53/3.86 tff(23920,plain,
% 3.53/3.86 (~b(z, s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[294, 23919, 286, 285])).
% 3.53/3.86 tff(23921,plain,
% 3.53/3.86 (r(z, s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[619, 23920])).
% 3.53/3.86 tff(23922,plain,
% 3.53/3.86 (r(z, s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2836, 23921, 23874])).
% 3.53/3.86 tff(23923,plain,
% 3.53/3.86 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23924,plain,
% 3.53/3.86 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.53/3.86 inference(rewrite,[status(thm)],[])).
% 3.53/3.86 tff(23925,plain,
% 3.53/3.86 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23924])).
% 3.53/3.86 tff(23926,plain,
% 3.53/3.86 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23925, 23923])).
% 3.53/3.86 tff(23927,plain,
% 3.53/3.86 ((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.53/3.86 inference(quant_inst,[status(thm)],[])).
% 3.53/3.86 tff(23928,plain,
% 3.53/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[23927, 23926])).
% 3.53/3.86 tff(23929,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23928, 333, 2737, 509, 4223, 4571])).
% 3.53/3.86 tff(23930,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23931,plain,
% 3.53/3.86 (~r(s(elem!1), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23930, 23922, 23896, 509])).
% 3.53/3.86 tff(23932,plain,
% 3.53/3.86 (~(s(elem!1) = s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2856, 23877])).
% 3.53/3.86 tff(23933,plain,
% 3.53/3.86 (~b(s(elem!1), s(s(elem!1)))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[15113, 144, 23918, 23894, 23888])).
% 3.53/3.86 tff(23934,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2860, 44, 23933, 23932, 23931])).
% 3.53/3.86 tff(23935,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23936,plain,
% 3.53/3.86 (~b(s(s(s(z))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23935, 509, 2484, 23873, 51, 2323, 23868, 11546, 322, 23869, 23320])).
% 3.53/3.86 tff(23937,plain,
% 3.53/3.86 (r(s(s(s(z))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[396, 23936])).
% 3.53/3.86 tff(23938,plain,
% 3.53/3.86 (r(s(s(elem!1)), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[6447, 23937, 57])).
% 3.53/3.86 tff(23939,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[13555, 333, 509, 51, 23938, 4571])).
% 3.53/3.86 tff(23940,plain,((~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23941,plain,
% 3.53/3.86 (~r(s(elem!1), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23940, 51, 23866, 57, 23280, 23272, 11546, 23305])).
% 3.53/3.86 tff(23942,plain,
% 3.53/3.86 (b(s(elem!1), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[507, 23941])).
% 3.53/3.86 tff(23943,plain,
% 3.53/3.86 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[22668, 1])).
% 3.53/3.86 tff(23944,plain,
% 3.53/3.86 (s(z) = elem!1),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[18838, 490, 23943, 11546, 322, 251])).
% 3.53/3.86 tff(23945,plain,
% 3.53/3.86 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23944])).
% 3.53/3.86 tff(23946,plain,
% 3.53/3.86 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 3.53/3.86 inference(transitivity,[status(thm)],[23945, 2])).
% 3.53/3.86 tff(23947,plain,
% 3.53/3.86 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 3.53/3.86 inference(transitivity,[status(thm)],[23946, 4795])).
% 3.53/3.86 tff(23948,plain,
% 3.53/3.86 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23947])).
% 3.53/3.86 tff(23949,plain,
% 3.53/3.86 (~(s(s(s(z))) = elem!1)),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[166, 23948])).
% 3.53/3.86 tff(23950,plain,
% 3.53/3.86 (~r(elem!1, z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2331, 51, 23943, 322])).
% 3.53/3.86 tff(23951,plain,
% 3.53/3.86 (b(elem!1, z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1380, 23950, 77])).
% 3.53/3.86 tff(23952,plain,
% 3.53/3.86 (~b(s(s(s(z))), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[10565, 23951, 251, 285])).
% 3.53/3.86 tff(23953,plain,
% 3.53/3.86 (r(s(s(s(z))), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[704, 23952, 23949])).
% 3.53/3.86 tff(23954,plain,
% 3.53/3.86 (s(s(z)) = s(elem!1)),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23944])).
% 3.53/3.86 tff(23955,plain,
% 3.53/3.86 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23954])).
% 3.53/3.86 tff(23956,plain,
% 3.53/3.86 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 3.53/3.86 inference(monotonicity,[status(thm)],[23955])).
% 3.53/3.86 tff(23957,plain,
% 3.53/3.86 (~(s(elem!1) = s(s(s(z))))),
% 3.53/3.86 inference(modus_ponens,[status(thm)],[217, 23956])).
% 3.53/3.86 tff(23958,plain,
% 3.53/3.86 (~b(z, s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[9320, 23953, 1, 23957, 285, 490, 491, 23891])).
% 3.53/3.86 tff(23959,plain,
% 3.53/3.86 (r(z, s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[619, 23958])).
% 3.53/3.86 tff(23960,plain,
% 3.53/3.86 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[17920, 23891, 11546, 322, 490, 51])).
% 3.53/3.86 tff(23961,plain,
% 3.53/3.86 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1451, 23960])).
% 3.53/3.86 tff(23962,plain,
% 3.53/3.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2689, 23961, 23944])).
% 3.53/3.86 tff(23963,plain,
% 3.53/3.86 (~b(s(elem!1), s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[15601, 23962, 491, 286, 23893])).
% 3.53/3.86 tff(23964,plain,
% 3.53/3.86 (r(s(elem!1), s(s(s(z))))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[965, 23963, 23957])).
% 3.53/3.86 tff(23965,plain,
% 3.53/3.86 (~(s(s(s(elem!1))) = elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2468, 23944])).
% 3.53/3.86 tff(23966,plain,
% 3.53/3.86 (~(elem!1 = s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[2482, 23965])).
% 3.53/3.86 tff(23967,plain,
% 3.53/3.86 (~(s(s(elem!1)) = s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1196, 23966])).
% 3.53/3.86 tff(23968,plain,
% 3.53/3.86 (~(s(elem!1) = elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[906, 23966])).
% 3.53/3.86 tff(23969,plain,
% 3.53/3.86 (~b(s(elem!1), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[916, 23951, 251, 491])).
% 3.53/3.86 tff(23970,plain,
% 3.53/3.86 (r(s(elem!1), elem!1)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[448, 23969, 23968])).
% 3.53/3.86 tff(23971,plain,
% 3.53/3.86 (~r(elem!1, s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[13399, 23970, 286, 2484, 23944, 251, 1, 51, 23951, 23967, 491])).
% 3.53/3.86 tff(23972,plain,
% 3.53/3.86 (b(elem!1, s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[560, 23971, 23966])).
% 3.53/3.86 tff(23973,plain,
% 3.53/3.86 (~b(z, s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[949, 23972, 491, 23951])).
% 3.53/3.86 tff(23974,plain,
% 3.53/3.86 (r(z, s(elem!1))),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[583, 23973])).
% 3.53/3.86 tff(23975,plain,
% 3.53/3.86 ($false),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[1929, 23974, 23964, 23959, 23953])).
% 3.53/3.86 tff(23976,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.86 tff(23977,plain,
% 3.53/3.86 (~b(s(s(s(z))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[23976, 23942, 23280, 23859, 51, 23292, 23324, 23325, 11546, 23305])).
% 3.53/3.86 tff(23978,plain,
% 3.53/3.86 (r(s(s(s(z))), z)),
% 3.53/3.86 inference(unit_resolution,[status(thm)],[396, 23977])).
% 3.53/3.87 tff(23979,plain,
% 3.53/3.87 (r(s(s(elem!1)), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[6447, 23978, 57])).
% 3.53/3.87 tff(23980,plain,
% 3.53/3.87 (~r(elem!1, z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[2331, 51, 23272, 23305])).
% 3.53/3.87 tff(23981,plain,
% 3.53/3.87 (b(elem!1, z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[1380, 23980, 23320])).
% 3.53/3.87 tff(23982,plain,
% 3.53/3.87 (~r(s(z), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[19114, 333, 11546, 23280, 23272])).
% 3.53/3.87 tff(23983,plain,
% 3.53/3.87 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23278, 23943])).
% 3.53/3.87 tff(23984,plain,
% 3.53/3.87 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[130, 23983, 2545])).
% 3.53/3.87 tff(23985,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 3.53/3.87 tff(23986,plain,
% 3.53/3.87 (~(s(z) = elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23303, 304, 2545])).
% 3.53/3.87 tff(23987,plain,
% 3.53/3.87 (b(s(z), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[406, 23986, 2310])).
% 3.53/3.87 tff(23988,plain,
% 3.53/3.87 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(23989,plain,
% 3.53/3.87 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(23990,plain,
% 3.53/3.87 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.87 inference(monotonicity,[status(thm)],[23989])).
% 3.53/3.87 tff(23991,plain,
% 3.53/3.87 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(transitivity,[status(thm)],[23990, 23988])).
% 3.53/3.87 tff(23992,plain,
% 3.53/3.87 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(quant_inst,[status(thm)],[])).
% 3.53/3.87 tff(23993,plain,
% 3.53/3.87 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.87 inference(modus_ponens,[status(thm)],[23992, 23991])).
% 3.53/3.87 tff(23994,plain,
% 3.53/3.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23993, 333, 670, 2484, 2323])).
% 3.53/3.87 tff(23995,plain,
% 3.53/3.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[279, 23994])).
% 3.53/3.87 tff(23996,plain,
% 3.53/3.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23855, 333, 670, 2484, 2323])).
% 3.53/3.87 tff(23997,plain,
% 3.53/3.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[302, 23996])).
% 3.53/3.87 tff(23998,plain,
% 3.53/3.87 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[17809, 3193, 2484, 11546])).
% 3.53/3.87 tff(23999,plain,
% 3.53/3.87 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[1137, 23998])).
% 3.53/3.87 tff(24000,plain,
% 3.53/3.87 (~b(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[14036, 144, 23999, 23997, 23995])).
% 3.53/3.87 tff(24001,plain,
% 3.53/3.87 (r(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[396, 24000])).
% 3.53/3.87 tff(24002,plain,
% 3.53/3.87 (~r(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[11212, 24001, 3193, 670])).
% 3.53/3.87 tff(24003,plain,
% 3.53/3.87 (b(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[348, 24002])).
% 3.53/3.87 tff(24004,plain,
% 3.53/3.87 (~b(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[7093, 24003, 304, 23997])).
% 3.53/3.87 tff(24005,plain,
% 3.53/3.87 (r(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[372, 24004])).
% 3.53/3.87 tff(24006,plain,
% 3.53/3.87 (((~![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(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24007,plain,
% 3.53/3.87 (((~r(s(z), s(s(s(s(s(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24008,plain,
% 3.53/3.87 (((~![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(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.87 inference(monotonicity,[status(thm)],[24007])).
% 3.53/3.87 tff(24009,plain,
% 3.53/3.87 (((~![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(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(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(transitivity,[status(thm)],[24008, 24006])).
% 3.53/3.87 tff(24010,plain,
% 3.53/3.87 ((~![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(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 3.53/3.87 inference(quant_inst,[status(thm)],[])).
% 3.53/3.87 tff(24011,plain,
% 3.53/3.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.87 inference(modus_ponens,[status(thm)],[24010, 24009])).
% 3.53/3.87 tff(24012,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24011, 333, 24005, 24001, 3193, 11546])).
% 3.53/3.87 tff(24013,plain,((~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24014,plain,
% 3.53/3.87 (~r(z, elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24013, 3193, 11546, 304, 2484, 2323])).
% 3.53/3.87 tff(24015,plain,
% 3.53/3.87 (b(z, elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[658, 74, 1575])).
% 3.53/3.87 tff(24016,plain,
% 3.53/3.87 (~r(s(z), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[19126, 2323, 321, 11546])).
% 3.53/3.87 tff(24017,plain,
% 3.53/3.87 (b(s(z), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[406, 6529, 24016])).
% 3.53/3.87 tff(24018,plain,
% 3.53/3.87 (~b(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[7079, 24015, 305, 24017])).
% 3.53/3.87 tff(24019,plain,
% 3.53/3.87 (r(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[372, 24018])).
% 3.53/3.87 tff(24020,plain,
% 3.53/3.87 (((~![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(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24021,plain,
% 3.53/3.87 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24022,plain,
% 3.53/3.87 (((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, 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(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.53/3.87 inference(monotonicity,[status(thm)],[24021])).
% 3.53/3.87 tff(24023,plain,
% 3.53/3.87 (((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, 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(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(transitivity,[status(thm)],[24022, 24020])).
% 3.53/3.87 tff(24024,plain,
% 3.53/3.87 ((~![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(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(quant_inst,[status(thm)],[])).
% 3.53/3.87 tff(24025,plain,
% 3.53/3.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.53/3.87 inference(modus_ponens,[status(thm)],[24024, 24023])).
% 3.53/3.87 tff(24026,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24025, 333, 354, 408, 2323, 321])).
% 3.53/3.87 tff(24027,plain,((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24028,plain,
% 3.53/3.87 (~r(elem!1, z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24027, 24019, 2323, 321])).
% 3.53/3.87 tff(24029,plain,
% 3.53/3.87 (b(elem!1, z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[1380, 24028, 730])).
% 3.53/3.87 tff(24030,plain,
% 3.53/3.87 (~b(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[1602, 24029, 24017, 24015])).
% 3.53/3.87 tff(24031,plain,
% 3.53/3.87 (r(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[348, 24030])).
% 3.53/3.87 tff(24032,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[19029, 333, 24019, 24031, 11546, 321])).
% 3.53/3.87 tff(24033,plain,((z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24034,plain,
% 3.53/3.87 (~b(elem!1, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24033, 321, 74, 2323, 11546, 1575])).
% 3.53/3.87 tff(24035,plain,
% 3.53/3.87 (~(elem!1 = s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23848, 321, 2323, 2484, 11546, 1575])).
% 3.53/3.87 tff(24036,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[720, 24035, 24034, 715])).
% 3.53/3.87 tff(24037,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24038,plain,
% 3.53/3.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24037, 24014, 2323, 2484, 11546, 715, 74])).
% 3.53/3.87 tff(24039,plain,
% 3.53/3.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[302, 24038])).
% 3.53/3.87 tff(24040,plain,
% 3.53/3.87 (~b(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[7093, 490, 304, 286])).
% 3.53/3.87 tff(24041,plain,
% 3.53/3.87 (r(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[348, 24040])).
% 3.53/3.87 tff(24042,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[19075, 333, 323, 11546, 2484, 51])).
% 3.53/3.87 tff(24043,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24044,plain,
% 3.53/3.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24043, 24041, 11546, 2484])).
% 3.53/3.87 tff(24045,plain,
% 3.53/3.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[279, 24044])).
% 3.53/3.87 tff(24046,plain,
% 3.53/3.87 (~b(z, s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[22484, 24045, 490, 304, 23999])).
% 3.53/3.87 tff(24047,plain,
% 3.53/3.87 (r(z, s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[619, 24046])).
% 3.53/3.87 tff(24048,plain,
% 3.53/3.87 (~b(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[14036, 144, 23999, 286, 24045])).
% 3.53/3.87 tff(24049,plain,
% 3.53/3.87 (r(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[396, 24048])).
% 3.53/3.87 tff(24050,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[16559, 333, 24041, 24049, 24047, 3193])).
% 3.53/3.87 tff(24051,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24052,plain,
% 3.53/3.87 (~b(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24051, 3193, 24039, 304, 11546, 2484])).
% 3.53/3.87 tff(24053,plain,
% 3.53/3.87 (r(z, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[372, 24052])).
% 3.53/3.87 tff(24054,plain,
% 3.53/3.87 (~r(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24011, 333, 24053, 3193, 11546])).
% 3.53/3.87 tff(24055,plain,
% 3.53/3.87 (b(s(s(s(z))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[396, 24054])).
% 3.53/3.87 tff(24056,plain,
% 3.53/3.87 (~r(z, s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[16763, 333, 24053, 3193, 11546])).
% 3.53/3.87 tff(24057,plain,
% 3.53/3.87 (b(z, s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[619, 24056])).
% 3.53/3.87 tff(24058,plain,
% 3.53/3.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[294, 24057, 24039, 24055])).
% 3.53/3.87 tff(24059,plain,
% 3.53/3.87 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[249, 24058])).
% 3.53/3.87 tff(24060,plain,
% 3.53/3.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[15576, 24059, 11546, 24053])).
% 3.53/3.87 tff(24061,plain,
% 3.53/3.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[279, 24060])).
% 3.53/3.87 tff(24062,plain,
% 3.53/3.87 ($false),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[14138, 144, 24055, 23999, 24039, 24061])).
% 3.53/3.87 tff(24063,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.87 tff(24064,plain,
% 3.53/3.87 (~r(s(s(s(z))), s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24063, 304, 11546, 23984, 23943, 715, 71])).
% 3.53/3.87 tff(24065,plain,
% 3.53/3.87 (b(s(s(s(z))), s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[2794, 24064])).
% 3.53/3.87 tff(24066,plain,
% 3.53/3.87 (~(elem!1 = s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[712, 23986])).
% 3.53/3.87 tff(24067,plain,
% 3.53/3.87 (b(elem!1, s(z))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[720, 24066, 715])).
% 3.53/3.87 tff(24068,plain,
% 3.53/3.87 (~b(s(s(s(z))), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[4375, 24067, 24065, 23987])).
% 3.53/3.87 tff(24069,plain,
% 3.53/3.87 (~b(s(s(s(z))), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[4375, 305, 56, 134])).
% 3.53/3.87 tff(24070,plain,
% 3.53/3.87 (~b(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[2273, 490, 56, 285])).
% 3.53/3.87 tff(24071,plain,
% 3.53/3.87 (r(s(z), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[348, 24070])).
% 3.53/3.87 tff(24072,plain,
% 3.53/3.87 (~b(z, elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[7079, 490, 134, 305])).
% 3.53/3.87 tff(24073,plain,
% 3.53/3.87 (r(z, elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[658, 24072, 71])).
% 3.53/3.87 tff(24074,plain,
% 3.53/3.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[21949, 24073, 11546, 24071])).
% 3.53/3.87 tff(24075,plain,
% 3.53/3.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[302, 24074])).
% 3.53/3.87 tff(24076,plain,
% 3.53/3.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24077,plain,
% 3.53/3.87 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(rewrite,[status(thm)],[])).
% 3.53/3.87 tff(24078,plain,
% 3.53/3.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.53/3.87 inference(monotonicity,[status(thm)],[24077])).
% 3.53/3.87 tff(24079,plain,
% 3.53/3.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.87 inference(transitivity,[status(thm)],[24078, 24076])).
% 3.53/3.87 tff(24080,plain,
% 3.53/3.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.87 inference(quant_inst,[status(thm)],[])).
% 3.53/3.87 tff(24081,plain,
% 3.53/3.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.53/3.87 inference(modus_ponens,[status(thm)],[24080, 24079])).
% 3.53/3.87 tff(24082,plain,
% 3.53/3.87 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24081, 144, 490, 285, 56, 24075])).
% 3.53/3.87 tff(24083,plain,
% 3.53/3.87 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[1137, 24082])).
% 3.53/3.87 tff(24084,plain,
% 3.53/3.87 (~r(s(s(s(z))), elem!1)),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[23315, 24083, 23943, 2484])).
% 3.53/3.87 tff(24085,plain,
% 3.53/3.87 (s(s(s(z))) = elem!1),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[704, 24084, 24069])).
% 3.53/3.87 tff(24086,plain,
% 3.53/3.87 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[12214, 24085])).
% 3.53/3.87 tff(24087,plain,
% 3.53/3.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.87 inference(unit_resolution,[status(thm)],[24043, 24071, 11546, 2484])).
% 3.53/3.87 tff(24088,plain,
% 3.53/3.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[279, 24087])).
% 3.53/3.88 tff(24089,plain,
% 3.53/3.88 (~(s(s(elem!1)) = elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7595, 24085, 1184])).
% 3.53/3.88 tff(24090,plain,
% 3.53/3.88 (~(elem!1 = s(s(elem!1)))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[5603, 24089])).
% 3.53/3.88 tff(24091,plain,
% 3.53/3.88 (~(s(elem!1) = elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[5813, 24090])).
% 3.53/3.88 tff(24092,plain,
% 3.53/3.88 (~(elem!1 = s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1569, 24091])).
% 3.53/3.88 tff(24093,plain,
% 3.53/3.88 (~r(s(elem!1), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7112, 24092, 490, 305, 24071, 1, 24073])).
% 3.53/3.88 tff(24094,plain,
% 3.53/3.88 (b(s(elem!1), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[507, 24093])).
% 3.53/3.88 tff(24095,plain,
% 3.53/3.88 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[10345, 144, 24094, 24075, 24088])).
% 3.53/3.88 tff(24096,plain,
% 3.53/3.88 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[472, 24095, 24086])).
% 3.53/3.88 tff(24097,plain,
% 3.53/3.88 (b(elem!1, z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[380, 24085, 285])).
% 3.53/3.88 tff(24098,plain,
% 3.53/3.88 (~b(elem!1, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7124, 144, 24097, 24094, 490, 305])).
% 3.53/3.88 tff(24099,plain,
% 3.53/3.88 (r(elem!1, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[560, 24098, 24092])).
% 3.53/3.88 tff(24100,plain,
% 3.53/3.88 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[20734, 24086])).
% 3.53/3.88 tff(24101,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24102,plain,
% 3.53/3.88 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24103,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24102])).
% 3.53/3.88 tff(24104,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.53/3.88 inference(transitivity,[status(thm)],[24103, 24101])).
% 3.53/3.88 tff(24105,plain,
% 3.53/3.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.53/3.88 inference(quant_inst,[status(thm)],[])).
% 3.53/3.88 tff(24106,plain,
% 3.53/3.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[24105, 24104])).
% 3.53/3.88 tff(24107,plain,
% 3.53/3.88 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24106, 144, 24094, 490, 304, 24075])).
% 3.53/3.88 tff(24108,plain,
% 3.53/3.88 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[542, 24107, 24100])).
% 3.53/3.88 tff(24109,plain,
% 3.53/3.88 ($false),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[12088, 24108, 24099, 2484, 24096])).
% 3.53/3.88 tff(24110,plain,((~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.88 tff(24111,plain,
% 3.53/3.88 (~b(z, s(z))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24110, 285, 304, 305, 1, 2484, 863, 56, 11546, 134])).
% 3.53/3.88 tff(24112,plain,
% 3.53/3.88 (r(z, s(z))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[372, 24111])).
% 3.53/3.88 tff(24113,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24114,plain,
% 3.53/3.88 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24115,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24114])).
% 3.53/3.88 tff(24116,plain,
% 3.53/3.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(transitivity,[status(thm)],[24115, 24113])).
% 3.53/3.88 tff(24117,plain,
% 3.53/3.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 3.53/3.88 inference(quant_inst,[status(thm)],[])).
% 3.53/3.88 tff(24118,plain,
% 3.53/3.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[24117, 24116])).
% 3.53/3.88 tff(24119,plain,
% 3.53/3.88 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24118, 144, 285, 56, 304, 259])).
% 3.53/3.88 tff(24120,plain,
% 3.53/3.88 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1137, 24119])).
% 3.53/3.88 tff(24121,plain,
% 3.53/3.88 (~r(s(s(s(z))), elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[23315, 24120, 23943, 2484])).
% 3.53/3.88 tff(24122,plain,
% 3.53/3.88 (s(s(s(z))) = elem!1),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[704, 24121, 24069])).
% 3.53/3.88 tff(24123,plain,
% 3.53/3.88 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[12214, 24122])).
% 3.53/3.88 tff(24124,plain,
% 3.53/3.88 (~(s(s(elem!1)) = elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7595, 24122, 863])).
% 3.53/3.88 tff(24125,plain,
% 3.53/3.88 (~(elem!1 = s(s(elem!1)))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[5603, 24124])).
% 3.53/3.88 tff(24126,plain,
% 3.53/3.88 (~(s(elem!1) = elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[5813, 24125])).
% 3.53/3.88 tff(24127,plain,
% 3.53/3.88 (s(s(s(s(z)))) = s(elem!1)),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24122])).
% 3.53/3.88 tff(24128,plain,
% 3.53/3.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24127])).
% 3.53/3.88 tff(24129,plain,
% 3.53/3.88 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24128])).
% 3.53/3.88 tff(24130,plain,
% 3.53/3.88 (~r(s(elem!1), elem!1)),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[23985, 24129])).
% 3.53/3.88 tff(24131,plain,
% 3.53/3.88 (b(s(elem!1), elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[448, 24130, 24126])).
% 3.53/3.88 tff(24132,plain,
% 3.53/3.88 (~b(s(elem!1), s(z))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[4344, 144, 24131, 134, 305])).
% 3.53/3.88 tff(24133,plain,
% 3.53/3.88 (r(s(elem!1), s(z))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[486, 24132, 1])).
% 3.53/3.88 tff(24134,plain,
% 3.53/3.88 (~r(s(elem!1), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[22626, 333, 24112, 24133, 11546])).
% 3.53/3.88 tff(24135,plain,
% 3.53/3.88 (b(s(elem!1), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[507, 24134])).
% 3.53/3.88 tff(24136,plain,
% 3.53/3.88 (~(s(s(z)) = elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[14611, 24122, 706])).
% 3.53/3.88 tff(24137,plain,
% 3.53/3.88 (~(s(elem!1) = s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1508, 24136])).
% 3.53/3.88 tff(24138,plain,
% 3.53/3.88 (~(s(s(s(z))) = s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1934, 24137])).
% 3.53/3.88 tff(24139,plain,
% 3.53/3.88 (((~![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(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), 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(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24140,plain,
% 3.53/3.88 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24141,plain,
% 3.53/3.88 (((~![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(s(s(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24140])).
% 3.53/3.88 tff(24142,plain,
% 3.53/3.88 (((~![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(s(s(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(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(transitivity,[status(thm)],[24141, 24139])).
% 3.53/3.88 tff(24143,plain,
% 3.53/3.88 ((~![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(s(s(z))))))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 3.53/3.88 inference(quant_inst,[status(thm)],[])).
% 3.53/3.88 tff(24144,plain,
% 3.53/3.88 ((~![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(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[24143, 24142])).
% 3.53/3.88 tff(24145,plain,
% 3.53/3.88 (~r(z, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24144, 333, 24112, 24133, 11546])).
% 3.53/3.88 tff(24146,plain,
% 3.53/3.88 (b(z, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[583, 24145])).
% 3.53/3.88 tff(24147,plain,
% 3.53/3.88 (b(elem!1, z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[380, 24122, 285])).
% 3.53/3.88 tff(24148,plain,
% 3.53/3.88 (~b(z, elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[916, 24135, 24131, 24147])).
% 3.53/3.88 tff(24149,plain,
% 3.53/3.88 (r(z, elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[658, 24148, 71])).
% 3.53/3.88 tff(24150,plain,
% 3.53/3.88 (~(elem!1 = s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1569, 24126])).
% 3.53/3.88 tff(24151,plain,
% 3.53/3.88 (~b(elem!1, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[949, 24146, 24147, 24135])).
% 3.53/3.88 tff(24152,plain,
% 3.53/3.88 (r(elem!1, s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[560, 24151, 24150])).
% 3.53/3.88 tff(24153,plain,
% 3.53/3.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[8367, 24152, 24149, 2484])).
% 3.53/3.88 tff(24154,plain,
% 3.53/3.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[302, 24153])).
% 3.53/3.88 tff(24155,plain,
% 3.53/3.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[14148, 24154, 24146, 285, 259, 2484, 24138, 24135])).
% 3.53/3.88 tff(24156,plain,
% 3.53/3.88 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[472, 24155, 24123])).
% 3.53/3.88 tff(24157,plain,
% 3.53/3.88 ($false),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[10345, 144, 24135, 24154, 24156, 259])).
% 3.53/3.88 tff(24158,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | (s(z) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.88 tff(24159,plain,
% 3.53/3.88 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24158, 285, 2484, 11546, 1, 134, 305, 23985, 706, 56, 304])).
% 3.53/3.88 tff(24160,plain,
% 3.53/3.88 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[279, 24159])).
% 3.53/3.88 tff(24161,plain,
% 3.53/3.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[15183, 24160, 11546, 24112])).
% 3.53/3.88 tff(24162,plain,
% 3.53/3.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[302, 24161])).
% 3.53/3.88 tff(24163,plain,
% 3.53/3.88 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[15576, 24160, 11546, 24112])).
% 3.53/3.88 tff(24164,plain,
% 3.53/3.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[249, 24163])).
% 3.53/3.88 tff(24165,plain,
% 3.53/3.88 (~b(z, s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[294, 24164, 24162, 285])).
% 3.53/3.88 tff(24166,plain,
% 3.53/3.88 (r(z, s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[619, 24165])).
% 3.53/3.88 tff(24167,plain,
% 3.53/3.88 (~b(s(z), s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[846, 24164, 304, 56])).
% 3.53/3.88 tff(24168,plain,
% 3.53/3.88 (r(s(z), s(s(s(z))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[172, 24167])).
% 3.53/3.88 tff(24169,plain,
% 3.53/3.88 (~r(s(s(s(z))), elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[1519, 24168, 24166, 24112])).
% 3.53/3.88 tff(24170,plain,
% 3.53/3.88 (s(s(s(z))) = elem!1),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[704, 24169, 24069])).
% 3.53/3.88 tff(24171,plain,
% 3.53/3.88 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24170])).
% 3.53/3.88 tff(24172,plain,
% 3.53/3.88 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.53/3.88 inference(symmetry,[status(thm)],[24171])).
% 3.53/3.88 tff(24173,plain,
% 3.53/3.88 (b(s(z), s(s(s(z))))),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[134, 24172])).
% 3.53/3.88 tff(24174,plain,
% 3.53/3.88 ($false),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24167, 24173])).
% 3.53/3.88 tff(24175,plain,((~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.88 tff(24176,plain,
% 3.53/3.88 (~b(s(s(s(z))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24175, 23987, 304, 24065, 11546, 23984, 1, 24067, 23985, 23986])).
% 3.53/3.88 tff(24177,plain,
% 3.53/3.88 (~(s(s(z)) = s(elem!1))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[855, 23986])).
% 3.53/3.88 tff(24178,plain,
% 3.53/3.88 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[862, 24177])).
% 3.53/3.88 tff(24179,plain,
% 3.53/3.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[23855, 333, 24073, 2484, 23943])).
% 3.53/3.88 tff(24180,plain,
% 3.53/3.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[302, 24179])).
% 3.53/3.88 tff(24181,plain,
% 3.53/3.88 (~b(s(z), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7093, 24180, 304, 490])).
% 3.53/3.88 tff(24182,plain,
% 3.53/3.88 (r(s(z), z)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[348, 24181])).
% 3.53/3.88 tff(24183,plain,
% 3.53/3.88 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(rewrite,[status(thm)],[])).
% 3.53/3.88 tff(24184,plain,
% 3.53/3.88 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.88 inference(monotonicity,[status(thm)],[24183])).
% 3.53/3.88 tff(24185,plain,
% 3.53/3.88 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.88 inference(transitivity,[status(thm)],[24184, 23988])).
% 3.53/3.88 tff(24186,plain,
% 3.53/3.88 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))),
% 3.53/3.88 inference(quant_inst,[status(thm)],[])).
% 3.53/3.88 tff(24187,plain,
% 3.53/3.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.88 inference(modus_ponens,[status(thm)],[24186, 24185])).
% 3.53/3.88 tff(24188,plain,
% 3.53/3.88 (~r(z, elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24187, 333, 2484, 2323, 51])).
% 3.53/3.88 tff(24189,plain,
% 3.53/3.88 (b(z, elem!1)),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[658, 24188, 74])).
% 3.53/3.88 tff(24190,plain,
% 3.53/3.88 ($false),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[7079, 24189, 22551, 134, 305])).
% 3.53/3.88 tff(24191,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.88 tff(24192,plain,
% 3.53/3.88 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.88 inference(unit_resolution,[status(thm)],[24191, 134, 305, 71, 2484, 23943, 11546])).
% 3.53/3.89 tff(24193,plain,
% 3.53/3.89 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[279, 24192])).
% 3.53/3.89 tff(24194,plain,
% 3.53/3.89 (b(s(s(s(z))), z)),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[624, 375])).
% 3.53/3.89 tff(24195,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1963, 24194])).
% 3.53/3.89 tff(24196,plain,(b(s(s(s(z))), z) | (~b(elem!1, z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24197,plain,
% 3.53/3.89 (~b(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24196, 78, 1963])).
% 3.53/3.89 tff(24198,plain,
% 3.53/3.89 (~b(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[20903, 24197, 11546, 2484, 305, 1, 134, 14872, 24180, 24193])).
% 3.53/3.89 tff(24199,plain,
% 3.53/3.89 (r(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[507, 24198])).
% 3.53/3.89 tff(24200,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[7112, 13979, 24199, 490, 305, 323, 1, 24073])).
% 3.53/3.89 tff(24201,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | b(s(s(s(z))), z) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24202,plain,
% 3.53/3.89 (~(s(s(s(z))) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24201, 490, 305, 24182, 1, 11546, 2484, 134, 1963, 1184])).
% 3.53/3.89 tff(24203,plain,
% 3.53/3.89 (r(s(s(s(z))), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[704, 24202, 24069])).
% 3.53/3.89 tff(24204,plain,
% 3.53/3.89 (~r(s(z), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[11246, 333, 24073, 24182, 1964])).
% 3.53/3.89 tff(24205,plain,
% 3.53/3.89 (b(s(z), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[172, 24204])).
% 3.53/3.89 tff(24206,plain,
% 3.53/3.89 (~b(elem!1, s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[17829, 144, 305, 56, 24205])).
% 3.53/3.89 tff(24207,plain,
% 3.53/3.89 (~(elem!1 = s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[10997, 24202])).
% 3.53/3.89 tff(24208,plain,
% 3.53/3.89 (r(elem!1, s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1538, 24207, 24206])).
% 3.53/3.89 tff(24209,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[21925, 333, 24073, 24208, 1964, 24203])).
% 3.53/3.89 tff(24210,plain,((~b(z, s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | b(s(s(s(z))), z) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24211,plain,
% 3.53/3.89 (~b(z, s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24210, 24067, 1, 11546, 23984, 23987, 24176, 24178, 24065, 304])).
% 3.53/3.89 tff(24212,plain,
% 3.53/3.89 (r(z, s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[372, 24211])).
% 3.53/3.89 tff(24213,plain,
% 3.53/3.89 (~r(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24027, 321, 2323, 354])).
% 3.53/3.89 tff(24214,plain,
% 3.53/3.89 (b(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1380, 24213, 730])).
% 3.53/3.89 tff(24215,plain,
% 3.53/3.89 (~(s(s(s(z))) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24196, 24214, 1963])).
% 3.53/3.89 tff(24216,plain,
% 3.53/3.89 (r(s(s(s(z))), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[704, 24215, 55])).
% 3.53/3.89 tff(24217,plain,
% 3.53/3.89 (r(z, elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24033, 321, 74, 2323, 11546, 305])).
% 3.53/3.89 tff(24218,plain,
% 3.53/3.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.89 inference(rewrite,[status(thm)],[])).
% 3.53/3.89 tff(24219,plain,
% 3.53/3.89 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.89 inference(rewrite,[status(thm)],[])).
% 3.53/3.89 tff(24220,plain,
% 3.53/3.89 (((~![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(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24219])).
% 3.53/3.89 tff(24221,plain,
% 3.53/3.89 (((~![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(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.53/3.89 inference(transitivity,[status(thm)],[24220, 24218])).
% 3.53/3.89 tff(24222,plain,
% 3.53/3.89 ((~![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(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 3.53/3.89 inference(quant_inst,[status(thm)],[])).
% 3.53/3.89 tff(24223,plain,
% 3.53/3.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[24222, 24221])).
% 3.53/3.89 tff(24224,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24223, 333, 24217, 1964, 24216, 2323])).
% 3.53/3.89 tff(24225,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1) | b(s(s(s(z))), z) | (~r(z, s(z))) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24226,plain,
% 3.53/3.89 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24225, 24068, 23943, 24176, 24212, 71, 11546, 24067])).
% 3.53/3.89 tff(24227,plain,
% 3.53/3.89 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[302, 24226])).
% 3.53/3.89 tff(24228,plain,
% 3.53/3.89 (~b(z, s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24210, 305, 1, 11546, 2484, 134, 1963, 863, 56, 304])).
% 3.53/3.89 tff(24229,plain,
% 3.53/3.89 (r(z, s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[372, 24228])).
% 3.53/3.89 tff(24230,plain,
% 3.53/3.89 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[23278, 2323])).
% 3.53/3.89 tff(24231,plain,
% 3.53/3.89 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[116, 24230])).
% 3.53/3.89 tff(24232,plain,
% 3.53/3.89 (~r(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[2122, 707, 1699, 354])).
% 3.53/3.89 tff(24233,plain,
% 3.53/3.89 (b(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1380, 24232, 1368])).
% 3.53/3.89 tff(24234,plain,
% 3.53/3.89 (~b(s(z), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[19147, 24233, 11546, 24231, 304, 251, 259, 706])).
% 3.53/3.89 tff(24235,plain,
% 3.53/3.89 (r(s(z), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[348, 24234])).
% 3.53/3.89 tff(24236,plain,
% 3.53/3.89 (~r(s(z), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[7314, 24235, 354, 1699])).
% 3.53/3.89 tff(24237,plain,
% 3.53/3.89 (b(s(z), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[172, 24236])).
% 3.53/3.89 tff(24238,plain,
% 3.53/3.89 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[846, 24237, 304, 56])).
% 3.53/3.89 tff(24239,plain,
% 3.53/3.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[249, 24238])).
% 3.53/3.89 tff(24240,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[18738, 333, 707, 2484, 2323, 24239])).
% 3.53/3.89 tff(24241,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24242,plain,
% 3.53/3.89 (~r(s(s(s(z))), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24241, 13636, 23943, 304, 56, 24229, 1964, 11546, 2484, 24193, 706, 77])).
% 3.53/3.89 tff(24243,plain,
% 3.53/3.89 (s(s(s(z))) = elem!1),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[704, 24242, 24069])).
% 3.53/3.89 tff(24244,plain,
% 3.53/3.89 (~(s(s(elem!1)) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[7595, 24243, 863])).
% 3.53/3.89 tff(24245,plain,
% 3.53/3.89 (~(elem!1 = s(s(elem!1)))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[5603, 24244])).
% 3.53/3.89 tff(24246,plain,
% 3.53/3.89 (~(s(elem!1) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[5813, 24245])).
% 3.53/3.89 tff(24247,plain,
% 3.53/3.89 (~(elem!1 = s(elem!1))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1569, 24246])).
% 3.53/3.89 tff(24248,plain,
% 3.53/3.89 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24225, 24069, 23943, 1963, 24229, 71, 11546, 305])).
% 3.53/3.89 tff(24249,plain,
% 3.53/3.89 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[302, 24248])).
% 3.53/3.89 tff(24250,plain,
% 3.53/3.89 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[12214, 24243])).
% 3.53/3.89 tff(24251,plain,
% 3.53/3.89 (~b(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24196, 24243, 1963])).
% 3.53/3.89 tff(24252,plain,
% 3.53/3.89 (~b(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[20903, 24251, 11546, 2484, 305, 1, 134, 24250, 24249, 24193])).
% 3.53/3.89 tff(24253,plain,
% 3.53/3.89 (r(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[507, 24252])).
% 3.53/3.89 tff(24254,plain,
% 3.53/3.89 (b(s(elem!1), s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1653, 24253, 1, 24229, 706, 1575, 24247])).
% 3.53/3.89 tff(24255,plain,
% 3.53/3.89 (r(elem!1, z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[653, 24251, 77])).
% 3.53/3.89 tff(24256,plain,
% 3.53/3.89 (~r(s(elem!1), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[10646, 24253, 24255, 24254, 134, 13636])).
% 3.53/3.89 tff(24257,plain,
% 3.53/3.89 (b(s(elem!1), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[448, 24256, 24246])).
% 3.53/3.89 tff(24258,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[7338, 144, 24257, 134, 24254, 305])).
% 3.53/3.89 tff(24259,plain,(r(z, elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(s(s(z))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24260,plain,
% 3.53/3.89 (r(z, elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24259, 23987, 24067, 1, 23986, 11546, 23984, 24176, 304, 24065])).
% 3.53/3.89 tff(24261,plain,
% 3.53/3.89 (~b(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[20903, 24197, 11546, 2484, 305, 1, 134, 14872, 286, 24193])).
% 3.53/3.89 tff(24262,plain,
% 3.53/3.89 (r(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[507, 24261])).
% 3.53/3.89 tff(24263,plain,
% 3.53/3.89 (~(s(s(z)) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[14611, 78, 706])).
% 3.53/3.89 tff(24264,plain,
% 3.53/3.89 (~(s(elem!1) = s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1508, 24263])).
% 3.53/3.89 tff(24265,plain,
% 3.53/3.89 (~r(s(elem!1), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[5835, 24262, 670, 1964])).
% 3.53/3.89 tff(24266,plain,
% 3.53/3.89 (b(s(elem!1), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[965, 24265, 24264])).
% 3.53/3.89 tff(24267,plain,
% 3.53/3.89 (b(s(elem!1), elem!1)),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[24266, 19261])).
% 3.53/3.89 tff(24268,plain,
% 3.53/3.89 (~b(s(elem!1), s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[4344, 144, 24267, 134, 305])).
% 3.53/3.89 tff(24269,plain,
% 3.53/3.89 (r(s(elem!1), s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[486, 24268, 1])).
% 3.53/3.89 tff(24270,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[22626, 333, 354, 24269, 24262, 11546])).
% 3.53/3.89 tff(24271,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(s(z))), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24272,plain,
% 3.53/3.89 (~(s(s(s(z))) = elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24271, 24212, 11546, 1, 23987, 24067, 24260, 23984, 24227, 24176, 23986])).
% 3.53/3.89 tff(24273,plain,
% 3.53/3.89 (r(s(s(s(z))), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[704, 24272, 24068])).
% 3.53/3.89 tff(24274,plain,
% 3.53/3.89 (r(s(s(s(z))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[396, 24176])).
% 3.53/3.89 tff(24275,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24223, 333, 24260, 24274, 24273, 23943])).
% 3.53/3.89 tff(24276,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(z)) | r(s(z), elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24277,plain,
% 3.53/3.89 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24276, 11546, 1, 23985, 715, 2310, 2545])).
% 3.53/3.89 tff(24278,plain,
% 3.53/3.89 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[319, 24277])).
% 3.53/3.89 tff(24279,plain,
% 3.53/3.89 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24037, 1575, 23943, 23984, 11546, 715, 71])).
% 3.53/3.89 tff(24280,plain,
% 3.53/3.89 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[302, 24279])).
% 3.53/3.89 tff(24281,plain,
% 3.53/3.89 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 3.53/3.89 inference(monotonicity,[status(thm)],[23944])).
% 3.53/3.89 tff(24282,plain,
% 3.53/3.89 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 3.53/3.89 inference(symmetry,[status(thm)],[24281])).
% 3.53/3.89 tff(24283,plain,
% 3.53/3.89 (~b(elem!1, s(z))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[6528, 23944])).
% 3.53/3.89 tff(24284,plain,
% 3.53/3.89 (elem!1 = s(z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[720, 24283, 715])).
% 3.53/3.89 tff(24285,plain,
% 3.53/3.89 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.89 inference(symmetry,[status(thm)],[203])).
% 3.53/3.89 tff(24286,plain,
% 3.53/3.89 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.89 inference(monotonicity,[status(thm)],[23944])).
% 3.53/3.89 tff(24287,plain,
% 3.53/3.89 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(s(s(s(z)))))),
% 3.53/3.89 inference(transitivity,[status(thm)],[24286, 203])).
% 3.53/3.89 tff(24288,plain,
% 3.53/3.89 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.89 inference(transitivity,[status(thm)],[24287, 24285])).
% 3.53/3.89 tff(24289,plain,
% 3.53/3.89 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24288])).
% 3.53/3.89 tff(24290,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 3.53/3.89 tff(24291,plain,
% 3.53/3.89 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24290])).
% 3.53/3.89 tff(24292,plain,
% 3.53/3.89 (s(s(s(z))) = z),
% 3.53/3.89 inference(transitivity,[status(thm)],[13297, 24291, 16])).
% 3.53/3.89 tff(24293,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[392, 24292])).
% 3.53/3.89 tff(24294,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24295,plain,
% 3.53/3.89 (~(s(s(s(s(z)))) = elem!1)),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[24294, 24289])).
% 3.53/3.89 tff(24296,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 3.53/3.89 tff(24297,plain,
% 3.53/3.89 (((~![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))),
% 3.53/3.89 inference(rewrite,[status(thm)],[])).
% 3.53/3.89 tff(24298,plain,
% 3.53/3.89 ((~![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))),
% 3.53/3.89 inference(quant_inst,[status(thm)],[])).
% 3.53/3.89 tff(24299,plain,
% 3.53/3.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[24298, 24297])).
% 3.53/3.89 tff(24300,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24299, 44, 3586, 23985, 24296])).
% 3.53/3.89 tff(24301,plain,(r(s(s(s(s(z)))), elem!1) | b(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24302,plain,
% 3.53/3.89 (b(s(s(s(s(z)))), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24301, 24295, 23985])).
% 3.53/3.89 tff(24303,plain,
% 3.53/3.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[23954])).
% 3.53/3.89 tff(24304,plain,
% 3.53/3.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.53/3.89 inference(transitivity,[status(thm)],[24303, 174])).
% 3.53/3.89 tff(24305,plain,
% 3.53/3.89 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(transitivity,[status(thm)],[24304, 175])).
% 3.53/3.89 tff(24306,plain,
% 3.53/3.89 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24305])).
% 3.53/3.89 tff(24307,plain,
% 3.53/3.89 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[1446, 24306])).
% 3.53/3.89 tff(24308,plain,
% 3.53/3.89 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[4281, 23967])).
% 3.53/3.89 tff(24309,plain,
% 3.53/3.89 (~(s(elem!1) = s(s(elem!1)))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[2856, 23967])).
% 3.53/3.89 tff(24310,plain,
% 3.53/3.89 (r(s(s(elem!1)), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[6447, 1699, 23944])).
% 3.53/3.89 tff(24311,plain,
% 3.53/3.89 (~b(s(s(s(s(z)))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[12662, 144, 251, 23951, 3529])).
% 3.53/3.89 tff(24312,plain,
% 3.53/3.89 (r(s(s(s(s(z)))), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24311])).
% 3.53/3.89 tff(24313,plain,
% 3.53/3.89 (~r(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[13565, 24312, 24310, 24309, 24308, 23944, 51])).
% 3.53/3.89 tff(24314,plain,
% 3.53/3.89 (b(s(elem!1), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[507, 24313])).
% 3.53/3.89 tff(24315,plain,
% 3.53/3.89 (~b(s(elem!1), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[916, 24314, 251, 23951])).
% 3.53/3.89 tff(24316,plain,
% 3.53/3.89 (r(s(elem!1), elem!1)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[448, 24315, 23968])).
% 3.53/3.89 tff(24317,plain,
% 3.53/3.89 (s(s(s(z))) = s(s(elem!1))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[23954])).
% 3.53/3.89 tff(24318,plain,
% 3.53/3.89 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24317])).
% 3.53/3.89 tff(24319,plain,
% 3.53/3.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(modus_ponens,[status(thm)],[23893, 24318])).
% 3.53/3.89 tff(24320,plain,
% 3.53/3.89 (~b(s(s(elem!1)), s(elem!1))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[15019, 24316, 23943, 2484, 24319, 23944])).
% 3.53/3.89 tff(24321,plain,
% 3.53/3.89 (r(s(s(elem!1)), s(elem!1))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[1283, 24320, 23967])).
% 3.53/3.89 tff(24322,plain,
% 3.53/3.89 (~r(elem!1, s(elem!1))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[13399, 24316, 286, 2484, 23944, 251, 1, 23951, 51, 23967, 24314])).
% 3.53/3.89 tff(24323,plain,
% 3.53/3.89 (b(elem!1, s(elem!1))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[560, 24322, 23966])).
% 3.53/3.89 tff(24324,plain,
% 3.53/3.89 ($false),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[13461, 24323, 24321, 1699, 51, 709, 23951, 24316])).
% 3.53/3.89 tff(24325,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.89 tff(24326,plain,
% 3.53/3.89 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[24325, 1964, 709, 286, 23984, 251, 1, 3529, 11546, 322, 490])).
% 3.53/3.89 tff(24327,plain,
% 3.53/3.89 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[279, 24326])).
% 3.53/3.89 tff(24328,plain,
% 3.53/3.89 (r(s(s(elem!1)), z)),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[6447, 1964, 23944])).
% 3.53/3.89 tff(24329,plain,
% 3.53/3.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.53/3.89 inference(monotonicity,[status(thm)],[24317])).
% 3.53/3.89 tff(24330,plain,
% 3.53/3.89 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[20837, 3193, 322, 8530])).
% 3.53/3.89 tff(24331,plain,
% 3.53/3.89 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[249, 24330])).
% 3.53/3.89 tff(24332,plain,
% 3.53/3.89 (~b(z, s(s(s(z))))),
% 3.53/3.89 inference(unit_resolution,[status(thm)],[16228, 24331, 23999, 259])).
% 3.53/3.89 tff(24333,plain,
% 3.53/3.89 (r(z, s(s(s(z))))),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[619, 24332])).
% 3.53/3.90 tff(24334,plain,
% 3.53/3.90 (r(z, s(s(elem!1)))),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[2836, 24333, 57])).
% 3.53/3.90 tff(24335,plain,
% 3.53/3.90 (((~![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)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 3.53/3.90 inference(rewrite,[status(thm)],[])).
% 3.53/3.90 tff(24336,plain,
% 3.53/3.90 (((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 3.53/3.90 inference(rewrite,[status(thm)],[])).
% 3.53/3.90 tff(24337,plain,
% 3.53/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))))),
% 3.53/3.90 inference(monotonicity,[status(thm)],[24336])).
% 3.53/3.90 tff(24338,plain,
% 3.53/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 3.53/3.90 inference(transitivity,[status(thm)],[24337, 24335])).
% 3.53/3.90 tff(24339,plain,
% 3.53/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 3.53/3.90 inference(quant_inst,[status(thm)],[])).
% 3.53/3.90 tff(24340,plain,
% 3.53/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))),
% 3.53/3.90 inference(modus_ponens,[status(thm)],[24339, 24338])).
% 3.53/3.90 tff(24341,plain,
% 3.53/3.90 (~r(s(s(elem!1)), elem!1)),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[24340, 333, 408, 24334, 5497])).
% 3.53/3.90 tff(24342,plain,
% 3.53/3.90 (~r(s(s(s(z))), s(z))),
% 3.53/3.90 inference(modus_ponens,[status(thm)],[24341, 2773])).
% 3.53/3.90 tff(24343,plain,
% 3.53/3.90 ($false),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[3193, 24342])).
% 3.53/3.90 tff(24344,plain,((~r(s(s(s(z))), s(z))) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.90 tff(24345,plain,
% 3.53/3.90 (~r(s(s(s(z))), s(z))),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[24344, 2322, 23944, 24328, 259, 322, 23984, 11546])).
% 3.53/3.90 tff(24346,plain,
% 3.53/3.90 (b(s(s(s(z))), s(z))),
% 3.53/3.90 inference(unit_resolution,[status(thm)],[2794, 24345])).
% 3.53/3.90 tff(24347,plain,
% 3.53/3.90 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 3.53/3.90 inference(monotonicity,[status(thm)],[23944])).
% 3.53/3.90 tff(24348,plain,
% 3.53/3.90 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 3.53/3.90 inference(transitivity,[status(thm)],[24347, 1218])).
% 3.53/3.90 tff(24349,plain,
% 3.53/3.90 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 3.53/3.90 inference(transitivity,[status(thm)],[24348, 4572])).
% 3.53/3.90 tff(24350,plain,
% 3.53/3.90 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.53/3.90 inference(monotonicity,[status(thm)],[24349])).
% 3.53/3.90 tff(24351,plain,
% 3.53/3.90 (~(s(s(elem!1)) = elem!1)),
% 3.53/3.90 inference(modus_ponens,[status(thm)],[107, 24350])).
% 3.53/3.90 tff(24352,plain,
% 3.53/3.90 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.53/3.90 inference(monotonicity,[status(thm)],[24317])).
% 3.53/3.90 tff(24353,plain,
% 3.53/3.90 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 3.63/3.90 inference(monotonicity,[status(thm)],[23944])).
% 3.63/3.90 tff(24354,plain,
% 3.63/3.90 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 3.63/3.90 inference(transitivity,[status(thm)],[24353, 24352])).
% 3.63/3.90 tff(24355,plain,
% 3.63/3.90 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(elem!1)), elem!1))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24354])).
% 3.63/3.90 tff(24356,plain,
% 3.63/3.90 (~r(s(s(elem!1)), elem!1)),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24345, 24355])).
% 3.63/3.90 tff(24357,plain,
% 3.63/3.90 (b(s(s(elem!1)), elem!1)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1260, 44, 24356, 24351])).
% 3.63/3.90 tff(24358,plain,
% 3.63/3.90 (r(s(z), z)),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[2322, 8529])).
% 3.63/3.90 tff(24359,plain,
% 3.63/3.90 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[472, 20108, 4762])).
% 3.63/3.90 tff(24360,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[13998, 333, 323, 434, 322, 525])).
% 3.63/3.90 tff(24361,plain,((~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24362,plain,
% 3.63/3.90 (~r(s(elem!1), s(z))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24361, 24359, 322, 24358])).
% 3.63/3.90 tff(24363,plain,
% 3.63/3.90 (b(s(elem!1), s(z))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[486, 24362, 1])).
% 3.63/3.90 tff(24364,plain,
% 3.63/3.90 (~r(s(elem!1), elem!1)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[13988, 24359, 2545, 286, 377, 77])).
% 3.63/3.90 tff(24365,plain,
% 3.63/3.90 (b(s(elem!1), elem!1)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[448, 24364, 2681])).
% 3.63/3.90 tff(24366,plain,
% 3.63/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.90 inference(rewrite,[status(thm)],[])).
% 3.63/3.90 tff(24367,plain,
% 3.63/3.90 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.90 inference(rewrite,[status(thm)],[])).
% 3.63/3.90 tff(24368,plain,
% 3.63/3.90 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24367])).
% 3.63/3.90 tff(24369,plain,
% 3.63/3.90 (((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.90 inference(transitivity,[status(thm)],[24368, 24366])).
% 3.63/3.90 tff(24370,plain,
% 3.63/3.90 ((~![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(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 3.63/3.90 inference(quant_inst,[status(thm)],[])).
% 3.63/3.90 tff(24371,plain,
% 3.63/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24370, 24369])).
% 3.63/3.90 tff(24372,plain,
% 3.63/3.90 (~r(elem!1, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24371, 333, 23984, 23943, 24359])).
% 3.63/3.90 tff(24373,plain,
% 3.63/3.90 (b(elem!1, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[560, 24372, 2483])).
% 3.63/3.90 tff(24374,plain,
% 3.63/3.90 (~b(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1642, 24373, 251, 24365])).
% 3.63/3.90 tff(24375,plain,
% 3.63/3.90 (r(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[583, 24374])).
% 3.63/3.90 tff(24376,plain,
% 3.63/3.90 (~r(z, s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1990, 24375, 1963, 24358, 491, 56, 24363])).
% 3.63/3.90 tff(24377,plain,
% 3.63/3.90 (b(z, s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[619, 24376])).
% 3.63/3.90 tff(24378,plain,
% 3.63/3.90 (b(z, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[2828, 24377, 57])).
% 3.63/3.90 tff(24379,plain,
% 3.63/3.90 (~b(elem!1, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[11841, 24378, 251, 4972])).
% 3.63/3.90 tff(24380,plain,
% 3.63/3.90 (r(elem!1, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[2522, 24379, 2462])).
% 3.63/3.90 tff(24381,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[14759, 333, 2322, 24375, 24380, 14744])).
% 3.63/3.90 tff(24382,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | b(s(s(s(z))), z) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24383,plain,
% 3.63/3.90 (~b(s(elem!1), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24382, 24357, 251, 23944, 1963, 24346, 1, 322, 2545, 286, 377, 259])).
% 3.63/3.90 tff(24384,plain,
% 3.63/3.90 (r(s(elem!1), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[507, 24383])).
% 3.63/3.90 tff(24385,plain,
% 3.63/3.90 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24304])).
% 3.63/3.90 tff(24386,plain,
% 3.63/3.90 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[1446, 24385])).
% 3.63/3.90 tff(24387,plain,
% 3.63/3.90 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[13988, 435, 2545, 286, 377, 1368])).
% 3.63/3.90 tff(24388,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[14780, 24387, 435, 2545, 377, 537, 509, 286])).
% 3.63/3.90 tff(24389,plain,((~r(s(elem!1), elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, z) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24390,plain,
% 3.63/3.90 (~r(s(elem!1), elem!1)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24389, 377, 2545, 24386, 24384, 286, 77])).
% 3.63/3.90 tff(24391,plain,
% 3.63/3.90 (b(s(elem!1), elem!1)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[448, 24390, 23968])).
% 3.63/3.90 tff(24392,plain,
% 3.63/3.90 (r(s(z), z) <=> r(elem!1, z)),
% 3.63/3.90 inference(monotonicity,[status(thm)],[23944])).
% 3.63/3.90 tff(24393,plain,
% 3.63/3.90 (r(elem!1, z) <=> r(s(z), z)),
% 3.63/3.90 inference(symmetry,[status(thm)],[24392])).
% 3.63/3.90 tff(24394,plain,
% 3.63/3.90 (r(s(z), z)),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[2322, 24393])).
% 3.63/3.90 tff(24395,plain,
% 3.63/3.90 (b(s(elem!1), s(z))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24391, 24282])).
% 3.63/3.90 tff(24396,plain,
% 3.63/3.90 (~r(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[8142, 24395, 24394, 1964, 23957, 24384])).
% 3.63/3.90 tff(24397,plain,
% 3.63/3.90 (b(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[583, 24396])).
% 3.63/3.90 tff(24398,plain,
% 3.63/3.90 (~b(elem!1, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1642, 24397, 251, 24391])).
% 3.63/3.90 tff(24399,plain,
% 3.63/3.90 (r(elem!1, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[560, 24398, 23966])).
% 3.63/3.90 tff(24400,plain,
% 3.63/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 3.63/3.90 inference(rewrite,[status(thm)],[])).
% 3.63/3.90 tff(24401,plain,
% 3.63/3.90 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 3.63/3.90 inference(rewrite,[status(thm)],[])).
% 3.63/3.90 tff(24402,plain,
% 3.63/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24401])).
% 3.63/3.90 tff(24403,plain,
% 3.63/3.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, 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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 3.63/3.90 inference(transitivity,[status(thm)],[24402, 24400])).
% 3.63/3.90 tff(24404,plain,
% 3.63/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 3.63/3.90 inference(quant_inst,[status(thm)],[])).
% 3.63/3.90 tff(24405,plain,
% 3.63/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24404, 24403])).
% 3.63/3.90 tff(24406,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24405, 333, 563, 408, 509, 4223])).
% 3.63/3.90 tff(24407,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24408,plain,
% 3.63/3.90 (~r(z, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24407, 24399, 2322, 24384])).
% 3.63/3.90 tff(24409,plain,
% 3.63/3.90 (~r(z, s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[2836, 24408, 23944])).
% 3.63/3.90 tff(24410,plain,
% 3.63/3.90 (b(z, s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[619, 24409])).
% 3.63/3.90 tff(24411,plain,
% 3.63/3.90 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[16453, 24410, 11546, 322, 490])).
% 3.63/3.90 tff(24412,plain,
% 3.63/3.90 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1137, 24411])).
% 3.63/3.90 tff(24413,plain,
% 3.63/3.90 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[16228, 24412, 24410, 259])).
% 3.63/3.90 tff(24414,plain,
% 3.63/3.90 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[249, 24413])).
% 3.63/3.90 tff(24415,plain,
% 3.63/3.90 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24414, 24329])).
% 3.63/3.90 tff(24416,plain,
% 3.63/3.90 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24348])).
% 3.63/3.90 tff(24417,plain,
% 3.63/3.90 (~(elem!1 = s(s(elem!1)))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[107, 24416])).
% 3.63/3.90 tff(24418,plain,
% 3.63/3.90 (b(z, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[2828, 24410, 23944])).
% 3.63/3.90 tff(24419,plain,
% 3.63/3.90 (~b(elem!1, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[11841, 24418, 251, 24357])).
% 3.63/3.90 tff(24420,plain,
% 3.63/3.90 (r(elem!1, s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[2522, 24419, 24417])).
% 3.63/3.90 tff(24421,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[23493, 333, 24420, 24415, 23943, 24328])).
% 3.63/3.90 tff(24422,plain,(b(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(s(z))), z) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24423,plain,
% 3.63/3.90 (b(elem!1, z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24422, 24327, 251, 11546, 322, 490, 2545, 286, 1963, 1])).
% 3.63/3.90 tff(24424,plain,
% 3.63/3.90 (b(s(z), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[3965, 24423, 23944])).
% 3.63/3.90 tff(24425,plain,
% 3.63/3.90 (~b(s(elem!1), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[20117, 24424, 11546, 490, 24327, 1, 286, 24307])).
% 3.63/3.90 tff(24426,plain,
% 3.63/3.90 (r(s(elem!1), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[507, 24425])).
% 3.63/3.90 tff(24427,plain,
% 3.63/3.90 (~b(s(s(s(s(z)))), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[12662, 144, 251, 24423, 3529])).
% 3.63/3.90 tff(24428,plain,
% 3.63/3.90 (r(s(s(s(s(z)))), z)),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24427])).
% 3.63/3.90 tff(24429,plain,
% 3.63/3.90 (~b(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[8386, 15010, 259, 2698, 15000])).
% 3.63/3.90 tff(24430,plain,
% 3.63/3.90 (r(z, s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[583, 24429])).
% 3.63/3.90 tff(24431,plain,
% 3.63/3.90 (((~![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(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.90 inference(rewrite,[status(thm)],[])).
% 3.63/3.90 tff(24432,plain,
% 3.63/3.90 ((~![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(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.90 inference(quant_inst,[status(thm)],[])).
% 3.63/3.90 tff(24433,plain,
% 3.63/3.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24432, 24431])).
% 3.63/3.90 tff(24434,plain,
% 3.63/3.90 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24433, 333, 24430, 5497, 12719])).
% 3.63/3.90 tff(24435,plain,
% 3.63/3.90 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24434, 4623])).
% 3.63/3.90 tff(24436,plain,
% 3.63/3.90 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[1116, 24435, 4283])).
% 3.63/3.90 tff(24437,plain,
% 3.63/3.90 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24436, 13534])).
% 3.63/3.90 tff(24438,plain,
% 3.63/3.90 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[2668])).
% 3.63/3.90 tff(24439,plain,
% 3.63/3.90 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.90 inference(symmetry,[status(thm)],[24438])).
% 3.63/3.90 tff(24440,plain,
% 3.63/3.90 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24439])).
% 3.63/3.90 tff(24441,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 3.63/3.90 tff(24442,plain,
% 3.63/3.90 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 3.63/3.90 inference(monotonicity,[status(thm)],[24441])).
% 3.63/3.90 tff(24443,plain,
% 3.63/3.90 (s(s(s(z))) = s(z)),
% 3.63/3.90 inference(transitivity,[status(thm)],[13297, 24442, 80])).
% 3.63/3.90 tff(24444,plain,
% 3.63/3.90 ($false),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[166, 24443])).
% 3.63/3.90 tff(24445,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.90 tff(24446,plain,
% 3.63/3.90 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.90 inference(modus_ponens,[status(thm)],[24445, 24440])).
% 3.63/3.90 tff(24447,plain,
% 3.63/3.90 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[23661, 333, 509, 24430, 12719])).
% 3.63/3.90 tff(24448,plain,
% 3.63/3.90 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[23673, 44])).
% 3.63/3.90 tff(24449,plain,
% 3.63/3.90 (b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.90 inference(unit_resolution,[status(thm)],[24448, 24447, 24446])).
% 3.63/3.90 tff(24450,plain,
% 3.63/3.90 (((~![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)), z)) | (~r(s(elem!1), z)) | (~r(z, 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(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24451,plain,
% 3.63/3.91 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24452,plain,
% 3.63/3.91 (((~![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(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24451])).
% 3.63/3.91 tff(24453,plain,
% 3.63/3.91 (((~![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(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.91 inference(transitivity,[status(thm)],[24452, 24450])).
% 3.63/3.91 tff(24454,plain,
% 3.63/3.91 ((~![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(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24455,plain,
% 3.63/3.91 ((~![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)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24454, 24453])).
% 3.63/3.91 tff(24456,plain,
% 3.63/3.91 (~r(s(elem!1), s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24455, 333, 509, 24430, 5497])).
% 3.63/3.91 tff(24457,plain,
% 3.63/3.91 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2860, 44, 2857, 24456])).
% 3.63/3.91 tff(24458,plain,
% 3.63/3.91 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[5505, 24430, 5497, 435])).
% 3.63/3.91 tff(24459,plain,
% 3.63/3.91 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1283, 24458, 2507])).
% 3.63/3.91 tff(24460,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24461,plain,
% 3.63/3.91 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24462,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24461])).
% 3.63/3.91 tff(24463,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(transitivity,[status(thm)],[24462, 24460])).
% 3.63/3.91 tff(24464,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24465,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24464, 24463])).
% 3.63/3.91 tff(24466,plain,
% 3.63/3.91 ($false),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24465, 144, 24459, 24457, 24449, 24437])).
% 3.63/3.91 tff(24467,plain,((~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.91 tff(24468,plain,
% 3.63/3.91 (~r(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24467, 24328, 23944, 24428, 24426, 24327, 23984, 23943])).
% 3.63/3.91 tff(24469,plain,
% 3.63/3.91 (b(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[448, 24468, 23968])).
% 3.63/3.91 tff(24470,plain,
% 3.63/3.91 (~r(z, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[23676, 547, 251, 3529, 57, 624, 451, 509])).
% 3.63/3.91 tff(24471,plain,
% 3.63/3.91 (~b(z, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1642, 547, 251, 451])).
% 3.63/3.91 tff(24472,plain,
% 3.63/3.91 ($false),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[583, 24471, 24470])).
% 3.63/3.91 tff(24473,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.91 tff(24474,plain,
% 3.63/3.91 (~b(elem!1, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24473, 24469, 251, 3529, 23944, 24423, 24426])).
% 3.63/3.91 tff(24475,plain,
% 3.63/3.91 (r(elem!1, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[560, 24474, 23966])).
% 3.63/3.91 tff(24476,plain,
% 3.63/3.91 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.91 inference(symmetry,[status(thm)],[13534])).
% 3.63/3.91 tff(24477,plain,
% 3.63/3.91 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24476])).
% 3.63/3.91 tff(24478,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(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(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24479,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24480,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24479, 24478])).
% 3.63/3.91 tff(24481,plain,
% 3.63/3.91 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24480, 333, 509, 4223, 12719])).
% 3.63/3.91 tff(24482,plain,
% 3.63/3.91 (b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24448, 24481, 24446])).
% 3.63/3.91 tff(24483,plain,
% 3.63/3.91 (((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24484,plain,
% 3.63/3.91 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24485,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24484])).
% 3.63/3.91 tff(24486,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~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(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.63/3.91 inference(transitivity,[status(thm)],[24485, 24483])).
% 3.63/3.91 tff(24487,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24488,plain,
% 3.63/3.91 ((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24487, 24486])).
% 3.63/3.91 tff(24489,plain,
% 3.63/3.91 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24488, 333, 509, 4223, 5497])).
% 3.63/3.91 tff(24490,plain,
% 3.63/3.91 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1283, 24489, 2507])).
% 3.63/3.91 tff(24491,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24492,plain,
% 3.63/3.91 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24493,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24492])).
% 3.63/3.91 tff(24494,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(transitivity,[status(thm)],[24493, 24491])).
% 3.63/3.91 tff(24495,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24496,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24495, 24494])).
% 3.63/3.91 tff(24497,plain,
% 3.63/3.91 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24496, 144, 451, 24490, 3529, 24482])).
% 3.63/3.91 tff(24498,plain,
% 3.63/3.91 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24497, 24477])).
% 3.63/3.91 tff(24499,plain,
% 3.63/3.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(rewrite,[status(thm)],[])).
% 3.63/3.91 tff(24500,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.91 inference(quant_inst,[status(thm)],[])).
% 3.63/3.91 tff(24501,plain,
% 3.63/3.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24500, 24499])).
% 3.63/3.91 tff(24502,plain,
% 3.63/3.91 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24501, 333, 4223, 5497, 12719])).
% 3.63/3.91 tff(24503,plain,
% 3.63/3.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24502, 4623])).
% 3.63/3.91 tff(24504,plain,
% 3.63/3.91 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1116, 24503, 4283])).
% 3.63/3.91 tff(24505,plain,
% 3.63/3.91 ($false),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24504, 24498])).
% 3.63/3.91 tff(24506,plain,((~r(z, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.91 tff(24507,plain,
% 3.63/3.91 (~r(z, s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24506, 24469, 23944, 3529, 24328, 24428, 24426])).
% 3.63/3.91 tff(24508,plain,
% 3.63/3.91 (~r(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2836, 24507, 23944])).
% 3.63/3.91 tff(24509,plain,
% 3.63/3.91 (b(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[619, 24508])).
% 3.63/3.91 tff(24510,plain,
% 3.63/3.91 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[16453, 24509, 11546, 322, 490])).
% 3.63/3.91 tff(24511,plain,
% 3.63/3.91 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1137, 24510])).
% 3.63/3.91 tff(24512,plain,
% 3.63/3.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[16228, 24511, 24509, 24327])).
% 3.63/3.91 tff(24513,plain,
% 3.63/3.91 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[249, 24512])).
% 3.63/3.91 tff(24514,plain,
% 3.63/3.91 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24513, 24329])).
% 3.63/3.91 tff(24515,plain,
% 3.63/3.91 (b(z, s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2828, 24509, 23944])).
% 3.63/3.91 tff(24516,plain,
% 3.63/3.91 (r(s(s(elem!1)), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[23496, 24514, 23943, 23944, 251, 24423, 24515])).
% 3.63/3.91 tff(24517,plain,
% 3.63/3.91 ($false),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[13396, 24516, 24514, 23984, 24475])).
% 3.63/3.91 tff(24518,plain,(b(s(s(s(z))), z) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.91 tff(24519,plain,
% 3.63/3.91 (b(s(s(s(z))), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24518, 490, 11546, 322, 251, 24302, 1, 286, 2545, 24284])).
% 3.63/3.91 tff(24520,plain,
% 3.63/3.91 (s(s(elem!1)) = s(s(s(z)))),
% 3.63/3.91 inference(symmetry,[status(thm)],[24317])).
% 3.63/3.91 tff(24521,plain,
% 3.63/3.91 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24520])).
% 3.63/3.91 tff(24522,plain,
% 3.63/3.91 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24521])).
% 3.63/3.91 tff(24523,plain,
% 3.63/3.91 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24317])).
% 3.63/3.91 tff(24524,plain,
% 3.63/3.91 (b(s(s(elem!1)), z)),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[285, 24523])).
% 3.63/3.91 tff(24525,plain,
% 3.63/3.91 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[23976, 491, 286, 23984, 251, 1, 285, 490, 11546, 322])).
% 3.63/3.91 tff(24526,plain,
% 3.63/3.91 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[279, 24525])).
% 3.63/3.91 tff(24527,plain,
% 3.63/3.91 (~b(s(z), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[20117, 24526, 11546, 490, 491, 1, 286, 24307])).
% 3.63/3.91 tff(24528,plain,
% 3.63/3.91 (~b(elem!1, z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[3965, 24527, 23944])).
% 3.63/3.91 tff(24529,plain,
% 3.63/3.91 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[10345, 144, 491, 286, 24526])).
% 3.63/3.91 tff(24530,plain,
% 3.63/3.91 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[472, 24529, 24307])).
% 3.63/3.91 tff(24531,plain,
% 3.63/3.91 (~r(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[13988, 24530, 2545, 286, 24528, 77])).
% 3.63/3.91 tff(24532,plain,
% 3.63/3.91 (b(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[448, 24531, 23968])).
% 3.63/3.91 tff(24533,plain,
% 3.63/3.91 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[14738, 144, 24532, 251, 491, 24524])).
% 3.63/3.91 tff(24534,plain,
% 3.63/3.91 (~b(s(elem!1), s(s(s(z))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24533, 24522])).
% 3.63/3.91 tff(24535,plain,
% 3.63/3.91 (~r(elem!1, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24371, 333, 23984, 23943, 24530])).
% 3.63/3.91 tff(24536,plain,
% 3.63/3.91 (b(elem!1, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[560, 24535, 23966])).
% 3.63/3.91 tff(24537,plain,
% 3.63/3.91 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.63/3.91 inference(transitivity,[status(thm)],[23955, 998])).
% 3.63/3.91 tff(24538,plain,
% 3.63/3.91 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24537])).
% 3.63/3.91 tff(24539,plain,
% 3.63/3.91 (~(s(s(s(z))) = s(elem!1))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[217, 24538])).
% 3.63/3.91 tff(24540,plain,
% 3.63/3.91 (~b(z, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[14148, 24530, 286, 285, 24526, 23984, 24539, 491])).
% 3.63/3.91 tff(24541,plain,
% 3.63/3.91 (r(z, s(elem!1))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[583, 24540])).
% 3.63/3.91 tff(24542,plain,
% 3.63/3.91 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(symmetry,[status(thm)],[24318])).
% 3.63/3.91 tff(24543,plain,
% 3.63/3.91 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.91 inference(monotonicity,[status(thm)],[24542])).
% 3.63/3.91 tff(24544,plain,
% 3.63/3.91 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[8153, 144, 286, 24526, 24524])).
% 3.63/3.91 tff(24545,plain,
% 3.63/3.91 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24544, 24543])).
% 3.63/3.91 tff(24546,plain,
% 3.63/3.91 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1137, 24545])).
% 3.63/3.91 tff(24547,plain,
% 3.63/3.91 (~b(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[16453, 24546, 11546, 322, 490])).
% 3.63/3.91 tff(24548,plain,
% 3.63/3.91 (r(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[619, 24547])).
% 3.63/3.91 tff(24549,plain,
% 3.63/3.91 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[10934, 24548, 24532, 24528, 23957, 24541, 24536])).
% 3.63/3.91 tff(24550,plain,
% 3.63/3.91 ($false),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24549, 24534])).
% 3.63/3.91 tff(24551,plain,((~b(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.91 tff(24552,plain,
% 3.63/3.91 (~b(s(elem!1), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24551, 490, 322, 11546, 251, 286, 24519, 2545, 1])).
% 3.63/3.91 tff(24553,plain,
% 3.63/3.91 (r(s(elem!1), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[507, 24552])).
% 3.63/3.91 tff(24554,plain,
% 3.63/3.91 (b(s(s(elem!1)), z)),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24519, 24523])).
% 3.63/3.91 tff(24555,plain,
% 3.63/3.91 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[23935, 24553, 286, 24519, 23984, 23943, 251, 11546, 322, 490, 77])).
% 3.63/3.91 tff(24556,plain,
% 3.63/3.91 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[279, 24555])).
% 3.63/3.91 tff(24557,plain,
% 3.63/3.91 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[8153, 144, 286, 24556, 24554])).
% 3.63/3.91 tff(24558,plain,
% 3.63/3.91 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24557, 24543])).
% 3.63/3.91 tff(24559,plain,
% 3.63/3.91 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[1137, 24558])).
% 3.63/3.91 tff(24560,plain,
% 3.63/3.91 (~r(s(s(s(z))), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[23315, 24559, 23943, 23984])).
% 3.63/3.91 tff(24561,plain,
% 3.63/3.91 (b(s(s(s(z))), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[704, 24560, 23949])).
% 3.63/3.91 tff(24562,plain,
% 3.63/3.91 (~b(elem!1, z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[10565, 24561, 251, 24519])).
% 3.63/3.91 tff(24563,plain,
% 3.63/3.91 (~r(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[24389, 24562, 2545, 24386, 24553, 286, 77])).
% 3.63/3.91 tff(24564,plain,
% 3.63/3.91 (b(s(elem!1), elem!1)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[448, 24563, 23968])).
% 3.63/3.91 tff(24565,plain,
% 3.63/3.91 (b(s(elem!1), s(z))),
% 3.63/3.91 inference(modus_ponens,[status(thm)],[24564, 24282])).
% 3.63/3.91 tff(24566,plain,
% 3.63/3.91 (~r(s(s(s(z))), s(z))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[15720, 24559, 11546, 322])).
% 3.63/3.91 tff(24567,plain,
% 3.63/3.91 (b(s(s(s(z))), s(z))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2794, 24566])).
% 3.63/3.91 tff(24568,plain,
% 3.63/3.91 (~b(s(z), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2273, 24567, 490, 24519])).
% 3.63/3.91 tff(24569,plain,
% 3.63/3.91 (r(s(z), z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[348, 24568])).
% 3.63/3.91 tff(24570,plain,
% 3.63/3.91 (~b(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[16453, 24559, 11546, 322, 490])).
% 3.63/3.91 tff(24571,plain,
% 3.63/3.91 (r(z, s(s(s(z))))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[619, 24570])).
% 3.63/3.91 tff(24572,plain,
% 3.63/3.91 (r(z, s(s(elem!1)))),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[2836, 24571, 23944])).
% 3.63/3.91 tff(24573,plain,
% 3.63/3.91 (r(elem!1, z)),
% 3.63/3.91 inference(unit_resolution,[status(thm)],[653, 24562, 77])).
% 3.63/3.91 tff(24574,plain,
% 3.63/3.91 (~r(elem!1, s(elem!1))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24407, 24573, 24572, 24553])).
% 3.63/3.92 tff(24575,plain,
% 3.63/3.92 (b(elem!1, s(elem!1))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[560, 24574, 23966])).
% 3.63/3.92 tff(24576,plain,
% 3.63/3.92 (~b(z, s(elem!1))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[1642, 24575, 251, 24564])).
% 3.63/3.92 tff(24577,plain,
% 3.63/3.92 (r(z, s(elem!1))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[583, 24576])).
% 3.63/3.92 tff(24578,plain,
% 3.63/3.92 (~b(s(elem!1), s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[1960, 24577, 1229, 24553, 24571, 24539, 24567, 24569])).
% 3.63/3.92 tff(24579,plain,
% 3.63/3.92 ($false),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24578, 24565])).
% 3.63/3.92 tff(24580,plain,((~b(z, s(z))) | (~b(z, elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.92 tff(24581,plain,
% 3.63/3.92 (~b(z, s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24580, 13636, 2545, 24280, 11546, 24278, 1, 23985, 715])).
% 3.63/3.92 tff(24582,plain,
% 3.63/3.92 (~(s(z) = elem!1)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[9366, 24581, 13636])).
% 3.63/3.92 tff(24583,plain,
% 3.63/3.92 (~(elem!1 = s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[712, 24582])).
% 3.63/3.92 tff(24584,plain,
% 3.63/3.92 (b(elem!1, s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[720, 24583, 715])).
% 3.63/3.92 tff(24585,plain,
% 3.63/3.92 (b(s(z), elem!1)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[406, 24582, 2310])).
% 3.63/3.92 tff(24586,plain,
% 3.63/3.92 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24191, 24585, 24584, 71, 23984, 23943, 11546])).
% 3.63/3.92 tff(24587,plain,
% 3.63/3.92 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[279, 24586])).
% 3.63/3.92 tff(24588,plain,
% 3.63/3.92 (r(z, s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[372, 24581])).
% 3.63/3.92 tff(24589,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z)))), elem!1)))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24590,plain,
% 3.63/3.92 (((~b(s(z), elem!1)) | (~b(s(s(s(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)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24591,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z)))), elem!1))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24590])).
% 3.63/3.92 tff(24592,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(z)))), elem!1)))),
% 3.63/3.92 inference(transitivity,[status(thm)],[24591, 24589])).
% 3.63/3.92 tff(24593,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.63/3.92 inference(quant_inst,[status(thm)],[])).
% 3.63/3.92 tff(24594,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.63/3.92 inference(modus_ponens,[status(thm)],[24593, 24592])).
% 3.63/3.92 tff(24595,plain,
% 3.63/3.92 (~b(s(s(s(s(z)))), s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24594, 144, 134, 305, 3529])).
% 3.63/3.92 tff(24596,assumption,(~(s(s(s(s(z)))) = s(z))), introduced(assumption)).
% 3.63/3.92 tff(24597,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 3.63/3.92 tff(24598,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 3.63/3.92 tff(24599,plain,
% 3.63/3.92 ($false),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[18491, 44, 24598, 24597, 24596])).
% 3.63/3.92 tff(24600,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,[]))).
% 3.63/3.92 tff(24601,plain,
% 3.63/3.92 (r(s(s(s(s(z)))), s(z))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24600, 24595, 24294])).
% 3.63/3.92 tff(24602,plain,
% 3.63/3.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[20413, 333, 24601, 11546, 322])).
% 3.63/3.92 tff(24603,plain,
% 3.63/3.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[9761, 24602])).
% 3.63/3.92 tff(24604,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24605,plain,
% 3.63/3.92 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24606,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24605])).
% 3.63/3.92 tff(24607,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(transitivity,[status(thm)],[24606, 24604])).
% 3.63/3.92 tff(24608,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(quant_inst,[status(thm)],[])).
% 3.63/3.92 tff(24609,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(modus_ponens,[status(thm)],[24608, 24607])).
% 3.63/3.92 tff(24610,plain,
% 3.63/3.92 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24609, 144, 251, 3529, 286])).
% 3.63/3.92 tff(24611,plain,
% 3.63/3.92 (~b(s(s(s(s(z)))), z)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24610, 24603])).
% 3.63/3.92 tff(24612,plain,
% 3.63/3.92 (((~![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(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24613,plain,
% 3.63/3.92 (((~r(s(z), s(s(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)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24614,plain,
% 3.63/3.92 (((~![X0: $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(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)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24613])).
% 3.63/3.92 tff(24615,plain,
% 3.63/3.92 (((~![X0: $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(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)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(transitivity,[status(thm)],[24614, 24612])).
% 3.63/3.92 tff(24616,plain,
% 3.63/3.92 ((~![X0: $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(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 3.63/3.92 inference(quant_inst,[status(thm)],[])).
% 3.63/3.92 tff(24617,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(modus_ponens,[status(thm)],[24616, 24615])).
% 3.63/3.92 tff(24618,plain,
% 3.63/3.92 (~r(s(s(s(s(z)))), z)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24617, 333, 354, 24601, 11546])).
% 3.63/3.92 tff(24619,plain,
% 3.63/3.92 ($false),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24618, 24611])).
% 3.63/3.92 tff(24620,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.92 tff(24621,plain,
% 3.63/3.92 (~b(s(s(s(s(z)))), elem!1)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24620, 13636, 24280, 11546, 24278, 24588, 24585, 24584])).
% 3.63/3.92 tff(24622,plain,
% 3.63/3.92 (s(s(s(s(z)))) = elem!1),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24301, 24621, 23985])).
% 3.63/3.92 tff(24623,plain,
% 3.63/3.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24622])).
% 3.63/3.92 tff(24624,plain,
% 3.63/3.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 3.63/3.92 inference(transitivity,[status(thm)],[24623, 4795])).
% 3.63/3.92 tff(24625,plain,
% 3.63/3.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24624])).
% 3.63/3.92 tff(24626,plain,
% 3.63/3.92 (~(s(s(s(z))) = elem!1)),
% 3.63/3.92 inference(modus_ponens,[status(thm)],[219, 24625])).
% 3.63/3.92 tff(24627,plain,
% 3.63/3.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.63/3.92 inference(monotonicity,[status(thm)],[6165])).
% 3.63/3.92 tff(24628,plain,
% 3.63/3.92 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.63/3.92 inference(symmetry,[status(thm)],[24627])).
% 3.63/3.92 tff(24629,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 3.63/3.92 tff(24630,plain,
% 3.63/3.92 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24629])).
% 3.63/3.92 tff(24631,plain,
% 3.63/3.92 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.63/3.92 inference(symmetry,[status(thm)],[24630])).
% 3.63/3.92 tff(24632,plain,
% 3.63/3.92 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24631])).
% 3.63/3.92 tff(24633,plain,
% 3.63/3.92 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 3.63/3.92 inference(symmetry,[status(thm)],[24632])).
% 3.63/3.92 tff(24634,plain,
% 3.63/3.92 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.63/3.92 inference(symmetry,[status(thm)],[1203])).
% 3.63/3.92 tff(24635,plain,
% 3.63/3.92 (elem!1 = s(s(elem!1))),
% 3.63/3.92 inference(transitivity,[status(thm)],[1193, 24634, 20, 24633])).
% 3.63/3.92 tff(24636,plain,
% 3.63/3.92 ($false),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[1221, 24635])).
% 3.63/3.92 tff(24637,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (elem!1 = s(s(elem!1))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.92 tff(24638,plain,
% 3.63/3.92 (~(s(s(s(s(z)))) = elem!1)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24637, 14202, 3326])).
% 3.63/3.92 tff(24639,plain,
% 3.63/3.92 (b(s(s(s(s(z)))), elem!1)),
% 3.63/3.92 inference(unit_resolution,[status(thm)],[24301, 24638, 23985])).
% 3.63/3.92 tff(24640,plain,
% 3.63/3.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.63/3.92 inference(modus_ponens,[status(thm)],[24639, 24628])).
% 3.63/3.92 tff(24641,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24642,plain,
% 3.63/3.92 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(rewrite,[status(thm)],[])).
% 3.63/3.92 tff(24643,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.63/3.92 inference(monotonicity,[status(thm)],[24642])).
% 3.63/3.92 tff(24644,plain,
% 3.63/3.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(transitivity,[status(thm)],[24643, 24641])).
% 3.63/3.92 tff(24645,plain,
% 3.63/3.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.63/3.92 inference(quant_inst,[status(thm)],[])).
% 3.63/3.93 tff(24646,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24645, 24644])).
% 3.63/3.93 tff(24647,plain,
% 3.63/3.93 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24646, 144, 14209, 14200])).
% 3.63/3.93 tff(24648,plain,
% 3.63/3.93 (~b(s(s(s(s(z)))), s(z))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24647, 24640])).
% 3.63/3.93 tff(24649,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), s(z))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24600, 24648, 24294])).
% 3.63/3.93 tff(24650,plain,
% 3.63/3.93 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[20413, 333, 24649, 11546, 322])).
% 3.63/3.93 tff(24651,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[9761, 24650])).
% 3.63/3.93 tff(24652,plain,
% 3.63/3.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(rewrite,[status(thm)],[])).
% 3.63/3.93 tff(24653,plain,
% 3.63/3.93 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(rewrite,[status(thm)],[])).
% 3.63/3.93 tff(24654,plain,
% 3.63/3.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24653])).
% 3.63/3.93 tff(24655,plain,
% 3.63/3.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(transitivity,[status(thm)],[24654, 24652])).
% 3.63/3.93 tff(24656,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(quant_inst,[status(thm)],[])).
% 3.63/3.93 tff(24657,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24656, 24655])).
% 3.63/3.93 tff(24658,plain,
% 3.63/3.93 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24657, 144, 286, 20667])).
% 3.63/3.93 tff(24659,plain,
% 3.63/3.93 (~b(s(s(s(s(z)))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24658, 24651, 24640])).
% 3.63/3.93 tff(24660,plain,
% 3.63/3.93 (~r(s(s(s(s(z)))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24617, 333, 354, 24649, 11546])).
% 3.63/3.93 tff(24661,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24660, 24659])).
% 3.63/3.93 tff(24662,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24663,plain,
% 3.63/3.93 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24662, 24280, 11546, 24278, 24588, 24584, 24585, 23985, 13636])).
% 3.63/3.93 tff(24664,plain,
% 3.63/3.93 (b(elem!1, z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[20903, 491, 11546, 2484, 305, 1, 134, 432, 286, 24193])).
% 3.63/3.93 tff(24665,plain,
% 3.63/3.93 (~b(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[916, 24664, 251, 491])).
% 3.63/3.93 tff(24666,plain,
% 3.63/3.93 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[10345, 144, 491, 286, 24193])).
% 3.63/3.93 tff(24667,plain,
% 3.63/3.93 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[472, 24666, 432])).
% 3.63/3.93 tff(24668,plain,
% 3.63/3.93 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(rewrite,[status(thm)],[])).
% 3.63/3.93 tff(24669,plain,
% 3.63/3.93 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24668])).
% 3.63/3.93 tff(24670,plain,
% 3.63/3.93 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(transitivity,[status(thm)],[24669, 14994])).
% 3.63/3.93 tff(24671,plain,
% 3.63/3.93 ((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))),
% 3.63/3.93 inference(quant_inst,[status(thm)],[])).
% 3.63/3.93 tff(24672,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24671, 24670])).
% 3.63/3.93 tff(24673,plain,
% 3.63/3.93 (~r(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24672, 333, 2484, 23943, 24667])).
% 3.63/3.93 tff(24674,plain,
% 3.63/3.93 (s(elem!1) = elem!1),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[448, 24673, 24665])).
% 3.63/3.93 tff(24675,plain,
% 3.63/3.93 (elem!1 = s(elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[906, 24674])).
% 3.63/3.93 tff(24676,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[885])).
% 3.63/3.93 tff(24677,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(symmetry,[status(thm)],[24676])).
% 3.63/3.93 tff(24678,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 3.63/3.93 tff(24679,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24678, 24677])).
% 3.63/3.93 tff(24680,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[23985, 24679])).
% 3.63/3.93 tff(24681,plain,((~r(s(s(s(s(z)))), s(elem!1))) | r(s(s(s(s(z)))), elem!1) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24682,plain,
% 3.63/3.93 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24681, 24675, 23985])).
% 3.63/3.93 tff(24683,plain,
% 3.63/3.93 (s(s(s(elem!1))) = elem!1),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[2482, 24675])).
% 3.63/3.93 tff(24684,plain,
% 3.63/3.93 (s(elem!1) = s(s(s(elem!1)))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[2584, 24683, 24675])).
% 3.63/3.93 tff(24685,plain,
% 3.63/3.93 (~(s(elem!1) = s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[990, 24684, 1])).
% 3.63/3.93 tff(24686,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 3.63/3.93 tff(24687,plain,
% 3.63/3.93 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24686])).
% 3.63/3.93 tff(24688,plain,
% 3.63/3.93 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.63/3.93 inference(symmetry,[status(thm)],[24687])).
% 3.63/3.93 tff(24689,plain,
% 3.63/3.93 (s(elem!1) = s(s(s(z)))),
% 3.63/3.93 inference(transitivity,[status(thm)],[2470, 1193, 24688, 183])).
% 3.63/3.93 tff(24690,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[960, 24689])).
% 3.63/3.93 tff(24691,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24692,plain,
% 3.63/3.93 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24691, 24685, 24675])).
% 3.63/3.93 tff(24693,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24448, 24692, 24682])).
% 3.63/3.93 tff(24694,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[885])).
% 3.63/3.93 tff(24695,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(symmetry,[status(thm)],[24694])).
% 3.63/3.93 tff(24696,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 3.63/3.93 tff(24697,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24696, 24695])).
% 3.63/3.93 tff(24698,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[3586, 24697])).
% 3.63/3.93 tff(24699,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(s(z)))), elem!1) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24700,plain,
% 3.63/3.93 (b(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24699, 24693, 24675])).
% 3.63/3.93 tff(24701,plain,
% 3.63/3.93 (~b(s(s(s(s(z)))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[12662, 144, 251, 24664, 24700])).
% 3.63/3.93 tff(24702,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24701])).
% 3.63/3.93 tff(24703,plain,
% 3.63/3.93 (~b(s(s(s(s(z)))), s(z))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24594, 144, 134, 305, 24700])).
% 3.63/3.93 tff(24704,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), s(z))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24600, 24703, 24294])).
% 3.63/3.93 tff(24705,plain,
% 3.63/3.93 (~b(s(z), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1602, 24664, 251, 134])).
% 3.63/3.93 tff(24706,plain,
% 3.63/3.93 (r(s(z), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[348, 24705])).
% 3.63/3.93 tff(24707,plain,
% 3.63/3.93 (((~![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))))),
% 3.63/3.93 inference(rewrite,[status(thm)],[])).
% 3.63/3.93 tff(24708,plain,
% 3.63/3.93 ((~![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))))),
% 3.63/3.93 inference(quant_inst,[status(thm)],[])).
% 3.63/3.93 tff(24709,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24708, 24707])).
% 3.63/3.93 tff(24710,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24709, 333, 354, 24706, 24704, 24702])).
% 3.63/3.93 tff(24711,plain,((~b(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24712,plain,
% 3.63/3.93 (~b(s(elem!1), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24711, 24588, 24585, 24584, 13636, 1, 23985, 23984, 24663, 24280, 11546])).
% 3.63/3.93 tff(24713,plain,
% 3.63/3.93 (r(s(elem!1), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[507, 24712])).
% 3.63/3.93 tff(24714,plain,
% 3.63/3.93 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[20734, 24663])).
% 3.63/3.93 tff(24715,plain,
% 3.63/3.93 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24622])).
% 3.63/3.93 tff(24716,plain,
% 3.63/3.93 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24715])).
% 3.63/3.93 tff(24717,plain,
% 3.63/3.93 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.63/3.93 inference(symmetry,[status(thm)],[24716])).
% 3.63/3.93 tff(24718,plain,
% 3.63/3.93 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24717])).
% 3.63/3.93 tff(24719,plain,
% 3.63/3.93 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24718])).
% 3.63/3.93 tff(24720,plain,
% 3.63/3.93 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 3.63/3.93 inference(symmetry,[status(thm)],[24719])).
% 3.63/3.93 tff(24721,plain,
% 3.63/3.93 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24720])).
% 3.63/3.93 tff(24722,plain,
% 3.63/3.93 (~(s(s(s(elem!1))) = elem!1)),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[23983, 24721])).
% 3.63/3.93 tff(24723,plain,
% 3.63/3.93 (~(elem!1 = s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[2482, 24722])).
% 3.63/3.93 tff(24724,plain,
% 3.63/3.93 (~(s(elem!1) = elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[906, 24723])).
% 3.63/3.93 tff(24725,plain,
% 3.63/3.93 (b(s(elem!1), s(z))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1653, 24723, 1, 1575, 24582, 24588, 24713])).
% 3.63/3.93 tff(24726,plain,
% 3.63/3.93 (~b(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[7338, 144, 24585, 24725, 24584])).
% 3.63/3.93 tff(24727,plain,
% 3.63/3.93 (r(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[448, 24726, 24724])).
% 3.63/3.93 tff(24728,plain,
% 3.63/3.93 (b(elem!1, z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24389, 24727, 2545, 24714, 24713, 24280, 77])).
% 3.63/3.93 tff(24729,plain,
% 3.63/3.93 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 3.63/3.93 inference(commutativity,[status(thm)],[])).
% 3.63/3.93 tff(24730,plain,
% 3.63/3.93 (elem!1 = s(s(s(s(z))))),
% 3.63/3.93 inference(symmetry,[status(thm)],[24622])).
% 3.63/3.93 tff(24731,plain,
% 3.63/3.93 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24730])).
% 3.63/3.93 tff(24732,plain,
% 3.63/3.93 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 3.63/3.93 inference(transitivity,[status(thm)],[24731, 24729])).
% 3.63/3.93 tff(24733,plain,
% 3.63/3.93 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 3.63/3.93 inference(symmetry,[status(thm)],[24732])).
% 3.63/3.93 tff(24734,plain,
% 3.63/3.93 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24733])).
% 3.63/3.93 tff(24735,plain,
% 3.63/3.93 (~(s(s(z)) = elem!1)),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24445, 24734])).
% 3.63/3.93 tff(24736,plain,
% 3.63/3.93 (~(s(elem!1) = s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1508, 24735])).
% 3.63/3.93 tff(24737,plain,
% 3.63/3.93 (~b(s(z), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1602, 24728, 13636, 24585])).
% 3.63/3.93 tff(24738,plain,
% 3.63/3.93 (r(s(z), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[348, 24737])).
% 3.63/3.93 tff(24739,plain,
% 3.63/3.93 (~r(s(s(s(z))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[8561, 24738, 24588, 24713, 24725, 24736])).
% 3.63/3.93 tff(24740,plain,
% 3.63/3.93 (b(s(s(s(z))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[396, 24739])).
% 3.63/3.93 tff(24741,plain,
% 3.63/3.93 (~b(s(s(s(z))), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[10565, 24740, 13636, 24728])).
% 3.63/3.93 tff(24742,plain,
% 3.63/3.93 (r(s(s(s(z))), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[704, 24741, 24626])).
% 3.63/3.93 tff(24743,plain,
% 3.63/3.93 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[23315, 24742, 23943, 23984])).
% 3.63/3.93 tff(24744,plain,
% 3.63/3.93 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1137, 24743])).
% 3.63/3.93 tff(24745,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[14138, 144, 24740, 24744, 24280, 24587])).
% 3.63/3.93 tff(24746,plain,(r(z, elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z)) | r(s(s(s(s(z)))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24747,plain,
% 3.63/3.93 (r(s(s(s(s(z)))), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24746, 23323, 11546, 23292, 2545, 23287, 23982])).
% 3.63/3.93 tff(24748,plain,
% 3.63/3.93 (r(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[448, 7326, 2681])).
% 3.63/3.93 tff(24749,plain,
% 3.63/3.93 (~b(elem!1, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[949, 491, 624, 585])).
% 3.63/3.93 tff(24750,plain,
% 3.63/3.93 (r(elem!1, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[560, 24749, 2483])).
% 3.63/3.93 tff(24751,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[12797, 24750, 24748, 2484, 9507, 57])).
% 3.63/3.93 tff(24752,plain,((~b(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24753,plain,
% 3.63/3.93 (~b(z, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24752, 23942, 24747, 57, 23981, 23280, 23324])).
% 3.63/3.93 tff(24754,plain,
% 3.63/3.93 (r(z, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[583, 24753])).
% 3.63/3.93 tff(24755,plain,
% 3.63/3.93 (~b(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[916, 23942, 23981, 23324])).
% 3.63/3.93 tff(24756,plain,
% 3.63/3.93 (r(s(elem!1), elem!1)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[448, 24755, 2681])).
% 3.63/3.93 tff(24757,plain,
% 3.63/3.93 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[5505, 24756, 24754, 23979])).
% 3.63/3.93 tff(24758,plain,
% 3.63/3.93 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[15019, 24756, 23272, 23280, 6147, 57])).
% 3.63/3.93 tff(24759,plain,
% 3.63/3.93 ($false),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1283, 24758, 24757, 2507])).
% 3.63/3.93 tff(24760,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.93 tff(24761,plain,
% 3.63/3.93 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24760, 23322, 57, 11546, 23321, 2545])).
% 3.63/3.93 tff(24762,plain,
% 3.63/3.93 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[279, 24761])).
% 3.63/3.93 tff(24763,plain,
% 3.63/3.93 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(rewrite,[status(thm)],[])).
% 3.63/3.93 tff(24764,plain,
% 3.63/3.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24763])).
% 3.63/3.93 tff(24765,plain,
% 3.63/3.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(transitivity,[status(thm)],[24764, 8148])).
% 3.63/3.93 tff(24766,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.93 inference(quant_inst,[status(thm)],[])).
% 3.63/3.93 tff(24767,plain,
% 3.63/3.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24766, 24765])).
% 3.63/3.93 tff(24768,plain,
% 3.63/3.93 (~b(s(s(elem!1)), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24767, 144, 23859, 23321, 24762])).
% 3.63/3.93 tff(24769,plain,
% 3.63/3.93 (r(s(s(elem!1)), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[5509, 24768])).
% 3.63/3.93 tff(24770,plain,
% 3.63/3.93 (~r(elem!1, z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[24344, 24769, 57, 3193, 24762, 23305, 23280, 11546])).
% 3.63/3.93 tff(24771,plain,
% 3.63/3.93 (b(elem!1, z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1380, 24770, 23320])).
% 3.63/3.93 tff(24772,plain,
% 3.63/3.93 (~b(z, s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[16228, 24762, 283, 23317])).
% 3.63/3.93 tff(24773,plain,
% 3.63/3.93 (r(z, s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[619, 24772])).
% 3.63/3.93 tff(24774,plain,
% 3.63/3.93 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 3.63/3.93 inference(symmetry,[status(thm)],[2497])).
% 3.63/3.93 tff(24775,plain,
% 3.63/3.93 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(z))), z))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[24774])).
% 3.63/3.93 tff(24776,plain,
% 3.63/3.93 (~b(s(s(s(z))), z)),
% 3.63/3.93 inference(modus_ponens,[status(thm)],[24768, 24775])).
% 3.63/3.93 tff(24777,plain,
% 3.63/3.93 (r(s(s(s(z))), z)),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[396, 24776])).
% 3.63/3.93 tff(24778,plain,
% 3.63/3.93 (~r(elem!1, s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[3201, 23297, 623, 3193])).
% 3.63/3.93 tff(24779,plain,
% 3.63/3.93 (b(elem!1, s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[1538, 24778, 3516])).
% 3.63/3.93 tff(24780,plain,
% 3.63/3.93 (~r(elem!1, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[6585, 23297, 707, 1699])).
% 3.63/3.93 tff(24781,plain,
% 3.63/3.93 (b(elem!1, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[560, 24780, 2483])).
% 3.63/3.93 tff(24782,plain,
% 3.63/3.93 (~b(s(s(s(z))), s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[12903, 491, 2082, 624, 547])).
% 3.63/3.93 tff(24783,plain,
% 3.63/3.93 (~b(z, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[949, 491, 624, 547])).
% 3.63/3.93 tff(24784,plain,
% 3.63/3.93 (r(z, s(elem!1))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[583, 24783])).
% 3.63/3.93 tff(24785,plain,
% 3.63/3.93 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[4807, 24784, 11786, 623, 24782])).
% 3.63/3.93 tff(24786,plain,
% 3.63/3.93 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[15601, 24785, 2254, 286, 491])).
% 3.63/3.93 tff(24787,plain,
% 3.63/3.93 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.93 inference(unit_resolution,[status(thm)],[472, 24786, 4762])).
% 3.63/3.93 tff(24788,plain,
% 3.63/3.93 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.63/3.93 inference(monotonicity,[status(thm)],[2499])).
% 3.63/3.93 tff(24789,plain,
% 3.63/3.93 (b(s(s(s(z))), s(elem!1))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[1249, 24788])).
% 3.63/3.94 tff(24790,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[3296, 24789])).
% 3.63/3.94 tff(24791,plain,((~b(s(s(elem!1)), s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24792,plain,
% 3.63/3.94 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24791, 24782, 57])).
% 3.63/3.94 tff(24793,plain,
% 3.63/3.94 (r(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1283, 24792, 2507])).
% 3.63/3.94 tff(24794,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[8341, 333, 24793, 24784, 10049, 24787])).
% 3.63/3.94 tff(24795,plain,((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24796,plain,
% 3.63/3.94 (~b(s(elem!1), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24795, 24781, 286, 623, 57, 624, 2254, 24779])).
% 3.63/3.94 tff(24797,plain,
% 3.63/3.94 (r(s(elem!1), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[507, 24796])).
% 3.63/3.94 tff(24798,plain,
% 3.63/3.94 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[5835, 24797, 1699, 23297])).
% 3.63/3.94 tff(24799,plain,
% 3.63/3.94 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[965, 24798, 11786])).
% 3.63/3.94 tff(24800,plain,
% 3.63/3.94 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24799, 2501])).
% 3.63/3.94 tff(24801,plain,
% 3.63/3.94 (~r(s(z), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1519, 23299, 623, 707])).
% 3.63/3.94 tff(24802,plain,
% 3.63/3.94 (b(s(z), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[172, 24801])).
% 3.63/3.94 tff(24803,plain,
% 3.63/3.94 (b(elem!1, s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[5343, 24802, 57])).
% 3.63/3.94 tff(24804,plain,
% 3.63/3.94 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[6771, 333, 23297, 24797, 5497])).
% 3.63/3.94 tff(24805,plain,
% 3.63/3.94 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1283, 24804, 2507])).
% 3.63/3.94 tff(24806,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[6943, 144, 24781, 24805, 24803, 24800])).
% 3.63/3.94 tff(24807,plain,(b(z, elem!1) | (~r(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24808,plain,
% 3.63/3.94 (b(z, elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24807, 24769, 57, 24777, 23859, 24773, 24771, 23317, 707, 3193])).
% 3.63/3.94 tff(24809,plain,
% 3.63/3.94 (b(z, s(z))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[9366, 24808, 57])).
% 3.63/3.94 tff(24810,plain,
% 3.63/3.94 (r(s(s(s(s(z)))), elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24580, 24809, 2545, 23859, 11546, 23305, 23292, 24808, 23287])).
% 3.63/3.94 tff(24811,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24812,plain,
% 3.63/3.94 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24813,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), 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(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.94 inference(monotonicity,[status(thm)],[24812])).
% 3.63/3.94 tff(24814,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), 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(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24813, 24811])).
% 3.63/3.94 tff(24815,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(quant_inst,[status(thm)],[])).
% 3.63/3.94 tff(24816,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24815, 24814])).
% 3.63/3.94 tff(24817,plain,
% 3.63/3.94 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24816, 333, 24810, 23280, 23272])).
% 3.63/3.94 tff(24818,plain,
% 3.63/3.94 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[9761, 24817])).
% 3.63/3.94 tff(24819,plain,
% 3.63/3.94 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24820,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.94 inference(monotonicity,[status(thm)],[24819])).
% 3.63/3.94 tff(24821,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24820, 19700])).
% 3.63/3.94 tff(24822,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(quant_inst,[status(thm)],[])).
% 3.63/3.94 tff(24823,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24822, 24821])).
% 3.63/3.94 tff(24824,plain,
% 3.63/3.94 (~b(s(s(s(s(z)))), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24823, 144, 23859, 24762, 24818])).
% 3.63/3.94 tff(24825,plain,
% 3.63/3.94 (r(s(s(s(s(z)))), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24824])).
% 3.63/3.94 tff(24826,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24827,plain,
% 3.63/3.94 (((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24828,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.94 inference(monotonicity,[status(thm)],[24827])).
% 3.63/3.94 tff(24829,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24828, 24826])).
% 3.63/3.94 tff(24830,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(quant_inst,[status(thm)],[])).
% 3.63/3.94 tff(24831,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24830, 24829])).
% 3.63/3.94 tff(24832,plain,
% 3.63/3.94 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24831, 144, 23322, 23321, 24818])).
% 3.63/3.94 tff(24833,plain,
% 3.63/3.94 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24832, 24477])).
% 3.63/3.94 tff(24834,plain,
% 3.63/3.94 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1116, 24833, 4283])).
% 3.63/3.94 tff(24835,plain,
% 3.63/3.94 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24834, 4272])).
% 3.63/3.94 tff(24836,plain,
% 3.63/3.94 (r(z, s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[2836, 24773, 57])).
% 3.63/3.94 tff(24837,plain,
% 3.63/3.94 (b(s(z), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[3965, 24771, 57])).
% 3.63/3.94 tff(24838,plain,
% 3.63/3.94 (~b(s(elem!1), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[20117, 24809, 11546, 4762, 23292, 23859, 24762, 24837])).
% 3.63/3.94 tff(24839,plain,
% 3.63/3.94 (r(s(elem!1), z)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[507, 24838])).
% 3.63/3.94 tff(24840,plain,
% 3.63/3.94 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24488, 333, 24839, 24836, 24769])).
% 3.63/3.94 tff(24841,plain,
% 3.63/3.94 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1283, 24840, 2507])).
% 3.63/3.94 tff(24842,plain,
% 3.63/3.94 (~r(s(elem!1), elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[15019, 24841, 23272, 23280, 23321, 57])).
% 3.63/3.94 tff(24843,plain,
% 3.63/3.94 (b(s(elem!1), elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[448, 24842, 2681])).
% 3.63/3.94 tff(24844,plain,
% 3.63/3.94 (~r(s(elem!1), s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[15066, 333, 24839, 24836, 24769])).
% 3.63/3.94 tff(24845,plain,
% 3.63/3.94 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[2860, 44, 2857, 24844])).
% 3.63/3.94 tff(24846,plain,
% 3.63/3.94 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(rewrite,[status(thm)],[])).
% 3.63/3.94 tff(24847,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.94 inference(monotonicity,[status(thm)],[24846])).
% 3.63/3.94 tff(24848,plain,
% 3.63/3.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24847, 15108])).
% 3.63/3.94 tff(24849,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.63/3.94 inference(quant_inst,[status(thm)],[])).
% 3.63/3.94 tff(24850,plain,
% 3.63/3.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24849, 24848])).
% 3.63/3.94 tff(24851,plain,
% 3.63/3.94 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24850, 144, 23322, 24845, 23321])).
% 3.63/3.94 tff(24852,plain,
% 3.63/3.94 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[472, 24851, 4762])).
% 3.63/3.94 tff(24853,plain,
% 3.63/3.94 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[6819, 144, 24841, 23322, 24845])).
% 3.63/3.94 tff(24854,plain,
% 3.63/3.94 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[542, 24853, 2698])).
% 3.63/3.94 tff(24855,plain,
% 3.63/3.94 (~r(elem!1, s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[12088, 24854, 23280, 24852])).
% 3.63/3.94 tff(24856,plain,
% 3.63/3.94 (b(elem!1, s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[560, 24855, 2483])).
% 3.63/3.94 tff(24857,plain,
% 3.63/3.94 (~b(z, s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[1642, 24856, 24808, 24843])).
% 3.63/3.94 tff(24858,plain,
% 3.63/3.94 (r(z, s(elem!1))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[583, 24857])).
% 3.63/3.94 tff(24859,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24433, 333, 24858, 24835, 24769, 24825])).
% 3.63/3.94 tff(24860,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(z) = elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24861,plain,
% 3.63/3.94 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24860, 23308, 2545, 11546, 57, 23307])).
% 3.63/3.94 tff(24862,plain,
% 3.63/3.94 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[249, 24861])).
% 3.63/3.94 tff(24863,plain,
% 3.63/3.94 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24862, 8165])).
% 3.63/3.94 tff(24864,plain,
% 3.63/3.94 (r(s(s(elem!1)), elem!1)),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[23308, 2770])).
% 3.63/3.94 tff(24865,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[23916, 333, 24864, 24863, 23280, 23272])).
% 3.63/3.94 tff(24866,plain,(b(s(s(s(z))), elem!1) | (~(s(z) = elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24867,plain,
% 3.63/3.94 (b(s(s(s(z))), elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24866, 57, 2545, 11546])).
% 3.63/3.94 tff(24868,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 3.63/3.94 tff(24869,plain,
% 3.63/3.94 (s(s(s(s(z)))) = s(s(s(z)))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24868, 2499])).
% 3.63/3.94 tff(24870,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[219, 24869])).
% 3.63/3.94 tff(24871,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24872,plain,
% 3.63/3.94 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24871, 57])).
% 3.63/3.94 tff(24873,plain,
% 3.63/3.94 (b(elem!1, s(s(elem!1)))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[5343, 16449, 57])).
% 3.63/3.94 tff(24874,plain,
% 3.63/3.94 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 3.63/3.94 inference(transitivity,[status(thm)],[58, 6760])).
% 3.63/3.94 tff(24875,plain,
% 3.63/3.94 (b(s(s(elem!1)), elem!1)),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[56, 24874])).
% 3.63/3.94 tff(24876,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 3.63/3.94 tff(24877,plain,
% 3.63/3.94 ($false),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24876, 24875])).
% 3.63/3.94 tff(24878,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.94 tff(24879,plain,
% 3.63/3.94 (b(s(s(elem!1)), elem!1)),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[24878, 22973, 57])).
% 3.63/3.94 tff(24880,plain,
% 3.63/3.94 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.63/3.94 inference(monotonicity,[status(thm)],[57])).
% 3.63/3.94 tff(24881,plain,
% 3.63/3.94 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(s(s(s(z)))))),
% 3.63/3.94 inference(transitivity,[status(thm)],[24880, 203])).
% 3.63/3.94 tff(24882,plain,
% 3.63/3.94 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.63/3.94 inference(transitivity,[status(thm)],[24881, 24285])).
% 3.63/3.94 tff(24883,plain,
% 3.63/3.94 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.63/3.94 inference(monotonicity,[status(thm)],[24882])).
% 3.63/3.94 tff(24884,plain,
% 3.63/3.94 (~(s(s(s(s(z)))) = elem!1)),
% 3.63/3.94 inference(modus_ponens,[status(thm)],[24294, 24883])).
% 3.63/3.94 tff(24885,plain,
% 3.63/3.94 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[2541, 670, 2323, 322])).
% 3.63/3.94 tff(24886,plain,
% 3.63/3.94 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.94 inference(unit_resolution,[status(thm)],[279, 24885])).
% 3.63/3.95 tff(24887,plain,
% 3.63/3.95 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2689, 467, 57])).
% 3.63/3.95 tff(24888,plain,
% 3.63/3.95 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[1451, 24887])).
% 3.63/3.95 tff(24889,plain,
% 3.63/3.95 (~r(s(s(z)), s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[18163, 24888, 322, 6107])).
% 3.63/3.95 tff(24890,plain,
% 3.63/3.95 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[2495])).
% 3.63/3.95 tff(24891,plain,
% 3.63/3.95 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[24890])).
% 3.63/3.95 tff(24892,plain,
% 3.63/3.95 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[18130, 24891])).
% 3.63/3.95 tff(24893,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[1686, 24892])).
% 3.63/3.95 tff(24894,plain,((~r(s(elem!1), s(s(s(z))))) | r(s(s(z)), s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24895,plain,
% 3.63/3.95 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24894, 24889, 57])).
% 3.63/3.95 tff(24896,plain,
% 3.63/3.95 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[965, 24895, 11786])).
% 3.63/3.95 tff(24897,plain,
% 3.63/3.95 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24896, 2501])).
% 3.63/3.95 tff(24898,plain,
% 3.63/3.95 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24899,plain,
% 3.63/3.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[24898])).
% 3.63/3.95 tff(24900,plain,
% 3.63/3.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.63/3.95 inference(transitivity,[status(thm)],[24899, 6375])).
% 3.63/3.95 tff(24901,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.63/3.95 inference(quant_inst,[status(thm)],[])).
% 3.63/3.95 tff(24902,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24901, 24900])).
% 3.63/3.95 tff(24903,plain,
% 3.63/3.95 (~b(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24902, 144, 2812, 24897, 4972])).
% 3.63/3.95 tff(24904,plain,
% 3.63/3.95 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[472, 467, 4762])).
% 3.63/3.95 tff(24905,plain,
% 3.63/3.95 (~r(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24672, 333, 2484, 2323, 24904])).
% 3.63/3.95 tff(24906,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[448, 24905, 24903, 2681])).
% 3.63/3.95 tff(24907,plain,(b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24908,plain,
% 3.63/3.95 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24907, 24873, 2323, 2484, 24879, 57, 322, 6107])).
% 3.63/3.95 tff(24909,plain,
% 3.63/3.95 (~b(s(elem!1), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[8282, 144, 23873, 24908, 24886])).
% 3.63/3.95 tff(24910,plain,
% 3.63/3.95 (r(s(elem!1), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[507, 24909])).
% 3.63/3.95 tff(24911,plain,
% 3.63/3.95 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[2500])).
% 3.63/3.95 tff(24912,plain,
% 3.63/3.95 (((~![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, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, 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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24913,plain,
% 3.63/3.95 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24914,plain,
% 3.63/3.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[24913])).
% 3.63/3.95 tff(24915,plain,
% 3.63/3.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(transitivity,[status(thm)],[24914, 24912])).
% 3.63/3.95 tff(24916,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 3.63/3.95 inference(quant_inst,[status(thm)],[])).
% 3.63/3.95 tff(24917,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24916, 24915])).
% 3.63/3.95 tff(24918,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24917, 333, 435, 670, 509, 2323])).
% 3.63/3.95 tff(24919,plain,((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24920,plain,
% 3.63/3.95 (~r(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24919, 24910, 670, 2323])).
% 3.63/3.95 tff(24921,plain,
% 3.63/3.95 (b(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[448, 24920, 2681])).
% 3.63/3.95 tff(24922,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24902, 144, 451, 2812, 3627, 4972])).
% 3.63/3.95 tff(24923,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24924,plain,
% 3.63/3.95 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24923, 24921, 24873, 24879])).
% 3.63/3.95 tff(24925,plain,
% 3.63/3.95 (~b(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24924, 24911])).
% 3.63/3.95 tff(24926,plain,
% 3.63/3.95 (r(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[965, 24925, 11786])).
% 3.63/3.95 tff(24927,plain,
% 3.63/3.95 (~r(s(s(s(z))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[5835, 24926, 670, 24910])).
% 3.63/3.95 tff(24928,plain,
% 3.63/3.95 (b(s(s(s(z))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[396, 24927])).
% 3.63/3.95 tff(24929,plain,
% 3.63/3.95 (b(elem!1, s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[5343, 838, 57])).
% 3.63/3.95 tff(24930,plain,
% 3.63/3.95 (~r(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[3624, 509, 670, 563])).
% 3.63/3.95 tff(24931,plain,
% 3.63/3.95 (b(s(elem!1), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[448, 24930, 2681])).
% 3.63/3.95 tff(24932,plain,
% 3.63/3.95 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24923, 24931, 24929, 4972])).
% 3.63/3.95 tff(24933,plain,
% 3.63/3.95 (r(s(elem!1), s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2860, 44, 24932, 2857])).
% 3.63/3.95 tff(24934,plain,
% 3.63/3.95 (~r(s(z), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[1235, 509, 12624, 354])).
% 3.63/3.95 tff(24935,plain,
% 3.63/3.95 (b(s(z), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[348, 24934])).
% 3.63/3.95 tff(24936,plain,
% 3.63/3.95 (~b(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24932, 24911])).
% 3.63/3.95 tff(24937,plain,
% 3.63/3.95 (r(s(elem!1), s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[965, 24936, 11786])).
% 3.63/3.95 tff(24938,plain,
% 3.63/3.95 (~r(s(s(s(z))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[5835, 24937, 670, 509])).
% 3.63/3.95 tff(24939,plain,
% 3.63/3.95 (b(s(s(s(z))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[396, 24938])).
% 3.63/3.95 tff(24940,plain,
% 3.63/3.95 (~b(z, s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2156, 24939, 24935, 838])).
% 3.63/3.95 tff(24941,plain,
% 3.63/3.95 (r(z, s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[619, 24940])).
% 3.63/3.95 tff(24942,plain,
% 3.63/3.95 (r(z, s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2836, 24941, 57])).
% 3.63/3.95 tff(24943,plain,
% 3.63/3.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24944,plain,
% 3.63/3.95 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24945,plain,
% 3.63/3.95 (((~![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(s(s(z))))))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[24944])).
% 3.63/3.95 tff(24946,plain,
% 3.63/3.95 (((~![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(s(s(z))))))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(transitivity,[status(thm)],[24945, 24943])).
% 3.63/3.95 tff(24947,plain,
% 3.63/3.95 ((~![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(s(s(z))))))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.63/3.95 inference(quant_inst,[status(thm)],[])).
% 3.63/3.95 tff(24948,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24947, 24946])).
% 3.63/3.95 tff(24949,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24948, 333, 509, 24942, 24933, 8162])).
% 3.63/3.95 tff(24950,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24951,plain,
% 3.63/3.95 (~r(s(elem!1), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24950, 563, 57, 838, 670, 4972, 354, 8162])).
% 3.63/3.95 tff(24952,plain,
% 3.63/3.95 (b(s(elem!1), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[507, 24951])).
% 3.63/3.95 tff(24953,plain,
% 3.63/3.95 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[10345, 144, 24952, 286, 259])).
% 3.63/3.95 tff(24954,plain,
% 3.63/3.95 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[472, 24953, 4762])).
% 3.63/3.95 tff(24955,plain,
% 3.63/3.95 (~r(z, s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[4052, 24954, 670, 563])).
% 3.63/3.95 tff(24956,plain,
% 3.63/3.95 (b(z, s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[583, 24955])).
% 3.63/3.95 tff(24957,plain,
% 3.63/3.95 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[12088, 24954, 2484, 563])).
% 3.63/3.95 tff(24958,plain,
% 3.63/3.95 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[542, 24957, 2698])).
% 3.63/3.95 tff(24959,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[12069, 24958, 24956, 286, 24952])).
% 3.63/3.95 tff(24960,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24961,plain,
% 3.63/3.95 (~r(elem!1, s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24960, 16449, 2484, 670, 24886, 57, 23873, 24879, 354, 11793])).
% 3.63/3.95 tff(24962,plain,
% 3.63/3.95 (b(elem!1, s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[560, 24961, 2483])).
% 3.63/3.95 tff(24963,plain,
% 3.63/3.95 (~b(s(s(s(z))), s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[4819, 24921, 4367, 24962])).
% 3.63/3.95 tff(24964,plain,
% 3.63/3.95 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24791, 24963, 57])).
% 3.63/3.95 tff(24965,plain,
% 3.63/3.95 (r(s(s(elem!1)), s(elem!1))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[1283, 24964, 2507])).
% 3.63/3.95 tff(24966,plain,
% 3.63/3.95 (r(s(elem!1), s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2860, 44, 24924, 2857])).
% 3.63/3.95 tff(24967,plain,
% 3.63/3.95 (~r(z, s(s(elem!1)))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[23930, 24966, 24910, 24965])).
% 3.63/3.95 tff(24968,plain,
% 3.63/3.95 (~r(z, s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2836, 24967, 57])).
% 3.63/3.95 tff(24969,plain,
% 3.63/3.95 (b(z, s(s(s(z))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[619, 24968])).
% 3.63/3.95 tff(24970,plain,
% 3.63/3.95 (~b(s(z), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[2156, 24969, 24928, 16449])).
% 3.63/3.95 tff(24971,plain,
% 3.63/3.95 (~b(elem!1, z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[3965, 24970, 57])).
% 3.63/3.95 tff(24972,plain,
% 3.63/3.95 (r(elem!1, z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[653, 24971, 23320])).
% 3.63/3.95 tff(24973,plain,
% 3.63/3.95 (((~![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)))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24974,plain,
% 3.63/3.95 ((~![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)))),
% 3.63/3.95 inference(quant_inst,[status(thm)],[])).
% 3.63/3.95 tff(24975,plain,
% 3.63/3.95 ((~![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))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24974, 24973])).
% 3.63/3.95 tff(24976,plain,
% 3.63/3.95 (~r(s(s(s(s(z)))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24975, 333, 670, 408, 9507])).
% 3.63/3.95 tff(24977,plain,
% 3.63/3.95 (b(s(s(s(s(z)))), z)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[4243, 44, 242, 24976])).
% 3.63/3.95 tff(24978,plain,
% 3.63/3.95 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24979,plain,
% 3.63/3.95 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(rewrite,[status(thm)],[])).
% 3.63/3.95 tff(24980,plain,
% 3.63/3.95 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.95 inference(monotonicity,[status(thm)],[24979])).
% 3.63/3.95 tff(24981,plain,
% 3.63/3.95 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(transitivity,[status(thm)],[24980, 24978])).
% 3.63/3.95 tff(24982,plain,
% 3.63/3.95 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.95 inference(quant_inst,[status(thm)],[])).
% 3.63/3.95 tff(24983,plain,
% 3.63/3.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.95 inference(modus_ponens,[status(thm)],[24982, 24981])).
% 3.63/3.95 tff(24984,plain,
% 3.63/3.95 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24983, 333, 408, 9507, 2484])).
% 3.63/3.95 tff(24985,plain,
% 3.63/3.95 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[9761, 24984])).
% 3.63/3.95 tff(24986,plain,
% 3.63/3.95 ($false),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24823, 144, 286, 259, 24985, 24977])).
% 3.63/3.95 tff(24987,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.95 tff(24988,plain,
% 3.63/3.95 (~r(s(s(s(s(z)))), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24987, 24972, 23873, 24886, 2484, 670])).
% 3.63/3.95 tff(24989,plain,
% 3.63/3.95 (b(s(s(s(s(z)))), elem!1)),
% 3.63/3.95 inference(unit_resolution,[status(thm)],[24301, 24988, 24884])).
% 3.63/3.95 tff(24990,plain,
% 3.63/3.95 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[10534, 24989, 24879, 24873])).
% 3.63/3.96 tff(24991,plain,
% 3.63/3.96 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(24992,plain,
% 3.63/3.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 3.63/3.96 inference(monotonicity,[status(thm)],[24991])).
% 3.63/3.96 tff(24993,plain,
% 3.63/3.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.63/3.96 inference(transitivity,[status(thm)],[24992, 23663])).
% 3.63/3.96 tff(24994,plain,
% 3.63/3.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.96 inference(quant_inst,[status(thm)],[])).
% 3.63/3.96 tff(24995,plain,
% 3.63/3.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[24994, 24993])).
% 3.63/3.96 tff(24996,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24995, 144, 547, 451, 3529, 24696])).
% 3.63/3.96 tff(24997,plain,((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(24998,plain,
% 3.63/3.96 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24997, 24989, 24962, 24921])).
% 3.63/3.96 tff(24999,plain,
% 3.63/3.96 (r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24448, 24998, 24446])).
% 3.63/3.96 tff(25000,plain,
% 3.63/3.96 (((~![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(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(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(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(25001,plain,
% 3.63/3.96 ((~![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(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.63/3.96 inference(quant_inst,[status(thm)],[])).
% 3.63/3.96 tff(25002,plain,
% 3.63/3.96 ((~![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(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25001, 25000])).
% 3.63/3.96 tff(25003,plain,
% 3.63/3.96 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25002, 333, 24965, 24966, 24999])).
% 3.63/3.96 tff(25004,plain,
% 3.63/3.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(25005,plain,
% 3.63/3.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.63/3.96 inference(quant_inst,[status(thm)],[])).
% 3.63/3.96 tff(25006,plain,
% 3.63/3.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25005, 25004])).
% 3.63/3.96 tff(25007,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25006, 44, 25003, 24990, 24872])).
% 3.63/3.96 tff(25008,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25009,plain,
% 3.63/3.96 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25008, 23297, 23280, 57, 24867, 23272, 23305, 23299, 11546])).
% 3.63/3.96 tff(25010,plain,
% 3.63/3.96 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1137, 25009])).
% 3.63/3.96 tff(25011,plain,
% 3.63/3.96 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2541, 670, 23272, 23305])).
% 3.63/3.96 tff(25012,plain,
% 3.63/3.96 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[279, 25011])).
% 3.63/3.96 tff(25013,plain,
% 3.63/3.96 (~b(s(s(elem!1)), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24767, 144, 23859, 14453, 25012])).
% 3.63/3.96 tff(25014,plain,
% 3.63/3.96 (~b(s(s(s(z))), z)),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25013, 24775])).
% 3.63/3.96 tff(25015,plain,
% 3.63/3.96 (r(s(s(s(z))), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[396, 25014])).
% 3.63/3.96 tff(25016,plain,
% 3.63/3.96 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[10345, 144, 491, 23859, 25012])).
% 3.63/3.96 tff(25017,plain,
% 3.63/3.96 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2689, 25016, 57])).
% 3.63/3.96 tff(25018,plain,
% 3.63/3.96 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1451, 25017])).
% 3.63/3.96 tff(25019,plain,
% 3.63/3.96 (b(s(s(elem!1)), elem!1)),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[24867, 6760])).
% 3.63/3.96 tff(25020,plain,
% 3.63/3.96 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[472, 25016, 4762])).
% 3.63/3.96 tff(25021,plain,
% 3.63/3.96 (~r(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24371, 333, 23280, 23272, 25020])).
% 3.63/3.96 tff(25022,plain,
% 3.63/3.96 (b(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[560, 25021, 2483])).
% 3.63/3.96 tff(25023,plain,
% 3.63/3.96 (~r(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24672, 333, 23280, 23272, 25020])).
% 3.63/3.96 tff(25024,plain,
% 3.63/3.96 (b(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[448, 25023, 2681])).
% 3.63/3.96 tff(25025,plain,
% 3.63/3.96 (~b(s(s(s(z))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[4819, 25024, 24867, 25022])).
% 3.63/3.96 tff(25026,plain,
% 3.63/3.96 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24791, 25025, 57])).
% 3.63/3.96 tff(25027,plain,
% 3.63/3.96 (r(s(s(elem!1)), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1283, 25026, 2507])).
% 3.63/3.96 tff(25028,plain,
% 3.63/3.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[16228, 284, 259, 2254])).
% 3.63/3.96 tff(25029,plain,
% 3.63/3.96 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[249, 25028])).
% 3.63/3.96 tff(25030,plain,
% 3.63/3.96 (~r(s(s(z)), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[7412, 25029, 2671, 1699])).
% 3.63/3.96 tff(25031,plain,
% 3.63/3.96 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24894, 25030, 57])).
% 3.63/3.96 tff(25032,plain,
% 3.63/3.96 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[965, 25031, 11786])).
% 3.63/3.96 tff(25033,plain,
% 3.63/3.96 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25032, 2501])).
% 3.63/3.96 tff(25034,plain,
% 3.63/3.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(25035,plain,
% 3.63/3.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(25036,plain,
% 3.63/3.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 3.63/3.96 inference(monotonicity,[status(thm)],[25035])).
% 3.63/3.96 tff(25037,plain,
% 3.63/3.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.63/3.96 inference(transitivity,[status(thm)],[25036, 25034])).
% 3.63/3.96 tff(25038,plain,
% 3.63/3.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 3.63/3.96 inference(quant_inst,[status(thm)],[])).
% 3.63/3.96 tff(25039,plain,
% 3.63/3.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25038, 25037])).
% 3.63/3.96 tff(25040,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25039, 144, 451, 491, 14704, 25033, 4972])).
% 3.63/3.96 tff(25041,plain,((~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25042,plain,
% 3.63/3.96 (~b(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25041, 25024, 491, 25019, 57, 25018, 25015, 25012, 2254])).
% 3.63/3.96 tff(25043,plain,
% 3.63/3.96 (r(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[619, 25042])).
% 3.63/3.96 tff(25044,plain,
% 3.63/3.96 (r(z, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2836, 25043, 57])).
% 3.63/3.96 tff(25045,plain,
% 3.63/3.96 (~r(elem!1, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[4231, 25044, 670, 25027])).
% 3.63/3.96 tff(25046,plain,
% 3.63/3.96 (b(elem!1, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2522, 25045, 2462])).
% 3.63/3.96 tff(25047,plain,
% 3.63/3.96 (~r(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24371, 333, 23280, 23272, 525])).
% 3.63/3.96 tff(25048,plain,
% 3.63/3.96 (b(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[560, 25047, 2483])).
% 3.63/3.96 tff(25049,plain,
% 3.63/3.96 (b(s(z), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[4682, 25048, 57])).
% 3.63/3.96 tff(25050,plain,
% 3.63/3.96 (~r(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24672, 333, 23280, 23272, 525])).
% 3.63/3.96 tff(25051,plain,
% 3.63/3.96 (b(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[448, 25050, 2681])).
% 3.63/3.96 tff(25052,plain,
% 3.63/3.96 (b(z, elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[658, 23867, 74])).
% 3.63/3.96 tff(25053,plain,
% 3.63/3.96 (~r(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[13493, 51, 2484, 525])).
% 3.63/3.96 tff(25054,plain,
% 3.63/3.96 (b(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[507, 25053])).
% 3.63/3.96 tff(25055,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[916, 25054, 25052, 451, 23903])).
% 3.63/3.96 tff(25056,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (elem!1 = z) | (z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25057,plain,
% 3.63/3.96 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25056, 25051, 23320, 23296, 23280, 525, 23272, 23305])).
% 3.63/3.96 tff(25058,plain,
% 3.63/3.96 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[279, 25057])).
% 3.63/3.96 tff(25059,plain,
% 3.63/3.96 (~b(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[16228, 25058, 283, 2254])).
% 3.63/3.96 tff(25060,plain,
% 3.63/3.96 (r(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[619, 25059])).
% 3.63/3.96 tff(25061,plain,
% 3.63/3.96 (r(z, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2836, 25060, 57])).
% 3.63/3.96 tff(25062,plain,
% 3.63/3.96 (~b(s(s(s(z))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[4819, 25051, 4367, 25048])).
% 3.63/3.96 tff(25063,plain,
% 3.63/3.96 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24791, 25062, 57])).
% 3.63/3.96 tff(25064,plain,
% 3.63/3.96 (r(s(s(elem!1)), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1283, 25063, 2507])).
% 3.63/3.96 tff(25065,plain,
% 3.63/3.96 (~b(s(s(elem!1)), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24767, 144, 286, 14453, 25058])).
% 3.63/3.96 tff(25066,plain,
% 3.63/3.96 (~b(s(s(s(z))), z)),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25065, 24775])).
% 3.63/3.96 tff(25067,plain,
% 3.63/3.96 (~b(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1853, 490, 1262, 3924])).
% 3.63/3.96 tff(25068,plain,
% 3.63/3.96 (r(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[583, 25067])).
% 3.63/3.96 tff(25069,plain,
% 3.63/3.96 (b(z, elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[8102, 490, 57])).
% 3.63/3.96 tff(25070,plain,
% 3.63/3.96 (b(elem!1, z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24422, 25069, 11546, 1963, 23305, 490, 2545, 286, 259, 23292])).
% 3.63/3.96 tff(25071,plain,
% 3.63/3.96 (~b(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[916, 25070, 451, 25069])).
% 3.63/3.96 tff(25072,plain,
% 3.63/3.96 (r(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[507, 25071])).
% 3.63/3.96 tff(25073,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[8201, 333, 2737, 25072, 25068, 4223])).
% 3.63/3.96 tff(25074,plain,((~b(z, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), z) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25075,plain,
% 3.63/3.96 (~b(z, s(z))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25074, 25066, 25064, 25051, 11546, 25061, 2545, 286, 25058, 25049, 57])).
% 3.63/3.96 tff(25076,plain,
% 3.63/3.96 (~b(z, elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[9366, 25075, 57])).
% 3.63/3.96 tff(25077,plain,
% 3.63/3.96 (r(z, elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[658, 25076, 23296])).
% 3.63/3.96 tff(25078,plain,
% 3.63/3.96 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24923, 25051, 4972, 2812])).
% 3.63/3.96 tff(25079,plain,
% 3.63/3.96 (r(s(elem!1), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2860, 44, 25078, 2857])).
% 3.63/3.96 tff(25080,plain,
% 3.63/3.96 (~r(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[23930, 25079, 25061, 25064])).
% 3.63/3.96 tff(25081,plain,
% 3.63/3.96 (b(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[507, 25080])).
% 3.63/3.96 tff(25082,plain,
% 3.63/3.96 (~b(s(elem!1), s(s(s(z))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25078, 24911])).
% 3.63/3.96 tff(25083,plain,
% 3.63/3.96 (~r(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[4807, 25082, 11786, 25062, 25060])).
% 3.63/3.96 tff(25084,plain,
% 3.63/3.96 (b(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[583, 25083])).
% 3.63/3.96 tff(25085,plain,
% 3.63/3.96 (~b(elem!1, z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[949, 25084, 25081, 25048])).
% 3.63/3.96 tff(25086,plain,
% 3.63/3.96 (r(elem!1, z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[653, 25085, 23320])).
% 3.63/3.96 tff(25087,plain,
% 3.63/3.96 (~r(s(s(s(s(z)))), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24987, 25058, 286, 25086, 23280, 25077])).
% 3.63/3.96 tff(25088,plain,
% 3.63/3.96 (b(s(s(s(s(z)))), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24301, 25087, 24884])).
% 3.63/3.96 tff(25089,plain,
% 3.63/3.96 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[23668, 144, 25048, 25051, 25088])).
% 3.63/3.96 tff(25090,plain,
% 3.63/3.96 (r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24448, 25089, 24446])).
% 3.63/3.96 tff(25091,plain,
% 3.63/3.96 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25002, 333, 25064, 25079, 25090])).
% 3.63/3.96 tff(25092,plain,
% 3.63/3.96 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25091, 4623])).
% 3.63/3.96 tff(25093,plain,
% 3.63/3.96 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[10534, 25088, 4972, 2812])).
% 3.63/3.96 tff(25094,plain,
% 3.63/3.96 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25093, 24477])).
% 3.63/3.96 tff(25095,plain,
% 3.63/3.96 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1116, 25094, 4283])).
% 3.63/3.96 tff(25096,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25095, 25092])).
% 3.63/3.96 tff(25097,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25098,plain,
% 3.63/3.96 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25097, 286, 4972, 2812, 57, 11546, 2545, 283, 2254, 4367])).
% 3.63/3.96 tff(25099,plain,
% 3.63/3.96 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[21271, 25098, 57])).
% 3.63/3.96 tff(25100,plain,
% 3.63/3.96 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[15113, 144, 23322, 14453, 25099])).
% 3.63/3.96 tff(25101,plain,
% 3.63/3.96 (r(s(elem!1), s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2860, 44, 25100, 2857])).
% 3.63/3.96 tff(25102,plain,
% 3.63/3.96 (~b(s(elem!1), s(s(s(z))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25100, 24911])).
% 3.63/3.96 tff(25103,plain,
% 3.63/3.96 (r(s(elem!1), s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[965, 25102, 11786])).
% 3.63/3.96 tff(25104,plain,
% 3.63/3.96 (~b(s(s(s(z))), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[10565, 23324, 4367, 23981])).
% 3.63/3.96 tff(25105,plain,
% 3.63/3.96 (r(s(s(s(z))), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[396, 25104])).
% 3.63/3.96 tff(25106,plain,
% 3.63/3.96 (r(s(s(elem!1)), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[6447, 25105, 57])).
% 3.63/3.96 tff(25107,plain,
% 3.63/3.96 (~b(z, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[11841, 23324, 4972, 2812])).
% 3.63/3.96 tff(25108,plain,
% 3.63/3.96 (~b(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2828, 25107, 57])).
% 3.63/3.96 tff(25109,plain,
% 3.63/3.96 (r(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[619, 25108])).
% 3.63/3.96 tff(25110,plain,
% 3.63/3.96 (r(z, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2836, 25109, 57])).
% 3.63/3.96 tff(25111,plain,
% 3.63/3.96 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.96 inference(rewrite,[status(thm)],[])).
% 3.63/3.96 tff(25112,plain,
% 3.63/3.96 (((~![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)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.63/3.96 inference(monotonicity,[status(thm)],[25111])).
% 3.63/3.96 tff(25113,plain,
% 3.63/3.96 (((~![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)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.63/3.96 inference(transitivity,[status(thm)],[25112, 15061])).
% 3.63/3.96 tff(25114,plain,
% 3.63/3.96 ((~![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)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.63/3.96 inference(quant_inst,[status(thm)],[])).
% 3.63/3.96 tff(25115,plain,
% 3.63/3.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 3.63/3.96 inference(modus_ponens,[status(thm)],[25114, 25113])).
% 3.63/3.96 tff(25116,plain,
% 3.63/3.96 (~r(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25115, 333, 25110, 25106, 4571])).
% 3.63/3.96 tff(25117,plain,
% 3.63/3.96 (b(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[507, 25116])).
% 3.63/3.96 tff(25118,plain,
% 3.63/3.96 (~b(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[916, 25117, 23981, 23324])).
% 3.63/3.96 tff(25119,plain,
% 3.63/3.96 (r(s(elem!1), elem!1)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[448, 25118, 2681])).
% 3.63/3.96 tff(25120,plain,
% 3.63/3.96 (~r(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[1972, 25109, 1686, 25105])).
% 3.63/3.96 tff(25121,plain,
% 3.63/3.96 (b(z, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[583, 25120])).
% 3.63/3.96 tff(25122,plain,
% 3.63/3.96 (~b(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[949, 25117, 23981, 25121])).
% 3.63/3.96 tff(25123,plain,
% 3.63/3.96 (r(elem!1, s(elem!1))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[560, 25122, 2483])).
% 3.63/3.96 tff(25124,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[12797, 25123, 25119, 23280, 24747, 57])).
% 3.63/3.96 tff(25125,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.96 tff(25126,plain,
% 3.63/3.96 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[25125, 25101, 57, 25103, 4972, 2812, 4367, 11546, 2545])).
% 3.63/3.96 tff(25127,plain,
% 3.63/3.96 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[279, 25126])).
% 3.63/3.96 tff(25128,plain,
% 3.63/3.96 (~b(s(s(elem!1)), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[24767, 144, 286, 14453, 25127])).
% 3.63/3.96 tff(25129,plain,
% 3.63/3.96 (r(s(s(elem!1)), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[5509, 25128])).
% 3.63/3.96 tff(25130,plain,
% 3.63/3.96 (~b(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[16228, 25127, 283, 2254])).
% 3.63/3.96 tff(25131,plain,
% 3.63/3.96 (r(z, s(s(s(z))))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[619, 25130])).
% 3.63/3.96 tff(25132,plain,
% 3.63/3.96 (r(z, s(s(elem!1)))),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[2836, 25131, 57])).
% 3.63/3.96 tff(25133,plain,
% 3.63/3.96 (~b(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[8282, 144, 286, 25099, 25127])).
% 3.63/3.96 tff(25134,plain,
% 3.63/3.96 (r(s(elem!1), z)),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[507, 25133])).
% 3.63/3.96 tff(25135,plain,
% 3.63/3.96 ($false),
% 3.63/3.96 inference(unit_resolution,[status(thm)],[15066, 333, 25134, 25132, 25129, 25101])).
% 3.63/3.96 tff(25136,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25137,plain,
% 3.63/3.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25136, 25046, 23859, 57, 24867, 2254, 25019, 11546, 2545])).
% 3.63/3.97 tff(25138,plain,
% 3.63/3.97 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[249, 25137])).
% 3.63/3.97 tff(25139,plain,
% 3.63/3.97 (~r(s(s(z)), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[7412, 25138, 25018, 25015])).
% 3.63/3.97 tff(25140,plain,
% 3.63/3.97 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24894, 25139, 57])).
% 3.63/3.97 tff(25141,plain,
% 3.63/3.97 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[965, 25140, 11786])).
% 3.63/3.97 tff(25142,plain,
% 3.63/3.97 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25141, 2501])).
% 3.63/3.97 tff(25143,plain,
% 3.63/3.97 (~b(s(elem!1), s(s(elem!1)))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24923, 25046, 25024, 25019])).
% 3.63/3.97 tff(25144,plain,
% 3.63/3.97 ($false),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25143, 25142])).
% 3.63/3.97 tff(25145,plain,((~b(s(elem!1), z)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25146,plain,
% 3.63/3.97 (~b(s(elem!1), z)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25145, 25010, 57, 11546, 2545, 23297])).
% 3.63/3.97 tff(25147,plain,
% 3.63/3.97 (r(s(elem!1), z)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[507, 25146])).
% 3.63/3.97 tff(25148,plain,
% 3.63/3.97 (~r(s(elem!1), elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24919, 25147, 23297, 23272])).
% 3.63/3.97 tff(25149,plain,
% 3.63/3.97 (b(s(elem!1), elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[448, 25148, 2681])).
% 3.63/3.97 tff(25150,plain,
% 3.63/3.97 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[2541, 23297, 23272, 23305])).
% 3.63/3.97 tff(25151,plain,
% 3.63/3.97 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[279, 25150])).
% 3.63/3.97 tff(25152,plain,
% 3.63/3.97 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25010, 4584])).
% 3.63/3.97 tff(25153,plain,
% 3.63/3.97 (~b(s(s(elem!1)), z)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24767, 144, 23859, 25152, 25151])).
% 3.63/3.97 tff(25154,plain,
% 3.63/3.97 (r(s(s(elem!1)), z)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[5509, 25153])).
% 3.63/3.97 tff(25155,plain,
% 3.63/3.97 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[6771, 333, 23297, 25147, 25154])).
% 3.63/3.97 tff(25156,plain,
% 3.63/3.97 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[1283, 25155, 2507])).
% 3.63/3.97 tff(25157,plain,
% 3.63/3.97 (b(s(s(s(z))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24791, 25156, 57])).
% 3.63/3.97 tff(25158,plain,
% 3.63/3.97 (~b(elem!1, s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[4819, 25157, 24867, 25149])).
% 3.63/3.97 tff(25159,plain,
% 3.63/3.97 (r(elem!1, s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[560, 25158, 2483])).
% 3.63/3.97 tff(25160,plain,
% 3.63/3.97 (~b(s(s(s(z))), z)),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25153, 24775])).
% 3.63/3.97 tff(25161,plain,
% 3.63/3.97 (r(s(s(s(z))), z)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[396, 25160])).
% 3.63/3.97 tff(25162,plain,
% 3.63/3.97 (~r(s(elem!1), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[5835, 25147, 23297, 25161])).
% 3.63/3.97 tff(25163,plain,
% 3.63/3.97 (b(s(elem!1), s(s(s(z))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[965, 25162, 11786])).
% 3.63/3.97 tff(25164,plain,
% 3.63/3.97 (b(s(elem!1), s(s(elem!1)))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25163, 2501])).
% 3.63/3.97 tff(25165,plain,
% 3.63/3.97 (~b(elem!1, s(s(elem!1)))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24923, 25164, 25149, 25019])).
% 3.63/3.97 tff(25166,plain,
% 3.63/3.97 (r(elem!1, s(s(elem!1)))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[2522, 25165, 2462])).
% 3.63/3.97 tff(25167,plain,
% 3.63/3.97 ($false),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[14959, 333, 2736, 3654, 2484, 5497])).
% 3.63/3.97 tff(25168,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25169,plain,
% 3.63/3.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25168, 25166, 23280, 25154])).
% 3.63/3.97 tff(25170,plain,
% 3.63/3.97 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[2758, 25169, 10047])).
% 3.63/3.97 tff(25171,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25172,plain,
% 3.63/3.97 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25173,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[25172])).
% 3.63/3.97 tff(25174,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.63/3.97 inference(transitivity,[status(thm)],[25173, 25171])).
% 3.63/3.97 tff(25175,plain,
% 3.63/3.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(quant_inst,[status(thm)],[])).
% 3.63/3.97 tff(25176,plain,
% 3.63/3.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25175, 25174])).
% 3.63/3.97 tff(25177,plain,
% 3.63/3.97 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25176, 144, 25149, 25170, 25164, 25019])).
% 3.63/3.97 tff(25178,plain,
% 3.63/3.97 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[472, 25177, 4762])).
% 3.63/3.97 tff(25179,plain,
% 3.63/3.97 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[6819, 144, 25156, 25170, 25164])).
% 3.63/3.97 tff(25180,plain,
% 3.63/3.97 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[542, 25179, 2698])).
% 3.63/3.97 tff(25181,plain,
% 3.63/3.97 ($false),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[12088, 25180, 25178, 23280, 25159])).
% 3.63/3.97 tff(25182,plain,(b(z, elem!1) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25183,plain,
% 3.63/3.97 (b(z, elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25182, 57, 11546, 2545])).
% 3.63/3.97 tff(25184,plain,
% 3.63/3.97 (b(z, s(z))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[9366, 25183, 57])).
% 3.63/3.97 tff(25185,plain,
% 3.63/3.97 (r(s(s(s(s(z)))), elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24580, 25184, 2545, 23859, 11546, 23305, 23292, 25183, 23287])).
% 3.63/3.97 tff(25186,plain,
% 3.63/3.97 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[21271, 15000, 57])).
% 3.63/3.97 tff(25187,plain,
% 3.63/3.97 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[542, 15010, 2698])).
% 3.63/3.97 tff(25188,plain,
% 3.63/3.97 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24816, 333, 9507, 2484, 2323])).
% 3.63/3.97 tff(25189,plain,
% 3.63/3.97 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[9761, 25188])).
% 3.63/3.97 tff(25190,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 3.63/3.97 tff(25191,assumption,(~r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 3.63/3.97 tff(25192,plain,
% 3.63/3.97 (b(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24448, 25191, 25190])).
% 3.63/3.97 tff(25193,plain,
% 3.63/3.97 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25194,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[25193])).
% 3.63/3.97 tff(25195,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(transitivity,[status(thm)],[25194, 12646])).
% 3.63/3.97 tff(25196,plain,
% 3.63/3.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.97 inference(quant_inst,[status(thm)],[])).
% 3.63/3.97 tff(25197,plain,
% 3.63/3.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25196, 25195])).
% 3.63/3.97 tff(25198,plain,
% 3.63/3.97 ($false),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25197, 144, 546, 450, 25192, 25189])).
% 3.63/3.97 tff(25199,plain,(r(s(s(s(s(z)))), s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25200,plain,
% 3.63/3.97 (r(s(s(s(s(z)))), s(elem!1))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25199, 25187, 25186, 24446, 9507, 2484, 2323])).
% 3.63/3.97 tff(25201,plain,
% 3.63/3.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, 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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25202,plain,
% 3.63/3.97 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25203,plain,
% 3.63/3.97 (((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[25202])).
% 3.63/3.97 tff(25204,plain,
% 3.63/3.97 (((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, 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(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.97 inference(transitivity,[status(thm)],[25203, 25201])).
% 3.63/3.97 tff(25205,plain,
% 3.63/3.97 ((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.63/3.97 inference(quant_inst,[status(thm)],[])).
% 3.63/3.97 tff(25206,plain,
% 3.63/3.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25205, 25204])).
% 3.63/3.97 tff(25207,plain,
% 3.63/3.97 ($false),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25206, 333, 435, 9507, 2323, 25200])).
% 3.63/3.97 tff(25208,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.97 tff(25209,plain,
% 3.63/3.97 (~r(s(elem!1), elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25208, 25185, 23272, 23280, 57])).
% 3.63/3.97 tff(25210,plain,
% 3.63/3.97 (b(s(elem!1), elem!1)),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[448, 25209, 2681])).
% 3.63/3.97 tff(25211,plain,
% 3.63/3.97 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.97 inference(commutativity,[status(thm)],[])).
% 3.63/3.97 tff(25212,plain,
% 3.63/3.97 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[3525])).
% 3.63/3.97 tff(25213,plain,
% 3.63/3.97 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.97 inference(transitivity,[status(thm)],[25212, 25211])).
% 3.63/3.97 tff(25214,plain,
% 3.63/3.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.63/3.97 inference(symmetry,[status(thm)],[25213])).
% 3.63/3.97 tff(25215,plain,
% 3.63/3.97 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[25214])).
% 3.63/3.97 tff(25216,plain,
% 3.63/3.97 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[24446, 25215])).
% 3.63/3.97 tff(25217,plain,
% 3.63/3.97 (((~![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)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25218,plain,
% 3.63/3.97 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.97 inference(rewrite,[status(thm)],[])).
% 3.63/3.97 tff(25219,plain,
% 3.63/3.97 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.63/3.97 inference(monotonicity,[status(thm)],[25218])).
% 3.63/3.97 tff(25220,plain,
% 3.63/3.97 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.97 inference(transitivity,[status(thm)],[25219, 25217])).
% 3.63/3.97 tff(25221,plain,
% 3.63/3.97 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.97 inference(quant_inst,[status(thm)],[])).
% 3.63/3.97 tff(25222,plain,
% 3.63/3.97 ((~![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)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.63/3.97 inference(modus_ponens,[status(thm)],[25221, 25220])).
% 3.63/3.97 tff(25223,plain,
% 3.63/3.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25222, 333, 25185, 23280, 23272])).
% 3.63/3.97 tff(25224,plain,
% 3.63/3.97 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[12733, 44, 25223])).
% 3.63/3.97 tff(25225,plain,
% 3.63/3.97 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[25224, 12723])).
% 3.63/3.97 tff(25226,plain,
% 3.63/3.97 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[24816, 333, 25185, 23280, 23272])).
% 3.63/3.97 tff(25227,plain,
% 3.63/3.97 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[9761, 25226])).
% 3.63/3.97 tff(25228,plain,
% 3.63/3.97 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[13493, 525, 2484, 509])).
% 3.63/3.97 tff(25229,plain,
% 3.63/3.97 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.97 inference(unit_resolution,[status(thm)],[279, 25228])).
% 3.63/3.98 tff(25230,plain,
% 3.63/3.98 (~b(s(s(s(s(z)))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24823, 144, 286, 25229, 25189])).
% 3.63/3.98 tff(25231,plain,
% 3.63/3.98 (r(s(s(s(s(z)))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[4243, 44, 242, 25230])).
% 3.63/3.98 tff(25232,plain,
% 3.63/3.98 (~r(s(elem!1), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25208, 9507, 2323, 2484, 57])).
% 3.63/3.98 tff(25233,plain,
% 3.63/3.98 (b(s(elem!1), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[448, 25232, 2681])).
% 3.63/3.98 tff(25234,plain,
% 3.63/3.98 (~r(elem!1, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24371, 333, 2484, 2323, 525])).
% 3.63/3.98 tff(25235,plain,
% 3.63/3.98 (b(elem!1, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[560, 25234, 2483])).
% 3.63/3.98 tff(25236,plain,
% 3.63/3.98 (~b(z, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[1642, 25235, 251, 25233])).
% 3.63/3.98 tff(25237,plain,
% 3.63/3.98 (r(z, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[583, 25236])).
% 3.63/3.98 tff(25238,plain,
% 3.63/3.98 (~b(s(s(s(z))), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[4819, 25235, 4367, 25233])).
% 3.63/3.98 tff(25239,plain,
% 3.63/3.98 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24791, 25238, 57])).
% 3.63/3.98 tff(25240,plain,
% 3.63/3.98 (r(s(s(elem!1)), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[1283, 25239, 2507])).
% 3.63/3.98 tff(25241,plain,
% 3.63/3.98 (~r(s(s(elem!1)), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[20156, 333, 25240, 509, 25237])).
% 3.63/3.98 tff(25242,plain,
% 3.63/3.98 (~r(s(s(s(z))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[6447, 25241, 57])).
% 3.63/3.98 tff(25243,plain,
% 3.63/3.98 (b(s(s(s(z))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[396, 25242])).
% 3.63/3.98 tff(25244,plain,
% 3.63/3.98 (~b(elem!1, z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[10565, 25243, 4367, 251])).
% 3.63/3.98 tff(25245,plain,
% 3.63/3.98 (r(elem!1, z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[653, 25244, 23320])).
% 3.63/3.98 tff(25246,plain,
% 3.63/3.98 (((~![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(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25247,plain,
% 3.63/3.98 (((~r(z, s(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, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25248,plain,
% 3.63/3.98 (((~![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(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, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25247])).
% 3.63/3.98 tff(25249,plain,
% 3.63/3.98 (((~![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(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, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25248, 25246])).
% 3.63/3.98 tff(25250,plain,
% 3.63/3.98 ((~![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(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(quant_inst,[status(thm)],[])).
% 3.63/3.98 tff(25251,plain,
% 3.63/3.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25250, 25249])).
% 3.63/3.98 tff(25252,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25251, 333, 25245, 25237, 9507, 25231])).
% 3.63/3.98 tff(25253,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~(s(z) = elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25254,plain,
% 3.63/3.98 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25253, 509, 24867, 25183, 57, 25185, 23859, 23280, 23272])).
% 3.63/3.98 tff(25255,plain,
% 3.63/3.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[21271, 25254, 57])).
% 3.63/3.98 tff(25256,plain,
% 3.63/3.98 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[12743, 144, 25255, 25227, 25225])).
% 3.63/3.98 tff(25257,plain,
% 3.63/3.98 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25256, 3528])).
% 3.63/3.98 tff(25258,plain,
% 3.63/3.98 (r(s(elem!1), s(s(s(elem!1))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[1067, 25257, 25216])).
% 3.63/3.98 tff(25259,plain,
% 3.63/3.98 (r(s(elem!1), s(s(s(s(z)))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[3545, 25258, 57])).
% 3.63/3.98 tff(25260,plain,
% 3.63/3.98 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[19392, 23861, 11546, 23305, 25184, 51])).
% 3.63/3.98 tff(25261,plain,
% 3.63/3.98 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[1137, 25260])).
% 3.63/3.98 tff(25262,plain,
% 3.63/3.98 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25261, 4584])).
% 3.63/3.98 tff(25263,plain,
% 3.63/3.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24760, 25262, 57, 11546, 51, 2545])).
% 3.63/3.98 tff(25264,plain,
% 3.63/3.98 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[2758, 25263, 10047])).
% 3.63/3.98 tff(25265,plain,
% 3.63/3.98 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25264, 14410])).
% 3.63/3.98 tff(25266,plain,
% 3.63/3.98 (~b(s(s(s(z))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[23935, 51, 23280, 23859, 509, 23272, 25183, 11546, 23305, 25184, 23320])).
% 3.63/3.98 tff(25267,plain,
% 3.63/3.98 (r(s(s(s(z))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[396, 25266])).
% 3.63/3.98 tff(25268,plain,
% 3.63/3.98 (r(s(s(elem!1)), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[6447, 25267, 57])).
% 3.63/3.98 tff(25269,plain,
% 3.63/3.98 (~r(s(s(elem!1)), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[13691, 333, 509, 51, 25268])).
% 3.63/3.98 tff(25270,plain,
% 3.63/3.98 (b(s(s(elem!1)), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[1283, 25269, 2507])).
% 3.63/3.98 tff(25271,plain,
% 3.63/3.98 (b(s(s(s(z))), s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24791, 25270, 57])).
% 3.63/3.98 tff(25272,plain,
% 3.63/3.98 (~b(elem!1, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[4819, 25271, 24867, 25210])).
% 3.63/3.98 tff(25273,plain,
% 3.63/3.98 (r(elem!1, s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[560, 25272, 2483])).
% 3.63/3.98 tff(25274,plain,
% 3.63/3.98 (~r(s(s(elem!1)), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[13396, 25273, 23280, 25264])).
% 3.63/3.98 tff(25275,plain,
% 3.63/3.98 (~b(z, s(s(elem!1)))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[23496, 25274, 23272, 57, 25183, 23981, 25264])).
% 3.63/3.98 tff(25276,plain,
% 3.63/3.98 (~b(z, s(s(s(z))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[2828, 25275, 57])).
% 3.63/3.98 tff(25277,plain,
% 3.63/3.98 (r(z, s(s(s(z))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[619, 25276])).
% 3.63/3.98 tff(25278,plain,
% 3.63/3.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[15762, 25277, 51, 25267])).
% 3.63/3.98 tff(25279,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25278, 25265])).
% 3.63/3.98 tff(25280,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25281,plain,
% 3.63/3.98 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25280, 509, 11546, 2545, 57])).
% 3.63/3.98 tff(25282,plain,
% 3.63/3.98 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[279, 25281])).
% 3.63/3.98 tff(25283,plain,
% 3.63/3.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25284,plain,
% 3.63/3.98 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25285,plain,
% 3.63/3.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25284])).
% 3.63/3.98 tff(25286,plain,
% 3.63/3.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25285, 25283])).
% 3.63/3.98 tff(25287,plain,
% 3.63/3.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.98 inference(quant_inst,[status(thm)],[])).
% 3.63/3.98 tff(25288,plain,
% 3.63/3.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25287, 25286])).
% 3.63/3.98 tff(25289,plain,
% 3.63/3.98 (~b(z, s(s(s(s(z)))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25288, 144, 25282, 25227, 25225])).
% 3.63/3.98 tff(25290,plain,
% 3.63/3.98 (r(z, s(s(s(s(z)))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[4260, 25289])).
% 3.63/3.98 tff(25291,plain,
% 3.63/3.98 (((~![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(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25292,plain,
% 3.63/3.98 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(rewrite,[status(thm)],[])).
% 3.63/3.98 tff(25293,plain,
% 3.63/3.98 (((~![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)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(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(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25292])).
% 3.63/3.98 tff(25294,plain,
% 3.63/3.98 (((~![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)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(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(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25293, 25291])).
% 3.63/3.98 tff(25295,plain,
% 3.63/3.98 ((~![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)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 3.63/3.98 inference(quant_inst,[status(thm)],[])).
% 3.63/3.98 tff(25296,plain,
% 3.63/3.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[25295, 25294])).
% 3.63/3.98 tff(25297,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25296, 333, 509, 25185, 25290, 25259])).
% 3.63/3.98 tff(25298,plain,((~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25299,plain,
% 3.63/3.98 (~r(s(elem!1), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25298, 57, 2545, 11546])).
% 3.63/3.98 tff(25300,plain,
% 3.63/3.98 (b(s(elem!1), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[507, 25299])).
% 3.63/3.98 tff(25301,plain,
% 3.63/3.98 (~b(elem!1, z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[916, 25300, 25183, 25210])).
% 3.63/3.98 tff(25302,plain,
% 3.63/3.98 (~b(s(s(s(z))), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24551, 25300, 11546, 23305, 25184, 23859, 25183, 2545, 23292])).
% 3.63/3.98 tff(25303,plain,
% 3.63/3.98 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24422, 25302, 11546, 25183, 23305, 25184, 2545, 23859, 25301, 23292])).
% 3.63/3.98 tff(25304,plain,
% 3.63/3.98 (r(elem!1, z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[653, 25301, 23320])).
% 3.63/3.98 tff(25305,plain,
% 3.63/3.98 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[2331, 25304, 23272, 23305])).
% 3.63/3.98 tff(25306,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[279, 25305, 25303])).
% 3.63/3.98 tff(25307,plain,((~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25308,plain,
% 3.63/3.98 (~(s(z) = elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25307, 11546, 2545])).
% 3.63/3.98 tff(25309,plain,
% 3.63/3.98 (~(elem!1 = s(z))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[712, 25308])).
% 3.63/3.98 tff(25310,plain,
% 3.63/3.98 (b(elem!1, s(z))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[720, 25309, 23287])).
% 3.63/3.98 tff(25311,plain,
% 3.63/3.98 (b(s(z), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[406, 25308, 23982])).
% 3.63/3.98 tff(25312,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[23855, 333, 670, 2484, 2323, 321])).
% 3.63/3.98 tff(25313,plain,((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25314,plain,
% 3.63/3.98 (~r(z, elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25313, 321, 2323, 2484])).
% 3.63/3.98 tff(25315,plain,
% 3.63/3.98 (z = elem!1),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[24037, 25314, 2323, 2484, 11546, 23870, 321])).
% 3.63/3.98 tff(25316,plain,
% 3.63/3.98 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25315])).
% 3.63/3.98 tff(25317,plain,
% 3.63/3.98 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25316, 203])).
% 3.63/3.98 tff(25318,plain,
% 3.63/3.98 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.63/3.98 inference(transitivity,[status(thm)],[25317, 24285])).
% 3.63/3.98 tff(25319,plain,
% 3.63/3.98 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25318])).
% 3.63/3.98 tff(25320,plain,
% 3.63/3.98 (~(s(s(s(s(z)))) = elem!1)),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[242, 25319])).
% 3.63/3.98 tff(25321,plain,
% 3.63/3.98 (~r(s(z), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[19114, 333, 11546, 2484, 2323])).
% 3.63/3.98 tff(25322,plain,
% 3.63/3.98 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.63/3.98 inference(monotonicity,[status(thm)],[66])).
% 3.63/3.98 tff(25323,plain,
% 3.63/3.98 (r(s(z), elem!1) <=> r(s(z), z)),
% 3.63/3.98 inference(symmetry,[status(thm)],[25322])).
% 3.63/3.98 tff(25324,plain,
% 3.63/3.98 ((~r(s(z), elem!1)) <=> (~r(s(z), z))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25323])).
% 3.63/3.98 tff(25325,plain,
% 3.63/3.98 (~r(s(z), z)),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[2310, 25324])).
% 3.63/3.98 tff(25326,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[323, 25325])).
% 3.63/3.98 tff(25327,plain,((~(z = elem!1)) | (~r(s(z), z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25328,plain,
% 3.63/3.98 (~r(s(z), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25327, 25315, 25321])).
% 3.63/3.98 tff(25329,plain,
% 3.63/3.98 (b(s(z), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[348, 25328])).
% 3.63/3.98 tff(25330,plain,
% 3.63/3.98 (b(s(elem!1), z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[18064, 25329, 25315])).
% 3.63/3.98 tff(25331,plain,
% 3.63/3.98 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 3.63/3.98 inference(symmetry,[status(thm)],[18060])).
% 3.63/3.98 tff(25332,plain,
% 3.63/3.98 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), z))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25331])).
% 3.63/3.98 tff(25333,plain,
% 3.63/3.98 (~b(s(elem!1), z)),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[3616, 25332])).
% 3.63/3.98 tff(25334,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[491, 25333])).
% 3.63/3.98 tff(25335,plain,((~(z = elem!1)) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25336,plain,
% 3.63/3.98 (b(s(elem!1), elem!1)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25335, 25330, 25315])).
% 3.63/3.98 tff(25337,plain,
% 3.63/3.98 (s(elem!1) = s(z)),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[70, 25315])).
% 3.63/3.98 tff(25338,plain,
% 3.63/3.98 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25337])).
% 3.63/3.98 tff(25339,plain,
% 3.63/3.98 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 3.63/3.98 inference(symmetry,[status(thm)],[25338])).
% 3.63/3.98 tff(25340,plain,
% 3.63/3.98 (b(elem!1, s(elem!1))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[305, 25339])).
% 3.63/3.98 tff(25341,plain,
% 3.63/3.98 (s(s(s(s(z)))) = s(z)),
% 3.63/3.98 inference(transitivity,[status(thm)],[24686, 18054])).
% 3.63/3.98 tff(25342,plain,
% 3.63/3.98 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25341])).
% 3.63/3.98 tff(25343,plain,
% 3.63/3.98 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 3.63/3.98 inference(symmetry,[status(thm)],[25342])).
% 3.63/3.98 tff(25344,plain,
% 3.63/3.98 (elem!1 = z),
% 3.63/3.98 inference(symmetry,[status(thm)],[66])).
% 3.63/3.98 tff(25345,plain,
% 3.63/3.98 (elem!1 = s(s(s(z)))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25344, 8680, 25343, 183])).
% 3.63/3.98 tff(25346,plain,
% 3.63/3.98 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[22888])).
% 3.63/3.98 tff(25347,plain,
% 3.63/3.98 (~(elem!1 = s(s(s(z))))),
% 3.63/3.98 inference(modus_ponens,[status(thm)],[392, 25346])).
% 3.63/3.98 tff(25348,plain,
% 3.63/3.98 ($false),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25347, 25345])).
% 3.63/3.98 tff(25349,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.98 tff(25350,plain,
% 3.63/3.98 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.63/3.98 inference(unit_resolution,[status(thm)],[25349, 25315])).
% 3.63/3.98 tff(25351,plain,
% 3.63/3.98 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25315])).
% 3.63/3.98 tff(25352,plain,
% 3.63/3.98 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.63/3.98 inference(transitivity,[status(thm)],[25351, 2])).
% 3.63/3.98 tff(25353,plain,
% 3.63/3.98 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.63/3.98 inference(transitivity,[status(thm)],[25352, 4795])).
% 3.63/3.98 tff(25354,plain,
% 3.63/3.98 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.63/3.98 inference(monotonicity,[status(thm)],[25353])).
% 3.63/3.99 tff(25355,plain,
% 3.63/3.99 (~(s(s(s(z))) = elem!1)),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[392, 25354])).
% 3.63/3.99 tff(25356,plain,
% 3.63/3.99 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25352])).
% 3.63/3.99 tff(25357,plain,
% 3.63/3.99 (~(elem!1 = s(s(s(z))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[392, 25356])).
% 3.63/3.99 tff(25358,plain,
% 3.63/3.99 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[23183, 25357, 2484, 134, 25355, 305, 11546, 321])).
% 3.63/3.99 tff(25359,plain,
% 3.63/3.99 (s(s(elem!1)) = s(s(z))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[18054])).
% 3.63/3.99 tff(25360,plain,
% 3.63/3.99 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25359])).
% 3.63/3.99 tff(25361,plain,
% 3.63/3.99 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25359, 25360])).
% 3.63/3.99 tff(25362,plain,
% 3.63/3.99 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.63/3.99 inference(symmetry,[status(thm)],[25361])).
% 3.63/3.99 tff(25363,plain,
% 3.63/3.99 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25362])).
% 3.63/3.99 tff(25364,plain,
% 3.63/3.99 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[217, 25363])).
% 3.63/3.99 tff(25365,plain,
% 3.63/3.99 (s(s(z)) = s(s(elem!1))),
% 3.63/3.99 inference(symmetry,[status(thm)],[25359])).
% 3.63/3.99 tff(25366,plain,
% 3.63/3.99 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25365])).
% 3.63/3.99 tff(25367,plain,
% 3.63/3.99 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 3.63/3.99 inference(symmetry,[status(thm)],[25366])).
% 3.63/3.99 tff(25368,plain,
% 3.63/3.99 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[18054])).
% 3.63/3.99 tff(25369,plain,
% 3.63/3.99 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 3.63/3.99 inference(transitivity,[status(thm)],[25368, 25367])).
% 3.63/3.99 tff(25370,plain,
% 3.63/3.99 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[18054])).
% 3.63/3.99 tff(25371,plain,
% 3.63/3.99 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.63/3.99 inference(symmetry,[status(thm)],[25370])).
% 3.63/3.99 tff(25372,plain,
% 3.63/3.99 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25371])).
% 3.63/3.99 tff(25373,plain,
% 3.63/3.99 (~(s(s(elem!1)) = s(elem!1))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[107, 25372])).
% 3.63/3.99 tff(25374,plain,
% 3.63/3.99 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.63/3.99 inference(monotonicity,[status(thm)],[66])).
% 3.63/3.99 tff(25375,plain,
% 3.63/3.99 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25374])).
% 3.63/3.99 tff(25376,plain,
% 3.63/3.99 (~(s(s(z)) = elem!1)),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[164, 25375])).
% 3.63/3.99 tff(25377,plain,
% 3.63/3.99 (~b(s(s(z)), elem!1)),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[23000, 144, 134, 305, 1417])).
% 3.63/3.99 tff(25378,plain,
% 3.63/3.99 (r(s(s(z)), elem!1)),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[7970, 25377, 1506])).
% 3.63/3.99 tff(25379,plain,
% 3.63/3.99 (((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25380,plain,
% 3.63/3.99 (((~r(elem!1, s(s(s(s(s(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(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(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25381,plain,
% 3.63/3.99 (((~![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(s(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(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(s(s(s(s(s(z)))))))))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25380])).
% 3.63/3.99 tff(25382,plain,
% 3.63/3.99 (((~![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(s(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(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(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(transitivity,[status(thm)],[25381, 25379])).
% 3.63/3.99 tff(25383,plain,
% 3.63/3.99 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.63/3.99 inference(quant_inst,[status(thm)],[])).
% 3.63/3.99 tff(25384,plain,
% 3.63/3.99 ((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[25383, 25382])).
% 3.63/3.99 tff(25385,plain,
% 3.63/3.99 (~r(s(s(z)), s(s(s(z))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[25384, 333, 707, 2323, 7155])).
% 3.63/3.99 tff(25386,plain,
% 3.63/3.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[18132, 25385, 8677])).
% 3.63/3.99 tff(25387,plain,
% 3.63/3.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25388,plain,
% 3.63/3.99 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25389,plain,
% 3.63/3.99 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25388])).
% 3.63/3.99 tff(25390,plain,
% 3.63/3.99 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(transitivity,[status(thm)],[25389, 25387])).
% 3.63/3.99 tff(25391,plain,
% 3.63/3.99 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(quant_inst,[status(thm)],[])).
% 3.63/3.99 tff(25392,plain,
% 3.63/3.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[25391, 25390])).
% 3.63/3.99 tff(25393,plain,
% 3.63/3.99 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[25392, 333, 2484, 2323, 7155])).
% 3.63/3.99 tff(25394,plain,
% 3.63/3.99 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[1451, 25393])).
% 3.63/3.99 tff(25395,plain,
% 3.63/3.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25396,plain,
% 3.63/3.99 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25397,plain,
% 3.63/3.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25396])).
% 3.63/3.99 tff(25398,plain,
% 3.63/3.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(transitivity,[status(thm)],[25397, 25395])).
% 3.63/3.99 tff(25399,plain,
% 3.63/3.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.63/3.99 inference(quant_inst,[status(thm)],[])).
% 3.63/3.99 tff(25400,plain,
% 3.63/3.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[25399, 25398])).
% 3.63/3.99 tff(25401,plain,
% 3.63/3.99 (~b(s(s(z)), s(s(s(z))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[25400, 144, 1417, 25394, 23368, 304])).
% 3.63/3.99 tff(25402,plain,
% 3.63/3.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[18122, 25401, 8677])).
% 3.63/3.99 tff(25403,plain,
% 3.63/3.99 ($false),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[4311, 25402, 25386, 22826])).
% 3.63/3.99 tff(25404,plain,((~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/3.99 tff(25405,plain,
% 3.63/3.99 (~r(s(s(s(z))), elem!1)),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[25404, 1417, 8677, 304, 2323, 25378, 2484])).
% 3.63/3.99 tff(25406,plain,
% 3.63/3.99 (b(s(s(s(z))), elem!1)),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[704, 25405, 698])).
% 3.63/3.99 tff(25407,plain,
% 3.63/3.99 (~b(s(s(s(z))), s(z))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[4375, 25406, 305, 134])).
% 3.63/3.99 tff(25408,plain,
% 3.63/3.99 (r(s(s(s(z))), s(z))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[2794, 25407])).
% 3.63/3.99 tff(25409,plain,
% 3.63/3.99 (~(s(s(z)) = s(elem!1))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[855, 6529])).
% 3.63/3.99 tff(25410,plain,
% 3.63/3.99 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[862, 25409])).
% 3.63/3.99 tff(25411,plain,
% 3.63/3.99 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.63/3.99 inference(symmetry,[status(thm)],[22809])).
% 3.63/3.99 tff(25412,plain,
% 3.63/3.99 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25411])).
% 3.63/3.99 tff(25413,plain,
% 3.63/3.99 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[18125])).
% 3.63/3.99 tff(25414,plain,
% 3.63/3.99 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25413])).
% 3.63/3.99 tff(25415,plain,
% 3.63/3.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(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(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25416,plain,
% 3.63/3.99 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(rewrite,[status(thm)],[])).
% 3.63/3.99 tff(25417,plain,
% 3.63/3.99 (((~![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(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/3.99 inference(monotonicity,[status(thm)],[25416])).
% 3.63/3.99 tff(25418,plain,
% 3.63/3.99 (((~![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(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/3.99 inference(transitivity,[status(thm)],[25417, 25415])).
% 3.63/3.99 tff(25419,plain,
% 3.63/3.99 ((~![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(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.63/3.99 inference(quant_inst,[status(thm)],[])).
% 3.63/3.99 tff(25420,plain,
% 3.63/3.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/3.99 inference(modus_ponens,[status(thm)],[25419, 25418])).
% 3.63/3.99 tff(25421,plain,
% 3.63/3.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.63/3.99 inference(unit_resolution,[status(thm)],[25420, 333, 2484, 2323, 25378])).
% 3.63/4.00 tff(25422,plain,
% 3.63/4.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25421, 25414])).
% 3.63/4.00 tff(25423,plain,
% 3.63/4.00 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[2758, 25422, 23135])).
% 3.63/4.00 tff(25424,plain,
% 3.63/4.00 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25423, 23136])).
% 3.63/4.00 tff(25425,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25426,plain,
% 3.63/4.00 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25427,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.63/4.00 inference(monotonicity,[status(thm)],[25426])).
% 3.63/4.00 tff(25428,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(transitivity,[status(thm)],[25427, 25425])).
% 3.63/4.00 tff(25429,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(quant_inst,[status(thm)],[])).
% 3.63/4.00 tff(25430,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25429, 25428])).
% 3.63/4.00 tff(25431,plain,
% 3.63/4.00 (~b(s(z), s(s(z)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25430, 144, 1417, 304, 9739])).
% 3.63/4.00 tff(25432,plain,
% 3.63/4.00 ($false),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25431, 22796])).
% 3.63/4.00 tff(25433,plain,((~b(s(z), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.00 tff(25434,plain,
% 3.63/4.00 (~b(s(z), s(s(elem!1)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25433, 1417, 8677, 304, 25424])).
% 3.63/4.00 tff(25435,plain,
% 3.63/4.00 (r(s(z), s(s(elem!1)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[5484, 25434])).
% 3.63/4.00 tff(25436,plain,
% 3.63/4.00 (r(s(z), s(s(z)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[22807, 25435, 8677])).
% 3.63/4.00 tff(25437,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25438,plain,
% 3.63/4.00 (((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25439,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), 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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.63/4.00 inference(monotonicity,[status(thm)],[25438])).
% 3.63/4.00 tff(25440,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), 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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.63/4.00 inference(transitivity,[status(thm)],[25439, 25437])).
% 3.63/4.00 tff(25441,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.63/4.00 inference(quant_inst,[status(thm)],[])).
% 3.63/4.00 tff(25442,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25441, 25440])).
% 3.63/4.00 tff(25443,plain,
% 3.63/4.00 ($false),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25442, 333, 3193, 7155, 19432, 22831])).
% 3.63/4.00 tff(25444,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.00 tff(25445,plain,
% 3.63/4.00 (~r(s(s(s(z))), s(s(z)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25444, 25408, 25378, 25436])).
% 3.63/4.00 tff(25446,plain,
% 3.63/4.00 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25445, 25412])).
% 3.63/4.00 tff(25447,plain,
% 3.63/4.00 (b(s(s(s(z))), s(s(elem!1)))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[1301, 25446, 25410])).
% 3.63/4.00 tff(25448,plain,
% 3.63/4.00 (b(s(s(s(z))), s(s(z)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25447, 22810])).
% 3.63/4.00 tff(25449,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25450,plain,
% 3.63/4.00 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(rewrite,[status(thm)],[])).
% 3.63/4.00 tff(25451,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.63/4.00 inference(monotonicity,[status(thm)],[25450])).
% 3.63/4.00 tff(25452,plain,
% 3.63/4.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.63/4.00 inference(transitivity,[status(thm)],[25451, 25449])).
% 3.63/4.00 tff(25453,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.63/4.00 inference(quant_inst,[status(thm)],[])).
% 3.63/4.00 tff(25454,plain,
% 3.63/4.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25453, 25452])).
% 3.63/4.00 tff(25455,plain,
% 3.63/4.00 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25454, 144, 1417, 304, 25424, 25448])).
% 3.63/4.00 tff(25456,plain,
% 3.63/4.00 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25392, 333, 2484, 2323, 25378])).
% 3.63/4.00 tff(25457,plain,
% 3.63/4.00 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[1451, 25456])).
% 3.63/4.00 tff(25458,plain,
% 3.63/4.00 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[9783, 144, 25457, 25424, 25448])).
% 3.63/4.00 tff(25459,plain,
% 3.63/4.00 ($false),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[16045, 25458, 25455, 11546, 25408])).
% 3.63/4.00 tff(25460,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.63/4.00 tff(25461,plain,
% 3.63/4.00 (~b(s(s(z)), s(z))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[25460, 304, 11546, 18054, 305, 134, 22891, 2323, 2484, 25376])).
% 3.63/4.00 tff(25462,plain,
% 3.63/4.00 (~b(s(s(elem!1)), s(elem!1))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[18895, 25461, 18054])).
% 3.63/4.00 tff(25463,plain,
% 3.63/4.00 (r(s(s(elem!1)), s(elem!1))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[1283, 25462, 25373])).
% 3.63/4.00 tff(25464,plain,
% 3.63/4.00 (r(s(s(z)), s(z))),
% 3.63/4.00 inference(modus_ponens,[status(thm)],[25463, 25369])).
% 3.63/4.00 tff(25465,plain,
% 3.63/4.00 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[21056, 25464, 2484, 11546])).
% 3.63/4.00 tff(25466,plain,
% 3.63/4.00 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[1451, 25465])).
% 3.63/4.00 tff(25467,plain,
% 3.63/4.00 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[23315, 20613, 2484, 2323])).
% 3.63/4.00 tff(25468,plain,
% 3.63/4.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[18738, 333, 20613, 2484, 2323])).
% 3.63/4.00 tff(25469,plain,
% 3.63/4.00 (~b(s(s(z)), s(s(s(z))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[7952, 25468, 1398, 25467])).
% 3.63/4.00 tff(25470,plain,
% 3.63/4.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.00 inference(unit_resolution,[status(thm)],[18122, 25469, 8677])).
% 3.63/4.00 tff(25471,plain,
% 3.63/4.00 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[4311, 25470, 22826])).
% 3.63/4.01 tff(25472,plain,
% 3.63/4.01 (r(s(s(z)), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18132, 25471, 8677])).
% 3.63/4.01 tff(25473,plain,
% 3.63/4.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[249, 25468])).
% 3.63/4.01 tff(25474,plain,
% 3.63/4.01 (~b(s(z), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[846, 56, 25473, 304])).
% 3.63/4.01 tff(25475,plain,
% 3.63/4.01 (r(s(z), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[172, 25474])).
% 3.63/4.01 tff(25476,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), 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))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25477,plain,
% 3.63/4.01 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25478,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25477])).
% 3.63/4.01 tff(25479,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.63/4.01 inference(transitivity,[status(thm)],[25478, 25476])).
% 3.63/4.01 tff(25480,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 3.63/4.01 inference(quant_inst,[status(thm)],[])).
% 3.63/4.01 tff(25481,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[25480, 25479])).
% 3.63/4.01 tff(25482,plain,
% 3.63/4.01 ($false),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25481, 333, 20613, 25475, 25472, 9770])).
% 3.63/4.01 tff(25483,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.01 tff(25484,plain,
% 3.63/4.01 (~b(s(s(s(z))), s(z))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25483, 25464, 304, 18054, 25466, 2484, 2323, 22891, 305, 134])).
% 3.63/4.01 tff(25485,plain,
% 3.63/4.01 (r(s(s(s(z))), s(z))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[2794, 25484])).
% 3.63/4.01 tff(25486,plain,
% 3.63/4.01 (~r(s(s(z)), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[20223, 333, 25485, 11546, 25464])).
% 3.63/4.01 tff(25487,plain,
% 3.63/4.01 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18132, 25486, 18054])).
% 3.63/4.01 tff(25488,plain,
% 3.63/4.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[4311, 25487, 25364])).
% 3.63/4.01 tff(25489,plain,
% 3.63/4.01 (b(s(s(z)), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18122, 25488, 18054])).
% 3.63/4.01 tff(25490,plain,
% 3.63/4.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[17809, 25485, 11546, 2484])).
% 3.63/4.01 tff(25491,plain,
% 3.63/4.01 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[7952, 25490, 25466, 25489])).
% 3.63/4.01 tff(25492,plain,
% 3.63/4.01 (~b(z, s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[2156, 22401, 489, 285])).
% 3.63/4.01 tff(25493,plain,
% 3.63/4.01 (r(z, s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[619, 25492])).
% 3.63/4.01 tff(25494,plain,
% 3.63/4.01 (r(elem!1, s(s(s(z))))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[25493, 22906])).
% 3.63/4.01 tff(25495,plain,
% 3.63/4.01 (((~![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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25496,plain,
% 3.63/4.01 (((~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(z)))))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25497,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25496])).
% 3.63/4.01 tff(25498,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/4.01 inference(transitivity,[status(thm)],[25497, 25495])).
% 3.63/4.01 tff(25499,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(z))))))))))),
% 3.63/4.01 inference(quant_inst,[status(thm)],[])).
% 3.63/4.01 tff(25500,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[25499, 25498])).
% 3.63/4.01 tff(25501,plain,
% 3.63/4.01 ($false),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25500, 333, 25494, 3193, 2323, 224])).
% 3.63/4.01 tff(25502,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.01 tff(25503,plain,
% 3.63/4.01 (~b(s(s(s(z))), z)),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25502, 25491, 2323, 66, 489, 25485, 11546])).
% 3.63/4.01 tff(25504,plain,
% 3.63/4.01 (r(s(s(s(z))), z)),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[396, 25503])).
% 3.63/4.01 tff(25505,plain,
% 3.63/4.01 (r(s(s(s(z))), elem!1)),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[22912, 25504, 66])).
% 3.63/4.01 tff(25506,plain,
% 3.63/4.01 ($false),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18738, 333, 25505, 2484, 2323, 25491])).
% 3.63/4.01 tff(25507,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.01 tff(25508,plain,
% 3.63/4.01 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25507, 25329, 2323, 2484, 25315, 11546, 305, 134])).
% 3.63/4.01 tff(25509,plain,
% 3.63/4.01 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[319, 25508])).
% 3.63/4.01 tff(25510,plain,
% 3.63/4.01 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25315])).
% 3.63/4.01 tff(25511,plain,
% 3.63/4.01 (b(elem!1, s(z)) <=> b(z, s(z))),
% 3.63/4.01 inference(symmetry,[status(thm)],[25510])).
% 3.63/4.01 tff(25512,plain,
% 3.63/4.01 (b(z, s(z))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[305, 25511])).
% 3.63/4.01 tff(25513,plain,
% 3.63/4.01 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25315])).
% 3.63/4.01 tff(25514,plain,
% 3.63/4.01 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(symmetry,[status(thm)],[25513])).
% 3.63/4.01 tff(25515,plain,
% 3.63/4.01 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[2323, 25514])).
% 3.63/4.01 tff(25516,plain,
% 3.63/4.01 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[17920, 25515, 11546, 25509, 25512, 25329])).
% 3.63/4.01 tff(25517,plain,
% 3.63/4.01 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[1451, 25516])).
% 3.63/4.01 tff(25518,plain,
% 3.63/4.01 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[8677])).
% 3.63/4.01 tff(25519,plain,
% 3.63/4.01 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.63/4.01 inference(symmetry,[status(thm)],[25518])).
% 3.63/4.01 tff(25520,plain,
% 3.63/4.01 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25519])).
% 3.63/4.01 tff(25521,plain,
% 3.63/4.01 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18738, 333, 707, 2484, 2323])).
% 3.63/4.01 tff(25522,plain,
% 3.63/4.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[249, 25521])).
% 3.63/4.01 tff(25523,plain,
% 3.63/4.01 (~b(s(s(z)), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[7952, 25521, 1398, 7927])).
% 3.63/4.01 tff(25524,plain,
% 3.63/4.01 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18122, 25523, 8677])).
% 3.63/4.01 tff(25525,plain,
% 3.63/4.01 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[4311, 25524, 22826])).
% 3.63/4.01 tff(25526,plain,
% 3.63/4.01 (r(s(s(z)), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[18132, 25525, 8677])).
% 3.63/4.01 tff(25527,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 3.63/4.01 tff(25528,plain,
% 3.63/4.01 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[20413, 333, 25527, 11546, 322])).
% 3.63/4.01 tff(25529,plain,
% 3.63/4.01 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[9761, 25528])).
% 3.63/4.01 tff(25530,plain,
% 3.63/4.01 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[23700, 144, 283, 2254, 25529])).
% 3.63/4.01 tff(25531,plain,
% 3.63/4.01 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[9821, 44, 219, 25530])).
% 3.63/4.01 tff(25532,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25533,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.63/4.01 inference(quant_inst,[status(thm)],[])).
% 3.63/4.01 tff(25534,plain,
% 3.63/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[25533, 25532])).
% 3.63/4.01 tff(25535,plain,
% 3.63/4.01 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25534, 333, 707, 6330, 25531])).
% 3.63/4.01 tff(25536,plain,
% 3.63/4.01 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[20431, 333, 25527, 11546, 322])).
% 3.63/4.01 tff(25537,plain,
% 3.63/4.01 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[12733, 44, 25536])).
% 3.63/4.01 tff(25538,plain,
% 3.63/4.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25537, 12723])).
% 3.63/4.01 tff(25539,plain,
% 3.63/4.01 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[20469, 144, 1398, 25529, 25538])).
% 3.63/4.01 tff(25540,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 3.63/4.01 tff(25541,plain,
% 3.63/4.01 (s(s(s(s(z)))) = s(s(z))),
% 3.63/4.01 inference(symmetry,[status(thm)],[25540])).
% 3.63/4.01 tff(25542,plain,
% 3.63/4.01 ($false),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[24445, 25541])).
% 3.63/4.01 tff(25543,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.01 tff(25544,plain,
% 3.63/4.01 ($false),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[20473, 44, 25543, 25539, 25535])).
% 3.63/4.01 tff(25545,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.63/4.01 tff(25546,plain,
% 3.63/4.01 (~r(s(s(s(s(z)))), s(z))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[25545, 707, 25526, 1398, 25522, 23185, 11546, 322])).
% 3.63/4.01 tff(25547,plain,
% 3.63/4.01 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.63/4.01 inference(modus_ponens,[status(thm)],[25546, 25520])).
% 3.63/4.01 tff(25548,plain,
% 3.63/4.01 (b(s(s(s(s(z)))), s(elem!1))),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[24448, 25547, 25190])).
% 3.63/4.01 tff(25549,plain,
% 3.63/4.01 (~b(s(s(s(s(z)))), elem!1)),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[24997, 25548, 547, 451])).
% 3.63/4.01 tff(25550,plain,
% 3.63/4.01 (r(s(s(s(s(z)))), elem!1)),
% 3.63/4.01 inference(unit_resolution,[status(thm)],[24301, 25549, 24296])).
% 3.63/4.01 tff(25551,plain,
% 3.63/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25552,plain,
% 3.63/4.01 (((~r(elem!1, s(s(s(s(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)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.63/4.01 inference(rewrite,[status(thm)],[])).
% 3.63/4.01 tff(25553,plain,
% 3.63/4.01 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.63/4.01 inference(monotonicity,[status(thm)],[25552])).
% 3.63/4.01 tff(25554,plain,
% 3.63/4.01 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.01 inference(transitivity,[status(thm)],[25553, 25551])).
% 3.73/4.01 tff(25555,plain,
% 3.73/4.01 ((~![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(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))))))),
% 3.73/4.01 inference(quant_inst,[status(thm)],[])).
% 3.73/4.01 tff(25556,plain,
% 3.73/4.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.01 inference(modus_ponens,[status(thm)],[25555, 25554])).
% 3.73/4.01 tff(25557,plain,
% 3.73/4.01 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[25556, 333, 707, 25550, 2323])).
% 3.73/4.01 tff(25558,plain,
% 3.73/4.01 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[9821, 44, 219, 25557])).
% 3.73/4.01 tff(25559,plain,
% 3.73/4.01 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[24816, 333, 25550, 2484, 2323])).
% 3.73/4.01 tff(25560,plain,
% 3.73/4.01 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[9761, 25559])).
% 3.73/4.01 tff(25561,plain,
% 3.73/4.01 ($false),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[18464, 144, 25522, 23185, 25560, 25558])).
% 3.73/4.01 tff(25562,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.01 tff(25563,plain,
% 3.73/4.01 (~r(s(s(s(z))), elem!1)),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[25562, 25320, 2323, 2484, 25340, 25336, 25350, 25337, 25517, 11546, 25509, 25358])).
% 3.73/4.01 tff(25564,plain,
% 3.73/4.01 (b(s(s(s(z))), elem!1)),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[704, 25563, 25355])).
% 3.73/4.01 tff(25565,plain,
% 3.73/4.01 (~b(s(s(s(z))), s(z))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[4375, 25564, 134, 305])).
% 3.73/4.01 tff(25566,plain,
% 3.73/4.01 (r(s(s(s(z))), s(z))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[2794, 25565])).
% 3.73/4.01 tff(25567,plain,
% 3.73/4.01 (~r(s(s(s(z))), z)),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[22912, 25563, 25315])).
% 3.73/4.01 tff(25568,plain,
% 3.73/4.01 (b(s(s(s(z))), z)),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[396, 25567])).
% 3.73/4.01 tff(25569,plain,
% 3.73/4.01 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[25502, 25566, 11546, 2323, 25315, 25329, 25568])).
% 3.73/4.01 tff(25570,plain,
% 3.73/4.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[249, 25569])).
% 3.73/4.01 tff(25571,plain,
% 3.73/4.01 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[24997, 3529, 547, 451])).
% 3.73/4.01 tff(25572,plain,
% 3.73/4.01 (r(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.01 inference(unit_resolution,[status(thm)],[24448, 25571, 25190])).
% 3.73/4.01 tff(25573,plain,
% 3.73/4.01 (r(s(s(s(s(z)))), s(z))),
% 3.73/4.01 inference(modus_ponens,[status(thm)],[25572, 25518])).
% 3.73/4.01 tff(25574,plain,
% 3.73/4.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(s(s(s(s(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(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.01 inference(rewrite,[status(thm)],[])).
% 3.73/4.01 tff(25575,plain,
% 3.73/4.01 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), 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(s(s(s(s(z))))))))))),
% 3.73/4.01 inference(rewrite,[status(thm)],[])).
% 3.73/4.01 tff(25576,plain,
% 3.73/4.01 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), 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(z))), 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(s(s(s(s(z)))))))))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25575])).
% 3.73/4.02 tff(25577,plain,
% 3.73/4.02 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), 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(z))), 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(s(s(s(s(z))))))))))),
% 3.73/4.02 inference(transitivity,[status(thm)],[25576, 25574])).
% 3.73/4.02 tff(25578,plain,
% 3.73/4.02 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.02 inference(quant_inst,[status(thm)],[])).
% 3.73/4.02 tff(25579,plain,
% 3.73/4.02 ((~![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(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(s(s(s(s(z)))))))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25578, 25577])).
% 3.73/4.02 tff(25580,plain,
% 3.73/4.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25579, 333, 3193, 25573, 11546])).
% 3.73/4.02 tff(25581,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[9821, 44, 219, 25580])).
% 3.73/4.02 tff(25582,plain,
% 3.73/4.02 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[20413, 333, 25573, 11546, 322])).
% 3.73/4.02 tff(25583,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[9761, 25582])).
% 3.73/4.02 tff(25584,plain,
% 3.73/4.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.02 inference(rewrite,[status(thm)],[])).
% 3.73/4.02 tff(25585,plain,
% 3.73/4.02 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.02 inference(rewrite,[status(thm)],[])).
% 3.73/4.02 tff(25586,plain,
% 3.73/4.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25585])).
% 3.73/4.02 tff(25587,plain,
% 3.73/4.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.02 inference(transitivity,[status(thm)],[25586, 25584])).
% 3.73/4.02 tff(25588,plain,
% 3.73/4.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.02 inference(quant_inst,[status(thm)],[])).
% 3.73/4.02 tff(25589,plain,
% 3.73/4.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25588, 25587])).
% 3.73/4.02 tff(25590,plain,
% 3.73/4.02 ($false),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25589, 144, 3529, 283, 4367, 25583, 25581])).
% 3.73/4.02 tff(25591,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.02 tff(25592,plain,
% 3.73/4.02 (~b(s(s(s(s(z)))), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25591, 25570, 25564, 11546, 25509, 25566, 25337, 25350, 25340, 25336])).
% 3.73/4.02 tff(25593,plain,
% 3.73/4.02 (r(s(s(s(s(z)))), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24301, 25592, 25320])).
% 3.73/4.02 tff(25594,plain,
% 3.73/4.02 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24816, 333, 25593, 2484, 2323])).
% 3.73/4.02 tff(25595,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[9761, 25594])).
% 3.73/4.02 tff(25596,plain,
% 3.73/4.02 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[1137, 25358])).
% 3.73/4.02 tff(25597,plain,
% 3.73/4.02 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[23700, 144, 25570, 25596, 25595])).
% 3.73/4.02 tff(25598,plain,
% 3.73/4.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[9821, 44, 219, 25597])).
% 3.73/4.02 tff(25599,plain,
% 3.73/4.02 (s(s(elem!1)) = s(s(z))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25337])).
% 3.73/4.02 tff(25600,plain,
% 3.73/4.02 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25599])).
% 3.73/4.02 tff(25601,plain,
% 3.73/4.02 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25599, 25600])).
% 3.73/4.02 tff(25602,plain,
% 3.73/4.02 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.73/4.02 inference(symmetry,[status(thm)],[25601])).
% 3.73/4.02 tff(25603,plain,
% 3.73/4.02 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25602])).
% 3.73/4.02 tff(25604,plain,
% 3.73/4.02 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[217, 25603])).
% 3.73/4.02 tff(25605,plain,
% 3.73/4.02 (~b(s(s(z)), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[7952, 25569, 25517, 25358])).
% 3.73/4.02 tff(25606,plain,
% 3.73/4.02 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[18122, 25605, 25337])).
% 3.73/4.02 tff(25607,plain,
% 3.73/4.02 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[4311, 25606, 25604])).
% 3.73/4.02 tff(25608,plain,
% 3.73/4.02 (r(s(s(z)), s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[18132, 25607, 25337])).
% 3.73/4.02 tff(25609,plain,
% 3.73/4.02 (((~![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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.73/4.02 inference(rewrite,[status(thm)],[])).
% 3.73/4.02 tff(25610,plain,
% 3.73/4.02 ((~![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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.73/4.02 inference(quant_inst,[status(thm)],[])).
% 3.73/4.02 tff(25611,plain,
% 3.73/4.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25610, 25609])).
% 3.73/4.02 tff(25612,plain,
% 3.73/4.02 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25611, 333, 25566, 25608, 25598])).
% 3.73/4.02 tff(25613,plain,
% 3.73/4.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25222, 333, 25593, 2484, 2323])).
% 3.73/4.02 tff(25614,plain,
% 3.73/4.02 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[12733, 44, 25613])).
% 3.73/4.02 tff(25615,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25614, 12723])).
% 3.73/4.02 tff(25616,plain,
% 3.73/4.02 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[20469, 144, 25517, 25595, 25615])).
% 3.73/4.02 tff(25617,plain,
% 3.73/4.02 ($false),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[20473, 44, 25543, 25616, 25612])).
% 3.73/4.02 tff(25618,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.02 tff(25619,plain,
% 3.73/4.02 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25618, 23280, 23272, 11546, 25311, 25310])).
% 3.73/4.02 tff(25620,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[302, 25619])).
% 3.73/4.02 tff(25621,plain,
% 3.73/4.02 (~(elem!1 = z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[14770, 25620, 2545])).
% 3.73/4.02 tff(25622,plain,
% 3.73/4.02 (~(z = elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[18287, 25621])).
% 3.73/4.02 tff(25623,plain,
% 3.73/4.02 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24191, 25622, 23280, 25311, 25310, 23272, 11546])).
% 3.73/4.02 tff(25624,plain,
% 3.73/4.02 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[279, 25623])).
% 3.73/4.02 tff(25625,plain,
% 3.73/4.02 (~r(s(s(s(z))), s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[17809, 6107, 23280, 11546])).
% 3.73/4.02 tff(25626,plain,
% 3.73/4.02 (b(s(s(s(z))), s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[2794, 25625])).
% 3.73/4.02 tff(25627,plain,
% 3.73/4.02 (~(s(elem!1) = s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[8683, 25622])).
% 3.73/4.02 tff(25628,plain,
% 3.73/4.02 (r(s(s(s(s(z)))), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24276, 304, 11546, 25627, 23287, 23982, 2545])).
% 3.73/4.02 tff(25629,plain,
% 3.73/4.02 (b(elem!1, s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[720, 713, 23870])).
% 3.73/4.02 tff(25630,plain,
% 3.73/4.02 (b(s(z), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[406, 706, 25321])).
% 3.73/4.02 tff(25631,plain,
% 3.73/4.02 (~(z = elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[18287, 1368])).
% 3.73/4.02 tff(25632,plain,
% 3.73/4.02 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24191, 25631, 2484, 25630, 25629, 2323, 11546])).
% 3.73/4.02 tff(25633,plain,
% 3.73/4.02 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[279, 25632])).
% 3.73/4.02 tff(25634,plain,
% 3.73/4.02 (~r(s(s(s(z))), s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24063, 304, 11546, 2323, 2484, 23870, 25631])).
% 3.73/4.02 tff(25635,plain,
% 3.73/4.02 (b(s(s(s(z))), s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[2794, 25634])).
% 3.73/4.02 tff(25636,plain,
% 3.73/4.02 (~(s(elem!1) = s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[8683, 25631])).
% 3.73/4.02 tff(25637,plain,
% 3.73/4.02 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.02 inference(rewrite,[status(thm)],[])).
% 3.73/4.02 tff(25638,plain,
% 3.73/4.02 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.02 inference(rewrite,[status(thm)],[])).
% 3.73/4.02 tff(25639,plain,
% 3.73/4.02 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25638])).
% 3.73/4.02 tff(25640,plain,
% 3.73/4.02 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.02 inference(transitivity,[status(thm)],[25639, 25637])).
% 3.73/4.02 tff(25641,plain,
% 3.73/4.02 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 3.73/4.02 inference(quant_inst,[status(thm)],[])).
% 3.73/4.02 tff(25642,plain,
% 3.73/4.02 ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25641, 25640])).
% 3.73/4.02 tff(25643,plain,
% 3.73/4.02 (~r(elem!1, s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25642, 333, 2484, 2323, 6107])).
% 3.73/4.02 tff(25644,plain,
% 3.73/4.02 (~b(elem!1, s(s(s(z))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[22776, 17819, 25629, 56])).
% 3.73/4.02 tff(25645,plain,
% 3.73/4.02 (elem!1 = s(s(s(z)))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[1538, 25644, 25643])).
% 3.73/4.02 tff(25646,plain,
% 3.73/4.02 (s(elem!1) = s(s(s(s(z))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25645])).
% 3.73/4.02 tff(25647,plain,
% 3.73/4.02 (s(s(s(s(z)))) = s(elem!1)),
% 3.73/4.02 inference(symmetry,[status(thm)],[25646])).
% 3.73/4.02 tff(25648,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25647])).
% 3.73/4.02 tff(25649,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.02 inference(symmetry,[status(thm)],[25648])).
% 3.73/4.02 tff(25650,plain,
% 3.73/4.02 (~b(s(s(s(z))), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[4375, 56, 25630, 25629])).
% 3.73/4.02 tff(25651,plain,
% 3.73/4.02 (~r(s(s(s(z))), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[23315, 6107, 2323, 2484])).
% 3.73/4.02 tff(25652,plain,
% 3.73/4.02 (s(s(s(z))) = elem!1),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[704, 25651, 25650])).
% 3.73/4.02 tff(25653,plain,
% 3.73/4.02 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[12214, 25652])).
% 3.73/4.02 tff(25654,plain,
% 3.73/4.02 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[20734, 25653])).
% 3.73/4.02 tff(25655,plain,
% 3.73/4.02 (~(s(s(elem!1)) = elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[7595, 25652, 863])).
% 3.73/4.02 tff(25656,plain,
% 3.73/4.02 (~(elem!1 = s(s(elem!1)))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[5603, 25655])).
% 3.73/4.02 tff(25657,plain,
% 3.73/4.02 (~(s(elem!1) = elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[5813, 25656])).
% 3.73/4.02 tff(25658,plain,
% 3.73/4.02 (r(s(elem!1), elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[448, 25657, 3616])).
% 3.73/4.02 tff(25659,plain,
% 3.73/4.02 (~(elem!1 = s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[1569, 25657])).
% 3.73/4.02 tff(25660,plain,
% 3.73/4.02 (r(elem!1, s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[560, 25659, 5775])).
% 3.73/4.02 tff(25661,plain,
% 3.73/4.02 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[12793, 333, 25660, 25658, 2484])).
% 3.73/4.02 tff(25662,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[542, 25661, 25654])).
% 3.73/4.02 tff(25663,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25662, 25649])).
% 3.73/4.02 tff(25664,plain,
% 3.73/4.02 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25646])).
% 3.73/4.02 tff(25665,plain,
% 3.73/4.02 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[20897, 25659, 2484, 3616, 5775])).
% 3.73/4.02 tff(25666,plain,
% 3.73/4.02 (~b(z, s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[8386, 25661, 259, 25665, 25654])).
% 3.73/4.02 tff(25667,plain,
% 3.73/4.02 (r(z, s(elem!1))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[583, 25666])).
% 3.73/4.02 tff(25668,plain,
% 3.73/4.02 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25645])).
% 3.73/4.02 tff(25669,plain,
% 3.73/4.02 (r(s(s(s(z))), s(elem!1))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25660, 25668])).
% 3.73/4.02 tff(25670,plain,
% 3.73/4.02 (~r(s(s(s(z))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[12891, 25669, 25658, 25667])).
% 3.73/4.02 tff(25671,plain,
% 3.73/4.02 (b(s(s(s(z))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[396, 25670])).
% 3.73/4.02 tff(25672,plain,
% 3.73/4.02 (~b(z, s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24110, 25671, 25629, 1, 304, 2484, 863, 56, 11546, 25630])).
% 3.73/4.02 tff(25673,plain,
% 3.73/4.02 (r(z, s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[372, 25672])).
% 3.73/4.02 tff(25674,plain,
% 3.73/4.02 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25645])).
% 3.73/4.02 tff(25675,plain,
% 3.73/4.02 (r(s(elem!1), s(s(s(z))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25658, 25674])).
% 3.73/4.02 tff(25676,plain,
% 3.73/4.02 (~r(z, elem!1)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[5074, 25675, 25667, 25660])).
% 3.73/4.02 tff(25677,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25647])).
% 3.73/4.02 tff(25678,plain,
% 3.73/4.02 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(elem!1), z))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25677])).
% 3.73/4.02 tff(25679,plain,
% 3.73/4.02 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(monotonicity,[status(thm)],[25646])).
% 3.73/4.02 tff(25680,plain,
% 3.73/4.02 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[472, 25665, 25653])).
% 3.73/4.02 tff(25681,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25680, 25679])).
% 3.73/4.02 tff(25682,plain,
% 3.73/4.02 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[25618, 2484, 2323, 11546, 25630, 25629])).
% 3.73/4.02 tff(25683,plain,
% 3.73/4.02 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[302, 25682])).
% 3.73/4.02 tff(25684,plain,
% 3.73/4.02 (~b(s(s(s(s(z)))), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[24823, 144, 25683, 259, 25681])).
% 3.73/4.02 tff(25685,plain,
% 3.73/4.02 (~b(s(elem!1), z)),
% 3.73/4.02 inference(modus_ponens,[status(thm)],[25684, 25678])).
% 3.73/4.02 tff(25686,plain,
% 3.73/4.02 (r(s(elem!1), z)),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[507, 25685])).
% 3.73/4.02 tff(25687,plain,
% 3.73/4.02 (b(s(elem!1), s(z))),
% 3.73/4.02 inference(unit_resolution,[status(thm)],[1653, 25686, 706, 1, 25676, 25659, 25673])).
% 3.73/4.02 tff(25688,plain,
% 3.73/4.02 (b(s(s(s(s(z)))), s(z))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25687, 25664])).
% 3.73/4.03 tff(25689,plain,
% 3.73/4.03 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 3.73/4.03 inference(commutativity,[status(thm)],[])).
% 3.73/4.03 tff(25690,plain,
% 3.73/4.03 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 3.73/4.03 inference(symmetry,[status(thm)],[25689])).
% 3.73/4.03 tff(25691,plain,
% 3.73/4.03 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25690])).
% 3.73/4.03 tff(25692,plain,
% 3.73/4.03 (~(s(z) = s(s(s(s(z)))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[24294, 25691])).
% 3.73/4.03 tff(25693,plain,
% 3.73/4.03 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25645])).
% 3.73/4.03 tff(25694,plain,
% 3.73/4.03 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25693])).
% 3.73/4.03 tff(25695,plain,
% 3.73/4.03 (~b(s(s(s(z))), s(elem!1))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[5775, 25694])).
% 3.73/4.03 tff(25696,plain,
% 3.73/4.03 (~(s(s(z)) = elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[14611, 25652, 706])).
% 3.73/4.03 tff(25697,plain,
% 3.73/4.03 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1508, 25696])).
% 3.73/4.03 tff(25698,plain,
% 3.73/4.03 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25645])).
% 3.73/4.03 tff(25699,plain,
% 3.73/4.03 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25698])).
% 3.73/4.03 tff(25700,plain,
% 3.73/4.03 (~b(s(elem!1), s(s(s(z))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[3616, 25699])).
% 3.73/4.03 tff(25701,plain,
% 3.73/4.03 (~r(z, s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[4807, 25700, 25697, 25667, 25695])).
% 3.73/4.03 tff(25702,plain,
% 3.73/4.03 (b(z, s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[619, 25701])).
% 3.73/4.03 tff(25703,plain,
% 3.73/4.03 (~b(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[2156, 25702, 17819, 25671])).
% 3.73/4.03 tff(25704,plain,
% 3.73/4.03 (r(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[348, 25703])).
% 3.73/4.03 tff(25705,plain,
% 3.73/4.03 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[19631])).
% 3.73/4.03 tff(25706,plain,
% 3.73/4.03 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.73/4.03 inference(symmetry,[status(thm)],[25705])).
% 3.73/4.03 tff(25707,plain,
% 3.73/4.03 (r(z, s(s(s(s(z)))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[562, 25706])).
% 3.73/4.03 tff(25708,plain,
% 3.73/4.03 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 3.73/4.03 inference(monotonicity,[status(thm)],[19631, 3239])).
% 3.73/4.03 tff(25709,plain,
% 3.73/4.03 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.03 inference(symmetry,[status(thm)],[25708])).
% 3.73/4.03 tff(25710,plain,
% 3.73/4.03 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[435, 25709])).
% 3.73/4.03 tff(25711,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.73/4.03 tff(25712,plain,
% 3.73/4.03 (((~![X0: $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(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25713,plain,
% 3.73/4.03 (((~r(s(s(s(s(z)))), 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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25714,plain,
% 3.73/4.03 (((~![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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25713])).
% 3.73/4.03 tff(25715,plain,
% 3.73/4.03 (((~![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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.73/4.03 inference(transitivity,[status(thm)],[25714, 25712])).
% 3.73/4.03 tff(25716,plain,
% 3.73/4.03 ((~![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(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 3.73/4.03 inference(quant_inst,[status(thm)],[])).
% 3.73/4.03 tff(25717,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25716, 25715])).
% 3.73/4.03 tff(25718,plain,
% 3.73/4.03 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25717, 333, 323, 25711])).
% 3.73/4.03 tff(25719,plain,
% 3.73/4.03 ($false),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25718, 25710, 25707])).
% 3.73/4.03 tff(25720,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(z))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.03 tff(25721,plain,
% 3.73/4.03 (~r(s(z), s(s(s(s(z)))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25720, 25704, 25645, 25667, 25658])).
% 3.73/4.03 tff(25722,plain,
% 3.73/4.03 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[19906, 44, 25721])).
% 3.73/4.03 tff(25723,plain,
% 3.73/4.03 (b(s(z), s(s(s(s(z)))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25722, 25692])).
% 3.73/4.03 tff(25724,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25725,plain,
% 3.73/4.03 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25726,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25725])).
% 3.73/4.03 tff(25727,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.73/4.03 inference(transitivity,[status(thm)],[25726, 25724])).
% 3.73/4.03 tff(25728,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.73/4.03 inference(quant_inst,[status(thm)],[])).
% 3.73/4.03 tff(25729,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25728, 25727])).
% 3.73/4.03 tff(25730,plain,
% 3.73/4.03 ($false),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25729, 144, 25723, 25688, 304, 25663])).
% 3.73/4.03 tff(25731,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.03 tff(25732,plain,
% 3.73/4.03 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25731, 5775, 706, 25636, 25633, 2484, 25635, 11546, 3616, 304, 2323])).
% 3.73/4.03 tff(25733,plain,
% 3.73/4.03 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1137, 25732])).
% 3.73/4.03 tff(25734,plain,
% 3.73/4.03 (~b(s(s(s(z))), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24118, 144, 25635, 25733, 304, 25633])).
% 3.73/4.03 tff(25735,plain,
% 3.73/4.03 (r(s(s(s(z))), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[396, 25734])).
% 3.73/4.03 tff(25736,plain,
% 3.73/4.03 (r(z, elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24259, 25734, 11546, 25636, 706, 304, 2484, 25630, 25629, 25635])).
% 3.73/4.03 tff(25737,plain,
% 3.73/4.03 (~b(s(s(s(z))), elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[4375, 25635, 25630, 25629])).
% 3.73/4.03 tff(25738,plain,
% 3.73/4.03 (~b(z, s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24210, 25734, 11546, 25630, 2484, 25636, 25629, 863, 25635, 304])).
% 3.73/4.03 tff(25739,plain,
% 3.73/4.03 (r(z, s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[372, 25738])).
% 3.73/4.03 tff(25740,plain,
% 3.73/4.03 (~(s(s(s(z))) = elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24271, 25739, 11546, 25636, 25736, 25629, 25630, 2484, 25683, 25734, 706])).
% 3.73/4.03 tff(25741,plain,
% 3.73/4.03 (r(s(s(s(z))), elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[704, 25740, 25737])).
% 3.73/4.03 tff(25742,plain,
% 3.73/4.03 (~r(elem!1, s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[6585, 25741, 25736, 25735])).
% 3.73/4.03 tff(25743,plain,
% 3.73/4.03 (elem!1 = s(elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[560, 25742, 5775])).
% 3.73/4.03 tff(25744,plain,
% 3.73/4.03 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25743])).
% 3.73/4.03 tff(25745,plain,
% 3.73/4.03 (r(s(s(s(z))), s(elem!1))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25741, 25744])).
% 3.73/4.03 tff(25746,plain,
% 3.73/4.03 (~r(elem!1, z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24987, 25736, 25683, 25633, 2484, 9507])).
% 3.73/4.03 tff(25747,plain,
% 3.73/4.03 (b(elem!1, z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1380, 25746, 1368])).
% 3.73/4.03 tff(25748,plain,
% 3.73/4.03 (b(s(elem!1), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[12198, 25743, 25747])).
% 3.73/4.03 tff(25749,plain,
% 3.73/4.03 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[6057, 25748, 25734])).
% 3.73/4.03 tff(25750,plain,
% 3.73/4.03 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25743])).
% 3.73/4.03 tff(25751,plain,
% 3.73/4.03 (b(s(elem!1), s(z))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25629, 25750])).
% 3.73/4.03 tff(25752,plain,
% 3.73/4.03 (b(s(s(s(z))), s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[2794, 8558])).
% 3.73/4.03 tff(25753,plain,
% 3.73/4.03 (~b(s(s(s(z))), elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[4375, 25752, 305, 134])).
% 3.73/4.03 tff(25754,plain,
% 3.73/4.03 (r(s(s(s(z))), elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[704, 25753, 698])).
% 3.73/4.03 tff(25755,plain,
% 3.73/4.03 ($false),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24223, 333, 670, 1699, 25754, 2323])).
% 3.73/4.03 tff(25756,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.03 tff(25757,plain,
% 3.73/4.03 (~r(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25756, 25739, 2323, 25629, 25736, 25735, 25740, 25630])).
% 3.73/4.03 tff(25758,plain,
% 3.73/4.03 (b(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[348, 25757])).
% 3.73/4.03 tff(25759,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25760,plain,
% 3.73/4.03 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25761,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25760])).
% 3.73/4.03 tff(25762,plain,
% 3.73/4.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 3.73/4.03 inference(transitivity,[status(thm)],[25761, 25759])).
% 3.73/4.03 tff(25763,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.73/4.03 inference(quant_inst,[status(thm)],[])).
% 3.73/4.03 tff(25764,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25763, 25762])).
% 3.73/4.03 tff(25765,plain,
% 3.73/4.03 (~b(s(elem!1), s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25764, 144, 25748, 25758, 25751, 25635])).
% 3.73/4.03 tff(25766,plain,
% 3.73/4.03 (r(s(elem!1), s(s(s(z))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[965, 25765, 25749])).
% 3.73/4.03 tff(25767,plain,
% 3.73/4.03 (~b(z, elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24241, 25741, 304, 2323, 25635, 25739, 25735, 11546, 2484, 25633, 706, 1368])).
% 3.73/4.03 tff(25768,plain,
% 3.73/4.03 (~b(z, s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[2974, 25743, 25767])).
% 3.73/4.03 tff(25769,plain,
% 3.73/4.03 (r(z, s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[583, 25768])).
% 3.73/4.03 tff(25770,plain,
% 3.73/4.03 (((~![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(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~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(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25771,plain,
% 3.73/4.03 (((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.73/4.03 inference(rewrite,[status(thm)],[])).
% 3.73/4.03 tff(25772,plain,
% 3.73/4.03 (((~![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(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))))),
% 3.73/4.03 inference(monotonicity,[status(thm)],[25771])).
% 3.73/4.03 tff(25773,plain,
% 3.73/4.03 (((~![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(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.73/4.03 inference(transitivity,[status(thm)],[25772, 25770])).
% 3.73/4.03 tff(25774,plain,
% 3.73/4.03 ((~![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(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.73/4.03 inference(quant_inst,[status(thm)],[])).
% 3.73/4.03 tff(25775,plain,
% 3.73/4.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))),
% 3.73/4.03 inference(modus_ponens,[status(thm)],[25774, 25773])).
% 3.73/4.03 tff(25776,plain,
% 3.73/4.03 ($false),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25775, 333, 25769, 25735, 25766, 25745])).
% 3.73/4.03 tff(25777,plain,(b(elem!1, s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (elem!1 = z) | (~r(s(s(s(s(z)))), elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.03 tff(25778,plain,
% 3.73/4.03 (b(elem!1, s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[25777, 304, 23272, 11546, 23280, 25308, 25621, 25628, 3616])).
% 3.73/4.03 tff(25779,plain,
% 3.73/4.03 (~(s(elem!1) = elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[5885, 25778])).
% 3.73/4.03 tff(25780,plain,
% 3.73/4.03 (r(s(elem!1), elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[448, 25779, 3616])).
% 3.73/4.03 tff(25781,plain,
% 3.73/4.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[14999, 333, 25780, 23280, 23272])).
% 3.73/4.03 tff(25782,plain,
% 3.73/4.03 (~(elem!1 = z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[14770, 2097, 2545])).
% 3.73/4.03 tff(25783,plain,
% 3.73/4.03 (~(z = elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[18287, 25782])).
% 3.73/4.03 tff(25784,plain,
% 3.73/4.03 (~(s(elem!1) = s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[8683, 25783])).
% 3.73/4.03 tff(25785,plain,
% 3.73/4.03 (~(s(z) = s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1228, 25784])).
% 3.73/4.03 tff(25786,plain,
% 3.73/4.03 (~r(z, elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24919, 509, 435, 2323])).
% 3.73/4.03 tff(25787,plain,
% 3.73/4.03 (b(z, elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[658, 25786, 25783])).
% 3.73/4.03 tff(25788,plain,
% 3.73/4.03 (~b(z, s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[7079, 25787, 305, 134])).
% 3.73/4.03 tff(25789,plain,
% 3.73/4.03 (r(z, s(z))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[372, 25788])).
% 3.73/4.03 tff(25790,plain,
% 3.73/4.03 (b(elem!1, z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[24389, 509, 2545, 2097, 2900, 435, 25782])).
% 3.73/4.03 tff(25791,plain,
% 3.73/4.03 (~b(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1602, 25787, 134, 25790])).
% 3.73/4.03 tff(25792,plain,
% 3.73/4.03 (r(s(z), z)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[348, 25791])).
% 3.73/4.03 tff(25793,plain,
% 3.73/4.03 (~r(s(z), s(elem!1))),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[1235, 25792, 509, 25789])).
% 3.73/4.03 tff(25794,plain,
% 3.73/4.03 (~(s(elem!1) = elem!1)),
% 3.73/4.03 inference(unit_resolution,[status(thm)],[5885, 547])).
% 3.73/4.03 tff(25795,plain,
% 3.73/4.04 (~(elem!1 = s(elem!1))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1569, 25794])).
% 3.73/4.04 tff(25796,plain,
% 3.73/4.04 (b(s(elem!1), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1653, 25789, 706, 25784, 25786, 25795, 509])).
% 3.73/4.04 tff(25797,plain,
% 3.73/4.04 (~b(s(z), s(elem!1))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[4409, 25796, 305, 547])).
% 3.73/4.04 tff(25798,plain,
% 3.73/4.04 ($false),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1244, 25797, 25793, 25785])).
% 3.73/4.04 tff(25799,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (s(z) = elem!1) | (~b(s(z), elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.04 tff(25800,plain,
% 3.73/4.04 (~r(s(elem!1), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25799, 25778, 25310, 25308, 25311, 2545, 25780, 23272, 25619])).
% 3.73/4.04 tff(25801,plain,
% 3.73/4.04 (b(s(elem!1), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[507, 25800])).
% 3.73/4.04 tff(25802,plain,
% 3.73/4.04 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[10345, 144, 25801, 25620, 25624])).
% 3.73/4.04 tff(25803,plain,
% 3.73/4.04 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[472, 25802, 25781])).
% 3.73/4.04 tff(25804,plain,
% 3.73/4.04 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25803])).
% 3.73/4.04 tff(25805,plain,
% 3.73/4.04 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(elem!1))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25804])).
% 3.73/4.04 tff(25806,plain,
% 3.73/4.04 (r(elem!1, s(elem!1))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[23272, 25805])).
% 3.73/4.04 tff(25807,plain,
% 3.73/4.04 (~r(s(s(s(z))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[24063, 304, 11546, 23272, 23280, 23287, 25622])).
% 3.73/4.04 tff(25808,plain,
% 3.73/4.04 (b(s(s(s(z))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[2794, 25807])).
% 3.73/4.04 tff(25809,plain,
% 3.73/4.04 (~b(s(s(s(z))), elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[4375, 25808, 25311, 25310])).
% 3.73/4.04 tff(25810,plain,
% 3.73/4.04 (~(s(s(s(z))) = elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[12214, 25803])).
% 3.73/4.04 tff(25811,plain,
% 3.73/4.04 (r(s(s(s(z))), elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[704, 25810, 25809])).
% 3.73/4.04 tff(25812,plain,
% 3.73/4.04 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[23315, 25811, 23272, 23280])).
% 3.73/4.04 tff(25813,plain,
% 3.73/4.04 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1137, 25812])).
% 3.73/4.04 tff(25814,plain,
% 3.73/4.04 (~b(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14036, 144, 25813, 25620, 25624])).
% 3.73/4.04 tff(25815,plain,
% 3.73/4.04 (r(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[396, 25814])).
% 3.73/4.04 tff(25816,plain,
% 3.73/4.04 (r(z, elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[24259, 25814, 11546, 25627, 25308, 304, 23280, 25311, 25310, 25808])).
% 3.73/4.04 tff(25817,plain,
% 3.73/4.04 ($false),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[6585, 25816, 25815, 25811, 25806])).
% 3.73/4.04 tff(25818,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.04 tff(25819,plain,
% 3.73/4.04 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25818, 3616, 2545, 11546])).
% 3.73/4.04 tff(25820,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[319, 25819])).
% 3.73/4.04 tff(25821,plain,
% 3.73/4.04 (~r(s(z), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[16388, 6107, 11546, 25820])).
% 3.73/4.04 tff(25822,plain,
% 3.73/4.04 (b(s(z), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[172, 25821])).
% 3.73/4.04 tff(25823,plain,
% 3.73/4.04 (~b(elem!1, s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[22776, 25822, 25310, 25626])).
% 3.73/4.04 tff(25824,plain,
% 3.73/4.04 (~r(elem!1, s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25642, 333, 23280, 23272, 6107])).
% 3.73/4.04 tff(25825,plain,
% 3.73/4.04 (elem!1 = s(s(s(z)))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1538, 25824, 25823])).
% 3.73/4.04 tff(25826,plain,
% 3.73/4.04 (s(elem!1) = s(s(s(s(z))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25825])).
% 3.73/4.04 tff(25827,plain,
% 3.73/4.04 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25826])).
% 3.73/4.04 tff(25828,plain,
% 3.73/4.04 (~(s(s(z)) = s(elem!1))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[855, 25308])).
% 3.73/4.04 tff(25829,plain,
% 3.73/4.04 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[862, 25828])).
% 3.73/4.04 tff(25830,plain,
% 3.73/4.04 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[24191, 25631, 2484, 134, 305, 2323, 11546])).
% 3.73/4.04 tff(25831,plain,
% 3.73/4.04 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[279, 25830])).
% 3.73/4.04 tff(25832,plain,
% 3.73/4.04 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25618, 2484, 2323, 11546, 134, 305])).
% 3.73/4.04 tff(25833,plain,
% 3.73/4.04 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[302, 25832])).
% 3.73/4.04 tff(25834,plain,
% 3.73/4.04 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[10345, 144, 491, 25833, 25831])).
% 3.73/4.04 tff(25835,plain,
% 3.73/4.04 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[472, 14872, 467])).
% 3.73/4.04 tff(25836,plain,
% 3.73/4.04 (elem!1 = s(elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[20897, 25835, 2484, 3616, 5775])).
% 3.73/4.04 tff(25837,plain,
% 3.73/4.04 ($false),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1569, 25836, 13978])).
% 3.73/4.04 tff(25838,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1)) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.04 tff(25839,plain,
% 3.73/4.04 (~(s(s(s(z))) = elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25838, 25834, 3616, 5775, 2484, 1184])).
% 3.73/4.04 tff(25840,plain,
% 3.73/4.04 (r(s(s(s(z))), elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[704, 25839, 55])).
% 3.73/4.04 tff(25841,plain,
% 3.73/4.04 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[23315, 25840, 2323, 2484])).
% 3.73/4.04 tff(25842,plain,
% 3.73/4.04 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1137, 25841])).
% 3.73/4.04 tff(25843,plain,
% 3.73/4.04 (~b(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14036, 144, 25842, 25833, 25831])).
% 3.73/4.04 tff(25844,plain,
% 3.73/4.04 (r(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[396, 25843])).
% 3.73/4.04 tff(25845,plain,
% 3.73/4.04 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[23315, 707, 2323, 2484])).
% 3.73/4.04 tff(25846,plain,
% 3.73/4.04 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1137, 25845])).
% 3.73/4.04 tff(25847,plain,
% 3.73/4.04 (~b(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14036, 144, 25846, 25833, 25831])).
% 3.73/4.04 tff(25848,plain,
% 3.73/4.04 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[6057, 25847, 491])).
% 3.73/4.04 tff(25849,plain,
% 3.73/4.04 (~(elem!1 = s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[10997, 25839])).
% 3.73/4.04 tff(25850,plain,
% 3.73/4.04 (~b(z, s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[7079, 251, 305, 134])).
% 3.73/4.04 tff(25851,plain,
% 3.73/4.04 (r(z, s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[372, 25850])).
% 3.73/4.04 tff(25852,plain,
% 3.73/4.04 (r(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[396, 25847])).
% 3.73/4.04 tff(25853,plain,
% 3.73/4.04 (~r(elem!1, z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[2122, 25851, 707, 25852])).
% 3.73/4.04 tff(25854,plain,
% 3.73/4.04 (b(elem!1, z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1380, 25853, 1368])).
% 3.73/4.04 tff(25855,plain,
% 3.73/4.04 (~b(s(z), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1602, 25854, 134, 251])).
% 3.73/4.04 tff(25856,plain,
% 3.73/4.04 (r(s(z), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[348, 25855])).
% 3.73/4.04 tff(25857,plain,
% 3.73/4.04 (~r(s(s(s(z))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[6555, 25856, 25852, 25851])).
% 3.73/4.04 tff(25858,plain,
% 3.73/4.04 (b(s(s(s(z))), s(z))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[2794, 25857])).
% 3.73/4.04 tff(25859,plain,
% 3.73/4.04 (~r(s(z), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[7314, 25856, 25852, 25851])).
% 3.73/4.04 tff(25860,plain,
% 3.73/4.04 (b(s(z), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[172, 25859])).
% 3.73/4.04 tff(25861,plain,
% 3.73/4.04 (~b(elem!1, s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[22776, 25860, 305, 25858])).
% 3.73/4.04 tff(25862,plain,
% 3.73/4.04 (r(elem!1, s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1538, 25861, 25849])).
% 3.73/4.04 tff(25863,plain,
% 3.73/4.04 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14901, 333, 25862, 707, 2484])).
% 3.73/4.04 tff(25864,plain,
% 3.73/4.04 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[249, 25863])).
% 3.73/4.04 tff(25865,plain,
% 3.73/4.04 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[20897, 902, 2484, 3616, 5775])).
% 3.73/4.04 tff(25866,plain,
% 3.73/4.04 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[472, 25865, 467])).
% 3.73/4.04 tff(25867,plain,
% 3.73/4.04 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25866])).
% 3.73/4.04 tff(25868,plain,
% 3.73/4.04 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25867])).
% 3.73/4.04 tff(25869,plain,
% 3.73/4.04 (s(s(s(s(s(s(z)))))) = elem!1),
% 3.73/4.04 inference(transitivity,[status(thm)],[21, 25868, 850])).
% 3.73/4.04 tff(25870,plain,
% 3.73/4.04 (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25866])).
% 3.73/4.04 tff(25871,plain,
% 3.73/4.04 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25870])).
% 3.73/4.04 tff(25872,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(elem!1)), elem!1)),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25871, 25869])).
% 3.73/4.04 tff(25873,plain,
% 3.73/4.04 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25872])).
% 3.73/4.04 tff(25874,plain,
% 3.73/4.04 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25866])).
% 3.73/4.04 tff(25875,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(elem!1), s(z))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25874])).
% 3.73/4.04 tff(25876,plain,
% 3.73/4.04 (r(s(elem!1), s(z))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[322, 25875])).
% 3.73/4.04 tff(25877,plain,
% 3.73/4.04 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25866])).
% 3.73/4.04 tff(25878,plain,
% 3.73/4.04 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(elem!1))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25877])).
% 3.73/4.04 tff(25879,plain,
% 3.73/4.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25871])).
% 3.73/4.04 tff(25880,plain,
% 3.73/4.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(elem!1))),
% 3.73/4.04 inference(transitivity,[status(thm)],[25879, 25878])).
% 3.73/4.04 tff(25881,plain,
% 3.73/4.04 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25880])).
% 3.73/4.04 tff(25882,plain,
% 3.73/4.04 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25871])).
% 3.73/4.04 tff(25883,plain,
% 3.73/4.04 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25882])).
% 3.73/4.04 tff(25884,plain,
% 3.73/4.04 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25883])).
% 3.73/4.04 tff(25885,plain,
% 3.73/4.04 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[1184, 25884])).
% 3.73/4.04 tff(25886,plain,
% 3.73/4.04 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.04 inference(commutativity,[status(thm)],[])).
% 3.73/4.04 tff(25887,plain,
% 3.73/4.04 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25886])).
% 3.73/4.04 tff(25888,plain,
% 3.73/4.04 ((~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25887])).
% 3.73/4.04 tff(25889,assumption,(~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.73/4.04 tff(25890,plain,
% 3.73/4.04 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25889, 25888])).
% 3.73/4.04 tff(25891,plain,
% 3.73/4.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.04 inference(rewrite,[status(thm)],[])).
% 3.73/4.04 tff(25892,plain,
% 3.73/4.04 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.04 inference(rewrite,[status(thm)],[])).
% 3.73/4.04 tff(25893,plain,
% 3.73/4.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25892])).
% 3.73/4.04 tff(25894,plain,
% 3.73/4.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.04 inference(transitivity,[status(thm)],[25893, 25891])).
% 3.73/4.04 tff(25895,plain,
% 3.73/4.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.04 inference(quant_inst,[status(thm)],[])).
% 3.73/4.04 tff(25896,plain,
% 3.73/4.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25895, 25894])).
% 3.73/4.04 tff(25897,plain,
% 3.73/4.04 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25896, 144, 286, 259, 15712])).
% 3.73/4.04 tff(25898,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1333, 44, 1308, 25897])).
% 3.73/4.04 tff(25899,plain,
% 3.73/4.04 (~b(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14036, 144, 2254, 286, 259])).
% 3.73/4.04 tff(25900,plain,
% 3.73/4.04 (r(s(s(s(z))), z)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[396, 25899])).
% 3.73/4.04 tff(25901,plain,
% 3.73/4.04 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[17253, 333, 354, 25900, 25898])).
% 3.73/4.04 tff(25902,plain,
% 3.73/4.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[15317, 144, 283, 2254, 15712])).
% 3.73/4.04 tff(25903,plain,
% 3.73/4.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 3.73/4.04 inference(rewrite,[status(thm)],[])).
% 3.73/4.04 tff(25904,plain,
% 3.73/4.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 3.73/4.04 inference(quant_inst,[status(thm)],[])).
% 3.73/4.04 tff(25905,plain,
% 3.73/4.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25904, 25903])).
% 3.73/4.04 tff(25906,plain,
% 3.73/4.04 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25905, 44, 25902])).
% 3.73/4.04 tff(25907,plain,
% 3.73/4.04 ($false),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25906, 25901, 25890])).
% 3.73/4.04 tff(25908,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.04 tff(25909,plain,
% 3.73/4.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[25908, 25885, 354, 286, 259, 283, 2254])).
% 3.73/4.04 tff(25910,plain,
% 3.73/4.04 (~b(s(s(elem!1)), s(elem!1))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25909, 25881])).
% 3.73/4.04 tff(25911,plain,
% 3.73/4.04 (r(s(s(elem!1)), s(elem!1))),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[1283, 25910, 2727])).
% 3.73/4.04 tff(25912,plain,
% 3.73/4.04 (r(s(s(elem!1)), elem!1)),
% 3.73/4.04 inference(unit_resolution,[status(thm)],[14227, 25911, 134, 323, 305, 25866, 25876])).
% 3.73/4.04 tff(25913,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25912, 25873])).
% 3.73/4.04 tff(25914,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25869])).
% 3.73/4.04 tff(25915,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25914])).
% 3.73/4.04 tff(25916,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[2484, 25915])).
% 3.73/4.04 tff(25917,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25869])).
% 3.73/4.04 tff(25918,plain,
% 3.73/4.04 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25917])).
% 3.73/4.04 tff(25919,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[2323, 25918])).
% 3.73/4.04 tff(25920,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25871])).
% 3.73/4.04 tff(25921,plain,
% 3.73/4.04 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(symmetry,[status(thm)],[25920])).
% 3.73/4.04 tff(25922,plain,
% 3.73/4.04 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(monotonicity,[status(thm)],[25866])).
% 3.73/4.04 tff(25923,plain,
% 3.73/4.04 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(transitivity,[status(thm)],[25922, 25921])).
% 3.73/4.04 tff(25924,plain,
% 3.73/4.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.04 inference(modus_ponens,[status(thm)],[25911, 25923])).
% 3.73/4.04 tff(25925,plain,
% 3.73/4.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25926,plain,
% 3.73/4.05 ((~![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(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z)))))))))),
% 3.73/4.05 inference(quant_inst,[status(thm)],[])).
% 3.73/4.05 tff(25927,plain,
% 3.73/4.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25926, 25925])).
% 3.73/4.05 tff(25928,plain,
% 3.73/4.05 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25927, 333, 25924])).
% 3.73/4.05 tff(25929,plain,
% 3.73/4.05 ($false),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25928, 25919, 25916, 25913])).
% 3.73/4.05 tff(25930,plain,((elem!1 = s(elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.05 tff(25931,plain,
% 3.73/4.05 (elem!1 = s(elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25930, 25856, 2484, 134, 2323, 305, 25851, 25833, 25831, 25864, 25846, 1184, 322, 25834, 3616, 5775])).
% 3.73/4.05 tff(25932,plain,
% 3.73/4.05 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24691, 25931, 25848])).
% 3.73/4.05 tff(25933,plain,
% 3.73/4.05 (~b(s(s(s(s(z)))), elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24620, 25851, 11546, 25833, 322, 251, 134, 305])).
% 3.73/4.05 tff(25934,plain,
% 3.73/4.05 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24699, 25931, 25933])).
% 3.73/4.05 tff(25935,plain,
% 3.73/4.05 (r(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24448, 25934, 25932])).
% 3.73/4.05 tff(25936,plain,
% 3.73/4.05 (s(elem!1) = elem!1),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1569, 25931])).
% 3.73/4.05 tff(25937,plain,
% 3.73/4.05 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[903])).
% 3.73/4.05 tff(25938,plain,
% 3.73/4.05 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(symmetry,[status(thm)],[25937])).
% 3.73/4.05 tff(25939,plain,
% 3.73/4.05 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[2323, 25938])).
% 3.73/4.05 tff(25940,plain,
% 3.73/4.05 ($false),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[466, 25939])).
% 3.73/4.05 tff(25941,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.05 tff(25942,plain,
% 3.73/4.05 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25941, 25936, 2323])).
% 3.73/4.05 tff(25943,plain,
% 3.73/4.05 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[25931])).
% 3.73/4.05 tff(25944,plain,
% 3.73/4.05 (r(s(s(s(z))), s(elem!1))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[707, 25943])).
% 3.73/4.05 tff(25945,plain,
% 3.73/4.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25946,plain,
% 3.73/4.05 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25947,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(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(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[25946])).
% 3.73/4.05 tff(25948,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(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(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(transitivity,[status(thm)],[25947, 25945])).
% 3.73/4.05 tff(25949,plain,
% 3.73/4.05 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.05 inference(quant_inst,[status(thm)],[])).
% 3.73/4.05 tff(25950,plain,
% 3.73/4.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25949, 25948])).
% 3.73/4.05 tff(25951,plain,
% 3.73/4.05 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25950, 333, 25944, 25942, 25935])).
% 3.73/4.05 tff(25952,plain,
% 3.73/4.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[9821, 44, 219, 25951])).
% 3.73/4.05 tff(25953,plain,
% 3.73/4.05 (s(s(s(elem!1))) = elem!1),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[2482, 25931])).
% 3.73/4.05 tff(25954,plain,
% 3.73/4.05 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[12928, 25953])).
% 3.73/4.05 tff(25955,plain,
% 3.73/4.05 (~b(z, s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[16228, 25864, 25831, 25846])).
% 3.73/4.05 tff(25956,plain,
% 3.73/4.05 (r(z, s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[619, 25955])).
% 3.73/4.05 tff(25957,plain,
% 3.73/4.05 (~r(s(elem!1), s(z))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1670, 25954, 322, 25851, 25856, 491])).
% 3.73/4.05 tff(25958,plain,
% 3.73/4.05 (b(s(elem!1), s(z))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[486, 25957, 25636])).
% 3.73/4.05 tff(25959,plain,
% 3.73/4.05 (~r(z, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1990, 25958, 491, 25856, 25847, 25858, 25956])).
% 3.73/4.05 tff(25960,plain,
% 3.73/4.05 (b(z, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[583, 25959])).
% 3.73/4.05 tff(25961,plain,
% 3.73/4.05 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[12069, 25960, 25833, 491])).
% 3.73/4.05 tff(25962,plain,
% 3.73/4.05 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[542, 25961, 25954])).
% 3.73/4.05 tff(25963,plain,
% 3.73/4.05 (((~![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(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25964,plain,
% 3.73/4.05 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25965,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[25964])).
% 3.73/4.05 tff(25966,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(transitivity,[status(thm)],[25965, 25963])).
% 3.73/4.05 tff(25967,plain,
% 3.73/4.05 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(quant_inst,[status(thm)],[])).
% 3.73/4.05 tff(25968,plain,
% 3.73/4.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25967, 25966])).
% 3.73/4.05 tff(25969,plain,
% 3.73/4.05 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25968, 333, 25942, 25935, 25962])).
% 3.73/4.05 tff(25970,plain,
% 3.73/4.05 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[9761, 25969])).
% 3.73/4.05 tff(25971,plain,
% 3.73/4.05 ($false),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[18464, 144, 25864, 25846, 25970, 25952])).
% 3.73/4.05 tff(25972,plain,((~b(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1)) | (elem!1 = z) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.05 tff(25973,plain,
% 3.73/4.05 (~b(z, elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25972, 25840, 491, 322, 2323, 2484, 134, 305, 1184, 3616, 5775, 1368, 11546])).
% 3.73/4.05 tff(25974,plain,
% 3.73/4.05 (r(z, elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[658, 25973, 25631])).
% 3.73/4.05 tff(25975,plain,
% 3.73/4.05 (~r(elem!1, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[6585, 25974, 25840, 25844])).
% 3.73/4.05 tff(25976,plain,
% 3.73/4.05 (elem!1 = s(elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[560, 25975, 5775])).
% 3.73/4.05 tff(25977,plain,
% 3.73/4.05 (s(elem!1) = elem!1),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1569, 25976])).
% 3.73/4.05 tff(25978,plain,
% 3.73/4.05 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25941, 25977, 2323])).
% 3.73/4.05 tff(25979,plain,
% 3.73/4.05 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[25976])).
% 3.73/4.05 tff(25980,plain,
% 3.73/4.05 (r(s(s(s(z))), s(elem!1))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25840, 25979])).
% 3.73/4.05 tff(25981,plain,
% 3.73/4.05 (~b(z, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[2974, 25976, 25973])).
% 3.73/4.05 tff(25982,plain,
% 3.73/4.05 (r(z, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[583, 25981])).
% 3.73/4.05 tff(25983,plain,
% 3.73/4.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25984,plain,
% 3.73/4.05 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(25985,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[25984])).
% 3.73/4.05 tff(25986,plain,
% 3.73/4.05 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.05 inference(transitivity,[status(thm)],[25985, 25983])).
% 3.73/4.05 tff(25987,plain,
% 3.73/4.05 ((~![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(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.73/4.05 inference(quant_inst,[status(thm)],[])).
% 3.73/4.05 tff(25988,plain,
% 3.73/4.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25987, 25986])).
% 3.73/4.05 tff(25989,plain,
% 3.73/4.05 ($false),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25988, 333, 25982, 25844, 25980, 25978])).
% 3.73/4.05 tff(25990,plain,((~b(s(elem!1), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | b(s(elem!1), elem!1) | (elem!1 = z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.05 tff(25991,plain,
% 3.73/4.05 (~b(s(elem!1), z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[25990, 55, 5775, 25820, 23280, 25311, 25310, 25829, 3616, 25621, 11546, 23272])).
% 3.73/4.05 tff(25992,plain,
% 3.73/4.05 (r(s(elem!1), z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[507, 25991])).
% 3.73/4.05 tff(25993,plain,
% 3.73/4.05 (r(s(s(s(s(z)))), z)),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[25992, 25827])).
% 3.73/4.05 tff(25994,plain,
% 3.73/4.05 (~r(s(s(s(z))), elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[23315, 6107, 23272, 23280])).
% 3.73/4.05 tff(25995,plain,
% 3.73/4.05 (s(s(s(z))) = elem!1),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[704, 25994, 55])).
% 3.73/4.05 tff(25996,plain,
% 3.73/4.05 (~(s(s(elem!1)) = elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[7595, 25995, 25829])).
% 3.73/4.05 tff(25997,plain,
% 3.73/4.05 (~(elem!1 = s(s(elem!1)))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[5603, 25996])).
% 3.73/4.05 tff(25998,plain,
% 3.73/4.05 (~(s(elem!1) = elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[5813, 25997])).
% 3.73/4.05 tff(25999,plain,
% 3.73/4.05 (r(s(elem!1), elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[448, 25998, 3616])).
% 3.73/4.05 tff(26000,plain,
% 3.73/4.05 (~r(z, elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24919, 25999, 25992, 23272])).
% 3.73/4.05 tff(26001,plain,
% 3.73/4.05 (b(z, elem!1)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[658, 26000, 25622])).
% 3.73/4.05 tff(26002,plain,
% 3.73/4.05 (b(z, s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[257, 26001, 25995])).
% 3.73/4.05 tff(26003,plain,
% 3.73/4.05 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[2899, 25992, 25619])).
% 3.73/4.05 tff(26004,plain,
% 3.73/4.05 (b(elem!1, z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24389, 25999, 2545, 25620, 26003, 25992, 25621])).
% 3.73/4.05 tff(26005,plain,
% 3.73/4.05 (b(s(s(s(z))), z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[24196, 26004, 25995])).
% 3.73/4.05 tff(26006,plain,
% 3.73/4.05 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[294, 26005, 25620, 26002])).
% 3.73/4.05 tff(26007,plain,
% 3.73/4.05 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[249, 26006])).
% 3.73/4.05 tff(26008,plain,
% 3.73/4.05 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[19960, 26007, 11546, 25820, 6107, 25626])).
% 3.73/4.05 tff(26009,plain,
% 3.73/4.05 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1451, 26008])).
% 3.73/4.05 tff(26010,plain,
% 3.73/4.05 (~b(s(s(z)), z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[19968, 144, 26009, 25620, 25624])).
% 3.73/4.05 tff(26011,plain,
% 3.73/4.05 (r(s(s(z)), z)),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1462, 44, 164, 26010])).
% 3.73/4.05 tff(26012,plain,
% 3.73/4.05 (~b(z, s(z))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[7079, 26001, 25310, 25311])).
% 3.73/4.05 tff(26013,plain,
% 3.73/4.05 (r(z, s(z))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[372, 26012])).
% 3.73/4.05 tff(26014,plain,
% 3.73/4.05 (((~![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(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(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.73/4.05 inference(rewrite,[status(thm)],[])).
% 3.73/4.05 tff(26015,plain,
% 3.73/4.05 ((~![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(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.73/4.05 inference(quant_inst,[status(thm)],[])).
% 3.73/4.05 tff(26016,plain,
% 3.73/4.05 ((~![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(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.73/4.05 inference(modus_ponens,[status(thm)],[26015, 26014])).
% 3.73/4.05 tff(26017,plain,
% 3.73/4.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[26016, 333, 26013, 26011, 25993])).
% 3.73/4.05 tff(26018,plain,
% 3.73/4.05 (b(s(s(z)), s(s(s(s(z)))))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[20473, 44, 25543, 26017])).
% 3.73/4.05 tff(26019,plain,
% 3.73/4.05 (s(s(s(s(z)))) = s(elem!1)),
% 3.73/4.05 inference(symmetry,[status(thm)],[25826])).
% 3.73/4.05 tff(26020,plain,
% 3.73/4.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.05 inference(monotonicity,[status(thm)],[26019])).
% 3.73/4.05 tff(26021,plain,
% 3.73/4.05 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.05 inference(symmetry,[status(thm)],[26020])).
% 3.73/4.05 tff(26022,plain,
% 3.73/4.05 (~(elem!1 = s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[1569, 25998])).
% 3.73/4.05 tff(26023,plain,
% 3.73/4.05 (r(elem!1, s(elem!1))),
% 3.73/4.05 inference(unit_resolution,[status(thm)],[560, 26022, 5775])).
% 3.73/4.05 tff(26024,plain,
% 3.73/4.05 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[12793, 333, 26023, 25999, 23280])).
% 3.73/4.06 tff(26025,plain,
% 3.73/4.06 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[542, 26024, 26003])).
% 3.73/4.06 tff(26026,plain,
% 3.73/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26025, 26021])).
% 3.73/4.06 tff(26027,plain,
% 3.73/4.06 (((~![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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26028,plain,
% 3.73/4.06 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26029,plain,
% 3.73/4.06 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26028])).
% 3.73/4.06 tff(26030,plain,
% 3.73/4.06 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.06 inference(transitivity,[status(thm)],[26029, 26027])).
% 3.73/4.06 tff(26031,plain,
% 3.73/4.06 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.06 inference(quant_inst,[status(thm)],[])).
% 3.73/4.06 tff(26032,plain,
% 3.73/4.06 ((~![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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26031, 26030])).
% 3.73/4.06 tff(26033,plain,
% 3.73/4.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26032, 333, 6107, 322, 3559])).
% 3.73/4.06 tff(26034,plain,
% 3.73/4.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[9821, 44, 219, 26033])).
% 3.73/4.06 tff(26035,plain,
% 3.73/4.06 (~r(s(s(s(s(z)))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[19765, 333, 11546, 322, 3559])).
% 3.73/4.06 tff(26036,plain,
% 3.73/4.06 (b(s(s(s(s(z)))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24600, 26035, 24294])).
% 3.73/4.06 tff(26037,plain,
% 3.73/4.06 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26038,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26037])).
% 3.73/4.06 tff(26039,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))))),
% 3.73/4.06 inference(transitivity,[status(thm)],[26038, 18482])).
% 3.73/4.06 tff(26040,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.73/4.06 inference(quant_inst,[status(thm)],[])).
% 3.73/4.06 tff(26041,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26040, 26039])).
% 3.73/4.06 tff(26042,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26041, 144, 56, 26036, 838, 26034])).
% 3.73/4.06 tff(26043,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26044,plain,
% 3.73/4.06 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26043, 25626, 11546, 25820, 6107, 25822])).
% 3.73/4.06 tff(26045,plain,
% 3.73/4.06 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[9761, 26044])).
% 3.73/4.06 tff(26046,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[20469, 144, 26009, 26045, 26026, 26018])).
% 3.73/4.06 tff(26047,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(elem!1)) | b(s(elem!1), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26048,plain,
% 3.73/4.06 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26047, 55, 2545, 5775, 3616, 11546])).
% 3.73/4.06 tff(26049,plain,
% 3.73/4.06 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1137, 26048])).
% 3.73/4.06 tff(26050,plain,
% 3.73/4.06 (~b(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[14036, 144, 26049, 25620, 25624])).
% 3.73/4.06 tff(26051,plain,
% 3.73/4.06 (r(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[396, 26050])).
% 3.73/4.06 tff(26052,plain,
% 3.73/4.06 (~r(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24919, 12525, 25992, 23272])).
% 3.73/4.06 tff(26053,plain,
% 3.73/4.06 (b(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[658, 26052, 25622])).
% 3.73/4.06 tff(26054,plain,
% 3.73/4.06 (~b(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[7079, 26053, 25310, 25311])).
% 3.73/4.06 tff(26055,plain,
% 3.73/4.06 (r(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[372, 26054])).
% 3.73/4.06 tff(26056,plain,
% 3.73/4.06 (b(s(elem!1), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1653, 26055, 25308, 25627, 25992, 26052, 902])).
% 3.73/4.06 tff(26057,plain,
% 3.73/4.06 (b(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24389, 12525, 2545, 25620, 26003, 25992, 25621])).
% 3.73/4.06 tff(26058,plain,
% 3.73/4.06 (~b(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1602, 26053, 25311, 26057])).
% 3.73/4.06 tff(26059,plain,
% 3.73/4.06 (r(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[348, 26058])).
% 3.73/4.06 tff(26060,plain,
% 3.73/4.06 (s(elem!1) = s(s(s(z)))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[8561, 26059, 25992, 26051, 26055, 26056])).
% 3.73/4.06 tff(26061,plain,
% 3.73/4.06 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26060])).
% 3.73/4.06 tff(26062,plain,
% 3.73/4.06 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.73/4.06 inference(symmetry,[status(thm)],[26061])).
% 3.73/4.06 tff(26063,plain,
% 3.73/4.06 (s(s(z)) = elem!1),
% 3.73/4.06 inference(transitivity,[status(thm)],[87, 26062, 850])).
% 3.73/4.06 tff(26064,plain,
% 3.73/4.06 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26063])).
% 3.73/4.06 tff(26065,plain,
% 3.73/4.06 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 3.73/4.06 inference(symmetry,[status(thm)],[26064])).
% 3.73/4.06 tff(26066,plain,
% 3.73/4.06 (r(s(s(s(s(z)))), elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24746, 26052, 11546, 25627, 2545, 23287, 23982])).
% 3.73/4.06 tff(26067,plain,
% 3.73/4.06 (r(s(s(s(s(z)))), s(s(z)))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26066, 26065])).
% 3.73/4.06 tff(26068,plain,
% 3.73/4.06 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26060])).
% 3.73/4.06 tff(26069,plain,
% 3.73/4.06 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26068, 26060])).
% 3.73/4.06 tff(26070,plain,
% 3.73/4.06 (~(s(s(s(z))) = elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24196, 26057, 26050])).
% 3.73/4.06 tff(26071,plain,
% 3.73/4.06 (r(s(s(s(z))), elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[704, 26070, 55])).
% 3.73/4.06 tff(26072,plain,
% 3.73/4.06 (~r(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2122, 26071, 26055, 26051])).
% 3.73/4.06 tff(26073,plain,
% 3.73/4.06 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[20897, 902, 23280, 3616, 5775])).
% 3.73/4.06 tff(26074,plain,
% 3.73/4.06 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[11084, 26060])).
% 3.73/4.06 tff(26075,plain,
% 3.73/4.06 (~b(s(s(elem!1)), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[18494, 26074, 25308, 25627, 25820, 25624, 25992, 26051, 902, 12525, 26055, 26071, 26073, 26072, 26052])).
% 3.73/4.06 tff(26076,plain,
% 3.73/4.06 (r(s(s(elem!1)), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1283, 26075, 2727])).
% 3.73/4.06 tff(26077,plain,
% 3.73/4.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26076, 26069])).
% 3.73/4.06 tff(26078,plain,
% 3.73/4.06 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26063])).
% 3.73/4.06 tff(26079,plain,
% 3.73/4.06 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.73/4.06 inference(symmetry,[status(thm)],[26078])).
% 3.73/4.06 tff(26080,plain,
% 3.73/4.06 (~(elem!1 = s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[10997, 26070])).
% 3.73/4.06 tff(26081,plain,
% 3.73/4.06 (~r(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[6555, 26059, 26051, 26055])).
% 3.73/4.06 tff(26082,plain,
% 3.73/4.06 (b(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2794, 26081])).
% 3.73/4.06 tff(26083,plain,
% 3.73/4.06 (~r(s(z), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[7314, 26059, 26051, 26055])).
% 3.73/4.06 tff(26084,plain,
% 3.73/4.06 (b(s(z), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[172, 26083])).
% 3.73/4.06 tff(26085,plain,
% 3.73/4.06 (~b(elem!1, s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[22776, 26084, 25310, 26082])).
% 3.73/4.06 tff(26086,plain,
% 3.73/4.06 (r(elem!1, s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1538, 26085, 26080])).
% 3.73/4.06 tff(26087,plain,
% 3.73/4.06 (r(s(s(z)), s(s(s(z))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26086, 26079])).
% 3.73/4.06 tff(26088,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26089,plain,
% 3.73/4.06 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26090,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, 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(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26089])).
% 3.73/4.06 tff(26091,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, 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(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.73/4.06 inference(transitivity,[status(thm)],[26090, 26088])).
% 3.73/4.06 tff(26092,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.73/4.06 inference(quant_inst,[status(thm)],[])).
% 3.73/4.06 tff(26093,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26092, 26091])).
% 3.73/4.06 tff(26094,plain,
% 3.73/4.06 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26093, 333, 26051, 26087, 26077])).
% 3.73/4.06 tff(26095,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26094, 26067])).
% 3.73/4.06 tff(26096,plain,((elem!1 = s(elem!1)) | b(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26097,plain,
% 3.73/4.06 (elem!1 = s(elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26096, 55, 11546, 2545, 3616, 5775])).
% 3.73/4.06 tff(26098,plain,
% 3.73/4.06 (~b(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[12198, 26097, 25991])).
% 3.73/4.06 tff(26099,plain,
% 3.73/4.06 (r(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[653, 26098, 25621])).
% 3.73/4.06 tff(26100,plain,
% 3.73/4.06 (s(elem!1) = elem!1),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1569, 26097])).
% 3.73/4.06 tff(26101,plain,
% 3.73/4.06 (elem!1 = s(s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[5813, 26100])).
% 3.73/4.06 tff(26102,plain,
% 3.73/4.06 (s(s(elem!1)) = elem!1),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[5603, 26101])).
% 3.73/4.06 tff(26103,plain,
% 3.73/4.06 (~(s(s(s(z))) = elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[7595, 26102, 25829])).
% 3.73/4.06 tff(26104,plain,
% 3.73/4.06 (r(s(s(s(z))), elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[704, 26103, 55])).
% 3.73/4.06 tff(26105,plain,
% 3.73/4.06 (~r(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2122, 26104, 26099, 26051])).
% 3.73/4.06 tff(26106,plain,
% 3.73/4.06 (b(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[372, 26105])).
% 3.73/4.06 tff(26107,plain,
% 3.73/4.06 (~r(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2079, 26104, 26099, 26051])).
% 3.73/4.06 tff(26108,plain,
% 3.73/4.06 (b(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[658, 26107, 25622])).
% 3.73/4.06 tff(26109,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[7079, 26108, 26106, 25310, 25311])).
% 3.73/4.06 tff(26110,plain,(b(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26111,plain,
% 3.73/4.06 (b(s(s(s(z))), elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26110, 5775, 2545, 3616, 11546])).
% 3.73/4.06 tff(26112,plain,
% 3.73/4.06 (~b(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[4375, 26111, 25311, 25310])).
% 3.73/4.06 tff(26113,plain,
% 3.73/4.06 (r(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2794, 26112])).
% 3.73/4.06 tff(26114,plain,
% 3.73/4.06 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[17809, 26113, 23280, 11546])).
% 3.73/4.06 tff(26115,plain,
% 3.73/4.06 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1137, 26114])).
% 3.73/4.06 tff(26116,plain,
% 3.73/4.06 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[15703, 333, 26113, 11546, 25820])).
% 3.73/4.06 tff(26117,plain,
% 3.73/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[249, 26116])).
% 3.73/4.06 tff(26118,plain,
% 3.73/4.06 (~b(z, s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[16228, 26117, 25624, 26115])).
% 3.73/4.06 tff(26119,plain,
% 3.73/4.06 (r(z, s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[619, 26118])).
% 3.73/4.06 tff(26120,plain,
% 3.73/4.06 (~b(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[14036, 144, 26115, 25620, 25624])).
% 3.73/4.06 tff(26121,plain,
% 3.73/4.06 (r(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[396, 26120])).
% 3.73/4.06 tff(26122,plain,
% 3.73/4.06 (~b(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[4375, 4367, 134, 305])).
% 3.73/4.06 tff(26123,plain,
% 3.73/4.06 (r(s(s(s(z))), s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2794, 26122])).
% 3.73/4.06 tff(26124,plain,
% 3.73/4.06 (~b(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[14036, 144, 23999, 286, 259])).
% 3.73/4.06 tff(26125,plain,
% 3.73/4.06 (r(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[396, 26124])).
% 3.73/4.06 tff(26126,plain,
% 3.73/4.06 (~r(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[6555, 25851, 3193, 26125])).
% 3.73/4.06 tff(26127,plain,
% 3.73/4.06 (b(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[348, 26126])).
% 3.73/4.06 tff(26128,plain,
% 3.73/4.06 (~b(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1602, 26127, 134, 251])).
% 3.73/4.06 tff(26129,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[6012, 333, 354, 1699, 3193, 353])).
% 3.73/4.06 tff(26130,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26131,plain,
% 3.73/4.06 (~r(s(z), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26130, 25851, 3193, 26125])).
% 3.73/4.06 tff(26132,plain,
% 3.73/4.06 (b(s(z), s(s(s(z))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[172, 26131])).
% 3.73/4.06 tff(26133,plain,
% 3.73/4.06 (r(elem!1, z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[653, 26128, 1368])).
% 3.73/4.06 tff(26134,plain,
% 3.73/4.06 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[20695, 26133, 251, 25851, 26132, 20727, 26127, 134])).
% 3.73/4.06 tff(26135,plain,
% 3.73/4.06 (~r(s(elem!1), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[10865, 26133, 12930, 435])).
% 3.73/4.06 tff(26136,plain,
% 3.73/4.06 (b(s(elem!1), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[507, 26135])).
% 3.73/4.06 tff(26137,plain,
% 3.73/4.06 ($false),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[20903, 26136, 26134, 11546, 2484, 305, 286, 134, 26128, 25636, 259])).
% 3.73/4.06 tff(26138,plain,((~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z) | (~r(s(s(s(z))), s(z))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.06 tff(26139,plain,
% 3.73/4.06 (~b(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26138, 12525, 2484, 305, 25833, 134, 25831, 11546, 1368, 26123, 255])).
% 3.73/4.06 tff(26140,plain,
% 3.73/4.06 (r(z, elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[658, 26139, 25631])).
% 3.73/4.06 tff(26141,plain,
% 3.73/4.06 (~r(s(elem!1), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24919, 26140, 12525, 2323])).
% 3.73/4.06 tff(26142,plain,
% 3.73/4.06 (b(s(elem!1), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[507, 26141])).
% 3.73/4.06 tff(26143,plain,
% 3.73/4.06 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[10345, 144, 26142, 25833, 25831])).
% 3.73/4.06 tff(26144,plain,
% 3.73/4.06 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[472, 26143, 25865])).
% 3.73/4.06 tff(26145,plain,
% 3.73/4.06 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26144])).
% 3.73/4.06 tff(26146,plain,
% 3.73/4.06 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 3.73/4.06 inference(symmetry,[status(thm)],[26145])).
% 3.73/4.06 tff(26147,plain,
% 3.73/4.06 (s(s(s(s(s(s(z)))))) = elem!1),
% 3.73/4.06 inference(transitivity,[status(thm)],[21, 26146, 850])).
% 3.73/4.06 tff(26148,plain,
% 3.73/4.06 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26147])).
% 3.73/4.06 tff(26149,plain,
% 3.73/4.06 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.73/4.06 inference(symmetry,[status(thm)],[26148])).
% 3.73/4.06 tff(26150,plain,
% 3.73/4.06 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[12793, 333, 5787, 12525, 2484])).
% 3.73/4.06 tff(26151,plain,
% 3.73/4.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 3.73/4.06 inference(rewrite,[status(thm)],[])).
% 3.73/4.06 tff(26152,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 3.73/4.06 inference(quant_inst,[status(thm)],[])).
% 3.73/4.06 tff(26153,plain,
% 3.73/4.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[26152, 26151])).
% 3.73/4.06 tff(26154,plain,
% 3.73/4.06 (~r(z, s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[26153, 333, 5787, 12525, 26140])).
% 3.73/4.06 tff(26155,plain,
% 3.73/4.06 (b(z, s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[583, 26154])).
% 3.73/4.06 tff(26156,plain,
% 3.73/4.06 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[8386, 26155, 25831, 26150, 25865])).
% 3.73/4.06 tff(26157,plain,
% 3.73/4.06 (~(elem!1 = s(s(elem!1)))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1216, 26156])).
% 3.73/4.06 tff(26158,plain,
% 3.73/4.06 (~(s(s(s(s(z)))) = elem!1)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[24637, 26156, 26157])).
% 3.73/4.06 tff(26159,plain,
% 3.73/4.06 (b(s(s(s(s(s(s(z)))))), z) <=> b(elem!1, z)),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26147])).
% 3.73/4.06 tff(26160,plain,
% 3.73/4.06 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(elem!1, z))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26159])).
% 3.73/4.06 tff(26161,plain,
% 3.73/4.06 (elem!1 = s(s(s(s(s(s(z))))))),
% 3.73/4.06 inference(transitivity,[status(thm)],[1193, 26145, 20])).
% 3.73/4.06 tff(26162,plain,
% 3.73/4.06 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 3.73/4.06 inference(monotonicity,[status(thm)],[26161])).
% 3.73/4.06 tff(26163,plain,
% 3.73/4.06 (b(s(s(s(s(s(s(z)))))), s(z))),
% 3.73/4.06 inference(modus_ponens,[status(thm)],[305, 26162])).
% 3.73/4.06 tff(26164,plain,
% 3.73/4.06 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[17809, 26123, 2484, 11546])).
% 3.73/4.06 tff(26165,plain,
% 3.73/4.06 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1137, 26164])).
% 3.73/4.06 tff(26166,plain,
% 3.73/4.06 (~b(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[14036, 144, 26165, 25833, 25831])).
% 3.73/4.06 tff(26167,plain,
% 3.73/4.06 (r(s(s(s(z))), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[396, 26166])).
% 3.73/4.06 tff(26168,plain,
% 3.73/4.06 (~r(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[11212, 26140, 26123, 26167])).
% 3.73/4.06 tff(26169,plain,
% 3.73/4.06 (b(s(z), z)),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[348, 26168])).
% 3.73/4.06 tff(26170,plain,
% 3.73/4.06 (~(s(z) = s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1228, 25636])).
% 3.73/4.06 tff(26171,plain,
% 3.73/4.06 (~b(s(z), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[2383, 26155, 26169, 26142])).
% 3.73/4.06 tff(26172,plain,
% 3.73/4.06 (r(s(z), s(elem!1))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[1244, 26171, 26170])).
% 3.73/4.06 tff(26173,plain,
% 3.73/4.06 (~r(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[6565, 26172, 26123, 26167])).
% 3.73/4.06 tff(26174,plain,
% 3.73/4.06 (b(z, s(z))),
% 3.73/4.06 inference(unit_resolution,[status(thm)],[372, 26173])).
% 3.73/4.07 tff(26175,plain,
% 3.73/4.07 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26176,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26175])).
% 3.73/4.07 tff(26177,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.73/4.07 inference(transitivity,[status(thm)],[26176, 18545])).
% 3.73/4.07 tff(26178,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 3.73/4.07 inference(quant_inst,[status(thm)],[])).
% 3.73/4.07 tff(26179,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26178, 26177])).
% 3.73/4.07 tff(26180,plain,
% 3.73/4.07 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26179, 144, 26174, 26169, 26163])).
% 3.73/4.07 tff(26181,plain,
% 3.73/4.07 (~b(elem!1, z)),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26180, 26160])).
% 3.73/4.07 tff(26182,plain,
% 3.73/4.07 (r(elem!1, z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[653, 26181, 1368])).
% 3.73/4.07 tff(26183,plain,
% 3.73/4.07 (~r(s(s(s(s(z)))), elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24987, 26182, 25833, 25831, 2484, 26140])).
% 3.73/4.07 tff(26184,plain,
% 3.73/4.07 (b(s(s(s(s(z)))), elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24301, 26183, 26158])).
% 3.73/4.07 tff(26185,plain,
% 3.73/4.07 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26184, 26149])).
% 3.73/4.07 tff(26186,plain,
% 3.73/4.07 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26147])).
% 3.73/4.07 tff(26187,plain,
% 3.73/4.07 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.73/4.07 inference(symmetry,[status(thm)],[26186])).
% 3.73/4.07 tff(26188,plain,
% 3.73/4.07 (~r(elem!1, s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[3201, 26140, 26123, 12930])).
% 3.73/4.07 tff(26189,plain,
% 3.73/4.07 (~(s(s(s(z))) = elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[25838, 26143, 3616, 5775, 2484, 1184])).
% 3.73/4.07 tff(26190,plain,
% 3.73/4.07 (~(elem!1 = s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[10997, 26189])).
% 3.73/4.07 tff(26191,plain,
% 3.73/4.07 (b(elem!1, s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[1538, 26190, 26188])).
% 3.73/4.07 tff(26192,plain,
% 3.73/4.07 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26191, 26187])).
% 3.73/4.07 tff(26193,plain,
% 3.73/4.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26161])).
% 3.73/4.07 tff(26194,plain,
% 3.73/4.07 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[4367, 26193])).
% 3.73/4.07 tff(26195,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26196,plain,
% 3.73/4.07 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26197,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26196])).
% 3.73/4.07 tff(26198,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(transitivity,[status(thm)],[26197, 26195])).
% 3.73/4.07 tff(26199,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.73/4.07 inference(quant_inst,[status(thm)],[])).
% 3.73/4.07 tff(26200,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26199, 26198])).
% 3.73/4.07 tff(26201,plain,
% 3.73/4.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26200, 144, 26194, 26192, 26185])).
% 3.73/4.07 tff(26202,plain,
% 3.73/4.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[9821, 44, 219, 26201])).
% 3.73/4.07 tff(26203,plain,
% 3.73/4.07 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26161])).
% 3.73/4.07 tff(26204,plain,
% 3.73/4.07 (b(s(z), s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[134, 26203])).
% 3.73/4.07 tff(26205,plain,
% 3.73/4.07 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[2082, 20661])).
% 3.73/4.07 tff(26206,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.73/4.07 tff(26207,plain,
% 3.73/4.07 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[20956, 144, 838, 6169, 26206])).
% 3.73/4.07 tff(26208,plain,
% 3.73/4.07 ($false),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26207, 26205])).
% 3.73/4.07 tff(26209,plain,((~b(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.07 tff(26210,plain,
% 3.73/4.07 (~b(s(z), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26209, 26194, 26204, 26191, 26144])).
% 3.73/4.07 tff(26211,plain,
% 3.73/4.07 (r(s(z), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[172, 26210])).
% 3.73/4.07 tff(26212,plain,
% 3.73/4.07 (~b(s(s(s(s(z)))), s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24646, 144, 26163, 26204, 26185])).
% 3.73/4.07 tff(26213,plain,
% 3.73/4.07 (r(s(s(s(s(z)))), s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24600, 26212, 24294])).
% 3.73/4.07 tff(26214,plain,
% 3.73/4.07 ($false),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[23683, 333, 26123, 26213, 26211, 26202])).
% 3.73/4.07 tff(26215,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = z) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | b(s(elem!1), elem!1) | b(elem!1, s(elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.07 tff(26216,plain,
% 3.73/4.07 (elem!1 = s(elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26215, 26111, 25621, 23280, 25310, 25311, 3616, 5775, 25829, 23272, 11546, 26118])).
% 3.73/4.07 tff(26217,plain,
% 3.73/4.07 (s(elem!1) = elem!1),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[1569, 26216])).
% 3.73/4.07 tff(26218,plain,
% 3.73/4.07 (b(s(z), s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[3262, 26217, 25311])).
% 3.73/4.07 tff(26219,plain,
% 3.73/4.07 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26216])).
% 3.73/4.07 tff(26220,plain,
% 3.73/4.07 (b(s(elem!1), s(z))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[25310, 26219])).
% 3.73/4.07 tff(26221,plain,
% 3.73/4.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26216])).
% 3.73/4.07 tff(26222,plain,
% 3.73/4.07 (b(s(s(s(z))), s(elem!1))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26111, 26221])).
% 3.73/4.07 tff(26223,plain,
% 3.73/4.07 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[990, 3676, 25636])).
% 3.73/4.07 tff(26224,plain,
% 3.73/4.07 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24691, 26223, 885])).
% 3.73/4.07 tff(26225,plain,
% 3.73/4.07 (r(z, elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[658, 606, 25631])).
% 3.73/4.07 tff(26226,plain,
% 3.73/4.07 (~r(s(z), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[11212, 26225, 3193, 1699])).
% 3.73/4.07 tff(26227,plain,
% 3.73/4.07 (b(s(z), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[348, 26226])).
% 3.73/4.07 tff(26228,plain,
% 3.73/4.07 (~b(z, s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[2974, 606, 885])).
% 3.73/4.07 tff(26229,plain,
% 3.73/4.07 (r(z, s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[583, 26228])).
% 3.73/4.07 tff(26230,plain,
% 3.73/4.07 (~r(s(elem!1), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[1972, 26229, 623, 1699])).
% 3.73/4.07 tff(26231,plain,
% 3.73/4.07 (b(s(elem!1), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[965, 26230, 26223])).
% 3.73/4.07 tff(26232,plain,
% 3.73/4.07 (~b(s(z), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[12255, 144, 1262, 26231, 4811])).
% 3.73/4.07 tff(26233,plain,
% 3.73/4.07 (r(s(z), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[172, 26232])).
% 3.73/4.07 tff(26234,plain,
% 3.73/4.07 (~r(z, s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26130, 26233, 3193, 1699])).
% 3.73/4.07 tff(26235,plain,
% 3.73/4.07 (b(z, s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[372, 26234])).
% 3.73/4.07 tff(26236,plain,
% 3.73/4.07 (~b(s(elem!1), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[499, 26235, 488, 26227])).
% 3.73/4.07 tff(26237,plain,
% 3.73/4.07 (~b(elem!1, z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[12198, 26236, 885])).
% 3.73/4.07 tff(26238,plain,
% 3.73/4.07 (r(elem!1, z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[653, 26237, 1368])).
% 3.73/4.07 tff(26239,plain,
% 3.73/4.07 (~r(s(s(s(s(z)))), elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24987, 26238, 286, 259, 2484, 26225])).
% 3.73/4.07 tff(26240,plain,
% 3.73/4.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24681, 26239, 885])).
% 3.73/4.07 tff(26241,plain,
% 3.73/4.07 (b(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24448, 26240, 26224])).
% 3.73/4.07 tff(26242,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26243,plain,
% 3.73/4.07 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26244,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26243])).
% 3.73/4.07 tff(26245,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.07 inference(transitivity,[status(thm)],[26244, 26242])).
% 3.73/4.07 tff(26246,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.73/4.07 inference(quant_inst,[status(thm)],[])).
% 3.73/4.07 tff(26247,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26246, 26245])).
% 3.73/4.07 tff(26248,plain,
% 3.73/4.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26247, 144, 26231, 4811, 26241])).
% 3.73/4.07 tff(26249,plain,
% 3.73/4.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[9821, 44, 219, 26248])).
% 3.73/4.07 tff(26250,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26251,plain,
% 3.73/4.07 (((~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.73/4.07 inference(rewrite,[status(thm)],[])).
% 3.73/4.07 tff(26252,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))))),
% 3.73/4.07 inference(monotonicity,[status(thm)],[26251])).
% 3.73/4.07 tff(26253,plain,
% 3.73/4.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.73/4.07 inference(transitivity,[status(thm)],[26252, 26250])).
% 3.73/4.07 tff(26254,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.73/4.07 inference(quant_inst,[status(thm)],[])).
% 3.73/4.07 tff(26255,plain,
% 3.73/4.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))),
% 3.73/4.07 inference(modus_ponens,[status(thm)],[26254, 26253])).
% 3.73/4.07 tff(26256,plain,
% 3.73/4.07 (~b(s(s(s(s(z)))), s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26255, 144, 488, 1262, 26241])).
% 3.73/4.07 tff(26257,plain,
% 3.73/4.07 (r(s(s(s(s(z)))), s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[24600, 26256, 24294])).
% 3.73/4.07 tff(26258,plain,
% 3.73/4.07 ($false),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[23683, 333, 3193, 26257, 26233, 26249])).
% 3.73/4.07 tff(26259,plain,(b(z, elem!1) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~(elem!1 = s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = z) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.07 tff(26260,plain,
% 3.73/4.07 (b(z, elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26259, 26113, 26222, 26220, 26218, 26216, 25620, 25624, 23280, 25621, 26121, 26119])).
% 3.73/4.07 tff(26261,plain,
% 3.73/4.07 (~b(z, s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[7079, 26260, 25310, 25311])).
% 3.73/4.07 tff(26262,plain,
% 3.73/4.07 (r(z, s(z))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[372, 26261])).
% 3.73/4.07 tff(26263,plain,
% 3.73/4.07 ($false),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[16763, 333, 26262, 26119, 26113, 11546])).
% 3.73/4.07 tff(26264,plain,(b(elem!1, s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.07 tff(26265,plain,
% 3.73/4.07 (b(elem!1, s(elem!1))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[26264, 3616, 11546, 2545])).
% 3.73/4.07 tff(26266,plain,
% 3.73/4.07 (~(s(elem!1) = elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[5885, 26265])).
% 3.73/4.07 tff(26267,plain,
% 3.73/4.07 (r(s(elem!1), elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[448, 26266, 3616])).
% 3.73/4.07 tff(26268,plain,
% 3.73/4.07 (~r(s(elem!1), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[25799, 26267, 25310, 25308, 25311, 2545, 26265, 23272, 25619])).
% 3.73/4.07 tff(26269,plain,
% 3.73/4.07 (b(s(elem!1), z)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[507, 26268])).
% 3.73/4.07 tff(26270,plain,
% 3.73/4.07 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[10345, 144, 26269, 25620, 25624])).
% 3.73/4.07 tff(26271,plain,
% 3.73/4.07 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[14999, 333, 26267, 23280, 23272])).
% 3.73/4.07 tff(26272,plain,
% 3.73/4.07 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[472, 26271, 26270])).
% 3.73/4.07 tff(26273,plain,
% 3.73/4.07 (~(s(s(s(z))) = elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[12214, 26272])).
% 3.73/4.07 tff(26274,plain,
% 3.73/4.07 (b(s(s(s(z))), elem!1)),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[704, 25651, 698])).
% 3.73/4.07 tff(26275,plain,
% 3.73/4.07 ($false),
% 3.73/4.07 inference(unit_resolution,[status(thm)],[4375, 26274, 22973, 134, 305])).
% 3.73/4.07 tff(26276,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26277,plain,
% 3.73/4.08 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26276, 26273, 25310, 25311, 23272, 23280, 11546])).
% 3.73/4.08 tff(26278,plain,
% 3.73/4.08 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1137, 26277])).
% 3.73/4.08 tff(26279,plain,
% 3.73/4.08 (~b(s(s(s(z))), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[14036, 144, 26278, 25620, 25624])).
% 3.73/4.08 tff(26280,plain,
% 3.73/4.08 (r(s(s(s(z))), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[396, 26279])).
% 3.73/4.08 tff(26281,plain,
% 3.73/4.08 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26272])).
% 3.73/4.08 tff(26282,plain,
% 3.73/4.08 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(elem!1))),
% 3.73/4.08 inference(symmetry,[status(thm)],[26281])).
% 3.73/4.08 tff(26283,plain,
% 3.73/4.08 (r(s(z), s(elem!1))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[11546, 26282])).
% 3.73/4.08 tff(26284,plain,
% 3.73/4.08 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26272])).
% 3.73/4.08 tff(26285,plain,
% 3.73/4.08 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(elem!1))),
% 3.73/4.08 inference(symmetry,[status(thm)],[26284])).
% 3.73/4.08 tff(26286,plain,
% 3.73/4.08 (r(elem!1, s(elem!1))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[23272, 26285])).
% 3.73/4.08 tff(26287,plain,
% 3.73/4.08 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26272])).
% 3.73/4.08 tff(26288,plain,
% 3.73/4.08 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26265, 26287])).
% 3.73/4.08 tff(26289,plain,
% 3.73/4.08 (~b(elem!1, z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[8787, 26288, 26265, 26269, 25624])).
% 3.73/4.08 tff(26290,plain,
% 3.73/4.08 (r(elem!1, z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[653, 26289, 25621])).
% 3.73/4.08 tff(26291,plain,
% 3.73/4.08 (~r(s(s(s(z))), elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[6585, 670, 563, 1699])).
% 3.73/4.08 tff(26292,plain,
% 3.73/4.08 (b(s(s(s(z))), elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[704, 26291, 20929])).
% 3.73/4.08 tff(26293,plain,
% 3.73/4.08 (~b(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[4375, 26292, 134, 305])).
% 3.73/4.08 tff(26294,plain,
% 3.73/4.08 (r(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2794, 26293])).
% 3.73/4.08 tff(26295,plain,
% 3.73/4.08 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[23261, 26294, 305, 20930, 2254, 11546, 132, 2484])).
% 3.73/4.08 tff(26296,plain,
% 3.73/4.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[249, 26295])).
% 3.73/4.08 tff(26297,plain,
% 3.73/4.08 (~b(z, s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[16228, 26296, 259, 2254])).
% 3.73/4.08 tff(26298,plain,
% 3.73/4.08 (~r(s(z), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[11212, 26294, 670, 1699])).
% 3.73/4.08 tff(26299,plain,
% 3.73/4.08 (b(s(z), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[348, 26298])).
% 3.73/4.08 tff(26300,plain,
% 3.73/4.08 (~r(z, s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[20976, 26299, 11546, 132, 2484, 408, 670, 927, 1, 714, 134])).
% 3.73/4.08 tff(26301,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[619, 26300, 26297])).
% 3.73/4.08 tff(26302,plain,((~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26303,plain,
% 3.73/4.08 (~r(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26302, 26288, 11546, 23280, 26290, 26272, 25627, 25309, 25311, 25624, 26278, 26280, 25310, 26286])).
% 3.73/4.08 tff(26304,plain,
% 3.73/4.08 (b(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[658, 26303, 25622])).
% 3.73/4.08 tff(26305,plain,
% 3.73/4.08 (~b(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[7079, 26304, 25310, 25311])).
% 3.73/4.08 tff(26306,plain,
% 3.73/4.08 (r(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[372, 26305])).
% 3.73/4.08 tff(26307,plain,
% 3.73/4.08 (~r(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[6565, 26306, 26283, 26280])).
% 3.73/4.08 tff(26308,plain,
% 3.73/4.08 (b(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2794, 26307])).
% 3.73/4.08 tff(26309,plain,
% 3.73/4.08 (~r(s(s(s(z))), elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2122, 26306, 26290, 26280])).
% 3.73/4.08 tff(26310,plain,
% 3.73/4.08 (b(s(s(s(z))), elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[704, 26309, 26273])).
% 3.73/4.08 tff(26311,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[4375, 26310, 26308, 25311, 25310])).
% 3.73/4.08 tff(26312,plain,(b(s(elem!1), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26313,plain,
% 3.73/4.08 (b(s(elem!1), elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26312, 11546, 2545])).
% 3.73/4.08 tff(26314,plain,
% 3.73/4.08 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.08 inference(monotonicity,[status(thm)],[927])).
% 3.73/4.08 tff(26315,plain,
% 3.73/4.08 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.73/4.08 inference(symmetry,[status(thm)],[26314])).
% 3.73/4.08 tff(26316,plain,
% 3.73/4.08 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26315])).
% 3.73/4.08 tff(26317,plain,
% 3.73/4.08 (~b(s(elem!1), elem!1)),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[2545, 26316])).
% 3.73/4.08 tff(26318,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[451, 26317])).
% 3.73/4.08 tff(26319,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26320,plain,
% 3.73/4.08 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26319, 26313, 2545])).
% 3.73/4.08 tff(26321,plain,
% 3.73/4.08 (~r(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[22626, 333, 25851, 7522, 11546])).
% 3.73/4.08 tff(26322,plain,
% 3.73/4.08 (b(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[507, 26321])).
% 3.73/4.08 tff(26323,plain,
% 3.73/4.08 (~b(elem!1, z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[916, 26322, 451, 251])).
% 3.73/4.08 tff(26324,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[20903, 26323, 26322, 11546, 2484, 305, 286, 134, 432, 1, 259])).
% 3.73/4.08 tff(26325,plain,((~b(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26326,plain,
% 3.73/4.08 (~b(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26325, 11546, 2484, 25629, 25683, 25630, 432, 25636, 25633, 451])).
% 3.73/4.08 tff(26327,plain,
% 3.73/4.08 (r(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[658, 26326, 25631])).
% 3.73/4.08 tff(26328,plain,
% 3.73/4.08 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[24191, 74, 2484, 25630, 25629, 2323, 11546])).
% 3.73/4.08 tff(26329,plain,
% 3.73/4.08 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[279, 26328])).
% 3.73/4.08 tff(26330,plain,
% 3.73/4.08 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[14138, 144, 285, 25683, 26329])).
% 3.73/4.08 tff(26331,plain,
% 3.73/4.08 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1137, 26330])).
% 3.73/4.08 tff(26332,plain,
% 3.73/4.08 (~r(elem!1, s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[25642, 333, 2484, 2323, 26331])).
% 3.73/4.08 tff(26333,plain,
% 3.73/4.08 (~r(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[17809, 26331, 2484, 11546])).
% 3.73/4.08 tff(26334,plain,
% 3.73/4.08 (b(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2794, 26333])).
% 3.73/4.08 tff(26335,plain,
% 3.73/4.08 (~r(s(z), s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[17817, 333, 11546, 2484, 26331])).
% 3.73/4.08 tff(26336,plain,
% 3.73/4.08 (b(s(z), s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[172, 26335])).
% 3.73/4.08 tff(26337,plain,
% 3.73/4.08 (~b(elem!1, s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[22776, 26336, 25629, 26334])).
% 3.73/4.08 tff(26338,plain,
% 3.73/4.08 (elem!1 = s(s(s(z)))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1538, 26337, 26332])).
% 3.73/4.08 tff(26339,plain,
% 3.73/4.08 (s(elem!1) = s(s(s(s(z))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26338])).
% 3.73/4.08 tff(26340,plain,
% 3.73/4.08 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26339])).
% 3.73/4.08 tff(26341,plain,
% 3.73/4.08 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26338])).
% 3.73/4.08 tff(26342,plain,
% 3.73/4.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[2484, 26341])).
% 3.73/4.08 tff(26343,plain,
% 3.73/4.08 (s(s(s(z))) = elem!1),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26276, 26331, 25629, 25630, 2323, 2484, 11546])).
% 3.73/4.08 tff(26344,plain,
% 3.73/4.08 (b(elem!1, z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[380, 26343, 285])).
% 3.73/4.08 tff(26345,plain,
% 3.73/4.08 (~(s(s(elem!1)) = elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[7595, 26343, 863])).
% 3.73/4.08 tff(26346,plain,
% 3.73/4.08 (~(elem!1 = s(s(elem!1)))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[5603, 26345])).
% 3.73/4.08 tff(26347,plain,
% 3.73/4.08 (~(s(elem!1) = elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[5813, 26346])).
% 3.73/4.08 tff(26348,plain,
% 3.73/4.08 (~(elem!1 = s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1569, 26347])).
% 3.73/4.08 tff(26349,plain,
% 3.73/4.08 (b(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[658, 1575, 74])).
% 3.73/4.08 tff(26350,plain,
% 3.73/4.08 (~b(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[7079, 26349, 305, 134])).
% 3.73/4.08 tff(26351,plain,
% 3.73/4.08 (r(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[372, 26350])).
% 3.73/4.08 tff(26352,plain,
% 3.73/4.08 (~b(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[916, 26349, 451, 624])).
% 3.73/4.08 tff(26353,plain,
% 3.73/4.08 (r(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[507, 26352])).
% 3.73/4.08 tff(26354,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1653, 26353, 26351, 706, 8684, 7521, 1575, 902])).
% 3.73/4.08 tff(26355,plain,(r(z, elem!1) | (s(z) = elem!1) | (elem!1 = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26356,plain,
% 3.73/4.08 (r(z, elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26355, 26348, 706, 451, 26344, 25629, 25630, 74])).
% 3.73/4.08 tff(26357,plain,
% 3.73/4.08 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26339])).
% 3.73/4.08 tff(26358,plain,
% 3.73/4.08 (~b(s(elem!1), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[4344, 144, 451, 25630, 25629])).
% 3.73/4.08 tff(26359,plain,
% 3.73/4.08 (r(s(elem!1), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[486, 26358, 8684])).
% 3.73/4.08 tff(26360,plain,
% 3.73/4.08 (r(s(s(s(s(z)))), s(z))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26359, 26357])).
% 3.73/4.08 tff(26361,plain,
% 3.73/4.08 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26339])).
% 3.73/4.08 tff(26362,plain,
% 3.73/4.08 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26338])).
% 3.73/4.08 tff(26363,plain,
% 3.73/4.08 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.73/4.08 inference(transitivity,[status(thm)],[26362, 26361])).
% 3.73/4.08 tff(26364,plain,
% 3.73/4.08 (~(s(s(z)) = elem!1)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[14611, 26343, 706])).
% 3.73/4.08 tff(26365,plain,
% 3.73/4.08 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1508, 26364])).
% 3.73/4.08 tff(26366,plain,
% 3.73/4.08 (~(s(s(s(z))) = s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[1934, 26365])).
% 3.73/4.08 tff(26367,plain,
% 3.73/4.08 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[12214, 26343])).
% 3.73/4.08 tff(26368,plain,
% 3.73/4.08 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[19607])).
% 3.73/4.08 tff(26369,plain,
% 3.73/4.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(symmetry,[status(thm)],[26368])).
% 3.73/4.08 tff(26370,plain,
% 3.73/4.08 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26369])).
% 3.73/4.08 tff(26371,plain,
% 3.73/4.08 (~r(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[17809, 14140, 2484, 11546])).
% 3.73/4.08 tff(26372,plain,
% 3.73/4.08 (b(s(s(s(z))), s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2794, 26371])).
% 3.73/4.08 tff(26373,plain,
% 3.73/4.08 (~r(z, s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[2393, 670, 434, 563])).
% 3.73/4.08 tff(26374,plain,
% 3.73/4.08 (b(z, s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[583, 26373])).
% 3.73/4.08 tff(26375,plain,
% 3.73/4.08 (~r(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[7112, 24071, 305, 1, 902, 490, 670])).
% 3.73/4.08 tff(26376,plain,
% 3.73/4.08 (b(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[507, 26375])).
% 3.73/4.08 tff(26377,plain,
% 3.73/4.08 (b(s(s(s(s(z)))), z)),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26376, 19698])).
% 3.73/4.08 tff(26378,plain,
% 3.73/4.08 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[22512, 490, 11546, 1, 3238, 585, 224])).
% 3.73/4.08 tff(26379,plain,
% 3.73/4.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[9761, 26378])).
% 3.73/4.08 tff(26380,plain,
% 3.73/4.08 (~b(s(s(s(s(z)))), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[19705, 144, 286, 259, 26379])).
% 3.73/4.08 tff(26381,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26380, 26377])).
% 3.73/4.08 tff(26382,plain,((~b(z, s(z))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26383,plain,
% 3.73/4.08 (~b(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26382, 670, 286, 259, 305, 1, 902, 3238, 11546, 26374, 22490, 26372, 285])).
% 3.73/4.08 tff(26384,plain,
% 3.73/4.08 (r(z, s(z))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[372, 26383])).
% 3.73/4.08 tff(26385,plain,
% 3.73/4.08 (~r(s(s(s(s(z)))), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[24617, 333, 26384, 20422, 11546])).
% 3.73/4.08 tff(26386,plain,
% 3.73/4.08 (b(s(s(s(s(z)))), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[4243, 44, 242, 26385])).
% 3.73/4.08 tff(26387,plain,
% 3.73/4.08 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[19705, 144, 286, 259, 26386])).
% 3.73/4.08 tff(26388,plain,
% 3.73/4.08 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26387, 26370])).
% 3.73/4.08 tff(26389,plain,
% 3.73/4.08 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 3.73/4.08 inference(symmetry,[status(thm)],[19808])).
% 3.73/4.08 tff(26390,plain,
% 3.73/4.08 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(elem!1), z))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26389])).
% 3.73/4.08 tff(26391,plain,
% 3.73/4.08 (~r(s(elem!1), z)),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26385, 26390])).
% 3.73/4.08 tff(26392,plain,
% 3.73/4.08 (b(s(elem!1), z)),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[507, 26391])).
% 3.73/4.08 tff(26393,plain,
% 3.73/4.08 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[14148, 26392, 286, 285, 259, 2484, 1948, 26374])).
% 3.73/4.08 tff(26394,plain,
% 3.73/4.08 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[472, 26393, 432])).
% 3.73/4.08 tff(26395,plain,
% 3.73/4.08 ($false),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26394, 26388])).
% 3.73/4.08 tff(26396,plain,((~r(z, elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.08 tff(26397,plain,
% 3.73/4.08 (~r(elem!1, s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26396, 26356, 25683, 26329, 26367, 285, 2484, 26366, 11546, 25629, 8684, 26348, 26359, 26338])).
% 3.73/4.08 tff(26398,plain,
% 3.73/4.08 (b(elem!1, s(elem!1))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[560, 26397, 26348])).
% 3.73/4.08 tff(26399,plain,
% 3.73/4.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26398, 26363])).
% 3.73/4.08 tff(26400,plain,
% 3.73/4.08 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26339])).
% 3.73/4.08 tff(26401,plain,
% 3.73/4.08 (b(s(elem!1), s(s(s(z))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[19265, 26343, 451])).
% 3.73/4.08 tff(26402,plain,
% 3.73/4.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26401, 26400])).
% 3.73/4.08 tff(26403,plain,
% 3.73/4.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.08 inference(rewrite,[status(thm)],[])).
% 3.73/4.08 tff(26404,plain,
% 3.73/4.08 (((~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(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.08 inference(rewrite,[status(thm)],[])).
% 3.73/4.08 tff(26405,plain,
% 3.73/4.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.73/4.08 inference(monotonicity,[status(thm)],[26404])).
% 3.73/4.08 tff(26406,plain,
% 3.73/4.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.73/4.08 inference(transitivity,[status(thm)],[26405, 26403])).
% 3.73/4.08 tff(26407,plain,
% 3.73/4.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 3.73/4.08 inference(quant_inst,[status(thm)],[])).
% 3.73/4.08 tff(26408,plain,
% 3.73/4.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.73/4.08 inference(modus_ponens,[status(thm)],[26407, 26406])).
% 3.73/4.08 tff(26409,plain,
% 3.73/4.08 (~b(s(z), s(s(s(s(z)))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26408, 144, 26336, 26402, 26399])).
% 3.73/4.08 tff(26410,plain,
% 3.73/4.08 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[19906, 44, 26409])).
% 3.73/4.08 tff(26411,plain,
% 3.73/4.08 (r(s(z), s(s(s(s(z)))))),
% 3.73/4.08 inference(unit_resolution,[status(thm)],[26410, 25692])).
% 3.73/4.08 tff(26412,plain,
% 3.73/4.08 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 3.73/4.08 inference(symmetry,[status(thm)],[22521])).
% 3.73/4.08 tff(26413,plain,
% 3.73/4.08 (((~![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(z)))))) | (~r(s(z), 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(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.08 inference(rewrite,[status(thm)],[])).
% 3.73/4.08 tff(26414,plain,
% 3.73/4.08 (((~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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(rewrite,[status(thm)],[])).
% 3.73/4.09 tff(26415,plain,
% 3.73/4.09 (((~![X0: $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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26414])).
% 3.73/4.09 tff(26416,plain,
% 3.73/4.09 (((~![X0: $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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(transitivity,[status(thm)],[26415, 26413])).
% 3.73/4.09 tff(26417,plain,
% 3.73/4.09 ((~![X0: $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)))))))),
% 3.73/4.09 inference(quant_inst,[status(thm)],[])).
% 3.73/4.09 tff(26418,plain,
% 3.73/4.09 ((~![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(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26417, 26416])).
% 3.73/4.09 tff(26419,plain,
% 3.73/4.09 (~r(z, s(s(s(s(z)))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26418, 333, 354, 25711, 25527])).
% 3.73/4.09 tff(26420,plain,
% 3.73/4.09 (b(z, s(s(s(s(z)))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[4260, 26419])).
% 3.73/4.09 tff(26421,plain,
% 3.73/4.09 (b(z, s(elem!1))),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26420, 26412])).
% 3.73/4.09 tff(26422,plain,
% 3.73/4.09 (((~![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)))), 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), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(rewrite,[status(thm)],[])).
% 3.73/4.09 tff(26423,plain,
% 3.73/4.09 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(rewrite,[status(thm)],[])).
% 3.73/4.09 tff(26424,plain,
% 3.73/4.09 (((~![X0: $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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26423])).
% 3.73/4.09 tff(26425,plain,
% 3.73/4.09 (((~![X0: $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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(transitivity,[status(thm)],[26424, 26422])).
% 3.73/4.09 tff(26426,plain,
% 3.73/4.09 ((~![X0: $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)))),
% 3.73/4.09 inference(quant_inst,[status(thm)],[])).
% 3.73/4.09 tff(26427,plain,
% 3.73/4.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26426, 26425])).
% 3.73/4.09 tff(26428,plain,
% 3.73/4.09 (~r(s(s(s(s(z)))), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26427, 333, 354, 25711, 25527])).
% 3.73/4.09 tff(26429,plain,
% 3.73/4.09 (~r(s(elem!1), z)),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26428, 26390])).
% 3.73/4.09 tff(26430,plain,
% 3.73/4.09 (b(s(elem!1), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[507, 26429])).
% 3.73/4.09 tff(26431,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[949, 26430, 26421, 624, 547])).
% 3.73/4.09 tff(26432,plain,((~r(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26433,plain,
% 3.73/4.09 (~r(z, s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26432, 26344, 26398, 26338, 26411, 26360])).
% 3.73/4.09 tff(26434,plain,
% 3.73/4.09 (b(z, s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[372, 26433])).
% 3.73/4.09 tff(26435,plain,
% 3.73/4.09 (~b(z, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26382, 26434, 25683, 26329, 25629, 8684, 26348, 26338, 11546, 26356, 26342, 26334, 285])).
% 3.73/4.09 tff(26436,plain,
% 3.73/4.09 (r(z, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[583, 26435])).
% 3.73/4.09 tff(26437,plain,
% 3.73/4.09 (r(z, s(s(s(s(z)))))),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26436, 26340])).
% 3.73/4.09 tff(26438,plain,
% 3.73/4.09 (~b(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2273, 26434, 26334, 285])).
% 3.73/4.09 tff(26439,plain,
% 3.73/4.09 (r(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[348, 26438])).
% 3.73/4.09 tff(26440,plain,
% 3.73/4.09 (((~![X0: $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(z)))))) | (~r(s(z), 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(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(rewrite,[status(thm)],[])).
% 3.73/4.09 tff(26441,plain,
% 3.73/4.09 (((~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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(rewrite,[status(thm)],[])).
% 3.73/4.09 tff(26442,plain,
% 3.73/4.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26441])).
% 3.73/4.09 tff(26443,plain,
% 3.73/4.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.09 inference(transitivity,[status(thm)],[26442, 26440])).
% 3.73/4.09 tff(26444,plain,
% 3.73/4.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 3.73/4.09 inference(quant_inst,[status(thm)],[])).
% 3.73/4.09 tff(26445,plain,
% 3.73/4.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26444, 26443])).
% 3.73/4.09 tff(26446,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26445, 333, 26439, 26411, 26360, 26437])).
% 3.73/4.09 tff(26447,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26448,plain,
% 3.73/4.09 (~b(s(s(s(z))), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26447, 11546, 2484, 706, 451, 25631, 2323])).
% 3.73/4.09 tff(26449,plain,
% 3.73/4.09 (r(s(elem!1), s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[486, 26358, 25636])).
% 3.73/4.09 tff(26450,plain,
% 3.73/4.09 (~(s(s(s(z))) = elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24271, 354, 11546, 1, 1963, 25629, 25630, 2484, 25683, 670, 706])).
% 3.73/4.09 tff(26451,plain,
% 3.73/4.09 (~r(z, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24144, 333, 354, 434, 11546])).
% 3.73/4.09 tff(26452,plain,
% 3.73/4.09 (b(z, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[583, 26451])).
% 3.73/4.09 tff(26453,plain,
% 3.73/4.09 (~(elem!1 = s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2974, 26452, 606])).
% 3.73/4.09 tff(26454,plain,
% 3.73/4.09 (~r(s(elem!1), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[22626, 333, 354, 434, 11546])).
% 3.73/4.09 tff(26455,plain,
% 3.73/4.09 (b(s(elem!1), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[507, 26454])).
% 3.73/4.09 tff(26456,plain,
% 3.73/4.09 (b(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[20903, 26455, 11546, 2484, 25629, 25683, 25630, 432, 1, 259])).
% 3.73/4.09 tff(26457,plain,
% 3.73/4.09 (~b(elem!1, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[949, 26456, 26452, 26455])).
% 3.73/4.09 tff(26458,plain,
% 3.73/4.09 (r(elem!1, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[560, 26457, 26453])).
% 3.73/4.09 tff(26459,plain,
% 3.73/4.09 (~r(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[6585, 26458, 670, 1964])).
% 3.73/4.09 tff(26460,plain,
% 3.73/4.09 (~r(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[25756, 354, 2323, 25629, 1964, 670, 26450, 25630])).
% 3.73/4.09 tff(26461,plain,
% 3.73/4.09 (b(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[348, 26460])).
% 3.73/4.09 tff(26462,plain,
% 3.73/4.09 (~b(s(z), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2383, 26452, 26461, 26455])).
% 3.73/4.09 tff(26463,plain,
% 3.73/4.09 (r(s(z), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1244, 26462, 1229])).
% 3.73/4.09 tff(26464,plain,
% 3.73/4.09 (~r(s(s(s(z))), s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[6565, 26463, 354, 1964])).
% 3.73/4.09 tff(26465,plain,
% 3.73/4.09 (b(s(s(s(z))), s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2794, 26464])).
% 3.73/4.09 tff(26466,plain,
% 3.73/4.09 (~b(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[4375, 26465, 25630, 25629])).
% 3.73/4.09 tff(26467,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[704, 26466, 26459, 26450])).
% 3.73/4.09 tff(26468,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26469,plain,
% 3.73/4.09 (~r(z, s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26468, 26327, 11546, 2484, 432, 25636, 25633, 26326, 26449, 2323, 26448, 706])).
% 3.73/4.09 tff(26470,plain,
% 3.73/4.09 (b(z, s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[372, 26469])).
% 3.73/4.09 tff(26471,plain,
% 3.73/4.09 (~b(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[20117, 491, 11546, 286, 25636, 259, 432, 490])).
% 3.73/4.09 tff(26472,plain,
% 3.73/4.09 (r(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[348, 26471])).
% 3.73/4.09 tff(26473,plain,
% 3.73/4.09 (~r(s(s(s(z))), s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[11212, 26472, 670, 1964])).
% 3.73/4.09 tff(26474,plain,
% 3.73/4.09 (b(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[20903, 491, 11546, 2484, 305, 286, 134, 432, 25636, 259])).
% 3.73/4.09 tff(26475,plain,
% 3.73/4.09 (~(s(s(s(z))) = elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24196, 26474, 1963])).
% 3.73/4.09 tff(26476,plain,
% 3.73/4.09 (~r(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7127, 491, 490, 902, 305, 1368, 670, 1964])).
% 3.73/4.09 tff(26477,plain,
% 3.73/4.09 (b(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[704, 26476, 26475])).
% 3.73/4.09 tff(26478,plain,
% 3.73/4.09 (~b(s(s(s(z))), s(z))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[4375, 26477, 134, 305])).
% 3.73/4.09 tff(26479,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2794, 26478, 26473])).
% 3.73/4.09 tff(26480,plain,((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | b(s(s(s(z))), z) | (~b(z, s(z))) | (elem!1 = s(elem!1)) | (elem!1 = z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26481,plain,
% 3.73/4.09 (~b(s(elem!1), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26480, 902, 25629, 26327, 26448, 26470, 25630, 1368, 11546, 25683, 25633, 432, 2484])).
% 3.73/4.09 tff(26482,plain,
% 3.73/4.09 (r(s(elem!1), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[507, 26481])).
% 3.73/4.09 tff(26483,plain,
% 3.73/4.09 (~r(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7112, 26482, 25629, 25636, 902, 26470, 26327])).
% 3.73/4.09 tff(26484,plain,
% 3.73/4.09 (b(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[348, 26483])).
% 3.73/4.09 tff(26485,plain,
% 3.73/4.09 (~b(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[9125, 144, 26470, 26484, 25629])).
% 3.73/4.09 tff(26486,plain,
% 3.73/4.09 (r(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[653, 26485, 1368])).
% 3.73/4.09 tff(26487,plain,
% 3.73/4.09 (~r(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7112, 509, 305, 25636, 902, 490, 670])).
% 3.73/4.09 tff(26488,plain,
% 3.73/4.09 (b(s(z), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[348, 26487])).
% 3.73/4.09 tff(26489,plain,
% 3.73/4.09 (~r(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[678, 509, 563, 670])).
% 3.73/4.09 tff(26490,plain,
% 3.73/4.09 (b(elem!1, z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1380, 26489, 1368])).
% 3.73/4.09 tff(26491,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[387, 144, 26490, 490, 26488, 305])).
% 3.73/4.09 tff(26492,plain,((~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (elem!1 = z) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26493,plain,
% 3.73/4.09 (~r(elem!1, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26492, 26482, 25629, 1368, 902, 26327, 26470])).
% 3.73/4.09 tff(26494,plain,
% 3.73/4.09 (b(elem!1, s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[560, 26493, 902])).
% 3.73/4.09 tff(26495,plain,
% 3.73/4.09 (~r(s(elem!1), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24919, 26482, 26327, 2323])).
% 3.73/4.09 tff(26496,plain,
% 3.73/4.09 (~b(s(z), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1732, 26493, 25630, 902, 26495])).
% 3.73/4.09 tff(26497,plain,
% 3.73/4.09 (r(s(z), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1244, 26496, 26170])).
% 3.73/4.09 tff(26498,plain,
% 3.73/4.09 (~b(s(s(elem!1)), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[4996, 26497, 25630, 25629, 451, 2727, 26494, 26449])).
% 3.73/4.09 tff(26499,plain,
% 3.73/4.09 (r(s(s(s(z))), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[396, 26448])).
% 3.73/4.09 tff(26500,plain,
% 3.73/4.09 (~r(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[2079, 26486, 26327, 26499])).
% 3.73/4.09 tff(26501,plain,
% 3.73/4.09 (~r(s(s(s(s(z)))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24987, 26486, 25683, 25633, 2484, 26327])).
% 3.73/4.09 tff(26502,plain,
% 3.73/4.09 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.73/4.09 inference(monotonicity,[status(thm)],[19995])).
% 3.73/4.09 tff(26503,plain,
% 3.73/4.09 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.73/4.09 inference(symmetry,[status(thm)],[26502])).
% 3.73/4.09 tff(26504,plain,
% 3.73/4.09 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26503])).
% 3.73/4.09 tff(26505,plain,
% 3.73/4.09 (~b(s(s(s(s(z)))), elem!1)),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[24876, 26504])).
% 3.73/4.09 tff(26506,plain,
% 3.73/4.09 (~(elem!1 = s(s(elem!1)))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[5603, 11096])).
% 3.73/4.09 tff(26507,plain,
% 3.73/4.09 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.73/4.09 inference(symmetry,[status(thm)],[13198])).
% 3.73/4.09 tff(26508,plain,
% 3.73/4.09 (elem!1 = s(s(s(s(z))))),
% 3.73/4.09 inference(symmetry,[status(thm)],[24629])).
% 3.73/4.09 tff(26509,plain,
% 3.73/4.09 (elem!1 = s(s(elem!1))),
% 3.73/4.09 inference(transitivity,[status(thm)],[26508, 26507])).
% 3.73/4.09 tff(26510,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1221, 26509])).
% 3.73/4.09 tff(26511,plain,((~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26512,plain,
% 3.73/4.09 (~(s(s(s(s(z)))) = elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26511, 11076, 26506])).
% 3.73/4.09 tff(26513,plain,
% 3.73/4.09 (b(s(s(s(s(z)))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[24301, 26512, 23985])).
% 3.73/4.09 tff(26514,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26513, 26505])).
% 3.73/4.09 tff(26515,plain,((~(s(s(s(z))) = s(elem!1))) | b(s(s(elem!1)), elem!1) | r(s(s(s(s(z)))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26516,plain,
% 3.73/4.09 (~(s(s(s(z))) = s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26515, 26498, 26501, 25636])).
% 3.73/4.09 tff(26517,plain,
% 3.73/4.09 (~r(s(s(s(z))), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[5824, 333, 26327, 26482, 26499])).
% 3.73/4.09 tff(26518,plain,
% 3.73/4.09 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1951, 44, 26517])).
% 3.73/4.09 tff(26519,plain,
% 3.73/4.09 (b(s(s(s(z))), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26518, 26516])).
% 3.73/4.09 tff(26520,plain,
% 3.73/4.09 (~b(s(s(s(z))), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[4819, 26519, 451, 26494])).
% 3.73/4.09 tff(26521,plain,
% 3.73/4.09 (s(s(s(z))) = elem!1),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[704, 26520, 26500])).
% 3.73/4.09 tff(26522,plain,
% 3.73/4.09 (~(s(s(elem!1)) = elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7595, 26521, 863])).
% 3.73/4.09 tff(26523,plain,
% 3.73/4.09 (r(s(s(elem!1)), elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[1260, 44, 26522, 26498])).
% 3.73/4.09 tff(26524,plain,
% 3.73/4.09 (b(s(s(elem!1)), z)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[5047, 26523, 26486, 26327])).
% 3.73/4.09 tff(26525,plain,
% 3.73/4.09 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7608, 26521, 706])).
% 3.73/4.09 tff(26526,plain,
% 3.73/4.09 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7776, 26525])).
% 3.73/4.09 tff(26527,plain,
% 3.73/4.09 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[8261, 333, 26486, 26523, 2484])).
% 3.73/4.09 tff(26528,plain,
% 3.73/4.09 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[7819, 44, 26527, 26526])).
% 3.73/4.09 tff(26529,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[8153, 144, 25683, 26528, 25633, 26524])).
% 3.73/4.09 tff(26530,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~b(s(elem!1), elem!1)) | (elem!1 = z) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26531,plain,
% 3.73/4.09 (elem!1 = s(elem!1)),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26530, 23280, 25308, 26313, 25621, 23272, 11546, 26320])).
% 3.73/4.09 tff(26532,plain,
% 3.73/4.09 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(elem!1))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26531])).
% 3.73/4.09 tff(26533,plain,
% 3.73/4.09 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), elem!1)),
% 3.73/4.09 inference(symmetry,[status(thm)],[26532])).
% 3.73/4.09 tff(26534,plain,
% 3.73/4.09 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), elem!1))),
% 3.73/4.09 inference(monotonicity,[status(thm)],[26533])).
% 3.73/4.09 tff(26535,plain,
% 3.73/4.09 ((~![X: $i] : (~b(X, X))) | (~b(s(elem!1), s(elem!1)))),
% 3.73/4.09 inference(quant_inst,[status(thm)],[])).
% 3.73/4.09 tff(26536,plain,
% 3.73/4.09 (~b(s(elem!1), s(elem!1))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26535, 5880])).
% 3.73/4.09 tff(26537,plain,
% 3.73/4.09 (~b(s(elem!1), elem!1)),
% 3.73/4.09 inference(modus_ponens,[status(thm)],[26536, 26534])).
% 3.73/4.09 tff(26538,plain,
% 3.73/4.09 ($false),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26313, 26537])).
% 3.73/4.09 tff(26539,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.09 tff(26540,plain,
% 3.73/4.09 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[26539, 2545])).
% 3.73/4.09 tff(26541,plain,
% 3.73/4.09 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[130, 54, 2545])).
% 3.73/4.09 tff(26542,plain,
% 3.73/4.09 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.09 inference(unit_resolution,[status(thm)],[23278, 26541])).
% 3.73/4.09 tff(26543,plain,
% 3.73/4.09 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[22697])).
% 3.73/4.10 tff(26544,plain,
% 3.73/4.10 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[4, 26543])).
% 3.73/4.10 tff(26545,plain,
% 3.73/4.10 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[14770, 22679, 286])).
% 3.73/4.10 tff(26546,plain,
% 3.73/4.10 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[22670])).
% 3.73/4.10 tff(26547,plain,
% 3.73/4.10 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26546])).
% 3.73/4.10 tff(26548,plain,
% 3.73/4.10 (~(s(z) = elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[344, 26547])).
% 3.73/4.10 tff(26549,plain,
% 3.73/4.10 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[22670])).
% 3.73/4.10 tff(26550,plain,
% 3.73/4.10 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26549])).
% 3.73/4.10 tff(26551,plain,
% 3.73/4.10 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[273, 26550])).
% 3.73/4.10 tff(26552,plain,
% 3.73/4.10 (~b(s(z), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[9955, 26551, 123, 54, 3])).
% 3.73/4.10 tff(26553,plain,
% 3.73/4.10 (r(s(z), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[406, 26552, 26548])).
% 3.73/4.10 tff(26554,plain,
% 3.73/4.10 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26549, 2544])).
% 3.73/4.10 tff(26555,plain,
% 3.73/4.10 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26554])).
% 3.73/4.10 tff(26556,plain,
% 3.73/4.10 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[273, 26555])).
% 3.73/4.10 tff(26557,plain,
% 3.73/4.10 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[121, 26556, 3])).
% 3.73/4.10 tff(26558,plain,
% 3.73/4.10 ((s(z) = z) <=> (elem!1 = s(z))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26546, 53])).
% 3.73/4.10 tff(26559,plain,
% 3.73/4.10 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26558])).
% 3.73/4.10 tff(26560,plain,
% 3.73/4.10 (~(elem!1 = s(z))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[344, 26559])).
% 3.73/4.10 tff(26561,plain,
% 3.73/4.10 (~b(elem!1, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[313, 304, 123, 26557])).
% 3.73/4.10 tff(26562,plain,
% 3.73/4.10 (r(elem!1, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[720, 26561, 26560])).
% 3.73/4.10 tff(26563,plain,
% 3.73/4.10 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18019])).
% 3.73/4.10 tff(26564,plain,
% 3.73/4.10 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26563, 203])).
% 3.73/4.10 tff(26565,plain,
% 3.73/4.10 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.73/4.10 inference(transitivity,[status(thm)],[26564, 24285])).
% 3.73/4.10 tff(26566,plain,
% 3.73/4.10 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26565])).
% 3.73/4.10 tff(26567,plain,
% 3.73/4.10 (~(s(s(s(s(z)))) = elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[242, 26566])).
% 3.73/4.10 tff(26568,plain,
% 3.73/4.10 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[25349, 18019])).
% 3.73/4.10 tff(26569,plain,
% 3.73/4.10 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[8677])).
% 3.73/4.10 tff(26570,plain,
% 3.73/4.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26569])).
% 3.73/4.10 tff(26571,plain,
% 3.73/4.10 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26570])).
% 3.73/4.10 tff(26572,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 3.73/4.10 tff(26573,plain,
% 3.73/4.10 ($false),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[9573, 144, 26572, 123, 304, 9725])).
% 3.73/4.10 tff(26574,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.10 tff(26575,plain,
% 3.73/4.10 (~b(s(s(s(s(z)))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26574, 9725, 304, 123])).
% 3.73/4.10 tff(26576,plain,
% 3.73/4.10 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26575, 26571])).
% 3.73/4.10 tff(26577,plain,
% 3.73/4.10 (r(s(s(s(s(z)))), s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[24448, 26576, 26568])).
% 3.73/4.10 tff(26578,plain,
% 3.73/4.10 (r(s(s(s(s(z)))), s(z))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26577, 25518])).
% 3.73/4.10 tff(26579,plain,
% 3.73/4.10 (((~![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(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(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.10 inference(rewrite,[status(thm)],[])).
% 3.73/4.10 tff(26580,plain,
% 3.73/4.10 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.10 inference(rewrite,[status(thm)],[])).
% 3.73/4.10 tff(26581,plain,
% 3.73/4.10 (((~![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(s(z)))), 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26580])).
% 3.73/4.10 tff(26582,plain,
% 3.73/4.10 (((~![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(s(z)))), 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26581, 26579])).
% 3.73/4.10 tff(26583,plain,
% 3.73/4.10 ((~![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(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.73/4.10 inference(quant_inst,[status(thm)],[])).
% 3.73/4.10 tff(26584,plain,
% 3.73/4.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26583, 26582])).
% 3.73/4.10 tff(26585,plain,
% 3.73/4.10 (~r(s(s(s(s(z)))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26584, 333, 409, 722, 26578])).
% 3.73/4.10 tff(26586,plain,
% 3.73/4.10 (b(s(s(s(s(z)))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[24299, 44, 26585, 26567])).
% 3.73/4.10 tff(26587,plain,
% 3.73/4.10 ($false),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[3552, 144, 26586, 133, 132, 9725])).
% 3.73/4.10 tff(26588,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.10 tff(26589,plain,
% 3.73/4.10 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26588, 26562, 123, 26557, 26553, 22669, 304, 26545])).
% 3.73/4.10 tff(26590,plain,
% 3.73/4.10 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[9761, 26589])).
% 3.73/4.10 tff(26591,plain,
% 3.73/4.10 (~b(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[22716, 26552, 22679])).
% 3.73/4.10 tff(26592,plain,
% 3.73/4.10 (r(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[348, 26591])).
% 3.73/4.10 tff(26593,plain,
% 3.73/4.10 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[22670])).
% 3.73/4.10 tff(26594,plain,
% 3.73/4.10 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26593])).
% 3.73/4.10 tff(26595,plain,
% 3.73/4.10 ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26594])).
% 3.73/4.10 tff(26596,plain,
% 3.73/4.10 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[3, 26595])).
% 3.73/4.10 tff(26597,plain,
% 3.73/4.10 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[279, 26596])).
% 3.73/4.10 tff(26598,plain,
% 3.73/4.10 (~b(z, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[757, 304, 123, 26597])).
% 3.73/4.10 tff(26599,plain,
% 3.73/4.10 (r(z, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[372, 26598])).
% 3.73/4.10 tff(26600,plain,
% 3.73/4.10 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[22669])).
% 3.73/4.10 tff(26601,plain,
% 3.73/4.10 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26600])).
% 3.73/4.10 tff(26602,plain,
% 3.73/4.10 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[123, 26601])).
% 3.73/4.10 tff(26603,plain,
% 3.73/4.10 (~b(s(elem!1), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[464, 26551, 54, 3, 26602])).
% 3.73/4.10 tff(26604,plain,
% 3.73/4.10 (~b(s(elem!1), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[25335, 26603, 22670])).
% 3.73/4.10 tff(26605,plain,
% 3.73/4.10 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 3.73/4.10 inference(transitivity,[status(thm)],[26546, 22692, 199])).
% 3.73/4.10 tff(26606,plain,
% 3.73/4.10 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26605])).
% 3.73/4.10 tff(26607,plain,
% 3.73/4.10 (~(s(elem!1) = elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[344, 26606])).
% 3.73/4.10 tff(26608,plain,
% 3.73/4.10 (r(s(elem!1), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[448, 26603, 26607])).
% 3.73/4.10 tff(26609,plain,
% 3.73/4.10 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18019])).
% 3.73/4.10 tff(26610,plain,
% 3.73/4.10 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 3.73/4.10 inference(symmetry,[status(thm)],[26609])).
% 3.73/4.10 tff(26611,plain,
% 3.73/4.10 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26610])).
% 3.73/4.10 tff(26612,plain,
% 3.73/4.10 (~r(z, elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[9917, 26611])).
% 3.73/4.10 tff(26613,plain,
% 3.73/4.10 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18019])).
% 3.73/4.10 tff(26614,plain,
% 3.73/4.10 ((s(z) = z) <=> (elem!1 = s(z))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26613, 53])).
% 3.73/4.10 tff(26615,plain,
% 3.73/4.10 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26614])).
% 3.73/4.10 tff(26616,plain,
% 3.73/4.10 (~(elem!1 = s(z))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[344, 26615])).
% 3.73/4.10 tff(26617,plain,
% 3.73/4.10 (~b(elem!1, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[313, 304, 123, 132])).
% 3.73/4.10 tff(26618,plain,
% 3.73/4.10 (r(elem!1, s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[720, 26617, 26616])).
% 3.73/4.10 tff(26619,plain,
% 3.73/4.10 (r(s(s(s(z))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[22912, 1699, 18019])).
% 3.73/4.10 tff(26620,plain,
% 3.73/4.10 (~r(s(elem!1), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1694, 26619, 435, 26618])).
% 3.73/4.10 tff(26621,plain,
% 3.73/4.10 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26613])).
% 3.73/4.10 tff(26622,plain,
% 3.73/4.10 (~(s(z) = elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[344, 26621])).
% 3.73/4.10 tff(26623,plain,
% 3.73/4.10 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18932, 466, 435, 1699, 1221, 959, 1249, 502, 1575, 706, 2725, 707])).
% 3.73/4.10 tff(26624,plain,
% 3.73/4.10 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[319, 26623])).
% 3.73/4.10 tff(26625,plain,
% 3.73/4.10 (b(s(s(z)), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18895, 18054, 1249])).
% 3.73/4.10 tff(26626,plain,
% 3.73/4.10 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18054])).
% 3.73/4.10 tff(26627,plain,
% 3.73/4.10 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26626])).
% 3.73/4.10 tff(26628,plain,
% 3.73/4.10 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[466, 26627])).
% 3.73/4.10 tff(26629,plain,
% 3.73/4.10 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[49, 26628])).
% 3.73/4.10 tff(26630,plain,
% 3.73/4.10 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1425, 26629, 304, 26625])).
% 3.73/4.10 tff(26631,plain,
% 3.73/4.10 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18054])).
% 3.73/4.10 tff(26632,plain,
% 3.73/4.10 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26631])).
% 3.73/4.10 tff(26633,plain,
% 3.73/4.10 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[25360])).
% 3.73/4.10 tff(26634,plain,
% 3.73/4.10 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26633])).
% 3.73/4.10 tff(26635,plain,
% 3.73/4.10 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26634, 26632])).
% 3.73/4.10 tff(26636,plain,
% 3.73/4.10 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26635])).
% 3.73/4.10 tff(26637,plain,
% 3.73/4.10 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18054])).
% 3.73/4.10 tff(26638,plain,
% 3.73/4.10 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26637])).
% 3.73/4.10 tff(26639,plain,
% 3.73/4.10 (~r(s(z), s(s(s(z))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[959, 26638])).
% 3.73/4.10 tff(26640,plain,
% 3.73/4.10 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26639, 26636])).
% 3.73/4.10 tff(26641,plain,
% 3.73/4.10 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[18054])).
% 3.73/4.10 tff(26642,plain,
% 3.73/4.10 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26641, 3061])).
% 3.73/4.10 tff(26643,plain,
% 3.73/4.10 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26642])).
% 3.73/4.10 tff(26644,plain,
% 3.73/4.10 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26643])).
% 3.73/4.10 tff(26645,plain,
% 3.73/4.10 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[1096, 26644])).
% 3.73/4.10 tff(26646,plain,
% 3.73/4.10 (b(s(elem!1), s(s(s(elem!1))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1067, 26645, 26640])).
% 3.73/4.10 tff(26647,plain,
% 3.73/4.10 (b(s(z), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[170, 44, 167, 26639])).
% 3.73/4.10 tff(26648,plain,
% 3.73/4.10 (~b(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18064, 66, 502])).
% 3.73/4.10 tff(26649,plain,
% 3.73/4.10 (r(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[348, 26648])).
% 3.73/4.10 tff(26650,plain,
% 3.73/4.10 (~r(s(s(s(z))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6555, 26649, 1699, 354])).
% 3.73/4.10 tff(26651,plain,
% 3.73/4.10 (b(s(s(s(z))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[2794, 26650])).
% 3.73/4.10 tff(26652,plain,
% 3.73/4.10 (~b(s(s(z)), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18116, 56, 8677, 1417, 10356])).
% 3.73/4.10 tff(26653,plain,
% 3.73/4.10 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18122, 26652, 8677])).
% 3.73/4.10 tff(26654,plain,
% 3.73/4.10 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[4311, 26653, 4620])).
% 3.73/4.10 tff(26655,plain,
% 3.73/4.10 (r(s(s(z)), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18132, 26654, 8677])).
% 3.73/4.10 tff(26656,plain,
% 3.73/4.10 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6352, 26655, 56, 1417, 123, 1699, 838])).
% 3.73/4.10 tff(26657,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[319, 26656])).
% 3.73/4.10 tff(26658,plain,
% 3.73/4.10 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18163, 26657, 2671, 26655])).
% 3.73/4.10 tff(26659,plain,
% 3.73/4.10 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1137, 26658])).
% 3.73/4.10 tff(26660,plain,
% 3.73/4.10 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[2262, 26659, 123, 838])).
% 3.73/4.10 tff(26661,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[249, 26660])).
% 3.73/4.10 tff(26662,plain,
% 3.73/4.10 ($false),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6350, 333, 1699, 2671, 26661, 26655])).
% 3.73/4.10 tff(26663,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~(s(elem!1) = s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.10 tff(26664,plain,
% 3.73/4.10 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26663, 26629, 1699, 26625, 26651, 26647, 18054, 4620, 26646])).
% 3.73/4.10 tff(26665,plain,
% 3.73/4.10 ($false),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1451, 26664, 26630])).
% 3.73/4.10 tff(26666,plain,((~(z = elem!1)) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(z)))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.10 tff(26667,plain,
% 3.73/4.10 (~(z = elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26666, 354, 6691, 304, 466, 959, 1699, 1249, 502])).
% 3.73/4.10 tff(26668,plain,
% 3.73/4.10 (b(z, elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[658, 26667, 1575])).
% 3.73/4.10 tff(26669,plain,
% 3.73/4.10 (~(elem!1 = z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[76, 26667])).
% 3.73/4.10 tff(26670,plain,
% 3.73/4.10 (b(elem!1, z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1380, 26669, 1378])).
% 3.73/4.10 tff(26671,plain,
% 3.73/4.10 (((~![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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(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(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 3.73/4.10 inference(rewrite,[status(thm)],[])).
% 3.73/4.10 tff(26672,plain,
% 3.73/4.10 ((~![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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 3.73/4.10 inference(quant_inst,[status(thm)],[])).
% 3.73/4.10 tff(26673,plain,
% 3.73/4.10 ((~![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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26672, 26671])).
% 3.73/4.10 tff(26674,plain,
% 3.73/4.10 (~r(s(s(s(z))), s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[26673, 333, 354, 12191, 1699])).
% 3.73/4.10 tff(26675,plain,
% 3.73/4.10 (~(s(elem!1) = s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[8683, 26667])).
% 3.73/4.10 tff(26676,plain,
% 3.73/4.10 (b(s(elem!1), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1653, 26675, 706, 1575, 902, 12191, 354])).
% 3.73/4.10 tff(26677,plain,
% 3.73/4.10 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6099, 26676, 304, 466, 1699, 354, 26674, 959])).
% 3.73/4.10 tff(26678,plain,
% 3.73/4.10 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[49, 26677])).
% 3.73/4.10 tff(26679,plain,
% 3.73/4.10 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[19019, 354, 26678, 18436, 26670, 26668])).
% 3.73/4.10 tff(26680,plain,
% 3.73/4.10 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[278, 26679, 274])).
% 3.73/4.10 tff(26681,plain,
% 3.73/4.10 (~b(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[19147, 26678, 26670, 304, 26668, 26680, 18388, 706])).
% 3.73/4.10 tff(26682,plain,
% 3.73/4.10 (r(s(z), z)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[348, 26681])).
% 3.73/4.10 tff(26683,plain,
% 3.73/4.10 (~r(s(s(s(z))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6555, 26682, 1699, 354])).
% 3.73/4.10 tff(26684,plain,
% 3.73/4.10 (b(s(s(s(z))), s(z))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[2794, 26683])).
% 3.73/4.10 tff(26685,plain,
% 3.73/4.10 (s(elem!1) = s(s(s(z)))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1716, 26684, 1699, 12191, 354, 26676, 26682])).
% 3.73/4.10 tff(26686,plain,
% 3.73/4.10 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26685])).
% 3.73/4.10 tff(26687,plain,
% 3.73/4.10 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26686])).
% 3.73/4.10 tff(26688,plain,
% 3.73/4.10 (s(s(z)) = elem!1),
% 3.73/4.10 inference(transitivity,[status(thm)],[87, 26687, 850])).
% 3.73/4.10 tff(26689,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26688])).
% 3.73/4.10 tff(26690,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26689])).
% 3.73/4.10 tff(26691,plain,
% 3.73/4.10 (elem!1 = s(s(z))),
% 3.73/4.10 inference(transitivity,[status(thm)],[1193, 26686, 86])).
% 3.73/4.10 tff(26692,plain,
% 3.73/4.10 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26691])).
% 3.73/4.10 tff(26693,plain,
% 3.73/4.10 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26692])).
% 3.73/4.10 tff(26694,plain,
% 3.73/4.10 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26688])).
% 3.73/4.10 tff(26695,plain,
% 3.73/4.10 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.73/4.10 inference(symmetry,[status(thm)],[26694])).
% 3.73/4.10 tff(26696,plain,
% 3.73/4.10 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26685])).
% 3.73/4.10 tff(26697,plain,
% 3.73/4.10 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 3.73/4.10 inference(transitivity,[status(thm)],[26696, 26695])).
% 3.73/4.10 tff(26698,plain,
% 3.73/4.10 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[990, 26685, 26675])).
% 3.73/4.10 tff(26699,plain,
% 3.73/4.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[12459, 26698])).
% 3.73/4.10 tff(26700,plain,
% 3.73/4.10 (~(s(z) = s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1228, 26675])).
% 3.73/4.10 tff(26701,plain,
% 3.73/4.10 (s(s(s(z))) = s(elem!1)),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26685, 998])).
% 3.73/4.10 tff(26702,plain,
% 3.73/4.10 (~(s(s(s(elem!1))) = elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1010, 26701])).
% 3.73/4.10 tff(26703,plain,
% 3.73/4.10 (~b(elem!1, s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[18357, 26702, 435, 354, 26700, 26670, 26676, 26668, 26682, 26699, 713])).
% 3.73/4.10 tff(26704,plain,
% 3.73/4.10 (r(elem!1, s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[560, 26703, 902])).
% 3.73/4.10 tff(26705,plain,
% 3.73/4.10 (r(s(s(z)), s(s(s(z))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26704, 26697])).
% 3.73/4.10 tff(26706,plain,
% 3.73/4.10 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 3.73/4.10 inference(monotonicity,[status(thm)],[26685])).
% 3.73/4.10 tff(26707,plain,
% 3.73/4.10 (~r(s(z), s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1235, 26682, 12191, 354])).
% 3.73/4.10 tff(26708,plain,
% 3.73/4.10 (b(s(z), s(elem!1))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1244, 26707, 26700])).
% 3.73/4.10 tff(26709,plain,
% 3.73/4.10 (b(s(z), s(s(s(z))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26708, 26706])).
% 3.73/4.10 tff(26710,plain,
% 3.73/4.10 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[6335, 144, 26684, 26709, 304])).
% 3.73/4.10 tff(26711,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[249, 26710])).
% 3.73/4.10 tff(26712,plain,
% 3.73/4.10 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[7412, 26711, 26705, 1699])).
% 3.73/4.10 tff(26713,plain,
% 3.73/4.10 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[1451, 26712])).
% 3.73/4.10 tff(26714,plain,
% 3.73/4.10 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26713, 26693])).
% 3.73/4.10 tff(26715,plain,
% 3.73/4.10 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[267, 26714, 26668, 26680])).
% 3.73/4.10 tff(26716,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.73/4.10 inference(unit_resolution,[status(thm)],[130, 26715, 18436])).
% 3.73/4.10 tff(26717,plain,
% 3.73/4.10 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.73/4.10 inference(modus_ponens,[status(thm)],[26716, 26690])).
% 3.73/4.10 tff(26718,plain,
% 3.73/4.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.73/4.10 inference(rewrite,[status(thm)],[])).
% 3.73/4.10 tff(26719,plain,
% 3.73/4.11 ((~![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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.73/4.11 inference(quant_inst,[status(thm)],[])).
% 3.73/4.11 tff(26720,plain,
% 3.73/4.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26719, 26718])).
% 3.73/4.11 tff(26721,plain,
% 3.73/4.11 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26720, 333, 1699, 26711, 26705])).
% 3.73/4.11 tff(26722,plain,
% 3.73/4.11 ($false),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26721, 26717])).
% 3.73/4.11 tff(26723,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(z)))) | r(z, elem!1) | r(elem!1, z) | (~b(s(s(elem!1)), s(elem!1))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.73/4.11 tff(26724,plain,
% 3.73/4.11 (~r(z, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26723, 26624, 1699, 13418, 435, 706, 466, 959, 1575, 18017, 1249, 502])).
% 3.73/4.11 tff(26725,plain,
% 3.73/4.11 (b(z, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[372, 26724])).
% 3.73/4.11 tff(26726,plain,
% 3.73/4.11 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[757, 123, 26624, 26725])).
% 3.73/4.11 tff(26727,plain,
% 3.73/4.11 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[278, 26726, 274])).
% 3.73/4.11 tff(26728,plain,
% 3.73/4.11 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[66])).
% 3.73/4.11 tff(26729,plain,
% 3.73/4.11 (b(elem!1, s(z))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[490, 26728])).
% 3.73/4.11 tff(26730,plain,
% 3.73/4.11 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[313, 26629, 304, 26729])).
% 3.73/4.11 tff(26731,plain,
% 3.73/4.11 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[121, 26730, 18388])).
% 3.73/4.11 tff(26732,plain,
% 3.73/4.11 (b(s(elem!1), s(s(s(elem!1))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1067, 26640, 26645])).
% 3.73/4.11 tff(26733,plain,
% 3.73/4.11 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1451, 26630])).
% 3.73/4.11 tff(26734,plain,
% 3.73/4.11 (~b(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26663, 26733, 1699, 26625, 26629, 26647, 18054, 4620, 26732])).
% 3.73/4.11 tff(26735,plain,
% 3.73/4.11 (r(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[2794, 26734])).
% 3.73/4.11 tff(26736,plain,
% 3.73/4.11 (r(s(z), elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[18039, 18054, 435])).
% 3.73/4.11 tff(26737,plain,
% 3.73/4.11 (((~![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))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.11 inference(rewrite,[status(thm)],[])).
% 3.73/4.11 tff(26738,plain,
% 3.73/4.11 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.11 inference(rewrite,[status(thm)],[])).
% 3.73/4.11 tff(26739,plain,
% 3.73/4.11 (((~![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(s(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26738])).
% 3.73/4.11 tff(26740,plain,
% 3.73/4.11 (((~![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(s(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.11 inference(transitivity,[status(thm)],[26739, 26737])).
% 3.73/4.11 tff(26741,plain,
% 3.73/4.11 ((~![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(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 3.73/4.11 inference(quant_inst,[status(thm)],[])).
% 3.73/4.11 tff(26742,plain,
% 3.73/4.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26741, 26740])).
% 3.73/4.11 tff(26743,plain,
% 3.73/4.11 ($false),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26742, 333, 26736, 26735, 707, 26731])).
% 3.73/4.11 tff(26744,plain,((~(z = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.11 tff(26745,plain,
% 3.73/4.11 (~(z = elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26744, 26624, 1699, 18053, 707, 466, 959, 26725, 1249, 435])).
% 3.73/4.11 tff(26746,plain,
% 3.73/4.11 (~(s(elem!1) = s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[8683, 26745])).
% 3.73/4.11 tff(26747,plain,
% 3.73/4.11 (~r(z, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26723, 304, 1699, 13418, 435, 706, 466, 959, 1575, 1378, 1249, 502])).
% 3.73/4.11 tff(26748,plain,
% 3.73/4.11 (b(z, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[372, 26747])).
% 3.73/4.11 tff(26749,plain,
% 3.73/4.11 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[18718, 323, 435, 1699, 26748, 2725, 1249, 706, 959, 1378, 1575, 502, 1221, 466, 1, 51])).
% 3.73/4.11 tff(26750,plain,
% 3.73/4.11 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[472, 26749, 466])).
% 3.73/4.11 tff(26751,plain,
% 3.73/4.11 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26750])).
% 3.73/4.11 tff(26752,plain,
% 3.73/4.11 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(elem!1), s(z))),
% 3.73/4.11 inference(symmetry,[status(thm)],[26751])).
% 3.73/4.11 tff(26753,plain,
% 3.73/4.11 (b(s(elem!1), s(z))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[304, 26752])).
% 3.73/4.11 tff(26754,plain,
% 3.73/4.11 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26750])).
% 3.73/4.11 tff(26755,plain,
% 3.73/4.11 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(elem!1))),
% 3.73/4.11 inference(symmetry,[status(thm)],[26754])).
% 3.73/4.11 tff(26756,plain,
% 3.73/4.11 (r(z, s(elem!1))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[51, 26755])).
% 3.73/4.11 tff(26757,plain,
% 3.73/4.11 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26750])).
% 3.73/4.11 tff(26758,plain,
% 3.73/4.11 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.73/4.11 inference(symmetry,[status(thm)],[26757])).
% 3.73/4.11 tff(26759,plain,
% 3.73/4.11 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26758])).
% 3.73/4.11 tff(26760,plain,
% 3.73/4.11 (~(s(elem!1) = s(s(s(z))))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[244, 26759])).
% 3.73/4.11 tff(26761,plain,
% 3.73/4.11 ($false),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[8142, 26760, 26756, 12191, 1699, 26753, 323])).
% 3.73/4.11 tff(26762,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = elem!1) | r(s(elem!1), s(s(s(z)))) | r(elem!1, z) | r(z, elem!1) | b(s(elem!1), z) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.11 tff(26763,plain,
% 3.73/4.11 (~r(s(z), z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26762, 26727, 1699, 26624, 466, 435, 2725, 1249, 706, 959, 18017, 1575, 502, 1221, 26746])).
% 3.73/4.11 tff(26764,plain,
% 3.73/4.11 (b(s(z), z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[348, 26763])).
% 3.73/4.11 tff(26765,plain,
% 3.73/4.11 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[7093, 26764, 26624, 26725])).
% 3.73/4.11 tff(26766,plain,
% 3.73/4.11 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[302, 26765])).
% 3.73/4.11 tff(26767,plain,
% 3.73/4.11 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[2251, 333, 1699, 26766, 26727])).
% 3.73/4.11 tff(26768,plain,
% 3.73/4.11 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1137, 26767])).
% 3.73/4.11 tff(26769,plain,
% 3.73/4.11 (~b(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[6004, 144, 123, 26768, 26624])).
% 3.73/4.11 tff(26770,plain,
% 3.73/4.11 (r(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[2794, 26769])).
% 3.73/4.11 tff(26771,plain,
% 3.73/4.11 (~(elem!1 = z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[76, 26745])).
% 3.73/4.11 tff(26772,plain,
% 3.73/4.11 (b(elem!1, z)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1380, 26771, 18017])).
% 3.73/4.11 tff(26773,plain,
% 3.73/4.11 (~b(elem!1, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[387, 144, 26772, 26725, 26764])).
% 3.73/4.11 tff(26774,plain,
% 3.73/4.11 (r(elem!1, s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[720, 26773, 713])).
% 3.73/4.11 tff(26775,plain,
% 3.73/4.11 (b(z, elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[658, 26745, 1575])).
% 3.73/4.11 tff(26776,plain,
% 3.73/4.11 (~b(s(z), elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1602, 26764, 26772, 26775])).
% 3.73/4.11 tff(26777,plain,
% 3.73/4.11 (r(s(z), elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[406, 26776, 706])).
% 3.73/4.11 tff(26778,plain,
% 3.73/4.11 ($false),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[9908, 333, 26777, 26774, 26770, 707])).
% 3.73/4.11 tff(26779,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (s(z) = elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | r(s(elem!1), s(s(s(z)))) | r(z, elem!1) | b(s(elem!1), z) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.73/4.11 tff(26780,plain,
% 3.73/4.11 (~b(s(s(elem!1)), s(elem!1))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26779, 26619, 123, 26622, 435, 23135, 466, 1699, 26620, 26612, 502, 22705])).
% 3.73/4.11 tff(26781,plain,
% 3.73/4.11 (r(s(s(elem!1)), s(elem!1))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1283, 26780, 22759])).
% 3.73/4.11 tff(26782,plain,
% 3.73/4.11 (r(s(s(z)), s(z))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26781, 22867])).
% 3.73/4.11 tff(26783,plain,
% 3.73/4.11 (((~![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(z)), 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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.73/4.11 inference(rewrite,[status(thm)],[])).
% 3.73/4.11 tff(26784,plain,
% 3.73/4.11 (((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.73/4.11 inference(rewrite,[status(thm)],[])).
% 3.73/4.11 tff(26785,plain,
% 3.73/4.11 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26784])).
% 3.73/4.11 tff(26786,plain,
% 3.73/4.11 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.73/4.11 inference(transitivity,[status(thm)],[26785, 26783])).
% 3.73/4.11 tff(26787,plain,
% 3.73/4.11 ((~![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(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 3.73/4.11 inference(quant_inst,[status(thm)],[])).
% 3.73/4.11 tff(26788,plain,
% 3.73/4.11 ((~![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(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26787, 26786])).
% 3.73/4.11 tff(26789,plain,
% 3.73/4.11 (~r(elem!1, s(s(z)))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[26788, 333, 409, 26618, 26782])).
% 3.73/4.11 tff(26790,plain,
% 3.73/4.11 (~r(elem!1, s(s(elem!1)))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26789, 22710])).
% 3.73/4.11 tff(26791,plain,
% 3.73/4.11 (b(elem!1, s(s(elem!1)))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[2522, 26790, 22705])).
% 3.73/4.11 tff(26792,plain,
% 3.73/4.11 (b(elem!1, s(s(z)))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[26791, 22760])).
% 3.73/4.11 tff(26793,plain,
% 3.73/4.11 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.73/4.11 inference(monotonicity,[status(thm)],[18019])).
% 3.73/4.11 tff(26794,plain,
% 3.73/4.11 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26793])).
% 3.73/4.11 tff(26795,plain,
% 3.73/4.11 (~(s(s(z)) = elem!1)),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[164, 26794])).
% 3.73/4.11 tff(26796,plain,
% 3.73/4.11 (~r(s(s(z)), elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[7974, 333, 409, 26618, 26782])).
% 3.73/4.11 tff(26797,plain,
% 3.73/4.11 (b(s(s(z)), elem!1)),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[7970, 26796, 26795])).
% 3.73/4.11 tff(26798,plain,
% 3.73/4.11 (~r(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[6555, 1699, 323, 354])).
% 3.73/4.11 tff(26799,plain,
% 3.73/4.11 (b(s(s(s(z))), s(z))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[2794, 26798])).
% 3.73/4.11 tff(26800,plain,
% 3.73/4.11 (~r(s(z), s(s(s(z))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[7314, 1699, 354, 323])).
% 3.73/4.11 tff(26801,plain,
% 3.73/4.11 (b(s(z), s(s(s(z))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[172, 26800])).
% 3.73/4.11 tff(26802,plain,
% 3.73/4.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[18125])).
% 3.73/4.11 tff(26803,plain,
% 3.73/4.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.73/4.11 inference(transitivity,[status(thm)],[26802, 15186])).
% 3.73/4.11 tff(26804,plain,
% 3.73/4.11 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.73/4.11 inference(monotonicity,[status(thm)],[26803])).
% 3.73/4.11 tff(26805,plain,
% 3.73/4.11 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.73/4.11 inference(modus_ponens,[status(thm)],[217, 26804])).
% 3.73/4.11 tff(26806,plain,
% 3.73/4.11 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1124, 144, 26799, 123, 304])).
% 3.73/4.11 tff(26807,plain,
% 3.73/4.11 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[1137, 26806])).
% 3.73/4.11 tff(26808,plain,
% 3.73/4.11 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[846, 26801, 304, 26799])).
% 3.73/4.11 tff(26809,plain,
% 3.73/4.11 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.73/4.11 inference(unit_resolution,[status(thm)],[249, 26808])).
% 3.73/4.11 tff(26810,plain,
% 3.73/4.11 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.73/4.11 inference(rewrite,[status(thm)],[])).
% 3.73/4.11 tff(26811,plain,
% 3.73/4.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.11 inference(monotonicity,[status(thm)],[26810])).
% 3.82/4.11 tff(26812,plain,
% 3.82/4.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.11 inference(transitivity,[status(thm)],[26811, 11645])).
% 3.82/4.11 tff(26813,plain,
% 3.82/4.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))),
% 3.82/4.11 inference(quant_inst,[status(thm)],[])).
% 3.82/4.11 tff(26814,plain,
% 3.82/4.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.11 inference(modus_ponens,[status(thm)],[26813, 26812])).
% 3.82/4.11 tff(26815,plain,
% 3.82/4.11 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.11 inference(unit_resolution,[status(thm)],[26814, 144, 133, 132, 26797])).
% 3.82/4.11 tff(26816,plain,
% 3.82/4.11 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.11 inference(unit_resolution,[status(thm)],[1451, 26815])).
% 3.82/4.11 tff(26817,plain,
% 3.82/4.11 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.11 inference(rewrite,[status(thm)],[])).
% 3.82/4.11 tff(26818,plain,
% 3.82/4.11 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.11 inference(rewrite,[status(thm)],[])).
% 3.82/4.11 tff(26819,plain,
% 3.82/4.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.11 inference(monotonicity,[status(thm)],[26818])).
% 3.82/4.11 tff(26820,plain,
% 3.82/4.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.11 inference(transitivity,[status(thm)],[26819, 26817])).
% 3.82/4.11 tff(26821,plain,
% 3.82/4.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26822,plain,
% 3.82/4.12 ((~![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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26821, 26820])).
% 3.82/4.12 tff(26823,plain,
% 3.82/4.12 (~r(s(s(s(z))), s(s(z)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26822, 333, 26816, 26809, 26807])).
% 3.82/4.12 tff(26824,plain,
% 3.82/4.12 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26823, 25412])).
% 3.82/4.12 tff(26825,plain,
% 3.82/4.12 (b(s(s(s(z))), s(s(elem!1)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[1301, 26824, 26805])).
% 3.82/4.12 tff(26826,plain,
% 3.82/4.12 (b(s(s(s(z))), s(s(z)))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26825, 22810])).
% 3.82/4.12 tff(26827,plain,
% 3.82/4.12 (~r(s(s(z)), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[7412, 26816, 26809, 1699])).
% 3.82/4.12 tff(26828,plain,
% 3.82/4.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[18132, 26827, 8677])).
% 3.82/4.12 tff(26829,plain,
% 3.82/4.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[4311, 26828, 22826])).
% 3.82/4.12 tff(26830,plain,
% 3.82/4.12 (b(s(s(z)), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[18122, 26829, 8677])).
% 3.82/4.12 tff(26831,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26832,plain,
% 3.82/4.12 (((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26833,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[26832])).
% 3.82/4.12 tff(26834,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.12 inference(transitivity,[status(thm)],[26833, 26831])).
% 3.82/4.12 tff(26835,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26836,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26835, 26834])).
% 3.82/4.12 tff(26837,plain,
% 3.82/4.12 (~b(elem!1, s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26836, 144, 26830, 26826, 26792])).
% 3.82/4.12 tff(26838,plain,
% 3.82/4.12 (r(elem!1, s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[1538, 26837, 22768])).
% 3.82/4.12 tff(26839,plain,
% 3.82/4.12 (((~![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(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))))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26840,plain,
% 3.82/4.12 ((~![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(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))))))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26841,plain,
% 3.82/4.12 ((~![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(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)))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26840, 26839])).
% 3.82/4.12 tff(26842,plain,
% 3.82/4.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26841, 333, 1525, 707, 9507])).
% 3.82/4.12 tff(26843,plain,
% 3.82/4.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[9821, 44, 219, 26842])).
% 3.82/4.12 tff(26844,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26845,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26846,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26845, 26844])).
% 3.82/4.12 tff(26847,plain,
% 3.82/4.12 ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26846, 333])).
% 3.82/4.12 tff(26848,plain,
% 3.82/4.12 (~r(s(s(s(s(z)))), s(z))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26847, 9507, 722, 409])).
% 3.82/4.12 tff(26849,plain,
% 3.82/4.12 (b(s(s(s(s(z)))), s(z))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[24600, 26848, 24294])).
% 3.82/4.12 tff(26850,plain,
% 3.82/4.12 ($false),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26041, 144, 56, 26849, 838, 26843])).
% 3.82/4.12 tff(26851,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.12 tff(26852,plain,
% 3.82/4.12 (~r(s(s(s(s(z)))), elem!1)),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26851, 26838, 26801, 26799, 26619, 26618, 409])).
% 3.82/4.12 tff(26853,plain,
% 3.82/4.12 (b(s(s(s(s(z)))), elem!1)),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[24301, 26852, 26567])).
% 3.82/4.12 tff(26854,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26855,plain,
% 3.82/4.12 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26856,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[26855])).
% 3.82/4.12 tff(26857,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.82/4.12 inference(transitivity,[status(thm)],[26856, 26854])).
% 3.82/4.12 tff(26858,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26859,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26858, 26857])).
% 3.82/4.12 tff(26860,plain,
% 3.82/4.12 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26859, 144, 26853, 26797, 26792])).
% 3.82/4.12 tff(26861,plain,
% 3.82/4.12 (r(s(s(s(s(z)))), s(s(z)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 26860])).
% 3.82/4.12 tff(26862,plain,
% 3.82/4.12 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.12 inference(symmetry,[status(thm)],[25413])).
% 3.82/4.12 tff(26863,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26864,plain,
% 3.82/4.12 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26865,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[26864])).
% 3.82/4.12 tff(26866,plain,
% 3.82/4.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.12 inference(transitivity,[status(thm)],[26865, 26863])).
% 3.82/4.12 tff(26867,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26868,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26867, 26866])).
% 3.82/4.12 tff(26869,plain,
% 3.82/4.12 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26868, 144, 133, 26797, 26792])).
% 3.82/4.12 tff(26870,plain,
% 3.82/4.12 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26869, 23138])).
% 3.82/4.12 tff(26871,plain,
% 3.82/4.12 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[2758, 26870, 23135])).
% 3.82/4.12 tff(26872,plain,
% 3.82/4.12 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26871, 26862])).
% 3.82/4.12 tff(26873,plain,
% 3.82/4.12 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26588, 26618, 123, 132, 409, 8677, 304, 133])).
% 3.82/4.12 tff(26874,plain,
% 3.82/4.12 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[9761, 26873])).
% 3.82/4.12 tff(26875,plain,
% 3.82/4.12 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26876,plain,
% 3.82/4.12 ((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.82/4.12 inference(quant_inst,[status(thm)],[])).
% 3.82/4.12 tff(26877,plain,
% 3.82/4.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26876, 26875])).
% 3.82/4.12 tff(26878,plain,
% 3.82/4.12 ($false),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26877, 333, 26816, 26874, 26872, 26861])).
% 3.82/4.12 tff(26879,plain,((~r(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), z) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.12 tff(26880,plain,
% 3.82/4.12 (~r(s(s(s(z))), z)),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26879, 304, 22669, 26545, 26557, 123, 26553, 26608, 466, 26604, 26599, 26592])).
% 3.82/4.12 tff(26881,plain,
% 3.82/4.12 (b(s(s(s(z))), z)),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[396, 26880])).
% 3.82/4.12 tff(26882,plain,
% 3.82/4.12 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 3.82/4.12 inference(monotonicity,[status(thm)],[66])).
% 3.82/4.12 tff(26883,plain,
% 3.82/4.12 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 3.82/4.12 inference(symmetry,[status(thm)],[26882])).
% 3.82/4.12 tff(26884,plain,
% 3.82/4.12 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[26883])).
% 3.82/4.12 tff(26885,plain,
% 3.82/4.12 (~b(s(s(s(z))), z)),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[55, 26884])).
% 3.82/4.12 tff(26886,plain,
% 3.82/4.12 ($false),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[285, 26885])).
% 3.82/4.12 tff(26887,plain,((~(z = elem!1)) | (~b(s(s(s(z))), z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.82/4.12 tff(26888,plain,
% 3.82/4.12 (b(s(s(s(z))), elem!1)),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[26887, 26881, 22670])).
% 3.82/4.12 tff(26889,plain,
% 3.82/4.12 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[10110, 26888, 3, 26551, 54])).
% 3.82/4.12 tff(26890,plain,
% 3.82/4.12 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[1137, 26889])).
% 3.82/4.12 tff(26891,plain,
% 3.82/4.12 (~b(elem!1, s(elem!1))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[18030, 26598, 22669])).
% 3.82/4.12 tff(26892,plain,
% 3.82/4.12 (~b(z, s(elem!1))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[18176, 26891, 22679])).
% 3.82/4.12 tff(26893,plain,
% 3.82/4.12 (r(z, s(elem!1))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[583, 26892])).
% 3.82/4.12 tff(26894,plain,
% 3.82/4.12 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[18019])).
% 3.82/4.12 tff(26895,plain,
% 3.82/4.12 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 3.82/4.12 inference(symmetry,[status(thm)],[26894])).
% 3.82/4.12 tff(26896,plain,
% 3.82/4.12 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 3.82/4.12 inference(transitivity,[status(thm)],[22983, 23014, 26895])).
% 3.82/4.12 tff(26897,plain,
% 3.82/4.12 (~b(z, s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[294, 283, 286, 285])).
% 3.82/4.12 tff(26898,plain,
% 3.82/4.12 (r(z, s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[619, 26897])).
% 3.82/4.12 tff(26899,plain,
% 3.82/4.12 (r(z, s(s(s(elem!1))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26898, 26896])).
% 3.82/4.12 tff(26900,plain,
% 3.82/4.12 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[13102, 26899, 435, 562])).
% 3.82/4.12 tff(26901,plain,
% 3.82/4.12 (b(s(s(s(elem!1))), s(elem!1))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[4697, 26900, 23041])).
% 3.82/4.12 tff(26902,plain,
% 3.82/4.12 (b(s(s(s(z))), s(z))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[23075, 26901, 8677])).
% 3.82/4.12 tff(26903,plain,
% 3.82/4.12 (~b(s(z), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[846, 26902, 304, 283])).
% 3.82/4.12 tff(26904,plain,
% 3.82/4.12 (r(s(z), s(s(s(z))))),
% 3.82/4.12 inference(unit_resolution,[status(thm)],[172, 26903])).
% 3.82/4.12 tff(26905,plain,
% 3.82/4.12 (r(elem!1, s(s(s(z))))),
% 3.82/4.12 inference(modus_ponens,[status(thm)],[26898, 22983])).
% 3.82/4.12 tff(26906,plain,
% 3.82/4.12 (((~![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(z), s(s(s(z))))) | (~r(s(s(s(z))), 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(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26907,plain,
% 3.82/4.12 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.12 inference(rewrite,[status(thm)],[])).
% 3.82/4.12 tff(26908,plain,
% 3.82/4.12 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.12 inference(monotonicity,[status(thm)],[26907])).
% 3.82/4.12 tff(26909,plain,
% 3.82/4.12 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.13 inference(transitivity,[status(thm)],[26908, 26906])).
% 3.82/4.13 tff(26910,plain,
% 3.82/4.13 ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 3.82/4.13 inference(quant_inst,[status(thm)],[])).
% 3.82/4.13 tff(26911,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26910, 26909])).
% 3.82/4.13 tff(26912,plain,
% 3.82/4.13 ($false),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26911, 333, 409, 26905, 26904, 6107])).
% 3.82/4.13 tff(26913,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.13 tff(26914,plain,
% 3.82/4.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26913, 26890, 26553, 304, 22669, 26608, 26893, 286, 26881])).
% 3.82/4.13 tff(26915,plain,
% 3.82/4.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[249, 26914])).
% 3.82/4.13 tff(26916,plain,
% 3.82/4.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[9817, 333, 26915, 26890, 26590])).
% 3.82/4.13 tff(26917,plain,
% 3.82/4.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[9821, 44, 219, 26916])).
% 3.82/4.13 tff(26918,plain,
% 3.82/4.13 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.82/4.13 inference(monotonicity,[status(thm)],[22670])).
% 3.82/4.13 tff(26919,plain,
% 3.82/4.13 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.82/4.13 inference(transitivity,[status(thm)],[26918, 203])).
% 3.82/4.13 tff(26920,plain,
% 3.82/4.13 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.82/4.13 inference(transitivity,[status(thm)],[26919, 24285])).
% 3.82/4.13 tff(26921,plain,
% 3.82/4.13 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.82/4.13 inference(monotonicity,[status(thm)],[26920])).
% 3.82/4.13 tff(26922,plain,
% 3.82/4.13 (~(s(s(s(s(z)))) = elem!1)),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[242, 26921])).
% 3.82/4.13 tff(26923,plain,
% 3.82/4.13 (~r(s(s(s(s(z)))), s(z))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26847, 9507, 26618, 409])).
% 3.82/4.13 tff(26924,plain,
% 3.82/4.13 (b(s(s(s(s(z)))), s(z))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[24600, 26923, 24294])).
% 3.82/4.13 tff(26925,plain,
% 3.82/4.13 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[14770, 22711, 286])).
% 3.82/4.13 tff(26926,plain,
% 3.82/4.13 (b(s(s(s(z))), elem!1)),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26887, 285, 18019])).
% 3.82/4.13 tff(26927,plain,
% 3.82/4.13 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1425, 1417, 123, 304])).
% 3.82/4.13 tff(26928,plain,
% 3.82/4.13 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1451, 26927])).
% 3.82/4.13 tff(26929,plain,
% 3.82/4.13 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26930,plain,
% 3.82/4.13 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26931,plain,
% 3.82/4.13 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.82/4.13 inference(monotonicity,[status(thm)],[26930])).
% 3.82/4.13 tff(26932,plain,
% 3.82/4.13 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(transitivity,[status(thm)],[26931, 26929])).
% 3.82/4.13 tff(26933,plain,
% 3.82/4.13 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(quant_inst,[status(thm)],[])).
% 3.82/4.13 tff(26934,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26933, 26932])).
% 3.82/4.13 tff(26935,plain,
% 3.82/4.13 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26934, 333, 26928, 224, 3559])).
% 3.82/4.13 tff(26936,plain,
% 3.82/4.13 (~r(s(s(z)), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1469, 333, 26928, 224, 6107])).
% 3.82/4.13 tff(26937,plain,
% 3.82/4.13 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[18132, 26936, 8677])).
% 3.82/4.13 tff(26938,plain,
% 3.82/4.13 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[4311, 26937, 22826])).
% 3.82/4.13 tff(26939,plain,
% 3.82/4.13 (b(s(s(z)), s(s(s(z))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[18122, 26938, 8677])).
% 3.82/4.13 tff(26940,plain,
% 3.82/4.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[9806, 333, 224, 6107, 3559])).
% 3.82/4.13 tff(26941,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 3.82/4.13 tff(26942,plain,
% 3.82/4.13 (s(s(s(s(z)))) = s(s(s(z)))),
% 3.82/4.13 inference(symmetry,[status(thm)],[26941])).
% 3.82/4.13 tff(26943,plain,
% 3.82/4.13 ($false),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[219, 26942])).
% 3.82/4.13 tff(26944,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.13 tff(26945,plain,
% 3.82/4.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26946,plain,
% 3.82/4.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 3.82/4.13 inference(quant_inst,[status(thm)],[])).
% 3.82/4.13 tff(26947,plain,
% 3.82/4.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26946, 26945])).
% 3.82/4.13 tff(26948,plain,
% 3.82/4.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 26940])).
% 3.82/4.13 tff(26949,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26950,plain,
% 3.82/4.13 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), 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(z))) | (~b(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(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26951,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 3.82/4.13 inference(monotonicity,[status(thm)],[26950])).
% 3.82/4.13 tff(26952,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.82/4.13 inference(transitivity,[status(thm)],[26951, 26949])).
% 3.82/4.13 tff(26953,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.82/4.13 inference(quant_inst,[status(thm)],[])).
% 3.82/4.13 tff(26954,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26953, 26952])).
% 3.82/4.13 tff(26955,plain,
% 3.82/4.13 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26954, 144, 1417, 26572, 26948])).
% 3.82/4.13 tff(26956,plain,
% 3.82/4.13 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26955, 26939])).
% 3.82/4.13 tff(26957,plain,
% 3.82/4.13 ($false),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[20473, 44, 25543, 26956, 26935])).
% 3.82/4.13 tff(26958,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.13 tff(26959,plain,
% 3.82/4.13 (~b(s(s(z)), s(z))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26958, 224, 8677, 26572, 26874, 6107, 123, 304])).
% 3.82/4.13 tff(26960,plain,
% 3.82/4.13 (~b(s(s(elem!1)), s(elem!1))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[18895, 26959, 8677])).
% 3.82/4.13 tff(26961,plain,
% 3.82/4.13 (r(s(s(elem!1)), s(elem!1))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1283, 26960, 22759])).
% 3.82/4.13 tff(26962,plain,
% 3.82/4.13 (r(s(s(z)), s(z))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26961, 22867])).
% 3.82/4.13 tff(26963,plain,
% 3.82/4.13 (~r(s(s(z)), elem!1)),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[7974, 333, 409, 26618, 26962])).
% 3.82/4.13 tff(26964,plain,
% 3.82/4.13 (b(s(s(z)), elem!1)),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[7970, 26963, 26795])).
% 3.82/4.13 tff(26965,plain,
% 3.82/4.13 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26814, 144, 133, 132, 26964])).
% 3.82/4.13 tff(26966,plain,
% 3.82/4.13 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1451, 26965])).
% 3.82/4.13 tff(26967,plain,
% 3.82/4.13 (~r(s(s(s(z))), s(s(z)))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26822, 333, 26966, 224, 6107])).
% 3.82/4.13 tff(26968,plain,
% 3.82/4.13 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26967, 25412])).
% 3.82/4.13 tff(26969,plain,
% 3.82/4.13 (~r(elem!1, s(s(z)))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26788, 333, 409, 26618, 26962])).
% 3.82/4.13 tff(26970,plain,
% 3.82/4.13 (~r(elem!1, s(s(elem!1)))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26969, 22710])).
% 3.82/4.13 tff(26971,plain,
% 3.82/4.13 (b(elem!1, s(s(elem!1)))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[2522, 26970, 22705])).
% 3.82/4.13 tff(26972,plain,
% 3.82/4.13 (b(elem!1, s(s(z)))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26971, 22760])).
% 3.82/4.13 tff(26973,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26974,plain,
% 3.82/4.13 (((~b(s(s(z)), elem!1)) | (~b(s(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(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.13 inference(rewrite,[status(thm)],[])).
% 3.82/4.13 tff(26975,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.82/4.13 inference(monotonicity,[status(thm)],[26974])).
% 3.82/4.13 tff(26976,plain,
% 3.82/4.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.82/4.13 inference(transitivity,[status(thm)],[26975, 26973])).
% 3.82/4.13 tff(26977,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(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)))),
% 3.82/4.13 inference(quant_inst,[status(thm)],[])).
% 3.82/4.13 tff(26978,plain,
% 3.82/4.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26977, 26976])).
% 3.82/4.13 tff(26979,plain,
% 3.82/4.13 (~b(s(s(s(z))), s(s(z)))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26978, 144, 4367, 26964, 26972])).
% 3.82/4.13 tff(26980,plain,
% 3.82/4.13 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.82/4.13 inference(modus_ponens,[status(thm)],[26979, 22812])).
% 3.82/4.13 tff(26981,plain,
% 3.82/4.13 (r(s(s(s(z))), s(s(elem!1)))),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[1301, 26980, 26805])).
% 3.82/4.13 tff(26982,plain,
% 3.82/4.13 ($false),
% 3.82/4.13 inference(unit_resolution,[status(thm)],[26981, 26968])).
% 3.82/4.13 tff(26983,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.14 tff(26984,plain,
% 3.82/4.14 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26983, 26924, 6107, 26926, 26925, 132, 409, 8677, 123, 304])).
% 3.82/4.14 tff(26985,plain,
% 3.82/4.14 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[249, 26984])).
% 3.82/4.14 tff(26986,plain,
% 3.82/4.14 (~b(z, s(s(s(z))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[294, 26985, 286, 285])).
% 3.82/4.14 tff(26987,plain,
% 3.82/4.14 (r(z, s(s(s(z))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[619, 26986])).
% 3.82/4.14 tff(26988,plain,
% 3.82/4.14 (r(elem!1, s(s(s(z))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[26987, 22983])).
% 3.82/4.14 tff(26989,plain,
% 3.82/4.14 (((~![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(z), s(s(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(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(26990,plain,
% 3.82/4.14 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(26991,plain,
% 3.82/4.14 (((~![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(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[26990])).
% 3.82/4.14 tff(26992,plain,
% 3.82/4.14 (((~![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(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~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), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.82/4.14 inference(transitivity,[status(thm)],[26991, 26989])).
% 3.82/4.14 tff(26993,plain,
% 3.82/4.14 ((~![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(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.82/4.14 inference(quant_inst,[status(thm)],[])).
% 3.82/4.14 tff(26994,plain,
% 3.82/4.14 ((~![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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[26993, 26992])).
% 3.82/4.14 tff(26995,plain,
% 3.82/4.14 (~r(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26994, 333, 409, 26988, 9507])).
% 3.82/4.14 tff(26996,plain,
% 3.82/4.14 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[19906, 44, 26995])).
% 3.82/4.14 tff(26997,plain,
% 3.82/4.14 (b(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26996, 25692])).
% 3.82/4.14 tff(26998,plain,
% 3.82/4.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[25729, 144, 26997, 26924, 304])).
% 3.82/4.14 tff(26999,plain,
% 3.82/4.14 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[12733, 44, 26998])).
% 3.82/4.14 tff(27000,plain,
% 3.82/4.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26999, 12723])).
% 3.82/4.14 tff(27001,plain,
% 3.82/4.14 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26588, 26618, 123, 132, 409, 8677, 304, 26925])).
% 3.82/4.14 tff(27002,plain,
% 3.82/4.14 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[9761, 27001])).
% 3.82/4.14 tff(27003,plain,
% 3.82/4.14 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27004,plain,
% 3.82/4.14 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27005,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[27004])).
% 3.82/4.14 tff(27006,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(transitivity,[status(thm)],[27005, 27003])).
% 3.82/4.14 tff(27007,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(quant_inst,[status(thm)],[])).
% 3.82/4.14 tff(27008,plain,
% 3.82/4.14 ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[27007, 27006])).
% 3.82/4.14 tff(27009,plain,
% 3.82/4.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27008, 333, 6107, 27002, 27000])).
% 3.82/4.14 tff(27010,plain,
% 3.82/4.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 27009])).
% 3.82/4.14 tff(27011,plain,
% 3.82/4.14 (r(z, s(s(s(elem!1))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[26987, 26896])).
% 3.82/4.14 tff(27012,plain,
% 3.82/4.14 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[13102, 27011, 435, 562])).
% 3.82/4.14 tff(27013,plain,
% 3.82/4.14 (b(s(s(s(elem!1))), s(elem!1))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[4697, 27012, 23041])).
% 3.82/4.14 tff(27014,plain,
% 3.82/4.14 (b(s(s(s(z))), s(z))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[23075, 27013, 8677])).
% 3.82/4.14 tff(27015,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27016,plain,
% 3.82/4.14 (((~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(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27017,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[27016])).
% 3.82/4.14 tff(27018,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(transitivity,[status(thm)],[27017, 27015])).
% 3.82/4.14 tff(27019,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(quant_inst,[status(thm)],[])).
% 3.82/4.14 tff(27020,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[27019, 27018])).
% 3.82/4.14 tff(27021,plain,
% 3.82/4.14 ($false),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27020, 144, 27014, 26997, 26924, 27010])).
% 3.82/4.14 tff(27022,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.14 tff(27023,plain,
% 3.82/4.14 (~r(s(s(s(s(z)))), elem!1)),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27022, 26890, 304, 26553, 22669, 26608, 26893, 286, 26881, 26557, 123])).
% 3.82/4.14 tff(27024,plain,
% 3.82/4.14 (b(s(s(s(s(z)))), elem!1)),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[24301, 27023, 26922])).
% 3.82/4.14 tff(27025,plain,
% 3.82/4.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[9806, 333, 26915, 26890, 26590])).
% 3.82/4.14 tff(27026,plain,
% 3.82/4.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 27025])).
% 3.82/4.14 tff(27027,plain,
% 3.82/4.14 (~b(s(s(s(s(z)))), s(z))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[26983, 26915, 26890, 26888, 26545, 26557, 26553, 22669, 123, 304])).
% 3.82/4.14 tff(27028,plain,
% 3.82/4.14 (r(s(s(s(s(z)))), s(z))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[24600, 27027, 24294])).
% 3.82/4.14 tff(27029,plain,
% 3.82/4.14 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[26919])).
% 3.82/4.14 tff(27030,plain,
% 3.82/4.14 (~(elem!1 = s(s(s(s(z)))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[242, 27029])).
% 3.82/4.14 tff(27031,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 3.82/4.14 tff(27032,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 3.82/4.14 tff(27033,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27034,plain,
% 3.82/4.14 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27035,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[27034])).
% 3.82/4.14 tff(27036,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.82/4.14 inference(transitivity,[status(thm)],[27035, 27033])).
% 3.82/4.14 tff(27037,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 3.82/4.14 inference(quant_inst,[status(thm)],[])).
% 3.82/4.14 tff(27038,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[27037, 27036])).
% 3.82/4.14 tff(27039,plain,
% 3.82/4.14 ($false),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27038, 144, 3529, 4367, 27032, 27031])).
% 3.82/4.14 tff(27040,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.14 tff(27041,plain,
% 3.82/4.14 (~b(elem!1, s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27040, 27024, 26888, 27026])).
% 3.82/4.14 tff(27042,plain,
% 3.82/4.14 (r(elem!1, s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[6873, 27041, 27030])).
% 3.82/4.14 tff(27043,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27044,plain,
% 3.82/4.14 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27045,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, 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(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[27044])).
% 3.82/4.14 tff(27046,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, 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(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.82/4.14 inference(transitivity,[status(thm)],[27045, 27043])).
% 3.82/4.14 tff(27047,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 3.82/4.14 inference(quant_inst,[status(thm)],[])).
% 3.82/4.14 tff(27048,plain,
% 3.82/4.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 3.82/4.14 inference(modus_ponens,[status(thm)],[27047, 27046])).
% 3.82/4.14 tff(27049,plain,
% 3.82/4.14 ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27048, 333])).
% 3.82/4.14 tff(27050,plain,
% 3.82/4.14 (~r(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27049, 27042, 26562, 27028])).
% 3.82/4.14 tff(27051,plain,
% 3.82/4.14 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[19906, 44, 27050])).
% 3.82/4.14 tff(27052,plain,
% 3.82/4.14 (b(s(z), s(s(s(s(z)))))),
% 3.82/4.14 inference(unit_resolution,[status(thm)],[27051, 25692])).
% 3.82/4.14 tff(27053,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27054,plain,
% 3.82/4.14 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.14 inference(rewrite,[status(thm)],[])).
% 3.82/4.14 tff(27055,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.82/4.14 inference(monotonicity,[status(thm)],[27054])).
% 3.82/4.14 tff(27056,plain,
% 3.82/4.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.82/4.15 inference(transitivity,[status(thm)],[27055, 27053])).
% 3.82/4.15 tff(27057,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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))))),
% 3.82/4.15 inference(quant_inst,[status(thm)],[])).
% 3.82/4.15 tff(27058,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[27057, 27056])).
% 3.82/4.15 tff(27059,plain,
% 3.82/4.15 (~b(s(s(s(z))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[27058, 144, 27052, 27024, 26888, 27026])).
% 3.82/4.15 tff(27060,plain,
% 3.82/4.15 (r(s(s(s(z))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[2794, 27059])).
% 3.82/4.15 tff(27061,plain,
% 3.82/4.15 (((~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(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.82/4.15 inference(rewrite,[status(thm)],[])).
% 3.82/4.15 tff(27062,plain,
% 3.82/4.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27061])).
% 3.82/4.15 tff(27063,plain,
% 3.82/4.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.82/4.15 inference(transitivity,[status(thm)],[27062, 26403])).
% 3.82/4.15 tff(27064,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.82/4.15 inference(quant_inst,[status(thm)],[])).
% 3.82/4.15 tff(27065,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[27064, 27063])).
% 3.82/4.15 tff(27066,plain,
% 3.82/4.15 (~b(s(z), s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[27065, 144, 27052, 26917, 27026])).
% 3.82/4.15 tff(27067,plain,
% 3.82/4.15 (r(s(z), s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[172, 27066])).
% 3.82/4.15 tff(27068,plain,
% 3.82/4.15 (~r(elem!1, s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[11876, 27067, 26553, 27060])).
% 3.82/4.15 tff(27069,plain,
% 3.82/4.15 (b(elem!1, s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[1538, 27068, 22674])).
% 3.82/4.15 tff(27070,plain,
% 3.82/4.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.82/4.15 inference(rewrite,[status(thm)],[])).
% 3.82/4.15 tff(27071,plain,
% 3.82/4.15 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.82/4.15 inference(rewrite,[status(thm)],[])).
% 3.82/4.15 tff(27072,plain,
% 3.82/4.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27071])).
% 3.82/4.15 tff(27073,plain,
% 3.82/4.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.82/4.15 inference(transitivity,[status(thm)],[27072, 27070])).
% 3.82/4.15 tff(27074,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.82/4.15 inference(quant_inst,[status(thm)],[])).
% 3.82/4.15 tff(27075,plain,
% 3.82/4.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[27074, 27073])).
% 3.82/4.15 tff(27076,plain,
% 3.82/4.15 ($false),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[27075, 144, 27069, 27024, 26888, 26917])).
% 3.82/4.15 tff(27077,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.15 tff(27078,plain,
% 3.82/4.15 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[27077, 3, 2097, 50, 54, 26544])).
% 3.82/4.15 tff(27079,plain,
% 3.82/4.15 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[319, 27078])).
% 3.82/4.15 tff(27080,plain,
% 3.82/4.15 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22669])).
% 3.82/4.15 tff(27081,plain,
% 3.82/4.15 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.82/4.15 inference(symmetry,[status(thm)],[27080])).
% 3.82/4.15 tff(27082,plain,
% 3.82/4.15 (s(s(elem!1)) = s(s(z))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22669])).
% 3.82/4.15 tff(27083,plain,
% 3.82/4.15 (s(s(z)) = s(s(elem!1))),
% 3.82/4.15 inference(symmetry,[status(thm)],[27082])).
% 3.82/4.15 tff(27084,plain,
% 3.82/4.15 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27083])).
% 3.82/4.15 tff(27085,plain,
% 3.82/4.15 ((~b(s(z), s(s(z)))) <=> (~b(s(z), s(s(elem!1))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27084])).
% 3.82/4.15 tff(27086,plain,
% 3.82/4.15 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27082])).
% 3.82/4.15 tff(27087,plain,
% 3.82/4.15 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27083])).
% 3.82/4.15 tff(27088,plain,
% 3.82/4.15 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.82/4.15 inference(transitivity,[status(thm)],[27087, 13328])).
% 3.82/4.15 tff(27089,plain,
% 3.82/4.15 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27088])).
% 3.82/4.15 tff(27090,plain,
% 3.82/4.15 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[1446, 27089])).
% 3.82/4.15 tff(27091,plain,
% 3.82/4.15 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[27077, 3, 2097, 123, 54, 466])).
% 3.82/4.15 tff(27092,plain,
% 3.82/4.15 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[319, 27091])).
% 3.82/4.15 tff(27093,plain,
% 3.82/4.15 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[23169, 27092, 22669])).
% 3.82/4.15 tff(27094,plain,
% 3.82/4.15 (r(s(elem!1), z)),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[507, 26604])).
% 3.82/4.15 tff(27095,plain,
% 3.82/4.15 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22669])).
% 3.82/4.15 tff(27096,plain,
% 3.82/4.15 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.82/4.15 inference(symmetry,[status(thm)],[27095])).
% 3.82/4.15 tff(27097,plain,
% 3.82/4.15 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27096])).
% 3.82/4.15 tff(27098,plain,
% 3.82/4.15 (~(s(s(elem!1)) = s(elem!1))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[107, 27097])).
% 3.82/4.15 tff(27099,plain,
% 3.82/4.15 (~b(s(s(s(z))), elem!1)),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[10110, 2254, 3, 26551, 54])).
% 3.82/4.15 tff(27100,plain,
% 3.82/4.15 (~b(s(s(s(z))), z)),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[26887, 27099, 22670])).
% 3.82/4.15 tff(27101,plain,
% 3.82/4.15 (r(s(s(s(z))), z)),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[396, 27100])).
% 3.82/4.15 tff(27102,plain,
% 3.82/4.15 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22670])).
% 3.82/4.15 tff(27103,plain,
% 3.82/4.15 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.82/4.15 inference(transitivity,[status(thm)],[27102, 1218])).
% 3.82/4.15 tff(27104,plain,
% 3.82/4.15 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27103])).
% 3.82/4.15 tff(27105,plain,
% 3.82/4.15 (~(elem!1 = s(s(elem!1)))),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[1094, 27104])).
% 3.82/4.15 tff(27106,plain,
% 3.82/4.15 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22670])).
% 3.82/4.15 tff(27107,plain,
% 3.82/4.15 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 3.82/4.15 inference(symmetry,[status(thm)],[27106])).
% 3.82/4.15 tff(27108,plain,
% 3.82/4.15 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27107])).
% 3.82/4.15 tff(27109,plain,
% 3.82/4.15 (~r(z, elem!1)),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[9917, 27108])).
% 3.82/4.15 tff(27110,plain,
% 3.82/4.15 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22670])).
% 3.82/4.15 tff(27111,plain,
% 3.82/4.15 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 3.82/4.15 inference(symmetry,[status(thm)],[27110])).
% 3.82/4.15 tff(27112,plain,
% 3.82/4.15 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27111])).
% 3.82/4.15 tff(27113,plain,
% 3.82/4.15 (~b(elem!1, z)),
% 3.82/4.15 inference(modus_ponens,[status(thm)],[5882, 27112])).
% 3.82/4.15 tff(27114,plain,
% 3.82/4.15 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[22669])).
% 3.82/4.15 tff(27115,plain,
% 3.82/4.15 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.82/4.15 inference(symmetry,[status(thm)],[27114])).
% 3.82/4.15 tff(27116,plain,
% 3.82/4.15 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 3.82/4.15 inference(monotonicity,[status(thm)],[27115])).
% 3.82/4.15 tff(27117,plain,
% 3.82/4.15 (r(s(s(s(z))), elem!1)),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[704, 27099, 22677])).
% 3.82/4.15 tff(27118,plain,
% 3.82/4.15 (~b(s(z), s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[2262, 283, 123, 2254])).
% 3.82/4.15 tff(27119,plain,
% 3.82/4.15 (r(s(z), s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[172, 27118])).
% 3.82/4.15 tff(27120,plain,
% 3.82/4.15 (~b(elem!1, s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[18960, 283, 132, 2254])).
% 3.82/4.15 tff(27121,plain,
% 3.82/4.15 (r(elem!1, s(s(s(z))))),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[1538, 27120, 1524])).
% 3.82/4.15 tff(27122,plain,
% 3.82/4.15 ($false),
% 3.82/4.15 inference(unit_resolution,[status(thm)],[7032, 333, 409, 27121, 707, 27119])).
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% 3.82/4.16 inference(unit_resolution,[status(thm)],[5352, 2812, 450, 132, 547])).
% 3.82/4.16 tff(27184,plain,
% 3.82/4.16 (r(s(s(elem!1)), s(elem!1))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1283, 27183, 2854])).
% 3.82/4.16 tff(27185,plain,
% 3.82/4.16 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[8422, 2812, 132, 450, 547])).
% 3.82/4.16 tff(27186,plain,
% 3.82/4.16 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[2758, 27185, 2725])).
% 3.82/4.16 tff(27187,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[8191, 27186, 27184, 509, 524])).
% 3.82/4.16 tff(27188,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27189,plain,
% 3.82/4.16 (~b(elem!1, s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27188, 27182, 27093, 27090, 27098, 26557, 26602, 27094])).
% 3.82/4.16 tff(27190,plain,
% 3.82/4.16 (r(elem!1, s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[2522, 27189, 27105])).
% 3.82/4.16 tff(27191,plain,
% 3.82/4.16 (~r(s(elem!1), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[5242, 27154, 26608, 27190])).
% 3.82/4.16 tff(27192,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27191, 27174])).
% 3.82/4.16 tff(27193,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), z) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27194,plain,
% 3.82/4.16 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27193, 26544, 50, 297, 3, 54])).
% 3.82/4.16 tff(27195,plain,
% 3.82/4.16 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1137, 27194])).
% 3.82/4.16 tff(27196,plain,
% 3.82/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[50, 26601])).
% 3.82/4.16 tff(27197,plain,
% 3.82/4.16 (~b(s(elem!1), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[464, 26551, 54, 3, 27196])).
% 3.82/4.16 tff(27198,plain,
% 3.82/4.16 (~b(s(elem!1), z)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[25335, 27197, 22670])).
% 3.82/4.16 tff(27199,plain,
% 3.82/4.16 (r(s(elem!1), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[448, 27197, 26607])).
% 3.82/4.16 tff(27200,plain,
% 3.82/4.16 (~b(s(z), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[9955, 26551, 50, 54, 3])).
% 3.82/4.16 tff(27201,plain,
% 3.82/4.16 (r(s(z), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[406, 27200, 26548])).
% 3.82/4.16 tff(27202,plain,
% 3.82/4.16 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[8677])).
% 3.82/4.16 tff(27203,plain,
% 3.82/4.16 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.82/4.16 inference(symmetry,[status(thm)],[27202])).
% 3.82/4.16 tff(27204,plain,
% 3.82/4.16 ((~b(s(z), s(s(z)))) <=> (~b(s(z), s(s(elem!1))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[22794])).
% 3.82/4.16 tff(27205,plain,
% 3.82/4.16 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[23169, 322, 8677])).
% 3.82/4.16 tff(27206,plain,
% 3.82/4.16 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[8677])).
% 3.82/4.16 tff(27207,plain,
% 3.82/4.16 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.82/4.16 inference(symmetry,[status(thm)],[27206])).
% 3.82/4.16 tff(27208,plain,
% 3.82/4.16 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[27207])).
% 3.82/4.16 tff(27209,plain,
% 3.82/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[8677])).
% 3.82/4.16 tff(27210,plain,
% 3.82/4.16 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(symmetry,[status(thm)],[27209])).
% 3.82/4.16 tff(27211,plain,
% 3.82/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[123, 27210])).
% 3.82/4.16 tff(27212,plain,
% 3.82/4.16 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 3.82/4.16 inference(transitivity,[status(thm)],[26613, 22748])).
% 3.82/4.16 tff(27213,plain,
% 3.82/4.16 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[27212])).
% 3.82/4.16 tff(27214,plain,
% 3.82/4.16 (~(elem!1 = s(elem!1))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[344, 27213])).
% 3.82/4.16 tff(27215,plain,
% 3.82/4.16 (~r(elem!1, s(z))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27144, 1699, 409, 322, 8677, 502, 466, 435, 132, 297, 26619])).
% 3.82/4.16 tff(27216,plain,
% 3.82/4.16 (~r(elem!1, s(elem!1))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27215, 23089])).
% 3.82/4.16 tff(27217,plain,
% 3.82/4.16 (b(elem!1, s(elem!1))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[560, 27216, 27214])).
% 3.82/4.16 tff(27218,plain,
% 3.82/4.16 (~b(elem!1, s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27188, 27217, 27205, 23135, 22759, 132, 27211, 12191])).
% 3.82/4.16 tff(27219,plain,
% 3.82/4.16 (r(elem!1, s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[2522, 27218, 22705])).
% 3.82/4.16 tff(27220,plain,
% 3.82/4.16 (r(z, s(s(z)))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27219, 23018])).
% 3.82/4.16 tff(27221,plain,
% 3.82/4.16 (r(elem!1, s(s(z)))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27220, 23017])).
% 3.82/4.16 tff(27222,plain,
% 3.82/4.16 (((~![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))), elem!1)) | (~r(s(z), s(s(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.82/4.16 inference(rewrite,[status(thm)],[])).
% 3.82/4.16 tff(27223,plain,
% 3.82/4.16 (((~r(elem!1, 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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.82/4.16 inference(rewrite,[status(thm)],[])).
% 3.82/4.16 tff(27224,plain,
% 3.82/4.16 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z))))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[27223])).
% 3.82/4.16 tff(27225,plain,
% 3.82/4.16 (((~![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(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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 3.82/4.16 inference(transitivity,[status(thm)],[27224, 27222])).
% 3.82/4.16 tff(27226,plain,
% 3.82/4.16 ((~![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(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 3.82/4.16 inference(quant_inst,[status(thm)],[])).
% 3.82/4.16 tff(27227,plain,
% 3.82/4.16 ((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27226, 27225])).
% 3.82/4.16 tff(27228,plain,
% 3.82/4.16 ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27227, 333, 409, 26619])).
% 3.82/4.16 tff(27229,plain,
% 3.82/4.16 (~r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27228, 27221])).
% 3.82/4.16 tff(27230,plain,
% 3.82/4.16 (~r(s(elem!1), s(s(s(z))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27229, 27208])).
% 3.82/4.16 tff(27231,plain,
% 3.82/4.16 (~b(s(s(elem!1)), s(elem!1))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[18297, 27230, 18046, 26612, 502, 466, 435, 22705, 1699, 297])).
% 3.82/4.16 tff(27232,plain,
% 3.82/4.16 (r(s(s(elem!1)), s(elem!1))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1283, 27231, 22759])).
% 3.82/4.16 tff(27233,plain,
% 3.82/4.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[8191, 27232, 12191, 27205])).
% 3.82/4.16 tff(27234,plain,
% 3.82/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[2758, 27233, 23135])).
% 3.82/4.16 tff(27235,plain,
% 3.82/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27234, 23136])).
% 3.82/4.16 tff(27236,plain,
% 3.82/4.16 (r(s(s(z)), s(z))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27232, 22867])).
% 3.82/4.16 tff(27237,plain,
% 3.82/4.16 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27139, 333, 409, 322, 27236])).
% 3.82/4.16 tff(27238,plain,
% 3.82/4.16 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1451, 27237])).
% 3.82/4.16 tff(27239,plain,
% 3.82/4.16 (~b(s(z), s(s(z)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27170, 144, 27238, 123, 27235])).
% 3.82/4.16 tff(27240,plain,
% 3.82/4.16 (~b(s(z), s(s(elem!1)))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27239, 27204])).
% 3.82/4.16 tff(27241,plain,
% 3.82/4.16 (r(s(z), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[5484, 27240])).
% 3.82/4.16 tff(27242,plain,
% 3.82/4.16 (r(s(elem!1), s(s(elem!1)))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[27241, 27203])).
% 3.82/4.16 tff(27243,plain,
% 3.82/4.16 (~r(s(elem!1), s(s(elem!1)))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[5242, 27232, 435, 27219])).
% 3.82/4.16 tff(27244,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27243, 27242])).
% 3.82/4.16 tff(27245,plain,((~r(s(s(s(z))), z)) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), elem!1)) | b(s(elem!1), z) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), z) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27246,plain,
% 3.82/4.16 (~r(s(s(s(z))), z)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27245, 22669, 50, 27201, 27079, 27199, 27198, 26544, 297, 26557])).
% 3.82/4.16 tff(27247,plain,
% 3.82/4.16 (b(s(s(s(z))), z)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[396, 27246])).
% 3.82/4.16 tff(27248,plain,
% 3.82/4.16 (b(s(s(s(z))), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[26887, 27247, 22670])).
% 3.82/4.16 tff(27249,plain,
% 3.82/4.16 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[14770, 22679, 2097])).
% 3.82/4.16 tff(27250,plain,
% 3.82/4.16 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[22669])).
% 3.82/4.16 tff(27251,plain,
% 3.82/4.16 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 3.82/4.16 inference(transitivity,[status(thm)],[27250, 3061])).
% 3.82/4.16 tff(27252,plain,
% 3.82/4.16 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.82/4.16 inference(symmetry,[status(thm)],[27251])).
% 3.82/4.16 tff(27253,plain,
% 3.82/4.16 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[27252])).
% 3.82/4.16 tff(27254,plain,
% 3.82/4.16 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[1096, 27253])).
% 3.82/4.16 tff(27255,plain,
% 3.82/4.16 (r(s(elem!1), z)),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[507, 27198])).
% 3.82/4.16 tff(27256,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[8740, 333, 409, 3193, 6107, 322])).
% 3.82/4.16 tff(27257,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27258,plain,
% 3.82/4.16 (~r(s(s(s(z))), s(z))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27257, 409, 6107, 322])).
% 3.82/4.16 tff(27259,plain,
% 3.82/4.16 (b(s(s(s(z))), s(z))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[2794, 27258])).
% 3.82/4.16 tff(27260,plain,
% 3.82/4.16 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[23038])).
% 3.82/4.16 tff(27261,plain,
% 3.82/4.16 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[1096, 27260])).
% 3.82/4.16 tff(27262,plain,
% 3.82/4.16 (b(elem!1, s(z))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[720, 715, 26616])).
% 3.82/4.16 tff(27263,plain,
% 3.82/4.16 (~b(elem!1, s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27148, 27262, 27259, 123, 132])).
% 3.82/4.16 tff(27264,plain,
% 3.82/4.16 (r(elem!1, s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1538, 27263, 22768])).
% 3.82/4.16 tff(27265,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[26911, 333, 409, 1525, 353, 6107])).
% 3.82/4.16 tff(27266,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27267,plain,
% 3.82/4.16 (~r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27266, 27264, 409, 6107])).
% 3.82/4.16 tff(27268,plain,
% 3.82/4.16 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[18102])).
% 3.82/4.16 tff(27269,plain,
% 3.82/4.16 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[8677])).
% 3.82/4.16 tff(27270,plain,
% 3.82/4.16 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(transitivity,[status(thm)],[27269, 27268])).
% 3.82/4.16 tff(27271,plain,
% 3.82/4.16 (r(s(z), s(s(s(z))))),
% 3.82/4.16 inference(modus_ponens,[status(thm)],[3541, 27270])).
% 3.82/4.16 tff(27272,plain,
% 3.82/4.16 ($false),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[155, 27271])).
% 3.82/4.16 tff(27273,plain,((~r(s(elem!1), s(s(s(elem!1))))) | r(s(z), s(s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.16 tff(27274,plain,
% 3.82/4.16 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[27273, 27267, 8677])).
% 3.82/4.16 tff(27275,plain,
% 3.82/4.16 (b(s(elem!1), s(s(s(elem!1))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1067, 27274, 27261])).
% 3.82/4.16 tff(27276,plain,
% 3.82/4.16 (~b(s(s(z)), s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[18116, 1417, 8677, 10356, 56])).
% 3.82/4.16 tff(27277,plain,
% 3.82/4.16 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[18122, 27276, 8677])).
% 3.82/4.16 tff(27278,plain,
% 3.82/4.16 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[4311, 27277, 22826])).
% 3.82/4.16 tff(27279,plain,
% 3.82/4.16 (r(s(s(z)), s(s(s(z))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[18132, 27278, 8677])).
% 3.82/4.16 tff(27280,plain,
% 3.82/4.16 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[18163, 27279, 322, 6107])).
% 3.82/4.16 tff(27281,plain,
% 3.82/4.16 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.16 inference(unit_resolution,[status(thm)],[1451, 27280])).
% 3.82/4.16 tff(27282,plain,
% 3.82/4.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.16 inference(rewrite,[status(thm)],[])).
% 3.82/4.16 tff(27283,plain,
% 3.82/4.16 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.16 inference(rewrite,[status(thm)],[])).
% 3.82/4.16 tff(27284,plain,
% 3.82/4.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.82/4.16 inference(monotonicity,[status(thm)],[27283])).
% 3.82/4.16 tff(27285,plain,
% 3.82/4.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.16 inference(transitivity,[status(thm)],[27284, 27282])).
% 3.82/4.16 tff(27286,plain,
% 3.82/4.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.16 inference(quant_inst,[status(thm)],[])).
% 3.82/4.16 tff(27287,plain,
% 3.82/4.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27286, 27285])).
% 3.82/4.17 tff(27288,plain,
% 3.82/4.17 (~b(s(s(z)), elem!1)),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27287, 144, 305, 1417, 27281, 133])).
% 3.82/4.17 tff(27289,plain,
% 3.82/4.17 (((~![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(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), 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)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27290,plain,
% 3.82/4.17 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27291,plain,
% 3.82/4.17 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[27290])).
% 3.82/4.17 tff(27292,plain,
% 3.82/4.17 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(transitivity,[status(thm)],[27291, 27289])).
% 3.82/4.17 tff(27293,plain,
% 3.82/4.17 ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 3.82/4.17 inference(quant_inst,[status(thm)],[])).
% 3.82/4.17 tff(27294,plain,
% 3.82/4.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27293, 27292])).
% 3.82/4.17 tff(27295,plain,
% 3.82/4.17 (~r(s(s(z)), elem!1)),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27294, 333, 1525, 6107, 27279])).
% 3.82/4.17 tff(27296,plain,
% 3.82/4.17 ($false),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[7970, 27295, 27288, 26795])).
% 3.82/4.17 tff(27297,plain,((~b(s(s(z)), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.17 tff(27298,plain,
% 3.82/4.17 (~b(s(s(z)), s(z))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27297, 27264, 6107, 27262, 133, 322, 8677, 27275, 27259])).
% 3.82/4.17 tff(27299,plain,
% 3.82/4.17 (~b(s(s(elem!1)), s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18895, 27298, 8677])).
% 3.82/4.17 tff(27300,plain,
% 3.82/4.17 (r(s(s(elem!1)), s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1283, 27299, 22759])).
% 3.82/4.17 tff(27301,plain,
% 3.82/4.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[8191, 27300, 509, 27205])).
% 3.82/4.17 tff(27302,plain,
% 3.82/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[2758, 27301, 23135])).
% 3.82/4.17 tff(27303,plain,
% 3.82/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27302, 23136])).
% 3.82/4.17 tff(27304,plain,
% 3.82/4.17 (r(s(s(z)), s(z))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27300, 22867])).
% 3.82/4.17 tff(27305,plain,
% 3.82/4.17 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27139, 333, 409, 322, 27304])).
% 3.82/4.17 tff(27306,plain,
% 3.82/4.17 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1451, 27305])).
% 3.82/4.17 tff(27307,plain,
% 3.82/4.17 (~b(s(z), s(s(z)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27170, 144, 27306, 123, 27303])).
% 3.82/4.17 tff(27308,plain,
% 3.82/4.17 (~b(s(z), s(s(elem!1)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27307, 27204])).
% 3.82/4.17 tff(27309,plain,
% 3.82/4.17 (r(s(z), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5484, 27308])).
% 3.82/4.17 tff(27310,plain,
% 3.82/4.17 (r(s(elem!1), s(s(elem!1)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27309, 27203])).
% 3.82/4.17 tff(27311,plain,
% 3.82/4.17 (~r(elem!1, s(elem!1))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[715, 23089])).
% 3.82/4.17 tff(27312,plain,
% 3.82/4.17 (b(elem!1, s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[560, 27311, 27214])).
% 3.82/4.17 tff(27313,plain,
% 3.82/4.17 (~b(elem!1, s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27188, 27312, 27205, 23135, 22759, 132, 27211, 509])).
% 3.82/4.17 tff(27314,plain,
% 3.82/4.17 (r(elem!1, s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[2522, 27313, 22705])).
% 3.82/4.17 tff(27315,plain,
% 3.82/4.17 (~r(s(elem!1), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5242, 27300, 435, 27314])).
% 3.82/4.17 tff(27316,plain,
% 3.82/4.17 ($false),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27315, 27310])).
% 3.82/4.17 tff(27317,plain,(r(elem!1, s(z)) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.17 tff(27318,plain,
% 3.82/4.17 (r(elem!1, s(z))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27317, 22669, 50, 27201, 27079, 27199, 27255, 27195, 27249, 26557])).
% 3.82/4.17 tff(27319,plain,
% 3.82/4.17 (r(z, s(z)) <=> r(z, s(elem!1))),
% 3.82/4.17 inference(symmetry,[status(thm)],[18136])).
% 3.82/4.17 tff(27320,plain,
% 3.82/4.17 (r(elem!1, s(z)) <=> r(z, s(elem!1))),
% 3.82/4.17 inference(transitivity,[status(thm)],[22948, 27319])).
% 3.82/4.17 tff(27321,plain,
% 3.82/4.17 (r(z, s(elem!1))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[722, 27320])).
% 3.82/4.17 tff(27322,plain,
% 3.82/4.17 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 3.82/4.17 inference(monotonicity,[status(thm)],[18019])).
% 3.82/4.17 tff(27323,plain,
% 3.82/4.17 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.82/4.17 inference(symmetry,[status(thm)],[27322])).
% 3.82/4.17 tff(27324,plain,
% 3.82/4.17 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 3.82/4.17 inference(monotonicity,[status(thm)],[18101])).
% 3.82/4.17 tff(27325,plain,
% 3.82/4.17 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.82/4.17 inference(symmetry,[status(thm)],[27324])).
% 3.82/4.17 tff(27326,plain,
% 3.82/4.17 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.82/4.17 inference(transitivity,[status(thm)],[27325, 27323])).
% 3.82/4.17 tff(27327,plain,
% 3.82/4.17 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[27326])).
% 3.82/4.17 tff(27328,plain,
% 3.82/4.17 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18132, 19957, 8677])).
% 3.82/4.17 tff(27329,plain,
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[4311, 27328, 22826])).
% 3.82/4.17 tff(27330,plain,
% 3.82/4.17 (b(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18122, 27329, 8677])).
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% 3.82/4.17 (~b(s(s(z)), s(z))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18116, 27330, 8677, 10356, 27259])).
% 3.82/4.17 tff(27332,plain,
% 3.82/4.17 (~b(s(s(elem!1)), s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18895, 27331, 8677])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[1283, 27332, 22759])).
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% 3.82/4.17 inference(modus_ponens,[status(thm)],[27333, 22867])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[27139, 333, 409, 2671, 322, 27334])).
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% 3.82/4.17 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27336, 10356, 322, 8677, 409, 6107])).
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% 3.82/4.17 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1451, 27337])).
% 3.82/4.17 tff(27339,plain,
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% 3.82/4.17 inference(modus_ponens,[status(thm)],[27339, 27327])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[5509, 27340])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[5505, 27341, 27321, 435])).
% 3.82/4.17 tff(27343,plain,
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[1283, 27342, 22759])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[18895, 27343, 8677])).
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% 3.82/4.17 (~b(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18116, 27344, 8677, 10356, 27259])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[18122, 27345, 8677])).
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% 3.82/4.17 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[4311, 27346, 22826])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[18132, 27347, 8677])).
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[7970, 27339, 26795])).
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% 3.82/4.17 inference(monotonicity,[status(thm)],[18019])).
% 3.82/4.17 tff(27351,plain,
% 3.82/4.17 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 3.82/4.17 inference(symmetry,[status(thm)],[27350])).
% 3.82/4.17 tff(27352,plain,
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% 3.82/4.17 inference(modus_ponens,[status(thm)],[2082, 27351])).
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% 3.82/4.17 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[18101])).
% 3.82/4.17 tff(27354,plain,
% 3.82/4.17 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[27353])).
% 3.82/4.17 tff(27355,plain,
% 3.82/4.17 (~b(s(s(z)), s(z))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18116, 7943, 8677, 10356, 56])).
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% 3.82/4.17 (~b(s(s(elem!1)), s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18895, 27355, 8677])).
% 3.82/4.17 tff(27357,plain,
% 3.82/4.17 (r(s(s(elem!1)), s(elem!1))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1283, 27356, 22759])).
% 3.82/4.17 tff(27358,plain,
% 3.82/4.17 (~r(s(s(elem!1)), z)),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5505, 27357, 562, 435])).
% 3.82/4.17 tff(27359,plain,
% 3.82/4.17 (b(s(s(elem!1)), z)),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5509, 27358])).
% 3.82/4.17 tff(27360,plain,
% 3.82/4.17 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5708, 27359, 285, 284])).
% 3.82/4.17 tff(27361,plain,
% 3.82/4.17 (~b(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27360, 27354])).
% 3.82/4.17 tff(27362,plain,
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[7943, 27361])).
% 3.82/4.17 tff(27363,plain,((~b(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.17 tff(27364,plain,
% 3.82/4.17 (~b(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27363, 27352, 285, 8677, 27321, 435, 10356, 27259])).
% 3.82/4.17 tff(27365,plain,
% 3.82/4.17 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18122, 27364, 8677])).
% 3.82/4.17 tff(27366,plain,
% 3.82/4.17 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[4311, 27365, 22826])).
% 3.82/4.17 tff(27367,plain,
% 3.82/4.17 (r(s(s(z)), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18132, 27366, 8677])).
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% 3.82/4.17 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[18163, 27367, 322, 6107])).
% 3.82/4.17 tff(27369,plain,
% 3.82/4.17 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1451, 27368])).
% 3.82/4.17 tff(27370,plain,
% 3.82/4.17 (~b(s(s(z)), elem!1)),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[11650, 144, 27369, 133, 132])).
% 3.82/4.17 tff(27371,plain,
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% 3.82/4.17 inference(unit_resolution,[status(thm)],[7970, 27370, 26795])).
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% 3.82/4.17 (((~![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(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27373,plain,
% 3.82/4.17 (((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27374,plain,
% 3.82/4.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[27373])).
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% 3.82/4.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(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(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.82/4.17 inference(transitivity,[status(thm)],[27374, 27372])).
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% 3.82/4.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.82/4.17 inference(quant_inst,[status(thm)],[])).
% 3.82/4.17 tff(27377,plain,
% 3.82/4.17 ((~![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(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27376, 27375])).
% 3.82/4.17 tff(27378,plain,
% 3.82/4.17 (~r(s(z), s(s(z)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27377, 333, 409, 722, 27371])).
% 3.82/4.17 tff(27379,plain,
% 3.82/4.17 (~r(s(z), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[22807, 27378, 8677])).
% 3.82/4.17 tff(27380,plain,
% 3.82/4.17 (b(s(z), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[5484, 27379])).
% 3.82/4.17 tff(27381,plain,
% 3.82/4.17 (b(s(z), s(s(z)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27380, 22795])).
% 3.82/4.17 tff(27382,plain,
% 3.82/4.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[11026, 144, 2082, 133, 26926])).
% 3.82/4.17 tff(27383,plain,
% 3.82/4.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[249, 27382])).
% 3.82/4.17 tff(27384,plain,
% 3.82/4.17 (((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27385,plain,
% 3.82/4.17 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(rewrite,[status(thm)],[])).
% 3.82/4.17 tff(27386,plain,
% 3.82/4.17 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(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(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.17 inference(monotonicity,[status(thm)],[27385])).
% 3.82/4.17 tff(27387,plain,
% 3.82/4.17 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(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(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.17 inference(transitivity,[status(thm)],[27386, 27384])).
% 3.82/4.17 tff(27388,plain,
% 3.82/4.17 ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.82/4.17 inference(quant_inst,[status(thm)],[])).
% 3.82/4.17 tff(27389,plain,
% 3.82/4.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27388, 27387])).
% 3.82/4.17 tff(27390,plain,
% 3.82/4.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27389, 333, 27383, 6107, 27367])).
% 3.82/4.17 tff(27391,plain,
% 3.82/4.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27390, 25414])).
% 3.82/4.17 tff(27392,plain,
% 3.82/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[2758, 27391, 23135])).
% 3.82/4.17 tff(27393,plain,
% 3.82/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.82/4.17 inference(modus_ponens,[status(thm)],[27392, 23136])).
% 3.82/4.17 tff(27394,plain,
% 3.82/4.17 (~b(s(z), s(s(z)))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27170, 144, 27369, 123, 27393])).
% 3.82/4.17 tff(27395,plain,
% 3.82/4.17 ($false),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27394, 27381])).
% 3.82/4.17 tff(27396,plain,((~b(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.17 tff(27397,plain,
% 3.82/4.17 (~b(elem!1, s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27396, 10356, 123, 409, 722, 6107, 133, 132, 322, 285, 435, 8677])).
% 3.82/4.17 tff(27398,plain,
% 3.82/4.17 (r(elem!1, s(s(s(z))))),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[1538, 27397, 22768])).
% 3.82/4.17 tff(27399,plain,
% 3.82/4.17 ($false),
% 3.82/4.17 inference(unit_resolution,[status(thm)],[27294, 333, 27398, 6107, 27349, 27348])).
% 3.82/4.17 tff(27400,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.17 tff(27401,plain,
% 3.82/4.17 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27400, 27195, 22669, 27199, 27249, 26557, 27079, 27201, 50, 27318, 27247])).
% 3.82/4.18 tff(27402,plain,
% 3.82/4.18 (r(s(elem!1), s(s(s(elem!1))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1067, 27401, 27254])).
% 3.82/4.18 tff(27403,plain,
% 3.82/4.18 (r(s(z), s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27273, 27402, 22669])).
% 3.82/4.18 tff(27404,plain,
% 3.82/4.18 (~r(elem!1, s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27266, 27403, 27201, 27195])).
% 3.82/4.18 tff(27405,plain,
% 3.82/4.18 (b(elem!1, s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1538, 27404, 22674])).
% 3.82/4.18 tff(27406,plain,
% 3.82/4.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[11026, 144, 27405, 27249, 27248])).
% 3.82/4.18 tff(27407,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[249, 27406])).
% 3.82/4.18 tff(27408,plain,
% 3.82/4.18 (((~![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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.18 inference(rewrite,[status(thm)],[])).
% 3.82/4.18 tff(27409,plain,
% 3.82/4.18 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.18 inference(rewrite,[status(thm)],[])).
% 3.82/4.18 tff(27410,plain,
% 3.82/4.18 (((~![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(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27409])).
% 3.82/4.18 tff(27411,plain,
% 3.82/4.18 (((~![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(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.18 inference(transitivity,[status(thm)],[27410, 27408])).
% 3.82/4.18 tff(27412,plain,
% 3.82/4.18 ((~![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(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.82/4.18 inference(quant_inst,[status(thm)],[])).
% 3.82/4.18 tff(27413,plain,
% 3.82/4.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27412, 27411])).
% 3.82/4.18 tff(27414,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27413, 333, 27403, 27407, 27195, 27079])).
% 3.82/4.18 tff(27415,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27416,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27415, 26542, 54, 26540])).
% 3.82/4.18 tff(27417,plain,
% 3.82/4.18 (s(elem!1) = s(z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[22668, 26542])).
% 3.82/4.18 tff(27418,plain,
% 3.82/4.18 (z = elem!1),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[8683, 27417])).
% 3.82/4.18 tff(27419,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[22687, 27418, 27416, 54])).
% 3.82/4.18 tff(27420,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27421,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27420, 54])).
% 3.82/4.18 tff(27422,plain,
% 3.82/4.18 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[846, 838, 56, 283])).
% 3.82/4.18 tff(27423,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[319, 27422])).
% 3.82/4.18 tff(27424,plain,
% 3.82/4.18 (~r(s(z), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[18406, 27423, 11546, 23943])).
% 3.82/4.18 tff(27425,plain,
% 3.82/4.18 (~r(elem!1, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[18836, 333, 11546, 23943, 27423])).
% 3.82/4.18 tff(27426,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.82/4.18 inference(symmetry,[status(thm)],[9415])).
% 3.82/4.18 tff(27427,plain,
% 3.82/4.18 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27426])).
% 3.82/4.18 tff(27428,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 3.82/4.18 tff(27429,plain,
% 3.82/4.18 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27428, 27427])).
% 3.82/4.18 tff(27430,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[133, 27429])).
% 3.82/4.18 tff(27431,plain,((~(elem!1 = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27432,plain,
% 3.82/4.18 (~(elem!1 = s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27431, 27422, 133])).
% 3.82/4.18 tff(27433,plain,
% 3.82/4.18 (b(elem!1, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[720, 27432, 27425])).
% 3.82/4.18 tff(27434,plain,
% 3.82/4.18 (~(s(z) = elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[6528, 27433])).
% 3.82/4.18 tff(27435,plain,
% 3.82/4.18 (b(s(z), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[406, 27434, 27424])).
% 3.82/4.18 tff(27436,plain,
% 3.82/4.18 (~r(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[2331, 51, 322, 2323])).
% 3.82/4.18 tff(27437,plain,
% 3.82/4.18 (b(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1380, 27436, 730])).
% 3.82/4.18 tff(27438,plain,
% 3.82/4.18 (~r(z, elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[2541, 51, 322, 2323])).
% 3.82/4.18 tff(27439,plain,
% 3.82/4.18 (b(z, elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[658, 27438, 74])).
% 3.82/4.18 tff(27440,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1602, 23891, 27439, 134, 27437])).
% 3.82/4.18 tff(27441,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27442,plain,
% 3.82/4.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27441, 27435, 71, 11546, 27423, 23943])).
% 3.82/4.18 tff(27443,plain,
% 3.82/4.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[279, 27442])).
% 3.82/4.18 tff(27444,plain,
% 3.82/4.18 (~b(s(s(s(z))), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[4375, 27435, 56, 27433])).
% 3.82/4.18 tff(27445,plain,
% 3.82/4.18 (elem!1 = s(s(s(z)))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[78, 2])).
% 3.82/4.18 tff(27446,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1524, 27445])).
% 3.82/4.18 tff(27447,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27448,plain,
% 3.82/4.18 (elem!1 = s(s(s(z)))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27447, 78])).
% 3.82/4.18 tff(27449,plain,
% 3.82/4.18 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27448])).
% 3.82/4.18 tff(27450,plain,
% 3.82/4.18 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[23943, 27449])).
% 3.82/4.18 tff(27451,plain,
% 3.82/4.18 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[26043, 27450, 11546, 56, 322, 838])).
% 3.82/4.18 tff(27452,plain,
% 3.82/4.18 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[9761, 27451])).
% 3.82/4.18 tff(27453,plain,
% 3.82/4.18 (~r(s(z), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[18406, 322, 11546, 23943])).
% 3.82/4.18 tff(27454,plain,
% 3.82/4.18 (b(s(z), elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[406, 6529, 27453])).
% 3.82/4.18 tff(27455,plain,
% 3.82/4.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27441, 27454, 71, 11546, 322, 23943])).
% 3.82/4.18 tff(27456,plain,
% 3.82/4.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[279, 27455])).
% 3.82/4.18 tff(27457,plain,
% 3.82/4.18 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27448])).
% 3.82/4.18 tff(27458,plain,
% 3.82/4.18 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 3.82/4.18 inference(symmetry,[status(thm)],[27457])).
% 3.82/4.18 tff(27459,plain,
% 3.82/4.18 (s(elem!1) = s(s(s(s(z))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27448])).
% 3.82/4.18 tff(27460,plain,
% 3.82/4.18 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27459])).
% 3.82/4.18 tff(27461,plain,
% 3.82/4.18 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.82/4.18 inference(symmetry,[status(thm)],[27460])).
% 3.82/4.18 tff(27462,plain,
% 3.82/4.18 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 3.82/4.18 inference(transitivity,[status(thm)],[27461, 27458])).
% 3.82/4.18 tff(27463,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.82/4.18 tff(27464,plain,
% 3.82/4.18 (r(s(elem!1), elem!1)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27463, 27462])).
% 3.82/4.18 tff(27465,plain,
% 3.82/4.18 (r(s(elem!1), s(s(s(z))))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27463, 27461])).
% 3.82/4.18 tff(27466,plain,
% 3.82/4.18 (~(s(s(elem!1)) = elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[7595, 78, 25410])).
% 3.82/4.18 tff(27467,plain,
% 3.82/4.18 (~(elem!1 = s(s(elem!1)))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[5603, 27466])).
% 3.82/4.18 tff(27468,plain,
% 3.82/4.18 (~(s(elem!1) = elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[5813, 27467])).
% 3.82/4.18 tff(27469,plain,
% 3.82/4.18 (~(elem!1 = s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1569, 27468])).
% 3.82/4.18 tff(27470,plain,
% 3.82/4.18 (~b(z, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[7079, 13636, 305, 134])).
% 3.82/4.18 tff(27471,plain,
% 3.82/4.18 (r(z, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[372, 27470])).
% 3.82/4.18 tff(27472,plain,
% 3.82/4.18 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[24033, 1575, 11546, 23943, 71, 305])).
% 3.82/4.18 tff(27473,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[302, 27472])).
% 3.82/4.18 tff(27474,plain,
% 3.82/4.18 (b(s(s(s(s(z)))), z)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[491, 19698])).
% 3.82/4.18 tff(27475,plain,
% 3.82/4.18 (~b(s(s(s(s(z)))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[19705, 144, 286, 259, 9725])).
% 3.82/4.18 tff(27476,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27475, 27474])).
% 3.82/4.18 tff(27477,plain,((~b(s(elem!1), z)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27478,plain,
% 3.82/4.18 (~b(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27477, 27473, 3238, 259, 9725])).
% 3.82/4.18 tff(27479,plain,
% 3.82/4.18 (r(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[507, 27478])).
% 3.82/4.18 tff(27480,plain,
% 3.82/4.18 (~b(s(elem!1), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[10646, 27479, 435, 408, 134, 13636])).
% 3.82/4.18 tff(27481,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1653, 27480, 27479, 1, 6529, 1575, 27471, 902])).
% 3.82/4.18 tff(27482,plain,(r(z, elem!1) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27483,plain,
% 3.82/4.18 (r(z, elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27482, 2322, 27469, 435, 1, 134, 27448, 259, 9725, 305, 11546])).
% 3.82/4.18 tff(27484,plain,
% 3.82/4.18 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[3282, 27483, 2322, 23943])).
% 3.82/4.18 tff(27485,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[302, 27484])).
% 3.82/4.18 tff(27486,plain,
% 3.82/4.18 (~b(s(s(s(z))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[380, 377, 78])).
% 3.82/4.18 tff(27487,plain,
% 3.82/4.18 (r(s(s(s(z))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[396, 27486])).
% 3.82/4.18 tff(27488,plain,
% 3.82/4.18 (~r(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[5835, 27483, 1686, 27487])).
% 3.82/4.18 tff(27489,plain,
% 3.82/4.18 (b(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[507, 27488])).
% 3.82/4.18 tff(27490,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27477, 27489, 27485, 27448, 259, 9725])).
% 3.82/4.18 tff(27491,plain,(b(elem!1, z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27492,plain,
% 3.82/4.18 (b(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27491, 27465, 9725, 27456, 27464, 1, 27454, 305, 11546, 78])).
% 3.82/4.18 tff(27493,plain,
% 3.82/4.18 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[24033, 1575, 11546, 2323, 74, 305])).
% 3.82/4.18 tff(27494,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[302, 27493])).
% 3.82/4.18 tff(27495,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[880, 27494, 26349, 133, 624])).
% 3.82/4.18 tff(27496,plain,(r(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27497,plain,
% 3.82/4.18 (r(z, elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27496, 27492, 133, 71, 11546, 23943, 305])).
% 3.82/4.18 tff(27498,plain,
% 3.82/4.18 (~r(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[24919, 27497, 27464, 23943])).
% 3.82/4.18 tff(27499,plain,
% 3.82/4.18 (b(s(elem!1), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[507, 27498])).
% 3.82/4.18 tff(27500,plain,
% 3.82/4.18 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27477, 27499, 27448, 27456, 9725])).
% 3.82/4.18 tff(27501,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[302, 27500])).
% 3.82/4.18 tff(27502,plain,
% 3.82/4.18 (~r(s(z), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[21949, 27501, 11546, 27497])).
% 3.82/4.18 tff(27503,plain,
% 3.82/4.18 (b(s(z), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[348, 27502])).
% 3.82/4.18 tff(27504,plain,
% 3.82/4.18 (~b(z, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[19223, 27503, 11546, 27450, 27497, 27501])).
% 3.82/4.18 tff(27505,plain,
% 3.82/4.18 (r(z, s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[372, 27504])).
% 3.82/4.18 tff(27506,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[18394, 333, 27505, 11546, 322, 27501])).
% 3.82/4.18 tff(27507,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27508,plain,
% 3.82/4.18 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27507, 27452, 322, 11546, 133, 305, 1, 78])).
% 3.82/4.18 tff(27509,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.82/4.18 tff(27510,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.82/4.18 tff(27511,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[9821, 44, 219, 27510, 27509])).
% 3.82/4.18 tff(27512,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27513,plain,
% 3.82/4.18 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27512, 27508])).
% 3.82/4.18 tff(27514,plain,
% 3.82/4.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[22516, 3238, 9759])).
% 3.82/4.18 tff(27515,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.82/4.18 tff(27516,plain,
% 3.82/4.18 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[3238])).
% 3.82/4.18 tff(27517,plain,
% 3.82/4.18 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 3.82/4.18 inference(symmetry,[status(thm)],[27516])).
% 3.82/4.18 tff(27518,plain,
% 3.82/4.18 (b(s(z), elem!1)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[838, 27517])).
% 3.82/4.18 tff(27519,plain,
% 3.82/4.18 (~(s(elem!1) = elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[25941, 27514, 2323])).
% 3.82/4.18 tff(27520,plain,
% 3.82/4.18 (~(elem!1 = s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[1569, 27519])).
% 3.82/4.18 tff(27521,plain,
% 3.82/4.18 ((s(z) = elem!1) <=> (s(z) = s(s(s(z))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[3238])).
% 3.82/4.18 tff(27522,plain,
% 3.82/4.18 ((s(z) = elem!1) <=> (s(s(s(z))) = s(z))),
% 3.82/4.18 inference(transitivity,[status(thm)],[27521, 157])).
% 3.82/4.18 tff(27523,plain,
% 3.82/4.18 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 3.82/4.18 inference(symmetry,[status(thm)],[27522])).
% 3.82/4.18 tff(27524,plain,
% 3.82/4.18 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27523])).
% 3.82/4.18 tff(27525,plain,
% 3.82/4.18 (~(s(z) = elem!1)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[166, 27524])).
% 3.82/4.18 tff(27526,plain,
% 3.82/4.18 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[3238])).
% 3.82/4.18 tff(27527,plain,
% 3.82/4.18 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 3.82/4.18 inference(symmetry,[status(thm)],[27526])).
% 3.82/4.18 tff(27528,plain,
% 3.82/4.18 (b(elem!1, s(z))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[56, 27527])).
% 3.82/4.18 tff(27529,plain,
% 3.82/4.18 (b(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[380, 22465, 285])).
% 3.82/4.18 tff(27530,plain,
% 3.82/4.18 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 3.82/4.18 inference(symmetry,[status(thm)],[20396])).
% 3.82/4.18 tff(27531,plain,
% 3.82/4.18 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.82/4.18 inference(symmetry,[status(thm)],[20395])).
% 3.82/4.18 tff(27532,plain,
% 3.82/4.18 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 3.82/4.18 inference(transitivity,[status(thm)],[27531, 27530])).
% 3.82/4.18 tff(27533,plain,
% 3.82/4.18 (b(s(elem!1), elem!1)),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[20266, 27532])).
% 3.82/4.18 tff(27534,plain,
% 3.82/4.18 (r(z, elem!1)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[26355, 27533, 27529, 27528, 27525, 27520, 27518, 74])).
% 3.82/4.18 tff(27535,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[18487, 144, 56, 26572, 838, 20266])).
% 3.82/4.18 tff(27536,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27537,plain,
% 3.82/4.18 (~b(s(s(s(s(z)))), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27536, 20266, 838, 56])).
% 3.82/4.18 tff(27538,plain,
% 3.82/4.18 (r(s(s(s(s(z)))), s(z)) | b(s(s(s(s(z)))), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[24600, 24294])).
% 3.82/4.18 tff(27539,plain,
% 3.82/4.18 (r(s(s(s(s(z)))), s(z))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27538, 27537])).
% 3.82/4.18 tff(27540,plain,
% 3.82/4.18 (r(s(elem!1), s(z))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27539, 22491])).
% 3.82/4.18 tff(27541,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[19607])).
% 3.82/4.18 tff(27542,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.18 inference(symmetry,[status(thm)],[27541])).
% 3.82/4.18 tff(27543,plain,
% 3.82/4.18 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[12733, 44, 27515])).
% 3.82/4.18 tff(27544,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27543, 12723])).
% 3.82/4.18 tff(27545,plain,
% 3.82/4.18 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27544, 27542])).
% 3.82/4.18 tff(27546,plain,
% 3.82/4.18 (~b(elem!1, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[555, 27545, 133, 27533])).
% 3.82/4.18 tff(27547,plain,
% 3.82/4.18 (r(elem!1, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[560, 27546, 27520])).
% 3.82/4.18 tff(27548,plain,
% 3.82/4.18 (~r(z, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[2393, 27547, 27540, 27534])).
% 3.82/4.18 tff(27549,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[19607])).
% 3.82/4.18 tff(27550,plain,
% 3.82/4.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.18 inference(symmetry,[status(thm)],[27549])).
% 3.82/4.18 tff(27551,plain,
% 3.82/4.18 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27550])).
% 3.82/4.18 tff(27552,plain,
% 3.82/4.18 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.82/4.18 inference(modus_ponens,[status(thm)],[27515, 27551])).
% 3.82/4.18 tff(27553,plain,
% 3.82/4.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[2541, 27534, 322, 2323])).
% 3.82/4.18 tff(27554,plain,
% 3.82/4.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[279, 27553])).
% 3.82/4.18 tff(27555,plain,
% 3.82/4.18 (~b(z, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[8386, 27554, 22467, 27552, 27514])).
% 3.82/4.18 tff(27556,plain,
% 3.82/4.18 ($false),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[583, 27555, 27548])).
% 3.82/4.18 tff(27557,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (z = elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.18 tff(27558,plain,
% 3.82/4.18 (~b(s(s(s(z))), z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[27557, 3238, 2323, 133, 74, 27515, 20266, 56, 838, 322, 9759])).
% 3.82/4.18 tff(27559,plain,
% 3.82/4.18 (~b(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[24196, 27558, 22465])).
% 3.82/4.18 tff(27560,plain,
% 3.82/4.18 (r(elem!1, z)),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[653, 27559, 730])).
% 3.82/4.18 tff(27561,plain,
% 3.82/4.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[2331, 27560, 322, 2323])).
% 3.82/4.18 tff(27562,plain,
% 3.82/4.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[279, 27561])).
% 3.82/4.18 tff(27563,plain,
% 3.82/4.18 (~b(z, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[8386, 27552, 22467, 27562, 27514])).
% 3.82/4.18 tff(27564,plain,
% 3.82/4.18 (r(z, s(elem!1))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[583, 27563])).
% 3.82/4.18 tff(27565,plain,
% 3.82/4.18 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.18 inference(unit_resolution,[status(thm)],[472, 27514, 22466])).
% 3.82/4.18 tff(27566,plain,
% 3.82/4.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.18 inference(rewrite,[status(thm)],[])).
% 3.82/4.18 tff(27567,plain,
% 3.82/4.18 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.18 inference(rewrite,[status(thm)],[])).
% 3.82/4.18 tff(27568,plain,
% 3.82/4.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.18 inference(monotonicity,[status(thm)],[27567])).
% 3.82/4.18 tff(27569,plain,
% 3.82/4.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(transitivity,[status(thm)],[27568, 27566])).
% 3.82/4.19 tff(27570,plain,
% 3.82/4.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))),
% 3.82/4.19 inference(quant_inst,[status(thm)],[])).
% 3.82/4.19 tff(27571,plain,
% 3.82/4.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.19 inference(modus_ponens,[status(thm)],[27570, 27569])).
% 3.82/4.19 tff(27572,plain,
% 3.82/4.19 ($false),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27571, 144, 451, 491, 133, 450, 259])).
% 3.82/4.19 tff(27573,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.19 tff(27574,plain,
% 3.82/4.19 (~b(s(elem!1), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27573, 27533, 133, 27565, 27562])).
% 3.82/4.19 tff(27575,plain,
% 3.82/4.19 (r(s(elem!1), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[507, 27574])).
% 3.82/4.19 tff(27576,plain,
% 3.82/4.19 ($false),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[571, 27547, 27575, 27560, 27564])).
% 3.82/4.19 tff(27577,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.19 tff(27578,plain,
% 3.82/4.19 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27577, 27513, 27448, 27451, 322, 23943, 71, 56, 838, 133])).
% 3.82/4.19 tff(27579,plain,
% 3.82/4.19 (~b(s(s(s(s(z)))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27536, 27513, 838, 56])).
% 3.82/4.19 tff(27580,plain,
% 3.82/4.19 (r(s(s(s(s(z)))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27538, 27579])).
% 3.82/4.19 tff(27581,plain,
% 3.82/4.19 ($false),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[20431, 333, 27580, 11546, 322, 27578])).
% 3.82/4.19 tff(27582,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.19 tff(27583,plain,
% 3.82/4.19 (~(s(s(s(z))) = elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27582, 27423, 11546, 56, 838, 133, 27433, 1])).
% 3.82/4.19 tff(27584,plain,
% 3.82/4.19 (r(s(s(s(z))), elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[704, 27583, 27444])).
% 3.82/4.19 tff(27585,plain,
% 3.82/4.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27586,plain,
% 3.82/4.19 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27587,plain,
% 3.82/4.19 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.19 inference(monotonicity,[status(thm)],[27586])).
% 3.82/4.19 tff(27588,plain,
% 3.82/4.19 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(transitivity,[status(thm)],[27587, 27585])).
% 3.82/4.19 tff(27589,plain,
% 3.82/4.19 ((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 3.82/4.19 inference(quant_inst,[status(thm)],[])).
% 3.82/4.19 tff(27590,plain,
% 3.82/4.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.19 inference(modus_ponens,[status(thm)],[27589, 27588])).
% 3.82/4.19 tff(27591,plain,
% 3.82/4.19 ($false),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27590, 333, 707, 2323, 6107, 322])).
% 3.82/4.19 tff(27592,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.19 tff(27593,plain,
% 3.82/4.19 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27592, 27584, 23943, 27423])).
% 3.82/4.19 tff(27594,plain,
% 3.82/4.19 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[1137, 27593])).
% 3.82/4.19 tff(27595,plain,
% 3.82/4.19 (~b(elem!1, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[22776, 27433, 838, 56])).
% 3.82/4.19 tff(27596,plain,
% 3.82/4.19 (~(elem!1 = s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[10997, 27583])).
% 3.82/4.19 tff(27597,plain,
% 3.82/4.19 (r(elem!1, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[1538, 27596, 27595])).
% 3.82/4.19 tff(27598,plain,
% 3.82/4.19 (~b(z, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[16228, 27594, 283, 27443])).
% 3.82/4.19 tff(27599,plain,
% 3.82/4.19 (r(z, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[619, 27598])).
% 3.82/4.19 tff(27600,plain,
% 3.82/4.19 (~r(elem!1, z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[7510, 623, 1525, 707])).
% 3.82/4.19 tff(27601,plain,
% 3.82/4.19 (b(elem!1, z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[1380, 27600, 730])).
% 3.82/4.19 tff(27602,plain,
% 3.82/4.19 (~r(z, elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[11259, 333, 1525, 1699, 623])).
% 3.82/4.19 tff(27603,plain,
% 3.82/4.19 (b(z, elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[658, 27602, 74])).
% 3.82/4.19 tff(27604,plain,
% 3.82/4.19 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[24033, 27602, 11546, 2323, 74, 305])).
% 3.82/4.19 tff(27605,plain,
% 3.82/4.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[302, 27604])).
% 3.82/4.19 tff(27606,plain,
% 3.82/4.19 ($false),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[880, 27605, 27603, 133, 27601])).
% 3.82/4.19 tff(27607,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.19 tff(27608,plain,
% 3.82/4.19 (~r(s(s(s(z))), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27607, 27599, 71, 11546, 23943, 27433, 27597, 133, 27584])).
% 3.82/4.19 tff(27609,plain,
% 3.82/4.19 (b(s(s(s(z))), z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[396, 27608])).
% 3.82/4.19 tff(27610,plain,
% 3.82/4.19 (~r(elem!1, z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[7510, 27599, 27597, 27584])).
% 3.82/4.19 tff(27611,plain,
% 3.82/4.19 (b(elem!1, z)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[1380, 27610, 77])).
% 3.82/4.19 tff(27612,plain,
% 3.82/4.19 (r(z, elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27496, 27611, 133, 71, 11546, 23943, 27433])).
% 3.82/4.19 tff(27613,plain,
% 3.82/4.19 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[3955, 133, 305, 134])).
% 3.82/4.19 tff(27614,plain,
% 3.82/4.19 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[319, 27613])).
% 3.82/4.19 tff(27615,plain,
% 3.82/4.19 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27616,plain,
% 3.82/4.19 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27617,plain,
% 3.82/4.19 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.82/4.19 inference(monotonicity,[status(thm)],[27616])).
% 3.82/4.19 tff(27618,plain,
% 3.82/4.19 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.82/4.19 inference(transitivity,[status(thm)],[27617, 27615])).
% 3.82/4.19 tff(27619,plain,
% 3.82/4.19 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 3.82/4.19 inference(quant_inst,[status(thm)],[])).
% 3.82/4.19 tff(27620,plain,
% 3.82/4.19 ((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.82/4.19 inference(modus_ponens,[status(thm)],[27619, 27618])).
% 3.82/4.19 tff(27621,plain,
% 3.82/4.19 (~r(elem!1, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27620, 333, 2323, 6107, 27614])).
% 3.82/4.19 tff(27622,plain,
% 3.82/4.19 (b(elem!1, s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[1538, 27621, 1524])).
% 3.82/4.19 tff(27623,plain,
% 3.82/4.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27624,plain,
% 3.82/4.19 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.82/4.19 inference(rewrite,[status(thm)],[])).
% 3.82/4.19 tff(27625,plain,
% 3.82/4.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.82/4.19 inference(monotonicity,[status(thm)],[27624])).
% 3.82/4.19 tff(27626,plain,
% 3.82/4.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.82/4.19 inference(transitivity,[status(thm)],[27625, 27623])).
% 3.82/4.19 tff(27627,plain,
% 3.82/4.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.82/4.19 inference(quant_inst,[status(thm)],[])).
% 3.82/4.19 tff(27628,plain,
% 3.82/4.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.82/4.19 inference(modus_ponens,[status(thm)],[27627, 27626])).
% 3.82/4.19 tff(27629,plain,
% 3.82/4.19 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27628, 144, 27622, 285, 133, 286])).
% 3.82/4.19 tff(27630,plain,
% 3.82/4.19 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[249, 27629])).
% 3.82/4.19 tff(27631,plain,
% 3.82/4.19 (~r(s(s(s(z))), elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[27590, 333, 2323, 6107, 27614])).
% 3.82/4.19 tff(27632,plain,
% 3.82/4.19 (b(s(s(s(z))), elem!1)),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[704, 27631, 698])).
% 3.82/4.19 tff(27633,plain,
% 3.82/4.19 (~b(s(z), s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[10692, 144, 134, 27622, 27632])).
% 3.82/4.19 tff(27634,plain,
% 3.82/4.19 (r(s(z), s(s(s(z))))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[172, 27633])).
% 3.82/4.19 tff(27635,plain,
% 3.82/4.19 (~b(s(s(s(z))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[4375, 27632, 305, 134])).
% 3.82/4.19 tff(27636,plain,
% 3.82/4.19 (r(s(s(s(z))), s(z))),
% 3.82/4.19 inference(unit_resolution,[status(thm)],[2794, 27635])).
% 3.82/4.19 tff(27637,plain,
% 3.82/4.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.82/4.20 inference(rewrite,[status(thm)],[])).
% 3.82/4.20 tff(27638,plain,
% 3.82/4.20 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.82/4.20 inference(rewrite,[status(thm)],[])).
% 3.82/4.20 tff(27639,plain,
% 3.82/4.20 (((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 3.82/4.20 inference(monotonicity,[status(thm)],[27638])).
% 3.82/4.20 tff(27640,plain,
% 3.82/4.20 (((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.82/4.20 inference(transitivity,[status(thm)],[27639, 27637])).
% 3.82/4.20 tff(27641,plain,
% 3.82/4.20 ((~![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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.82/4.20 inference(quant_inst,[status(thm)],[])).
% 3.82/4.20 tff(27642,plain,
% 3.82/4.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.82/4.20 inference(modus_ponens,[status(thm)],[27641, 27640])).
% 3.82/4.20 tff(27643,plain,
% 3.82/4.20 ($false),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[27642, 333, 27636, 27634, 27630, 27614])).
% 3.82/4.20 tff(27644,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.82/4.20 tff(27645,plain,
% 3.82/4.20 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[27644, 285, 2323, 134, 133, 286, 305, 698, 12398])).
% 3.82/4.20 tff(27646,plain,
% 3.82/4.20 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[1137, 27645])).
% 3.82/4.20 tff(27647,plain,
% 3.82/4.20 ($false),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[14138, 144, 285, 27646, 286, 259])).
% 3.82/4.20 tff(27648,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.82/4.20 tff(27649,plain,
% 3.82/4.20 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[27648, 27609, 133, 23943, 27435, 27583, 27443, 27433])).
% 3.82/4.20 tff(27650,plain,
% 3.82/4.20 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[302, 27649])).
% 3.82/4.20 tff(27651,plain,
% 3.82/4.20 (~r(s(z), z)),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[21949, 27650, 11546, 27612])).
% 3.82/4.20 tff(27652,plain,
% 3.82/4.20 (b(s(z), z)),
% 3.82/4.20 inference(unit_resolution,[status(thm)],[348, 27651])).
% 3.82/4.20 tff(27653,plain,
% 3.82/4.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27654,plain,
% 3.90/4.20 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27655,plain,
% 3.90/4.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27654])).
% 3.90/4.20 tff(27656,plain,
% 3.90/4.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(transitivity,[status(thm)],[27655, 27653])).
% 3.90/4.20 tff(27657,plain,
% 3.90/4.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 3.90/4.20 inference(quant_inst,[status(thm)],[])).
% 3.90/4.20 tff(27658,plain,
% 3.90/4.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[27657, 27656])).
% 3.90/4.20 tff(27659,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27658, 144, 27652, 27609, 56, 27594, 27443])).
% 3.90/4.20 tff(27660,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.20 tff(27661,plain,
% 3.90/4.20 (~b(s(z), s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27660, 1, 11546, 133, 17795, 56])).
% 3.90/4.20 tff(27662,plain,
% 3.90/4.20 (r(s(z), s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[172, 27661])).
% 3.90/4.20 tff(27663,plain,
% 3.90/4.20 (r(s(z), s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[172, 156])).
% 3.90/4.20 tff(27664,plain,
% 3.90/4.20 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[21397, 321, 11546, 353])).
% 3.90/4.20 tff(27665,plain,
% 3.90/4.20 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[1137, 27664])).
% 3.90/4.20 tff(27666,plain,
% 3.90/4.20 (~r(z, s(z))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[24027, 321, 408, 2323])).
% 3.90/4.20 tff(27667,plain,
% 3.90/4.20 (b(z, s(z))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[372, 27666])).
% 3.90/4.20 tff(27668,plain,
% 3.90/4.20 (((~![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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27669,plain,
% 3.90/4.20 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27670,plain,
% 3.90/4.20 (((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27669])).
% 3.90/4.20 tff(27671,plain,
% 3.90/4.20 (((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(transitivity,[status(thm)],[27670, 27668])).
% 3.90/4.20 tff(27672,plain,
% 3.90/4.20 ((~![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(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 3.90/4.20 inference(quant_inst,[status(thm)],[])).
% 3.90/4.20 tff(27673,plain,
% 3.90/4.20 ((~![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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[27672, 27671])).
% 3.90/4.20 tff(27674,plain,
% 3.90/4.20 (~r(elem!1, s(z))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27673, 333, 11546, 2323, 321])).
% 3.90/4.20 tff(27675,plain,
% 3.90/4.20 (elem!1 = s(z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[720, 27674, 708])).
% 3.90/4.20 tff(27676,plain,
% 3.90/4.20 (s(z) = elem!1),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[712, 27675])).
% 3.90/4.20 tff(27677,plain,
% 3.90/4.20 (r(s(z), z) <=> r(elem!1, z)),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27676])).
% 3.90/4.20 tff(27678,plain,
% 3.90/4.20 (r(elem!1, z) <=> r(s(z), z)),
% 3.90/4.20 inference(symmetry,[status(thm)],[27677])).
% 3.90/4.20 tff(27679,plain,
% 3.90/4.20 (r(s(z), z)),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[408, 27678])).
% 3.90/4.20 tff(27680,plain,
% 3.90/4.20 (~r(z, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[19065, 27679, 11546, 321])).
% 3.90/4.20 tff(27681,plain,
% 3.90/4.20 (b(z, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[619, 27680])).
% 3.90/4.20 tff(27682,plain,
% 3.90/4.20 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[22484, 27681, 304, 27667, 27665])).
% 3.90/4.20 tff(27683,plain,
% 3.90/4.20 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[279, 27682])).
% 3.90/4.20 tff(27684,plain,
% 3.90/4.20 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27685,plain,
% 3.90/4.20 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27686,plain,
% 3.90/4.20 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27685])).
% 3.90/4.20 tff(27687,plain,
% 3.90/4.20 (((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(transitivity,[status(thm)],[27686, 27684])).
% 3.90/4.20 tff(27688,plain,
% 3.90/4.20 ((~![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(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))),
% 3.90/4.20 inference(quant_inst,[status(thm)],[])).
% 3.90/4.20 tff(27689,plain,
% 3.90/4.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[27688, 27687])).
% 3.90/4.20 tff(27690,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27689, 333, 408, 2323, 321, 27683])).
% 3.90/4.20 tff(27691,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.20 tff(27692,plain,
% 3.90/4.20 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27691, 408, 2323, 304, 11546, 708, 27663])).
% 3.90/4.20 tff(27693,plain,
% 3.90/4.20 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[302, 27692])).
% 3.90/4.20 tff(27694,plain,
% 3.90/4.20 (~b(z, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[21533, 27693, 56, 304, 283])).
% 3.90/4.20 tff(27695,plain,
% 3.90/4.20 (r(z, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[619, 27694])).
% 3.90/4.20 tff(27696,plain,
% 3.90/4.20 (~r(z, s(z))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[22294, 489, 133, 11546, 51, 251])).
% 3.90/4.20 tff(27697,plain,
% 3.90/4.20 (~b(z, s(z))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[7093, 489, 286, 304])).
% 3.90/4.20 tff(27698,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[372, 27697, 27696])).
% 3.90/4.20 tff(27699,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.20 tff(27700,plain,
% 3.90/4.20 (~b(s(z), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27699, 51, 304, 133, 11546, 286, 251])).
% 3.90/4.20 tff(27701,plain,
% 3.90/4.20 (r(s(z), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[348, 27700])).
% 3.90/4.20 tff(27702,plain,
% 3.90/4.20 (s(z) = elem!1),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[19519, 27701, 11546, 408, 623, 133, 51])).
% 3.90/4.20 tff(27703,plain,
% 3.90/4.20 (s(s(z)) = s(elem!1)),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27702])).
% 3.90/4.20 tff(27704,plain,
% 3.90/4.20 (s(s(s(z))) = s(s(elem!1))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27703])).
% 3.90/4.20 tff(27705,plain,
% 3.90/4.20 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27704])).
% 3.90/4.20 tff(27706,plain,
% 3.90/4.20 (~b(elem!1, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[13482, 27702, 156])).
% 3.90/4.20 tff(27707,plain,
% 3.90/4.20 (r(elem!1, s(s(s(z))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[1538, 27706, 1524])).
% 3.90/4.20 tff(27708,plain,
% 3.90/4.20 (r(elem!1, s(s(elem!1)))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[27707, 27705])).
% 3.90/4.20 tff(27709,plain,
% 3.90/4.20 (((~![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(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, 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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27710,plain,
% 3.90/4.20 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(rewrite,[status(thm)],[])).
% 3.90/4.20 tff(27711,plain,
% 3.90/4.20 (((~![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(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27710])).
% 3.90/4.20 tff(27712,plain,
% 3.90/4.20 (((~![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(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, 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)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.20 inference(transitivity,[status(thm)],[27711, 27709])).
% 3.90/4.20 tff(27713,plain,
% 3.90/4.20 ((~![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(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 3.90/4.20 inference(quant_inst,[status(thm)],[])).
% 3.90/4.20 tff(27714,plain,
% 3.90/4.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[27713, 27712])).
% 3.90/4.20 tff(27715,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27714, 333, 408, 2736, 51, 5497])).
% 3.90/4.20 tff(27716,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.20 tff(27717,plain,
% 3.90/4.20 (~r(s(s(elem!1)), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27716, 27708, 408, 51])).
% 3.90/4.20 tff(27718,plain,
% 3.90/4.20 (b(s(s(elem!1)), z)),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[5509, 27717])).
% 3.90/4.20 tff(27719,plain,
% 3.90/4.20 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.20 inference(monotonicity,[status(thm)],[27704])).
% 3.90/4.20 tff(27720,plain,
% 3.90/4.20 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.20 inference(modus_ponens,[status(thm)],[283, 27719])).
% 3.90/4.20 tff(27721,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[10010, 144, 251, 27720, 133, 286, 27718])).
% 3.90/4.20 tff(27722,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.20 tff(27723,plain,
% 3.90/4.20 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[27722, 27693, 133, 251, 408, 283, 1524, 156, 11546, 27695, 304])).
% 3.90/4.20 tff(27724,plain,
% 3.90/4.20 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[279, 27723])).
% 3.90/4.20 tff(27725,plain,
% 3.90/4.20 ($false),
% 3.90/4.20 inference(unit_resolution,[status(thm)],[16551, 333, 323, 1699, 623, 353])).
% 3.90/4.21 tff(27726,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.21 tff(27727,plain,
% 3.90/4.21 (~r(s(s(s(z))), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27726, 323, 623, 353])).
% 3.90/4.21 tff(27728,plain,
% 3.90/4.21 (b(s(s(s(z))), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[396, 27727])).
% 3.90/4.21 tff(27729,plain,
% 3.90/4.21 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[24118, 144, 56, 304, 259])).
% 3.90/4.21 tff(27730,plain,
% 3.90/4.21 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27729, 27728])).
% 3.90/4.21 tff(27731,plain,
% 3.90/4.21 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[1137, 27730])).
% 3.90/4.21 tff(27732,plain,
% 3.90/4.21 (((~![X0: $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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), 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(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27733,plain,
% 3.90/4.21 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27734,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27733])).
% 3.90/4.21 tff(27735,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.21 inference(transitivity,[status(thm)],[27734, 27732])).
% 3.90/4.21 tff(27736,plain,
% 3.90/4.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 3.90/4.21 inference(quant_inst,[status(thm)],[])).
% 3.90/4.21 tff(27737,plain,
% 3.90/4.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[27736, 27735])).
% 3.90/4.21 tff(27738,plain,
% 3.90/4.21 ($false),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27737, 333, 323, 623, 353, 27731])).
% 3.90/4.21 tff(27739,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.21 tff(27740,plain,
% 3.90/4.21 (~r(s(z), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27739, 27695, 27663, 56, 304, 27724])).
% 3.90/4.21 tff(27741,plain,
% 3.90/4.21 (b(s(z), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[348, 27740])).
% 3.90/4.21 tff(27742,plain,
% 3.90/4.21 (~b(z, s(z))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[7093, 27741, 27693, 304])).
% 3.90/4.21 tff(27743,plain,
% 3.90/4.21 (r(z, s(z))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[372, 27742])).
% 3.90/4.21 tff(27744,plain,
% 3.90/4.21 (~r(elem!1, s(z))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[20609, 27743, 11546, 408])).
% 3.90/4.21 tff(27745,plain,
% 3.90/4.21 (~(s(z) = elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[9366, 27742, 251])).
% 3.90/4.21 tff(27746,plain,
% 3.90/4.21 (~(elem!1 = s(z))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[712, 27745])).
% 3.90/4.21 tff(27747,plain,
% 3.90/4.21 ($false),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[720, 27746, 27744, 708])).
% 3.90/4.21 tff(27748,plain,((~r(elem!1, z)) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.21 tff(27749,plain,
% 3.90/4.21 (~r(elem!1, z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27748, 251, 11546, 708, 304, 56, 133, 17795, 1524, 156, 2323])).
% 3.90/4.21 tff(27750,plain,
% 3.90/4.21 (b(elem!1, z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[1380, 27749, 1368])).
% 3.90/4.21 tff(27751,plain,
% 3.90/4.21 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[880, 27750, 133, 251])).
% 3.90/4.21 tff(27752,plain,
% 3.90/4.21 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[302, 27751])).
% 3.90/4.21 tff(27753,plain,
% 3.90/4.21 (~r(elem!1, s(z))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27673, 333, 11546, 2323, 27752])).
% 3.90/4.21 tff(27754,plain,
% 3.90/4.21 (elem!1 = s(z)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[718, 44, 27753, 708])).
% 3.90/4.21 tff(27755,plain,
% 3.90/4.21 (s(elem!1) = s(s(z))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27754])).
% 3.90/4.21 tff(27756,plain,
% 3.90/4.21 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27755])).
% 3.90/4.21 tff(27757,plain,
% 3.90/4.21 (s(z) = elem!1),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[712, 27754])).
% 3.90/4.21 tff(27758,plain,
% 3.90/4.21 (~(s(s(s(elem!1))) = elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[2468, 27757])).
% 3.90/4.21 tff(27759,plain,
% 3.90/4.21 (~(elem!1 = s(elem!1))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[2482, 27758])).
% 3.90/4.21 tff(27760,plain,
% 3.90/4.21 (~(s(elem!1) = elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[906, 27759])).
% 3.90/4.21 tff(27761,plain,
% 3.90/4.21 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27754])).
% 3.90/4.21 tff(27762,plain,
% 3.90/4.21 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.90/4.21 inference(symmetry,[status(thm)],[27761])).
% 3.90/4.21 tff(27763,plain,
% 3.90/4.21 (s(s(elem!1)) = s(s(s(z)))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27755])).
% 3.90/4.21 tff(27764,plain,
% 3.90/4.21 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27763])).
% 3.90/4.21 tff(27765,plain,
% 3.90/4.21 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 3.90/4.21 inference(symmetry,[status(thm)],[27764])).
% 3.90/4.21 tff(27766,plain,
% 3.90/4.21 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.90/4.21 inference(transitivity,[status(thm)],[27765, 27762])).
% 3.90/4.21 tff(27767,plain,
% 3.90/4.21 (r(elem!1, s(s(elem!1)))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[27663, 27766])).
% 3.90/4.21 tff(27768,plain,
% 3.90/4.21 (~(s(s(elem!1)) = s(elem!1))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[1196, 27759])).
% 3.90/4.21 tff(27769,plain,
% 3.90/4.21 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27763])).
% 3.90/4.21 tff(27770,plain,
% 3.90/4.21 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(symmetry,[status(thm)],[27769])).
% 3.90/4.21 tff(27771,plain,
% 3.90/4.21 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[21397, 27752, 11546, 27663])).
% 3.90/4.21 tff(27772,plain,
% 3.90/4.21 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[1137, 27771])).
% 3.90/4.21 tff(27773,plain,
% 3.90/4.21 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[27772, 27770])).
% 3.90/4.21 tff(27774,plain,
% 3.90/4.21 (b(s(s(elem!1)), elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[24878, 27757, 56])).
% 3.90/4.21 tff(27775,plain,
% 3.90/4.21 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27754])).
% 3.90/4.21 tff(27776,plain,
% 3.90/4.21 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 3.90/4.21 inference(symmetry,[status(thm)],[27775])).
% 3.90/4.21 tff(27777,plain,
% 3.90/4.21 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27776])).
% 3.90/4.21 tff(27778,plain,
% 3.90/4.21 (~(s(s(z)) = elem!1)),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[1416, 27777])).
% 3.90/4.21 tff(27779,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27780,plain,
% 3.90/4.21 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27781,plain,
% 3.90/4.21 (((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27780])).
% 3.90/4.21 tff(27782,plain,
% 3.90/4.21 (((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(transitivity,[status(thm)],[27781, 27779])).
% 3.90/4.21 tff(27783,plain,
% 3.90/4.21 ((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 3.90/4.21 inference(quant_inst,[status(thm)],[])).
% 3.90/4.21 tff(27784,plain,
% 3.90/4.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[27783, 27782])).
% 3.90/4.21 tff(27785,plain,
% 3.90/4.21 (~r(s(s(z)), elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27784, 333, 2671, 2323, 321])).
% 3.90/4.21 tff(27786,plain,
% 3.90/4.21 (b(s(s(z)), elem!1)),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[7970, 1506, 27785])).
% 3.90/4.21 tff(27787,plain,
% 3.90/4.21 (~(elem!1 = s(s(z)))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[1506, 17962])).
% 3.90/4.21 tff(27788,plain,
% 3.90/4.21 (((~![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(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(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, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27789,plain,
% 3.90/4.21 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27790,plain,
% 3.90/4.21 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27789])).
% 3.90/4.21 tff(27791,plain,
% 3.90/4.21 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.21 inference(transitivity,[status(thm)],[27790, 27788])).
% 3.90/4.21 tff(27792,plain,
% 3.90/4.21 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 3.90/4.21 inference(quant_inst,[status(thm)],[])).
% 3.90/4.21 tff(27793,plain,
% 3.90/4.21 ((~![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(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[27792, 27791])).
% 3.90/4.21 tff(27794,plain,
% 3.90/4.21 (~r(elem!1, s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27793, 333, 2671, 2323, 321])).
% 3.90/4.21 tff(27795,plain,
% 3.90/4.21 ((elem!1 = s(s(z))) | b(elem!1, s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[18919, 44, 27794])).
% 3.90/4.21 tff(27796,plain,
% 3.90/4.21 (b(elem!1, s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27795, 27787])).
% 3.90/4.21 tff(27797,plain,
% 3.90/4.21 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[26868, 144, 133, 7928, 27796])).
% 3.90/4.21 tff(27798,plain,
% 3.90/4.21 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[9653, 44, 27797])).
% 3.90/4.21 tff(27799,plain,
% 3.90/4.21 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.21 inference(unit_resolution,[status(thm)],[27798, 9614])).
% 3.90/4.21 tff(27800,plain,
% 3.90/4.21 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 3.90/4.21 inference(commutativity,[status(thm)],[])).
% 3.90/4.21 tff(27801,plain,
% 3.90/4.21 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 3.90/4.21 inference(symmetry,[status(thm)],[27800])).
% 3.90/4.21 tff(27802,plain,
% 3.90/4.21 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27801])).
% 3.90/4.21 tff(27803,plain,
% 3.90/4.21 (~(z = s(s(z)))),
% 3.90/4.21 inference(modus_ponens,[status(thm)],[164, 27802])).
% 3.90/4.21 tff(27804,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27805,plain,
% 3.90/4.21 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.90/4.21 inference(rewrite,[status(thm)],[])).
% 3.90/4.21 tff(27806,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.90/4.21 inference(monotonicity,[status(thm)],[27805])).
% 3.90/4.21 tff(27807,plain,
% 3.90/4.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.90/4.22 inference(transitivity,[status(thm)],[27806, 27804])).
% 3.90/4.22 tff(27808,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 3.90/4.22 inference(quant_inst,[status(thm)],[])).
% 3.90/4.22 tff(27809,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27808, 27807])).
% 3.90/4.22 tff(27810,plain,
% 3.90/4.22 (~b(z, s(s(z)))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27809, 144, 251, 7928, 27796])).
% 3.90/4.22 tff(27811,plain,
% 3.90/4.22 (((~![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))))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27812,plain,
% 3.90/4.22 ((~![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))))),
% 3.90/4.22 inference(quant_inst,[status(thm)],[])).
% 3.90/4.22 tff(27813,plain,
% 3.90/4.22 ((~![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)))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27812, 27811])).
% 3.90/4.22 tff(27814,plain,
% 3.90/4.22 ((z = s(s(z))) | r(z, s(s(z)))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27813, 44, 27810])).
% 3.90/4.22 tff(27815,plain,
% 3.90/4.22 (r(z, s(s(z)))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27814, 27803])).
% 3.90/4.22 tff(27816,plain,
% 3.90/4.22 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27817,plain,
% 3.90/4.22 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27818,plain,
% 3.90/4.22 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27817])).
% 3.90/4.22 tff(27819,plain,
% 3.90/4.22 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.22 inference(transitivity,[status(thm)],[27818, 27816])).
% 3.90/4.22 tff(27820,plain,
% 3.90/4.22 ((~![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(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.90/4.22 inference(quant_inst,[status(thm)],[])).
% 3.90/4.22 tff(27821,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27820, 27819])).
% 3.90/4.22 tff(27822,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27821, 333, 2671, 321, 27815, 27799])).
% 3.90/4.22 tff(27823,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27824,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27823, 27786, 1506, 133, 2671, 251, 321, 2323])).
% 3.90/4.22 tff(27825,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27826,plain,
% 3.90/4.22 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27825, 27778, 133, 251, 27752, 2323])).
% 3.90/4.22 tff(27827,plain,
% 3.90/4.22 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1451, 27826])).
% 3.90/4.22 tff(27828,plain,
% 3.90/4.22 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2689, 27827, 27757])).
% 3.90/4.22 tff(27829,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27830,plain,
% 3.90/4.22 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27831,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27830])).
% 3.90/4.22 tff(27832,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.22 inference(transitivity,[status(thm)],[27831, 27829])).
% 3.90/4.22 tff(27833,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.90/4.22 inference(quant_inst,[status(thm)],[])).
% 3.90/4.22 tff(27834,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27833, 27832])).
% 3.90/4.22 tff(27835,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27834, 144, 1249, 133, 4972, 6147, 450])).
% 3.90/4.22 tff(27836,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27837,plain,
% 3.90/4.22 (~b(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27836, 27828, 133, 27774, 27773])).
% 3.90/4.22 tff(27838,plain,
% 3.90/4.22 (r(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1283, 27837, 27768])).
% 3.90/4.22 tff(27839,plain,
% 3.90/4.22 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27755, 27763])).
% 3.90/4.22 tff(27840,plain,
% 3.90/4.22 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.90/4.22 inference(symmetry,[status(thm)],[27839])).
% 3.90/4.22 tff(27841,plain,
% 3.90/4.22 (~b(s(s(z)), s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[7952, 27827, 7926, 27771])).
% 3.90/4.22 tff(27842,plain,
% 3.90/4.22 (r(s(s(z)), s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1473, 44, 27841, 217])).
% 3.90/4.22 tff(27843,plain,
% 3.90/4.22 (r(s(elem!1), s(s(elem!1)))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27842, 27840])).
% 3.90/4.22 tff(27844,plain,
% 3.90/4.22 (~r(s(elem!1), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[5242, 27843, 27838, 27767])).
% 3.90/4.22 tff(27845,plain,
% 3.90/4.22 (b(s(elem!1), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[448, 27844, 27760])).
% 3.90/4.22 tff(27846,plain,
% 3.90/4.22 (~b(s(elem!1), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[916, 27845, 251, 27750])).
% 3.90/4.22 tff(27847,plain,
% 3.90/4.22 (r(s(elem!1), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[507, 27846])).
% 3.90/4.22 tff(27848,plain,
% 3.90/4.22 (r(s(s(z)), z)),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27847, 27756])).
% 3.90/4.22 tff(27849,plain,
% 3.90/4.22 (b(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[9366, 27757, 251])).
% 3.90/4.22 tff(27850,plain,
% 3.90/4.22 (~r(z, s(s(elem!1)))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[23930, 27847, 27843, 27838])).
% 3.90/4.22 tff(27851,plain,
% 3.90/4.22 (~r(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2836, 27850, 27757])).
% 3.90/4.22 tff(27852,plain,
% 3.90/4.22 (b(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[619, 27851])).
% 3.90/4.22 tff(27853,plain,
% 3.90/4.22 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[22484, 27852, 304, 27849, 27772])).
% 3.90/4.22 tff(27854,plain,
% 3.90/4.22 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[279, 27853])).
% 3.90/4.22 tff(27855,plain,
% 3.90/4.22 (b(s(s(s(z))), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[63, 27757, 56])).
% 3.90/4.22 tff(27856,plain,
% 3.90/4.22 (~b(s(s(s(z))), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[10565, 27855, 251, 27750])).
% 3.90/4.22 tff(27857,plain,
% 3.90/4.22 (r(s(s(s(z))), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[396, 27856])).
% 3.90/4.22 tff(27858,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[18232, 333, 27857, 27854, 27842, 27848])).
% 3.90/4.22 tff(27859,plain,((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (elem!1 = s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27860,plain,
% 3.90/4.22 (~b(z, elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27859, 304, 133, 7926, 23943, 56, 708, 11546, 77, 1524, 27661])).
% 3.90/4.22 tff(27861,plain,
% 3.90/4.22 (r(z, elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[658, 27860, 71])).
% 3.90/4.22 tff(27862,plain,
% 3.90/4.22 (s(elem!1) = s(s(z))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27675])).
% 3.90/4.22 tff(27863,plain,
% 3.90/4.22 (s(s(elem!1)) = s(s(s(z)))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27862])).
% 3.90/4.22 tff(27864,plain,
% 3.90/4.22 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27863])).
% 3.90/4.22 tff(27865,plain,
% 3.90/4.22 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(symmetry,[status(thm)],[27864])).
% 3.90/4.22 tff(27866,plain,
% 3.90/4.22 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27665, 27865])).
% 3.90/4.22 tff(27867,plain,
% 3.90/4.22 (b(s(s(elem!1)), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[24878, 27676, 56])).
% 3.90/4.22 tff(27868,plain,
% 3.90/4.22 (~(s(s(s(elem!1))) = elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2468, 27676])).
% 3.90/4.22 tff(27869,plain,
% 3.90/4.22 (~(elem!1 = s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2482, 27868])).
% 3.90/4.22 tff(27870,plain,
% 3.90/4.22 (~(s(s(elem!1)) = s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1196, 27869])).
% 3.90/4.22 tff(27871,plain,
% 3.90/4.22 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27863, 27862])).
% 3.90/4.22 tff(27872,plain,
% 3.90/4.22 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(symmetry,[status(thm)],[27871])).
% 3.90/4.22 tff(27873,plain,
% 3.90/4.22 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27872])).
% 3.90/4.22 tff(27874,plain,
% 3.90/4.22 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27862])).
% 3.90/4.22 tff(27875,plain,
% 3.90/4.22 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(z))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27874])).
% 3.90/4.22 tff(27876,plain,
% 3.90/4.22 (~b(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[8102, 27676, 606])).
% 3.90/4.22 tff(27877,plain,
% 3.90/4.22 (r(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[372, 27876])).
% 3.90/4.22 tff(27878,plain,
% 3.90/4.22 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[15183, 27877, 11546, 321])).
% 3.90/4.22 tff(27879,plain,
% 3.90/4.22 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[279, 27878])).
% 3.90/4.22 tff(27880,plain,
% 3.90/4.22 (~b(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[16228, 27879, 283, 27665])).
% 3.90/4.22 tff(27881,plain,
% 3.90/4.22 (r(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[619, 27880])).
% 3.90/4.22 tff(27882,plain,
% 3.90/4.22 (~r(s(s(s(z))), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[3011, 27881, 353, 27877])).
% 3.90/4.22 tff(27883,plain,
% 3.90/4.22 (~r(s(s(s(z))), s(s(z)))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27882, 27875])).
% 3.90/4.22 tff(27884,plain,
% 3.90/4.22 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27883, 27873])).
% 3.90/4.22 tff(27885,plain,
% 3.90/4.22 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1283, 27884, 27870])).
% 3.90/4.22 tff(27886,plain,
% 3.90/4.22 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27836, 27885, 133, 27867, 27866])).
% 3.90/4.22 tff(27887,plain,
% 3.90/4.22 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[21271, 27886, 27676])).
% 3.90/4.22 tff(27888,plain,
% 3.90/4.22 (~b(elem!1, s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[14987, 27885, 133, 27867, 27866])).
% 3.90/4.22 tff(27889,plain,
% 3.90/4.22 (r(elem!1, s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[560, 27888, 27869])).
% 3.90/4.22 tff(27890,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[4103, 27889, 27887, 321, 2323])).
% 3.90/4.22 tff(27891,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, elem!1) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27892,plain,
% 3.90/4.22 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27891, 27860, 133, 27662, 17795, 11546, 23943, 56, 708])).
% 3.90/4.22 tff(27893,plain,
% 3.90/4.22 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[302, 27892])).
% 3.90/4.22 tff(27894,plain,
% 3.90/4.22 (~b(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[21533, 27893, 56, 304, 17795])).
% 3.90/4.22 tff(27895,plain,
% 3.90/4.22 (r(z, s(s(s(z))))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[619, 27894])).
% 3.90/4.22 tff(27896,plain,
% 3.90/4.22 (b(s(s(elem!1)), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[24878, 57, 56])).
% 3.90/4.22 tff(27897,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27898,plain,
% 3.90/4.22 (((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.90/4.22 inference(rewrite,[status(thm)],[])).
% 3.90/4.22 tff(27899,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27898])).
% 3.90/4.22 tff(27900,plain,
% 3.90/4.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.90/4.22 inference(transitivity,[status(thm)],[27899, 27897])).
% 3.90/4.22 tff(27901,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.90/4.22 inference(quant_inst,[status(thm)],[])).
% 3.90/4.22 tff(27902,plain,
% 3.90/4.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[27901, 27900])).
% 3.90/4.22 tff(27903,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27902, 144, 624, 23322, 133, 286, 27896])).
% 3.90/4.22 tff(27904,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27905,plain,
% 3.90/4.22 (~(s(z) = elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27904, 624, 133, 286, 283, 56])).
% 3.90/4.22 tff(27906,plain,
% 3.90/4.22 (~(elem!1 = s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[712, 27905])).
% 3.90/4.22 tff(27907,plain,
% 3.90/4.22 (r(elem!1, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[720, 27906, 708])).
% 3.90/4.22 tff(27908,plain,
% 3.90/4.22 (~b(s(z), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[3988, 624, 133, 304, 286])).
% 3.90/4.22 tff(27909,plain,
% 3.90/4.22 (~r(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[13826, 27905, 670, 27908, 708])).
% 3.90/4.22 tff(27910,plain,
% 3.90/4.22 (b(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[372, 27909])).
% 3.90/4.22 tff(27911,plain,
% 3.90/4.22 (~b(s(z), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[7093, 27910, 286, 304])).
% 3.90/4.22 tff(27912,plain,
% 3.90/4.22 (r(s(z), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[348, 27911])).
% 3.90/4.22 tff(27913,plain,
% 3.90/4.22 (r(s(z), elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[406, 27905, 27908])).
% 3.90/4.22 tff(27914,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1767, 333, 670, 27913, 27912, 27907])).
% 3.90/4.22 tff(27915,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27916,plain,
% 3.90/4.22 (~b(elem!1, z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27915, 27861, 27893, 304, 708, 133, 17795, 56])).
% 3.90/4.22 tff(27917,plain,
% 3.90/4.22 (r(elem!1, z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[653, 27916, 77])).
% 3.90/4.22 tff(27918,plain,
% 3.90/4.22 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2894, 51, 23943, 7265])).
% 3.90/4.22 tff(27919,plain,
% 3.90/4.22 (~r(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[20609, 6065, 11546, 408])).
% 3.90/4.22 tff(27920,plain,
% 3.90/4.22 (~r(s(z), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[19519, 706, 11546, 408, 623, 133, 51])).
% 3.90/4.22 tff(27921,plain,
% 3.90/4.22 (b(s(z), z)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[348, 27920])).
% 3.90/4.22 tff(27922,plain,
% 3.90/4.22 (~b(z, s(z))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[7093, 27921, 286, 304])).
% 3.90/4.22 tff(27923,plain,
% 3.90/4.22 ($false),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[372, 27922, 27919])).
% 3.90/4.22 tff(27924,plain,((s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | b(elem!1, s(z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.22 tff(27925,plain,
% 3.90/4.22 (s(z) = elem!1),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[27924, 51, 304, 11546, 408, 708, 623, 133, 286])).
% 3.90/4.22 tff(27926,plain,
% 3.90/4.22 (s(s(z)) = s(elem!1)),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27925])).
% 3.90/4.22 tff(27927,plain,
% 3.90/4.22 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27926])).
% 3.90/4.22 tff(27928,plain,
% 3.90/4.22 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.90/4.22 inference(transitivity,[status(thm)],[27927, 174])).
% 3.90/4.22 tff(27929,plain,
% 3.90/4.22 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27928])).
% 3.90/4.22 tff(27930,plain,
% 3.90/4.22 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.90/4.22 inference(modus_ponens,[status(thm)],[1446, 27929])).
% 3.90/4.22 tff(27931,plain,
% 3.90/4.22 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[542, 27930, 27918])).
% 3.90/4.22 tff(27932,plain,
% 3.90/4.22 (~(s(s(s(elem!1))) = elem!1)),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2468, 27925])).
% 3.90/4.22 tff(27933,plain,
% 3.90/4.22 (~(elem!1 = s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[2482, 27932])).
% 3.90/4.22 tff(27934,plain,
% 3.90/4.22 (~(s(s(elem!1)) = s(elem!1))),
% 3.90/4.22 inference(unit_resolution,[status(thm)],[1196, 27933])).
% 3.90/4.22 tff(27935,plain,
% 3.90/4.22 (s(s(s(z))) = s(s(elem!1))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27926])).
% 3.90/4.22 tff(27936,plain,
% 3.90/4.22 (s(s(elem!1)) = s(s(s(z)))),
% 3.90/4.22 inference(symmetry,[status(thm)],[27935])).
% 3.90/4.22 tff(27937,plain,
% 3.90/4.22 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.90/4.22 inference(monotonicity,[status(thm)],[27936])).
% 3.90/4.22 tff(27938,plain,
% 3.90/4.22 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.90/4.22 inference(symmetry,[status(thm)],[27937])).
% 3.90/4.23 tff(27939,plain,
% 3.90/4.23 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[27938])).
% 3.90/4.23 tff(27940,plain,
% 3.90/4.23 (~b(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[8102, 27925, 606])).
% 3.90/4.23 tff(27941,plain,
% 3.90/4.23 (r(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[372, 27940])).
% 3.90/4.23 tff(27942,plain,
% 3.90/4.23 (~r(s(s(s(z))), s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[3011, 27941, 27663, 623])).
% 3.90/4.23 tff(27943,plain,
% 3.90/4.23 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[27942, 27939])).
% 3.90/4.23 tff(27944,plain,
% 3.90/4.23 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1283, 27943, 27934])).
% 3.90/4.23 tff(27945,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[27935])).
% 3.90/4.23 tff(27946,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[283, 27945])).
% 3.90/4.23 tff(27947,plain,
% 3.90/4.23 (~b(s(elem!1), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[5667, 27931, 304, 27946, 27944])).
% 3.90/4.23 tff(27948,plain,
% 3.90/4.23 (r(s(elem!1), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[486, 27947, 1])).
% 3.90/4.23 tff(27949,plain,
% 3.90/4.23 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[27935])).
% 3.90/4.23 tff(27950,plain,
% 3.90/4.23 (~b(elem!1, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[13482, 27925, 156])).
% 3.90/4.23 tff(27951,plain,
% 3.90/4.23 (r(elem!1, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1538, 27950, 1524])).
% 3.90/4.23 tff(27952,plain,
% 3.90/4.23 (r(elem!1, s(s(elem!1)))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[27951, 27949])).
% 3.90/4.23 tff(27953,plain,
% 3.90/4.23 (~r(s(s(elem!1)), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27716, 27952, 408, 51])).
% 3.90/4.23 tff(27954,plain,
% 3.90/4.23 (b(s(s(elem!1)), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[5509, 27953])).
% 3.90/4.23 tff(27955,plain,
% 3.90/4.23 (r(s(z), z) <=> r(elem!1, z)),
% 3.90/4.23 inference(monotonicity,[status(thm)],[27925])).
% 3.90/4.23 tff(27956,plain,
% 3.90/4.23 (r(elem!1, z) <=> r(s(z), z)),
% 3.90/4.23 inference(symmetry,[status(thm)],[27955])).
% 3.90/4.23 tff(27957,plain,
% 3.90/4.23 (r(s(z), z)),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[408, 27956])).
% 3.90/4.23 tff(27958,plain,
% 3.90/4.23 (~r(s(elem!1), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1365, 27948, 27941, 27957])).
% 3.90/4.23 tff(27959,plain,
% 3.90/4.23 (b(s(elem!1), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[507, 27958])).
% 3.90/4.23 tff(27960,plain,
% 3.90/4.23 (~b(z, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[5572, 27959, 27944, 27954])).
% 3.90/4.23 tff(27961,plain,
% 3.90/4.23 (r(z, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[583, 27960])).
% 3.90/4.23 tff(27962,plain,
% 3.90/4.23 (~r(elem!1, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[2393, 27961, 27948, 7265])).
% 3.90/4.23 tff(27963,plain,
% 3.90/4.23 (b(elem!1, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[560, 27962, 27933])).
% 3.90/4.23 tff(27964,plain,
% 3.90/4.23 (~(s(elem!1) = elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[906, 27933])).
% 3.90/4.23 tff(27965,plain,
% 3.90/4.23 (~r(s(elem!1), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[5359, 27961, 27952, 7265])).
% 3.90/4.23 tff(27966,plain,
% 3.90/4.23 (b(s(elem!1), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[448, 27965, 27964])).
% 3.90/4.23 tff(27967,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[555, 27966, 27963, 133, 27931])).
% 3.90/4.23 tff(27968,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | b(z, elem!1) | b(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(27969,plain,
% 3.90/4.23 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27968, 304, 1, 133, 27917, 17795, 27895, 1524, 27860, 27661, 11546, 708, 27893])).
% 3.90/4.23 tff(27970,plain,
% 3.90/4.23 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[279, 27969])).
% 3.90/4.23 tff(27971,plain,
% 3.90/4.23 (~r(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27739, 27970, 27662, 56, 304, 27895])).
% 3.90/4.23 tff(27972,plain,
% 3.90/4.23 (b(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[348, 27971])).
% 3.90/4.23 tff(27973,plain,
% 3.90/4.23 (~b(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[7093, 27972, 27893, 304])).
% 3.90/4.23 tff(27974,plain,
% 3.90/4.23 (r(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[372, 27973])).
% 3.90/4.23 tff(27975,plain,
% 3.90/4.23 (~r(elem!1, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[19174, 27974, 11546, 27861])).
% 3.90/4.23 tff(27976,plain,
% 3.90/4.23 (elem!1 = s(z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[720, 27975, 708])).
% 3.90/4.23 tff(27977,plain,
% 3.90/4.23 (b(elem!1, z) <=> b(s(z), z)),
% 3.90/4.23 inference(monotonicity,[status(thm)],[27976])).
% 3.90/4.23 tff(27978,plain,
% 3.90/4.23 (b(s(z), z) <=> b(elem!1, z)),
% 3.90/4.23 inference(symmetry,[status(thm)],[27977])).
% 3.90/4.23 tff(27979,plain,
% 3.90/4.23 (b(elem!1, z)),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[27972, 27978])).
% 3.90/4.23 tff(27980,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27916, 27979])).
% 3.90/4.23 tff(27981,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(27982,plain,
% 3.90/4.23 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27981, 708, 11546, 56, 1, 133, 1524, 7926])).
% 3.90/4.23 tff(27983,plain,
% 3.90/4.23 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[319, 27982])).
% 3.90/4.23 tff(27984,plain,
% 3.90/4.23 (~(elem!1 = s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27431, 27982, 133])).
% 3.90/4.23 tff(27985,plain,
% 3.90/4.23 (r(elem!1, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[720, 27984, 708])).
% 3.90/4.23 tff(27986,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[18836, 333, 27985, 11546, 23943, 27983])).
% 3.90/4.23 tff(27987,plain,(b(elem!1, s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(27988,plain,
% 3.90/4.23 (b(elem!1, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27987, 1524, 133, 56, 1, 11546, 7926])).
% 3.90/4.23 tff(27989,plain,
% 3.90/4.23 (r(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[24033, 321, 11546, 2323, 74, 305])).
% 3.90/4.23 tff(27990,plain,
% 3.90/4.23 (~r(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[21949, 321, 11546, 27989])).
% 3.90/4.23 tff(27991,plain,
% 3.90/4.23 (b(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[348, 27990])).
% 3.90/4.23 tff(27992,plain,
% 3.90/4.23 (~r(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[19126, 321, 11546, 2323])).
% 3.90/4.23 tff(27993,plain,
% 3.90/4.23 (b(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[406, 27992, 6529])).
% 3.90/4.23 tff(27994,plain,
% 3.90/4.23 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[3955, 27993, 133, 305])).
% 3.90/4.23 tff(27995,plain,
% 3.90/4.23 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[319, 27994])).
% 3.90/4.23 tff(27996,plain,
% 3.90/4.23 (~r(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[362, 27995, 353, 321])).
% 3.90/4.23 tff(27997,plain,
% 3.90/4.23 (b(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[372, 27996])).
% 3.90/4.23 tff(27998,plain,
% 3.90/4.23 (~r(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[3282, 321, 27989, 2323])).
% 3.90/4.23 tff(27999,plain,
% 3.90/4.23 (b(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1380, 27998, 730])).
% 3.90/4.23 tff(28000,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[387, 144, 27999, 27997, 27991, 305])).
% 3.90/4.23 tff(28001,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(28002,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28001, 27988, 27662, 133, 11546, 23943, 71])).
% 3.90/4.23 tff(28003,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[302, 28002])).
% 3.90/4.23 tff(28004,plain,
% 3.90/4.23 (~(s(s(s(z))) = elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27447, 1524])).
% 3.90/4.23 tff(28005,plain,
% 3.90/4.23 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[16388, 322, 11546, 353])).
% 3.90/4.23 tff(28006,plain,
% 3.90/4.23 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1137, 28005])).
% 3.90/4.23 tff(28007,plain,
% 3.90/4.23 (~r(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[18406, 322, 11546, 2323])).
% 3.90/4.23 tff(28008,plain,
% 3.90/4.23 (b(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[406, 28007, 6529])).
% 3.90/4.23 tff(28009,plain,
% 3.90/4.23 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27441, 28008, 74, 11546, 322, 2323])).
% 3.90/4.23 tff(28010,plain,
% 3.90/4.23 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[279, 28009])).
% 3.90/4.23 tff(28011,plain,
% 3.90/4.23 (~b(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[16228, 28010, 283, 28006])).
% 3.90/4.23 tff(28012,plain,
% 3.90/4.23 (r(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[619, 28011])).
% 3.90/4.23 tff(28013,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28001, 305, 353, 133, 11546, 2323, 74])).
% 3.90/4.23 tff(28014,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[302, 28013])).
% 3.90/4.23 tff(28015,plain,
% 3.90/4.23 (~b(s(s(s(z))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27648, 28010, 133, 2323, 28014, 698, 28008, 305])).
% 3.90/4.23 tff(28016,plain,
% 3.90/4.23 (r(s(s(s(z))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[396, 28015])).
% 3.90/4.23 tff(28017,plain,
% 3.90/4.23 (~r(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27726, 28016, 28012, 353])).
% 3.90/4.23 tff(28018,plain,
% 3.90/4.23 (b(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[348, 28017])).
% 3.90/4.23 tff(28019,plain,
% 3.90/4.23 (~b(s(s(s(z))), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[4375, 28008, 56, 305])).
% 3.90/4.23 tff(28020,plain,
% 3.90/4.23 (r(s(s(s(z))), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[704, 28019, 698])).
% 3.90/4.23 tff(28021,plain,
% 3.90/4.23 (~r(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1519, 28012, 353, 28020])).
% 3.90/4.23 tff(28022,plain,
% 3.90/4.23 (b(z, s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[372, 28021])).
% 3.90/4.23 tff(28023,plain,
% 3.90/4.23 (~b(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[7079, 28022, 305, 28008])).
% 3.90/4.23 tff(28024,plain,
% 3.90/4.23 (r(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[658, 28023, 74])).
% 3.90/4.23 tff(28025,plain,
% 3.90/4.23 (~r(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[14255, 28024, 283, 28020, 28014])).
% 3.90/4.23 tff(28026,plain,
% 3.90/4.23 (b(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1380, 28025, 730])).
% 3.90/4.23 tff(28027,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[387, 144, 28026, 28022, 28018, 305])).
% 3.90/4.23 tff(28028,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (z = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(28029,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28028, 27988, 17795, 71, 27662, 133, 23943, 28004, 11546, 56])).
% 3.90/4.23 tff(28030,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[319, 28029])).
% 3.90/4.23 tff(28031,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[19486, 144, 489, 305, 133, 304, 286])).
% 3.90/4.23 tff(28032,plain,((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(28033,plain,
% 3.90/4.23 (~b(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28032, 27988, 133, 28030, 28003])).
% 3.90/4.23 tff(28034,plain,
% 3.90/4.23 (r(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[348, 28033])).
% 3.90/4.23 tff(28035,plain,
% 3.90/4.23 (~(s(z) = elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[6528, 27988])).
% 3.90/4.23 tff(28036,plain,
% 3.90/4.23 (~b(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[3955, 28030, 133, 27988])).
% 3.90/4.23 tff(28037,plain,
% 3.90/4.23 (r(s(z), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[406, 28036, 28035])).
% 3.90/4.23 tff(28038,plain,
% 3.90/4.23 (~b(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[21533, 28030, 56, 28003, 17795])).
% 3.90/4.23 tff(28039,plain,
% 3.90/4.23 (r(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[619, 28038])).
% 3.90/4.23 tff(28040,plain,
% 3.90/4.23 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27739, 28034, 27662, 56, 28030, 28039])).
% 3.90/4.23 tff(28041,plain,
% 3.90/4.23 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[279, 28040])).
% 3.90/4.23 tff(28042,plain,
% 3.90/4.23 (~r(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[19519, 28041, 11546, 28035, 28039, 133, 28034])).
% 3.90/4.23 tff(28043,plain,
% 3.90/4.23 (b(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[1380, 28042, 77])).
% 3.90/4.23 tff(28044,plain,
% 3.90/4.23 (r(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27496, 28043, 133, 71, 11546, 23943, 27988])).
% 3.90/4.23 tff(28045,plain,
% 3.90/4.23 (((~![X0: $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), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, 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(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.23 inference(rewrite,[status(thm)],[])).
% 3.90/4.23 tff(28046,plain,
% 3.90/4.23 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.23 inference(rewrite,[status(thm)],[])).
% 3.90/4.23 tff(28047,plain,
% 3.90/4.23 (((~![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(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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28046])).
% 3.90/4.23 tff(28048,plain,
% 3.90/4.23 (((~![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(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(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.23 inference(transitivity,[status(thm)],[28047, 28045])).
% 3.90/4.23 tff(28049,plain,
% 3.90/4.23 ((~![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(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 3.90/4.23 inference(quant_inst,[status(thm)],[])).
% 3.90/4.23 tff(28050,plain,
% 3.90/4.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[28049, 28048])).
% 3.90/4.23 tff(28051,plain,
% 3.90/4.23 ($false),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28050, 333, 28044, 28037, 28034, 23943])).
% 3.90/4.23 tff(28052,plain,((elem!1 = s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.23 tff(28053,plain,
% 3.90/4.23 (elem!1 = s(s(s(z)))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28052, 1, 11546, 56, 133, 7926])).
% 3.90/4.23 tff(28054,plain,
% 3.90/4.23 (s(elem!1) = s(s(s(s(z))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28055,plain,
% 3.90/4.23 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28054])).
% 3.90/4.23 tff(28056,plain,
% 3.90/4.23 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28057,plain,
% 3.90/4.23 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.23 inference(transitivity,[status(thm)],[28056, 28055])).
% 3.90/4.23 tff(28058,plain,
% 3.90/4.23 ((elem!1 = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28059,plain,
% 3.90/4.23 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 3.90/4.23 inference(transitivity,[status(thm)],[28058, 997])).
% 3.90/4.23 tff(28060,plain,
% 3.90/4.23 ((s(elem!1) = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.90/4.23 inference(symmetry,[status(thm)],[28059])).
% 3.90/4.23 tff(28061,plain,
% 3.90/4.23 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28054])).
% 3.90/4.23 tff(28062,plain,
% 3.90/4.23 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.90/4.23 inference(symmetry,[status(thm)],[28061])).
% 3.90/4.23 tff(28063,plain,
% 3.90/4.23 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 3.90/4.23 inference(transitivity,[status(thm)],[28062, 28060, 199])).
% 3.90/4.23 tff(28064,plain,
% 3.90/4.23 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28063])).
% 3.90/4.23 tff(28065,plain,
% 3.90/4.23 (~(s(elem!1) = elem!1)),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[219, 28064])).
% 3.90/4.23 tff(28066,plain,
% 3.90/4.23 (s(s(s(z))) = elem!1),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[10997, 28053])).
% 3.90/4.23 tff(28067,plain,
% 3.90/4.23 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28068,plain,
% 3.90/4.23 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 3.90/4.23 inference(symmetry,[status(thm)],[28067])).
% 3.90/4.23 tff(28069,plain,
% 3.90/4.23 (r(s(z), elem!1)),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[27662, 28068])).
% 3.90/4.23 tff(28070,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[19126, 28069, 11546, 23943])).
% 3.90/4.23 tff(28071,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[302, 28070])).
% 3.90/4.23 tff(28072,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[18406, 28069, 11546, 23943])).
% 3.90/4.23 tff(28073,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[319, 28072])).
% 3.90/4.23 tff(28074,plain,
% 3.90/4.23 (~b(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[21533, 28073, 56, 28071, 17795])).
% 3.90/4.23 tff(28075,plain,
% 3.90/4.23 (r(z, s(s(s(z))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[619, 28074])).
% 3.90/4.23 tff(28076,plain,
% 3.90/4.23 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28077,plain,
% 3.90/4.23 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 3.90/4.23 inference(symmetry,[status(thm)],[28076])).
% 3.90/4.23 tff(28078,plain,
% 3.90/4.23 (b(elem!1, s(z))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[56, 28077])).
% 3.90/4.23 tff(28079,plain,
% 3.90/4.23 (~b(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[28032, 28073, 133, 28078, 28071])).
% 3.90/4.23 tff(28080,plain,
% 3.90/4.23 (r(s(z), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[348, 28079])).
% 3.90/4.23 tff(28081,plain,
% 3.90/4.23 (~r(s(s(s(z))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27726, 28080, 28075, 27662])).
% 3.90/4.23 tff(28082,plain,
% 3.90/4.23 (b(s(s(s(z))), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[396, 28081])).
% 3.90/4.23 tff(28083,plain,
% 3.90/4.23 (b(elem!1, z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[380, 28082, 28066])).
% 3.90/4.23 tff(28084,plain,
% 3.90/4.23 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[12214, 28066])).
% 3.90/4.23 tff(28085,plain,
% 3.90/4.23 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[20734, 28084])).
% 3.90/4.23 tff(28086,plain,
% 3.90/4.23 (~b(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[257, 28074, 28066])).
% 3.90/4.23 tff(28087,plain,
% 3.90/4.23 (r(z, elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[658, 28086, 71])).
% 3.90/4.23 tff(28088,plain,
% 3.90/4.23 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[27739, 28080, 27662, 56, 28073, 28075])).
% 3.90/4.23 tff(28089,plain,
% 3.90/4.23 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[279, 28088])).
% 3.90/4.23 tff(28090,plain,
% 3.90/4.23 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[2894, 28089, 23943, 28087])).
% 3.90/4.23 tff(28091,plain,
% 3.90/4.23 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[542, 28090, 28085])).
% 3.90/4.23 tff(28092,plain,
% 3.90/4.23 (~b(s(elem!1), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[3500, 28091, 133, 28071, 28083])).
% 3.90/4.23 tff(28093,plain,
% 3.90/4.23 (r(s(elem!1), elem!1)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[448, 28092, 28065])).
% 3.90/4.23 tff(28094,plain,
% 3.90/4.23 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[28093, 28057])).
% 3.90/4.23 tff(28095,plain,
% 3.90/4.23 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28054])).
% 3.90/4.23 tff(28096,plain,
% 3.90/4.23 (~r(s(elem!1), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[24919, 28093, 28087, 23943])).
% 3.90/4.23 tff(28097,plain,
% 3.90/4.23 (b(s(elem!1), z)),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[507, 28096])).
% 3.90/4.23 tff(28098,plain,
% 3.90/4.23 (~b(z, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[12069, 28097, 28071, 28091])).
% 3.90/4.23 tff(28099,plain,
% 3.90/4.23 (r(z, s(elem!1))),
% 3.90/4.23 inference(unit_resolution,[status(thm)],[583, 28098])).
% 3.90/4.23 tff(28100,plain,
% 3.90/4.23 (r(z, s(s(s(s(z)))))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[28099, 28095])).
% 3.90/4.23 tff(28101,plain,
% 3.90/4.23 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(monotonicity,[status(thm)],[28053])).
% 3.90/4.23 tff(28102,plain,
% 3.90/4.23 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.23 inference(modus_ponens,[status(thm)],[23943, 28101])).
% 3.90/4.23 tff(28103,plain,
% 3.90/4.23 (((~![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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.23 inference(rewrite,[status(thm)],[])).
% 3.90/4.23 tff(28104,plain,
% 3.90/4.23 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.23 inference(rewrite,[status(thm)],[])).
% 3.90/4.24 tff(28105,plain,
% 3.90/4.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28104])).
% 3.90/4.24 tff(28106,plain,
% 3.90/4.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28105, 28103])).
% 3.90/4.24 tff(28107,plain,
% 3.90/4.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 3.90/4.24 inference(quant_inst,[status(thm)],[])).
% 3.90/4.24 tff(28108,plain,
% 3.90/4.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[28107, 28106])).
% 3.90/4.24 tff(28109,plain,
% 3.90/4.24 ($false),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28108, 333, 28075, 28102, 28100, 28094])).
% 3.90/4.24 tff(28110,plain,((s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.24 tff(28111,plain,
% 3.90/4.24 (s(elem!1) = s(z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28110, 7926, 56, 11546, 27421])).
% 3.90/4.24 tff(28112,plain,
% 3.90/4.24 (z = elem!1),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[8683, 28111])).
% 3.90/4.24 tff(28113,plain,
% 3.90/4.24 (elem!1 = z),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18287, 28112])).
% 3.90/4.24 tff(28114,plain,
% 3.90/4.24 ($false),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[708, 26729])).
% 3.90/4.24 tff(28115,plain,((~b(z, s(z))) | b(elem!1, s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.24 tff(28116,plain,
% 3.90/4.24 (~b(z, s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28115, 708, 28112])).
% 3.90/4.24 tff(28117,plain,
% 3.90/4.24 (~b(elem!1, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18030, 28116, 28111])).
% 3.90/4.24 tff(28118,plain,
% 3.90/4.24 (~b(z, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18176, 28117, 28113])).
% 3.90/4.24 tff(28119,plain,
% 3.90/4.24 (r(z, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[583, 28118])).
% 3.90/4.24 tff(28120,plain,
% 3.90/4.24 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28111])).
% 3.90/4.24 tff(28121,plain,
% 3.90/4.24 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28120])).
% 3.90/4.24 tff(28122,plain,
% 3.90/4.24 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[11546, 28121])).
% 3.90/4.24 tff(28123,plain,
% 3.90/4.24 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.24 tff(28124,plain,
% 3.90/4.24 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28123])).
% 3.90/4.24 tff(28125,plain,
% 3.90/4.24 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.24 tff(28126,plain,
% 3.90/4.24 ((s(z) = z) <=> (elem!1 = s(z))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28125, 53])).
% 3.90/4.24 tff(28127,plain,
% 3.90/4.24 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28126])).
% 3.90/4.24 tff(28128,plain,
% 3.90/4.24 (~(elem!1 = s(z))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[344, 28127])).
% 3.90/4.24 tff(28129,plain,
% 3.90/4.24 (r(elem!1, s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[720, 708, 28128])).
% 3.90/4.24 tff(28130,plain,
% 3.90/4.24 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.24 tff(28131,plain,
% 3.90/4.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[22687, 28112, 54])).
% 3.90/4.24 tff(28132,plain,
% 3.90/4.24 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[302, 28131])).
% 3.90/4.24 tff(28133,plain,
% 3.90/4.24 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28111])).
% 3.90/4.24 tff(28134,plain,
% 3.90/4.24 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28133, 3061])).
% 3.90/4.24 tff(28135,plain,
% 3.90/4.24 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28134])).
% 3.90/4.24 tff(28136,plain,
% 3.90/4.24 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28135])).
% 3.90/4.24 tff(28137,plain,
% 3.90/4.24 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[1096, 28136])).
% 3.90/4.24 tff(28138,plain,
% 3.90/4.24 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[27273, 155, 28111])).
% 3.90/4.24 tff(28139,plain,
% 3.90/4.24 (b(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1067, 28138, 28137])).
% 3.90/4.24 tff(28140,plain,
% 3.90/4.24 (b(s(elem!1), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18064, 489, 28112])).
% 3.90/4.24 tff(28141,plain,
% 3.90/4.24 (b(s(z), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[22716, 489, 28113])).
% 3.90/4.24 tff(28142,plain,
% 3.90/4.24 (elem!1 = z),
% 3.90/4.24 inference(symmetry,[status(thm)],[28112])).
% 3.90/4.24 tff(28143,plain,
% 3.90/4.24 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28142])).
% 3.90/4.24 tff(28144,plain,
% 3.90/4.24 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.90/4.24 inference(symmetry,[status(thm)],[28143])).
% 3.90/4.24 tff(28145,plain,
% 3.90/4.24 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28144])).
% 3.90/4.24 tff(28146,plain,
% 3.90/4.24 (~(s(s(z)) = elem!1)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[164, 28145])).
% 3.90/4.24 tff(28147,plain,
% 3.90/4.24 (s(s(elem!1)) = s(s(z))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28111])).
% 3.90/4.24 tff(28148,plain,
% 3.90/4.24 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28147])).
% 3.90/4.24 tff(28149,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28147, 28148])).
% 3.90/4.24 tff(28150,plain,
% 3.90/4.24 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28149])).
% 3.90/4.24 tff(28151,plain,
% 3.90/4.24 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28150])).
% 3.90/4.24 tff(28152,plain,
% 3.90/4.24 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[217, 28151])).
% 3.90/4.24 tff(28153,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28111])).
% 3.90/4.24 tff(28154,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28153])).
% 3.90/4.24 tff(28155,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28154])).
% 3.90/4.24 tff(28156,plain,
% 3.90/4.24 (~(s(s(elem!1)) = s(elem!1))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[107, 28155])).
% 3.90/4.24 tff(28157,plain,
% 3.90/4.24 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.24 tff(28158,plain,
% 3.90/4.24 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28157, 1218])).
% 3.90/4.24 tff(28159,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28158])).
% 3.90/4.24 tff(28160,plain,
% 3.90/4.24 (~(elem!1 = s(s(elem!1)))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[1094, 28159])).
% 3.90/4.24 tff(28161,plain,
% 3.90/4.24 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.90/4.24 inference(transitivity,[status(thm)],[28158, 4572])).
% 3.90/4.24 tff(28162,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28161])).
% 3.90/4.24 tff(28163,plain,
% 3.90/4.24 (~(s(s(elem!1)) = elem!1)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[1094, 28162])).
% 3.90/4.24 tff(28164,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 3.90/4.24 inference(symmetry,[status(thm)],[2502])).
% 3.90/4.24 tff(28165,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28154, 28164])).
% 3.90/4.24 tff(28166,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28165])).
% 3.90/4.24 tff(28167,plain,
% 3.90/4.24 (~(s(elem!1) = s(s(elem!1)))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[107, 28166])).
% 3.90/4.24 tff(28168,plain,
% 3.90/4.24 (s(s(z)) = s(s(elem!1))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28147])).
% 3.90/4.24 tff(28169,plain,
% 3.90/4.24 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28168])).
% 3.90/4.24 tff(28170,plain,
% 3.90/4.24 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28169, 13328])).
% 3.90/4.24 tff(28171,plain,
% 3.90/4.24 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28170])).
% 3.90/4.24 tff(28172,plain,
% 3.90/4.24 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[1446, 28171])).
% 3.90/4.24 tff(28173,plain,
% 3.90/4.24 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28111])).
% 3.90/4.24 tff(28174,plain,
% 3.90/4.24 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 3.90/4.24 inference(transitivity,[status(thm)],[28173, 52])).
% 3.90/4.24 tff(28175,plain,
% 3.90/4.24 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.90/4.24 inference(symmetry,[status(thm)],[28174])).
% 3.90/4.24 tff(28176,plain,
% 3.90/4.24 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28125, 28175])).
% 3.90/4.24 tff(28177,plain,
% 3.90/4.24 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28176])).
% 3.90/4.24 tff(28178,plain,
% 3.90/4.24 (~(elem!1 = s(elem!1))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[344, 28177])).
% 3.90/4.24 tff(28179,plain,
% 3.90/4.24 (~b(elem!1, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18030, 9362, 28111])).
% 3.90/4.24 tff(28180,plain,
% 3.90/4.24 (r(elem!1, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[560, 28179, 28178])).
% 3.90/4.24 tff(28181,plain,
% 3.90/4.24 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[8472, 28180, 27421, 28122, 28172, 28167, 28163, 28160, 451])).
% 3.90/4.24 tff(28182,plain,
% 3.90/4.24 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1283, 28181, 28156])).
% 3.90/4.24 tff(28183,plain,
% 3.90/4.24 (b(s(s(z)), s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18895, 28182, 28111])).
% 3.90/4.24 tff(28184,plain,
% 3.90/4.24 (~b(s(s(z)), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18116, 28183, 28111, 56, 10356])).
% 3.90/4.24 tff(28185,plain,
% 3.90/4.24 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18122, 28184, 28111])).
% 3.90/4.24 tff(28186,plain,
% 3.90/4.24 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[4311, 28185, 28152])).
% 3.90/4.24 tff(28187,plain,
% 3.90/4.24 (r(s(s(z)), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18132, 28186, 28111])).
% 3.90/4.24 tff(28188,plain,
% 3.90/4.24 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.24 tff(28189,plain,
% 3.90/4.24 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28188, 2544])).
% 3.90/4.24 tff(28190,plain,
% 3.90/4.24 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28189])).
% 3.90/4.24 tff(28191,plain,
% 3.90/4.24 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[273, 28190])).
% 3.90/4.24 tff(28192,plain,
% 3.90/4.24 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[121, 3, 28191])).
% 3.90/4.24 tff(28193,plain,
% 3.90/4.24 (~b(s(s(s(z))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[294, 284, 283, 286])).
% 3.90/4.24 tff(28194,plain,
% 3.90/4.24 (r(s(s(s(z))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[396, 28193])).
% 3.90/4.24 tff(28195,plain,
% 3.90/4.24 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[16228, 284, 283, 22725])).
% 3.90/4.24 tff(28196,plain,
% 3.90/4.24 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1137, 28195])).
% 3.90/4.24 tff(28197,plain,
% 3.90/4.24 (~b(z, s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[16453, 28196, 11546, 284, 322])).
% 3.90/4.24 tff(28198,plain,
% 3.90/4.24 (r(z, s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[372, 28197])).
% 3.90/4.24 tff(28199,plain,
% 3.90/4.24 (~r(s(z), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[16388, 28196, 11546, 322])).
% 3.90/4.24 tff(28200,plain,
% 3.90/4.24 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[27273, 28199, 8677])).
% 3.90/4.24 tff(28201,plain,
% 3.90/4.24 (b(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1067, 28200, 27261])).
% 3.90/4.24 tff(28202,plain,
% 3.90/4.24 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.90/4.24 inference(transitivity,[status(thm)],[22703, 4572])).
% 3.90/4.24 tff(28203,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28202])).
% 3.90/4.24 tff(28204,plain,
% 3.90/4.24 (~(s(s(elem!1)) = elem!1)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[1094, 28203])).
% 3.90/4.24 tff(28205,plain,
% 3.90/4.24 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 3.90/4.24 inference(transitivity,[status(thm)],[22757, 28164])).
% 3.90/4.24 tff(28206,plain,
% 3.90/4.24 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28205])).
% 3.90/4.24 tff(28207,plain,
% 3.90/4.24 (~(s(elem!1) = s(s(elem!1)))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[107, 28206])).
% 3.90/4.24 tff(28208,plain,
% 3.90/4.24 (~b(elem!1, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18030, 28197, 8677])).
% 3.90/4.24 tff(28209,plain,
% 3.90/4.24 (r(elem!1, s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[560, 28208, 27214])).
% 3.90/4.24 tff(28210,plain,
% 3.90/4.24 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[8472, 28209, 133, 22728, 23135, 28207, 28204, 22705, 451])).
% 3.90/4.24 tff(28211,plain,
% 3.90/4.24 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1283, 28210, 22759])).
% 3.90/4.24 tff(28212,plain,
% 3.90/4.24 (b(s(s(z)), s(z))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18895, 28211, 8677])).
% 3.90/4.24 tff(28213,plain,
% 3.90/4.24 (~b(s(s(z)), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18116, 28212, 8677, 56, 28201])).
% 3.90/4.24 tff(28214,plain,
% 3.90/4.24 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18122, 28213, 8677])).
% 3.90/4.24 tff(28215,plain,
% 3.90/4.24 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[4311, 28214, 22826])).
% 3.90/4.24 tff(28216,plain,
% 3.90/4.24 (r(s(s(z)), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18132, 28215, 8677])).
% 3.90/4.24 tff(28217,plain,
% 3.90/4.24 (~r(s(s(z)), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18145, 28216, 28198, 28194])).
% 3.90/4.24 tff(28218,plain,
% 3.90/4.24 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[66])).
% 3.90/4.24 tff(28219,plain,
% 3.90/4.24 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 3.90/4.24 inference(symmetry,[status(thm)],[28218])).
% 3.90/4.24 tff(28220,plain,
% 3.90/4.24 (r(s(s(z)), z)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[7155, 28219])).
% 3.90/4.24 tff(28221,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 3.90/4.24 tff(28222,plain,
% 3.90/4.24 ($false),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28221, 28220])).
% 3.90/4.24 tff(28223,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.24 tff(28224,plain,
% 3.90/4.24 (~r(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28223, 28217, 18019])).
% 3.90/4.24 tff(28225,plain,
% 3.90/4.24 (b(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[7970, 28224, 22830])).
% 3.90/4.24 tff(28226,plain,
% 3.90/4.24 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18163, 28216, 322, 28196])).
% 3.90/4.24 tff(28227,plain,
% 3.90/4.24 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1451, 28226])).
% 3.90/4.24 tff(28228,plain,
% 3.90/4.24 ($false),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[23209, 144, 134, 28212, 28227, 132, 28225])).
% 3.90/4.24 tff(28229,plain,((~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.24 tff(28230,plain,
% 3.90/4.24 (~b(z, s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28229, 134, 28192, 322, 28111, 56, 27421, 451, 11546, 17795, 28132])).
% 3.90/4.24 tff(28231,plain,
% 3.90/4.24 (r(z, s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[619, 28230])).
% 3.90/4.24 tff(28232,plain,
% 3.90/4.24 (r(elem!1, s(s(s(z))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[28231, 28130])).
% 3.90/4.24 tff(28233,plain,
% 3.90/4.24 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.90/4.24 inference(monotonicity,[status(thm)],[18019])).
% 3.90/4.24 tff(28234,plain,
% 3.90/4.24 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28233])).
% 3.90/4.24 tff(28235,plain,
% 3.90/4.24 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[273, 28234])).
% 3.90/4.24 tff(28236,plain,
% 3.90/4.24 (~b(s(s(s(z))), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[10110, 23185, 54, 28235, 3])).
% 3.90/4.24 tff(28237,plain,
% 3.90/4.24 (~b(s(s(s(z))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[26887, 28236, 18019])).
% 3.90/4.24 tff(28238,plain,
% 3.90/4.24 (r(s(s(s(z))), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[396, 28237])).
% 3.90/4.24 tff(28239,plain,
% 3.90/4.24 (~r(s(s(z)), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18145, 28238, 354, 6330])).
% 3.90/4.24 tff(28240,plain,
% 3.90/4.24 (~r(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28223, 28239, 18019])).
% 3.90/4.24 tff(28241,plain,
% 3.90/4.24 (b(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[7970, 28240, 22830])).
% 3.90/4.24 tff(28242,plain,
% 3.90/4.24 (b(s(s(elem!1)), elem!1)),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[28241, 27325])).
% 3.90/4.24 tff(28243,plain,
% 3.90/4.24 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28233, 2544])).
% 3.90/4.24 tff(28244,plain,
% 3.90/4.24 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28243])).
% 3.90/4.24 tff(28245,plain,
% 3.90/4.24 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[273, 28244])).
% 3.90/4.24 tff(28246,plain,
% 3.90/4.24 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[121, 3, 28245])).
% 3.90/4.24 tff(28247,plain,
% 3.90/4.24 (r(s(s(z)), s(s(s(z))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18132, 23044, 8677])).
% 3.90/4.24 tff(28248,plain,
% 3.90/4.24 (~r(s(s(z)), z)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[18145, 28247, 354, 1699])).
% 3.90/4.24 tff(28249,plain,
% 3.90/4.24 (~r(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28223, 28248, 18019])).
% 3.90/4.24 tff(28250,plain,
% 3.90/4.24 (b(s(s(z)), elem!1)),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[7970, 28249, 26795])).
% 3.90/4.24 tff(28251,plain,
% 3.90/4.24 ($false),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[11650, 144, 1398, 133, 132, 28250])).
% 3.90/4.24 tff(28252,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~(s(elem!1) = s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.24 tff(28253,plain,
% 3.90/4.24 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28252, 28238, 27421, 7926, 28246, 8677, 7927, 354])).
% 3.90/4.24 tff(28254,plain,
% 3.90/4.24 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[1451, 28253])).
% 3.90/4.24 tff(28255,plain,
% 3.90/4.24 (((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.24 inference(rewrite,[status(thm)],[])).
% 3.90/4.24 tff(28256,plain,
% 3.90/4.24 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.24 inference(rewrite,[status(thm)],[])).
% 3.90/4.24 tff(28257,plain,
% 3.90/4.24 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.24 inference(monotonicity,[status(thm)],[28256])).
% 3.90/4.24 tff(28258,plain,
% 3.90/4.24 (((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.24 inference(transitivity,[status(thm)],[28257, 28255])).
% 3.90/4.24 tff(28259,plain,
% 3.90/4.24 ((~![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(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 3.90/4.24 inference(quant_inst,[status(thm)],[])).
% 3.90/4.24 tff(28260,plain,
% 3.90/4.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.24 inference(modus_ponens,[status(thm)],[28259, 28258])).
% 3.90/4.24 tff(28261,plain,
% 3.90/4.24 (~r(s(z), s(s(z)))),
% 3.90/4.24 inference(unit_resolution,[status(thm)],[28260, 333, 28254, 11546, 322])).
% 3.90/4.25 tff(28262,plain,
% 3.90/4.25 (~r(s(z), s(s(elem!1)))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[22807, 28261, 8677])).
% 3.90/4.25 tff(28263,plain,
% 3.90/4.25 (b(s(z), s(s(elem!1)))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[5484, 28262])).
% 3.90/4.25 tff(28264,plain,
% 3.90/4.25 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[8677])).
% 3.90/4.25 tff(28265,plain,
% 3.90/4.25 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.90/4.25 inference(symmetry,[status(thm)],[28264])).
% 3.90/4.25 tff(28266,plain,
% 3.90/4.25 (b(s(elem!1), s(s(elem!1)))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[5486, 28265])).
% 3.90/4.25 tff(28267,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 3.90/4.25 tff(28268,plain,
% 3.90/4.25 ($false),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28267, 28266])).
% 3.90/4.25 tff(28269,plain,((~b(s(z), s(s(elem!1)))) | b(s(elem!1), s(s(elem!1))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.25 tff(28270,plain,
% 3.90/4.25 (b(s(elem!1), s(s(elem!1)))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28269, 28263, 8677])).
% 3.90/4.25 tff(28271,plain,
% 3.90/4.25 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[18101])).
% 3.90/4.25 tff(28272,plain,
% 3.90/4.25 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.90/4.25 inference(symmetry,[status(thm)],[28271])).
% 3.90/4.25 tff(28273,plain,
% 3.90/4.25 ((~r(elem!1, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28272])).
% 3.90/4.25 tff(28274,plain,
% 3.90/4.25 (r(s(s(s(z))), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[704, 28236, 22766])).
% 3.90/4.25 tff(28275,plain,
% 3.90/4.25 (~r(elem!1, s(s(z)))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[23084, 333, 1525, 28274, 6330])).
% 3.90/4.25 tff(28276,plain,
% 3.90/4.25 (~r(elem!1, s(s(elem!1)))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28275, 28273])).
% 3.90/4.25 tff(28277,plain,
% 3.90/4.25 (b(elem!1, s(s(elem!1)))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[2522, 28276, 22705])).
% 3.90/4.25 tff(28278,plain,
% 3.90/4.25 (~b(s(s(elem!1)), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[24923, 28277, 451, 28270])).
% 3.90/4.25 tff(28279,plain,
% 3.90/4.25 ($false),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28278, 28242])).
% 3.90/4.25 tff(28280,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~(s(elem!1) = s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(z, s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.25 tff(28281,plain,
% 3.90/4.25 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28280, 28187, 451, 11546, 322, 28232, 28111, 7926, 9363, 54, 3])).
% 3.90/4.25 tff(28282,plain,
% 3.90/4.25 (~r(s(s(z)), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[27294, 333, 28232, 28281, 28187])).
% 3.90/4.25 tff(28283,plain,
% 3.90/4.25 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[18163, 28281, 322, 28187])).
% 3.90/4.25 tff(28284,plain,
% 3.90/4.25 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[1451, 28283])).
% 3.90/4.25 tff(28285,plain,
% 3.90/4.25 (~b(s(s(z)), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[23209, 144, 134, 28183, 28284, 28192])).
% 3.90/4.25 tff(28286,plain,
% 3.90/4.25 ($false),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[7970, 28285, 28282, 28146])).
% 3.90/4.25 tff(28287,plain,(b(z, s(z)) | (~b(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.25 tff(28288,plain,
% 3.90/4.25 (~b(s(elem!1), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28287, 28141, 9362, 322, 11546, 7926, 54, 3, 56, 10356])).
% 3.90/4.25 tff(28289,plain,
% 3.90/4.25 ($false),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[25335, 28288, 28140, 28112])).
% 3.90/4.25 tff(28290,plain,((~b(s(z), z)) | b(z, s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.25 tff(28291,plain,
% 3.90/4.25 (~b(s(z), z)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28290, 28139, 322, 11546, 7926, 54, 3, 56, 9362])).
% 3.90/4.25 tff(28292,plain,
% 3.90/4.25 (r(s(z), z)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[348, 28291])).
% 3.90/4.25 tff(28293,plain,
% 3.90/4.25 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.25 tff(28294,plain,
% 3.90/4.25 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(symmetry,[status(thm)],[28293])).
% 3.90/4.25 tff(28295,plain,
% 3.90/4.25 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28192, 28294])).
% 3.90/4.25 tff(28296,plain,
% 3.90/4.25 (r(s(z), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[25327, 28292, 28112])).
% 3.90/4.25 tff(28297,plain,
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% 3.90/4.25 inference(modus_ponens,[status(thm)],[409, 22733])).
% 3.90/4.25 tff(28298,plain,
% 3.90/4.25 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[14540, 354, 28297, 22728])).
% 3.90/4.25 tff(28299,plain,
% 3.90/4.25 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[302, 28298])).
% 3.90/4.25 tff(28300,plain,
% 3.90/4.25 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[14770, 28299, 22711])).
% 3.90/4.25 tff(28301,plain,
% 3.90/4.25 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 3.90/4.25 inference(symmetry,[status(thm)],[24729])).
% 3.90/4.25 tff(28302,plain,
% 3.90/4.25 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28301])).
% 3.90/4.25 tff(28303,plain,
% 3.90/4.25 (~(s(s(z)) = s(s(s(s(z)))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[24445, 28302])).
% 3.90/4.25 tff(28304,plain,
% 3.90/4.25 (r(elem!1, s(z))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[354, 22947])).
% 3.90/4.25 tff(28305,plain,
% 3.90/4.25 (~r(s(s(s(s(z)))), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[26851, 1525, 838, 56, 26619, 28304, 409])).
% 3.90/4.25 tff(28306,plain,
% 3.90/4.25 (b(s(s(s(s(z)))), elem!1)),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[24299, 44, 28305, 26567])).
% 3.90/4.25 tff(28307,plain,
% 3.90/4.25 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[3552, 144, 28306, 28300, 132])).
% 3.90/4.25 tff(28308,plain,
% 3.90/4.25 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[9761, 28307])).
% 3.90/4.25 tff(28309,plain,
% 3.90/4.25 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[19765, 333, 11546, 322, 28308])).
% 3.90/4.25 tff(28310,plain,
% 3.90/4.25 (b(s(s(s(s(z)))), s(z))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[24600, 28309, 24294])).
% 3.90/4.25 tff(28311,plain,
% 3.90/4.25 (~r(s(z), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[19714, 333, 11546, 322, 28308])).
% 3.90/4.25 tff(28312,plain,
% 3.90/4.25 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[19906, 44, 28311])).
% 3.90/4.25 tff(28313,plain,
% 3.90/4.25 (b(s(z), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28312, 25692])).
% 3.90/4.25 tff(28314,plain,
% 3.90/4.25 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[26043, 28308, 838, 56, 322, 11546])).
% 3.90/4.25 tff(28315,plain,
% 3.90/4.25 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[26564])).
% 3.90/4.25 tff(28316,plain,
% 3.90/4.25 (~(elem!1 = s(s(s(s(z)))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[242, 28315])).
% 3.90/4.25 tff(28317,plain,
% 3.90/4.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[26041, 144, 56, 28310, 838])).
% 3.90/4.25 tff(28318,plain,
% 3.90/4.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[9821, 44, 219, 28317])).
% 3.90/4.25 tff(28319,plain,
% 3.90/4.25 (((~![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))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28320,plain,
% 3.90/4.25 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28321,plain,
% 3.90/4.25 (((~![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))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, 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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28320])).
% 3.90/4.25 tff(28322,plain,
% 3.90/4.25 (((~![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))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, 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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.90/4.25 inference(transitivity,[status(thm)],[28321, 28319])).
% 3.90/4.25 tff(28323,plain,
% 3.90/4.25 ((~![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))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.90/4.25 inference(quant_inst,[status(thm)],[])).
% 3.90/4.25 tff(28324,plain,
% 3.90/4.25 ((~![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))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28323, 28322])).
% 3.90/4.25 tff(28325,plain,
% 3.90/4.25 (~r(elem!1, s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28324, 333, 1525, 26619, 28318])).
% 3.90/4.25 tff(28326,plain,
% 3.90/4.25 (b(elem!1, s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[6873, 28325, 28316])).
% 3.90/4.25 tff(28327,plain,
% 3.90/4.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28328,plain,
% 3.90/4.25 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28329,plain,
% 3.90/4.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28328])).
% 3.90/4.25 tff(28330,plain,
% 3.90/4.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(transitivity,[status(thm)],[28329, 28327])).
% 3.90/4.25 tff(28331,plain,
% 3.90/4.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.90/4.25 inference(quant_inst,[status(thm)],[])).
% 3.90/4.25 tff(28332,plain,
% 3.90/4.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28331, 28330])).
% 3.90/4.25 tff(28333,plain,
% 3.90/4.25 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28332, 144, 28306, 28300, 28326])).
% 3.90/4.25 tff(28334,plain,
% 3.90/4.25 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[12733, 44, 28333])).
% 3.90/4.25 tff(28335,plain,
% 3.90/4.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28334, 12723])).
% 3.90/4.25 tff(28336,plain,
% 3.90/4.25 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 3.90/4.25 inference(commutativity,[status(thm)],[])).
% 3.90/4.25 tff(28337,plain,
% 3.90/4.25 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 3.90/4.25 inference(symmetry,[status(thm)],[28336])).
% 3.90/4.25 tff(28338,plain,
% 3.90/4.25 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28337])).
% 3.90/4.25 tff(28339,plain,
% 3.90/4.25 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[219, 28338])).
% 3.90/4.25 tff(28340,plain,
% 3.90/4.25 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28341,plain,
% 3.90/4.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28340])).
% 3.90/4.25 tff(28342,plain,
% 3.90/4.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(transitivity,[status(thm)],[28341, 27015])).
% 3.90/4.25 tff(28343,plain,
% 3.90/4.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 3.90/4.25 inference(quant_inst,[status(thm)],[])).
% 3.90/4.25 tff(28344,plain,
% 3.90/4.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28343, 28342])).
% 3.90/4.25 tff(28345,plain,
% 3.90/4.25 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28344, 144, 56, 28313, 28310])).
% 3.90/4.25 tff(28346,plain,
% 3.90/4.25 ((s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[26947, 44, 28345])).
% 3.90/4.25 tff(28347,plain,
% 3.90/4.25 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28346, 28339])).
% 3.90/4.25 tff(28348,plain,
% 3.90/4.25 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28349,plain,
% 3.90/4.25 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(rewrite,[status(thm)],[])).
% 3.90/4.25 tff(28350,plain,
% 3.90/4.25 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.90/4.25 inference(monotonicity,[status(thm)],[28349])).
% 3.90/4.25 tff(28351,plain,
% 3.90/4.25 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.90/4.25 inference(transitivity,[status(thm)],[28350, 28348])).
% 3.90/4.25 tff(28352,plain,
% 3.90/4.25 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.90/4.25 inference(quant_inst,[status(thm)],[])).
% 3.90/4.25 tff(28353,plain,
% 3.90/4.25 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.90/4.25 inference(modus_ponens,[status(thm)],[28352, 28351])).
% 3.90/4.25 tff(28354,plain,
% 3.90/4.25 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28353, 333, 28308, 28347, 28335])).
% 3.90/4.25 tff(28355,plain,
% 3.90/4.25 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[28252, 28354, 132, 354, 1699, 8677, 28300, 28314])).
% 3.90/4.25 tff(28356,plain,
% 3.90/4.25 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[1451, 28355])).
% 3.90/4.25 tff(28357,plain,
% 3.90/4.25 (~r(s(s(z)), s(z))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[17910, 333, 28356, 11546, 322])).
% 3.90/4.25 tff(28358,plain,
% 3.90/4.25 (b(s(s(z)), s(z))),
% 3.90/4.25 inference(unit_resolution,[status(thm)],[1429, 44, 28357, 1416])).
% 3.90/4.26 tff(28359,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28360,plain,
% 3.90/4.26 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28361,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28360])).
% 3.90/4.26 tff(28362,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(transitivity,[status(thm)],[28361, 28359])).
% 3.90/4.26 tff(28363,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 3.90/4.26 inference(quant_inst,[status(thm)],[])).
% 3.90/4.26 tff(28364,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28363, 28362])).
% 3.90/4.26 tff(28365,plain,
% 3.90/4.26 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28364, 144, 28358, 28313, 28310])).
% 3.90/4.26 tff(28366,plain,
% 3.90/4.26 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28367,plain,
% 3.90/4.26 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28368,plain,
% 3.90/4.26 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28367])).
% 3.90/4.26 tff(28369,plain,
% 3.90/4.26 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(transitivity,[status(thm)],[28368, 28366])).
% 3.90/4.26 tff(28370,plain,
% 3.90/4.26 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.90/4.26 inference(quant_inst,[status(thm)],[])).
% 3.90/4.26 tff(28371,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28370, 28369])).
% 3.90/4.26 tff(28372,plain,
% 3.90/4.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28371, 333, 28356, 322, 28308])).
% 3.90/4.26 tff(28373,plain,
% 3.90/4.26 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[20473, 44, 28372])).
% 3.90/4.26 tff(28374,plain,
% 3.90/4.26 ($false),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28373, 28365, 28303])).
% 3.90/4.26 tff(28375,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.26 tff(28376,plain,
% 3.90/4.26 (~r(elem!1, s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28375, 1699, 11546, 132, 354, 322, 8677, 26799, 19304, 409])).
% 3.90/4.26 tff(28377,plain,
% 3.90/4.26 (b(elem!1, s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[1538, 28376, 22768])).
% 3.90/4.26 tff(28378,plain,
% 3.90/4.26 (b(z, s(s(s(z))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28377, 27351])).
% 3.90/4.26 tff(28379,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26847, 25527, 722, 409])).
% 3.90/4.26 tff(28380,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24299, 44, 28379, 24296])).
% 3.90/4.26 tff(28381,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[3552, 144, 28380, 133, 132])).
% 3.90/4.26 tff(28382,plain,
% 3.90/4.26 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9761, 28381])).
% 3.90/4.26 tff(28383,plain,
% 3.90/4.26 ($false),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[22498, 333, 25527, 11546, 224, 28382])).
% 3.90/4.26 tff(28384,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.26 tff(28385,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28384, 224, 11546, 133, 132, 24296, 722, 409])).
% 3.90/4.26 tff(28386,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24600, 28385, 24294])).
% 3.90/4.26 tff(28387,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26041, 144, 56, 28386, 838])).
% 3.90/4.26 tff(28388,plain,
% 3.90/4.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9821, 44, 219, 28387])).
% 3.90/4.26 tff(28389,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28390,plain,
% 3.90/4.26 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28391,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28390])).
% 3.90/4.26 tff(28392,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.26 inference(transitivity,[status(thm)],[28391, 28389])).
% 3.90/4.26 tff(28393,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(z))))))))))),
% 3.90/4.26 inference(quant_inst,[status(thm)],[])).
% 3.90/4.26 tff(28394,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28393, 28392])).
% 3.90/4.26 tff(28395,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28394, 333, 707, 224, 28388])).
% 3.90/4.26 tff(28396,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9761, 28395])).
% 3.90/4.26 tff(28397,plain,
% 3.90/4.26 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28398,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28397])).
% 3.90/4.26 tff(28399,plain,
% 3.90/4.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.26 inference(transitivity,[status(thm)],[28398, 3547])).
% 3.90/4.26 tff(28400,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(s(s(z))))))))))),
% 3.90/4.26 inference(quant_inst,[status(thm)],[])).
% 3.90/4.26 tff(28401,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28400, 28399])).
% 3.90/4.26 tff(28402,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28401, 144, 133, 132, 28396])).
% 3.90/4.26 tff(28403,plain,
% 3.90/4.26 (r(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24299, 44, 28402, 24296])).
% 3.90/4.26 tff(28404,plain,
% 3.90/4.26 (((~![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(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(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))))))),
% 3.90/4.26 inference(rewrite,[status(thm)],[])).
% 3.90/4.26 tff(28405,plain,
% 3.90/4.26 ((~![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(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.90/4.26 inference(quant_inst,[status(thm)],[])).
% 3.90/4.26 tff(28406,plain,
% 3.90/4.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28405, 28404])).
% 3.90/4.26 tff(28407,plain,
% 3.90/4.26 ($false),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28406, 333, 722, 707, 28403, 28388])).
% 3.90/4.26 tff(28408,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.26 tff(28409,plain,
% 3.90/4.26 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28408, 26619, 28304, 26567, 28300, 132, 26799, 19304, 11546, 409])).
% 3.90/4.26 tff(28410,plain,
% 3.90/4.26 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[249, 28409])).
% 3.90/4.26 tff(28411,plain,
% 3.90/4.26 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[16228, 28410, 259, 28378])).
% 3.90/4.26 tff(28412,plain,
% 3.90/4.26 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[1137, 28411])).
% 3.90/4.26 tff(28413,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26043, 28412, 19304, 26799, 322, 11546])).
% 3.90/4.26 tff(28414,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9761, 28413])).
% 3.90/4.26 tff(28415,plain,
% 3.90/4.26 ($false),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[3552, 144, 3529, 133, 132, 9725])).
% 3.90/4.26 tff(28416,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.26 tff(28417,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28416, 28414, 132, 28300])).
% 3.90/4.26 tff(28418,plain,
% 3.90/4.26 (r(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24299, 44, 28417, 26567])).
% 3.90/4.26 tff(28419,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28406, 333, 28304, 26619, 28418])).
% 3.90/4.26 tff(28420,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9821, 44, 219, 28419])).
% 3.90/4.26 tff(28421,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26847, 28418, 28304, 409])).
% 3.90/4.26 tff(28422,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24600, 28421, 24294])).
% 3.90/4.26 tff(28423,plain,
% 3.90/4.26 ($false),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26041, 144, 26799, 28422, 19304, 28420])).
% 3.90/4.26 tff(28424,plain,((~r(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.26 tff(28425,plain,
% 3.90/4.26 (~r(s(s(s(z))), z)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28424, 28296, 11546, 28192, 322, 28295, 28292, 28111, 9363])).
% 3.90/4.26 tff(28426,plain,
% 3.90/4.26 (b(s(s(s(z))), z)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[396, 28425])).
% 3.90/4.26 tff(28427,plain,
% 3.90/4.26 (~b(z, s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[294, 28426, 17795, 28132])).
% 3.90/4.26 tff(28428,plain,
% 3.90/4.26 (r(z, s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[619, 28427])).
% 3.90/4.26 tff(28429,plain,
% 3.90/4.26 (r(elem!1, s(s(s(z))))),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[28428, 28130])).
% 3.90/4.26 tff(28430,plain,
% 3.90/4.26 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28188])).
% 3.90/4.26 tff(28431,plain,
% 3.90/4.26 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[273, 28430])).
% 3.90/4.26 tff(28432,plain,
% 3.90/4.26 (b(s(s(s(z))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26887, 28426, 28112])).
% 3.90/4.26 tff(28433,plain,
% 3.90/4.26 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[10110, 28432, 54, 28431, 3])).
% 3.90/4.26 tff(28434,plain,
% 3.90/4.26 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[1137, 28433])).
% 3.90/4.26 tff(28435,plain,
% 3.90/4.26 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.26 tff(28436,plain,
% 3.90/4.26 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.90/4.26 inference(transitivity,[status(thm)],[28435, 203])).
% 3.90/4.26 tff(28437,plain,
% 3.90/4.26 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.90/4.26 inference(transitivity,[status(thm)],[28436, 24285])).
% 3.90/4.26 tff(28438,plain,
% 3.90/4.26 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.90/4.26 inference(monotonicity,[status(thm)],[28437])).
% 3.90/4.26 tff(28439,plain,
% 3.90/4.26 (~(s(s(s(s(z)))) = elem!1)),
% 3.90/4.26 inference(modus_ponens,[status(thm)],[242, 28438])).
% 3.90/4.26 tff(28440,plain,
% 3.90/4.26 (b(s(z), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[172, 155])).
% 3.90/4.26 tff(28441,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26043, 28434, 11546, 56, 322, 28440])).
% 3.90/4.26 tff(28442,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[9761, 28441])).
% 3.90/4.26 tff(28443,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[28416, 28442, 27421, 28192])).
% 3.90/4.26 tff(28444,plain,
% 3.90/4.26 (r(s(s(s(s(z)))), elem!1)),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[24301, 28443, 28439])).
% 3.90/4.26 tff(28445,plain,
% 3.90/4.26 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[26847, 28444, 722, 28296])).
% 3.90/4.26 tff(28446,plain,
% 3.90/4.26 (b(s(s(s(s(z)))), s(z))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[27538, 28445])).
% 3.90/4.26 tff(28447,plain,
% 3.90/4.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.26 inference(unit_resolution,[status(thm)],[27536, 28446, 28440, 56])).
% 3.90/4.27 tff(28448,plain,
% 3.90/4.27 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[27512, 28447])).
% 3.90/4.27 tff(28449,plain,
% 3.90/4.27 (((~![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(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), 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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28450,plain,
% 3.90/4.27 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28451,plain,
% 3.90/4.27 (((~![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(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28450])).
% 3.90/4.27 tff(28452,plain,
% 3.90/4.27 (((~![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(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(transitivity,[status(thm)],[28451, 28449])).
% 3.90/4.27 tff(28453,plain,
% 3.90/4.27 ((~![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(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.90/4.27 inference(quant_inst,[status(thm)],[])).
% 3.90/4.27 tff(28454,plain,
% 3.90/4.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28453, 28452])).
% 3.90/4.27 tff(28455,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28454, 333, 1525, 9507, 6107, 27463])).
% 3.90/4.27 tff(28456,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28457,plain,
% 3.90/4.27 (~r(elem!1, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28456, 28448, 28444, 28434])).
% 3.90/4.27 tff(28458,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28457, 28429])).
% 3.90/4.27 tff(28459,plain,(r(s(z), s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28460,plain,
% 3.90/4.27 (r(s(z), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28459, 322, 722, 11546, 56, 54, 3, 7926, 9362])).
% 3.90/4.27 tff(28461,plain,
% 3.90/4.27 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28112])).
% 3.90/4.27 tff(28462,plain,
% 3.90/4.27 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.90/4.27 inference(transitivity,[status(thm)],[28461, 2])).
% 3.90/4.27 tff(28463,plain,
% 3.90/4.27 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.90/4.27 inference(transitivity,[status(thm)],[28462, 4795])).
% 3.90/4.27 tff(28464,plain,
% 3.90/4.27 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28463])).
% 3.90/4.27 tff(28465,plain,
% 3.90/4.27 (~(s(s(s(z))) = elem!1)),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[392, 28464])).
% 3.90/4.27 tff(28466,plain,
% 3.90/4.27 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[16388, 28460, 11546, 322])).
% 3.90/4.27 tff(28467,plain,
% 3.90/4.27 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[1137, 28466])).
% 3.90/4.27 tff(28468,plain,
% 3.90/4.27 (~b(elem!1, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[18960, 28467, 17795, 28192])).
% 3.90/4.27 tff(28469,plain,
% 3.90/4.27 (~b(s(s(s(z))), elem!1)),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[10110, 28467, 54, 28431, 3])).
% 3.90/4.27 tff(28470,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[12402, 28469, 28468, 28465, 722, 28460])).
% 3.90/4.27 tff(28471,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28472,plain,
% 3.90/4.27 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28471, 3, 54, 722, 11546, 56, 7926, 9362])).
% 3.90/4.27 tff(28473,plain,
% 3.90/4.27 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[319, 28472])).
% 3.90/4.27 tff(28474,plain,
% 3.90/4.27 (~b(z, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[21533, 28473, 56, 28132, 17795])).
% 3.90/4.27 tff(28475,plain,
% 3.90/4.27 (r(z, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[619, 28474])).
% 3.90/4.27 tff(28476,plain,
% 3.90/4.27 (r(elem!1, s(s(s(z))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28475, 28130])).
% 3.90/4.27 tff(28477,plain,
% 3.90/4.27 (~b(s(z), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[846, 28473, 56, 17795])).
% 3.90/4.27 tff(28478,plain,
% 3.90/4.27 (r(s(z), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[172, 28477])).
% 3.90/4.27 tff(28479,plain,
% 3.90/4.27 (~r(s(s(s(z))), elem!1)),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[1519, 28475, 9363, 28478])).
% 3.90/4.27 tff(28480,plain,
% 3.90/4.27 (b(s(s(s(z))), elem!1)),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[704, 28479, 28465])).
% 3.90/4.27 tff(28481,plain,
% 3.90/4.27 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[10110, 28480, 54, 28431, 3])).
% 3.90/4.27 tff(28482,plain,
% 3.90/4.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[1137, 28481])).
% 3.90/4.27 tff(28483,plain,
% 3.90/4.27 (((~![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(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), 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(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28484,plain,
% 3.90/4.27 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28485,plain,
% 3.90/4.27 (((~![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(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28484])).
% 3.90/4.27 tff(28486,plain,
% 3.90/4.27 (((~![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(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(transitivity,[status(thm)],[28485, 28483])).
% 3.90/4.27 tff(28487,plain,
% 3.90/4.27 ((~![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(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 3.90/4.27 inference(quant_inst,[status(thm)],[])).
% 3.90/4.27 tff(28488,plain,
% 3.90/4.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28487, 28486])).
% 3.90/4.27 tff(28489,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28488, 333, 1525, 722, 353, 6107])).
% 3.90/4.27 tff(28490,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28491,plain,
% 3.90/4.27 (~r(elem!1, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28490, 28482, 722, 28478])).
% 3.90/4.27 tff(28492,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28491, 28476])).
% 3.90/4.27 tff(28493,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28494,plain,
% 3.90/4.27 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28493, 28129, 54, 56, 11546, 7926, 28116])).
% 3.90/4.27 tff(28495,plain,
% 3.90/4.27 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28494, 28124])).
% 3.90/4.27 tff(28496,plain,
% 3.90/4.27 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[3607, 28495, 28122, 28119])).
% 3.90/4.27 tff(28497,plain,
% 3.90/4.27 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[23169, 28496, 28111])).
% 3.90/4.27 tff(28498,plain,
% 3.90/4.27 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[319, 28497])).
% 3.90/4.27 tff(28499,plain,
% 3.90/4.27 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28125])).
% 3.90/4.27 tff(28500,plain,
% 3.90/4.27 (~(s(z) = elem!1)),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[344, 28499])).
% 3.90/4.27 tff(28501,plain,
% 3.90/4.27 (~b(s(z), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[846, 28498, 56, 17795])).
% 3.90/4.27 tff(28502,plain,
% 3.90/4.27 (r(s(z), s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[172, 28501])).
% 3.90/4.27 tff(28503,plain,
% 3.90/4.27 (~b(z, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[21533, 28498, 56, 28132, 17795])).
% 3.90/4.27 tff(28504,plain,
% 3.90/4.27 (r(z, s(s(s(z))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[619, 28503])).
% 3.90/4.27 tff(28505,plain,
% 3.90/4.27 (r(elem!1, s(s(s(z))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28504, 28130])).
% 3.90/4.27 tff(28506,plain,
% 3.90/4.27 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28147])).
% 3.90/4.27 tff(28507,plain,
% 3.90/4.27 (r(z, s(z))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[372, 28116])).
% 3.90/4.27 tff(28508,plain,
% 3.90/4.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[18583, 28495, 11546, 28507])).
% 3.90/4.27 tff(28509,plain,
% 3.90/4.27 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[2758, 28508, 28172])).
% 3.90/4.27 tff(28510,plain,
% 3.90/4.27 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28509, 28506])).
% 3.90/4.27 tff(28511,plain,
% 3.90/4.27 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28490, 1525, 722, 353])).
% 3.90/4.27 tff(28512,plain,
% 3.90/4.27 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[1137, 28511])).
% 3.90/4.27 tff(28513,plain,
% 3.90/4.27 (((~![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))), 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), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28514,plain,
% 3.90/4.27 (((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28515,plain,
% 3.90/4.27 (((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 3.90/4.27 inference(monotonicity,[status(thm)],[28514])).
% 3.90/4.27 tff(28516,plain,
% 3.90/4.27 (((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), 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(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.90/4.27 inference(transitivity,[status(thm)],[28515, 28513])).
% 3.90/4.27 tff(28517,plain,
% 3.90/4.27 ((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 3.90/4.27 inference(quant_inst,[status(thm)],[])).
% 3.90/4.27 tff(28518,plain,
% 3.90/4.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28517, 28516])).
% 3.90/4.27 tff(28519,plain,
% 3.90/4.27 ($false),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28518, 333, 409, 1525, 353, 19432])).
% 3.90/4.27 tff(28520,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.27 tff(28521,plain,
% 3.90/4.27 (~r(s(s(s(z))), s(s(z)))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[28520, 409, 1525, 353])).
% 3.90/4.27 tff(28522,plain,
% 3.90/4.27 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28521, 25412])).
% 3.90/4.27 tff(28523,plain,
% 3.90/4.27 (b(s(s(s(z))), s(s(elem!1)))),
% 3.90/4.27 inference(unit_resolution,[status(thm)],[1301, 28522, 26805])).
% 3.90/4.27 tff(28524,plain,
% 3.90/4.27 (b(s(s(s(z))), s(s(z)))),
% 3.90/4.27 inference(modus_ponens,[status(thm)],[28523, 22810])).
% 3.90/4.27 tff(28525,plain,
% 3.90/4.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28526,plain,
% 3.90/4.27 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.27 inference(rewrite,[status(thm)],[])).
% 3.90/4.27 tff(28527,plain,
% 3.90/4.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28526])).
% 3.90/4.28 tff(28528,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28527, 28525])).
% 3.90/4.28 tff(28529,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28530,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28529, 28528])).
% 3.90/4.28 tff(28531,plain,
% 3.90/4.28 ($false),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28530, 144, 56, 1417, 2254, 9739, 23756])).
% 3.90/4.28 tff(28532,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.28 tff(28533,plain,
% 3.90/4.28 (~b(s(s(z)), s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28532, 28524, 28512, 9739, 56])).
% 3.90/4.28 tff(28534,plain,
% 3.90/4.28 (~b(s(s(elem!1)), s(elem!1))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[18895, 28533, 8677])).
% 3.90/4.28 tff(28535,plain,
% 3.90/4.28 (r(s(s(elem!1)), s(elem!1))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[1283, 28534, 22759])).
% 3.90/4.28 tff(28536,plain,
% 3.90/4.28 (r(s(s(z)), s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[22871, 28535, 8677])).
% 3.90/4.28 tff(28537,plain,
% 3.90/4.28 (~r(elem!1, s(s(z)))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[26788, 333, 409, 722, 28536])).
% 3.90/4.28 tff(28538,plain,
% 3.90/4.28 (~r(elem!1, s(s(elem!1)))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28537, 28273])).
% 3.90/4.28 tff(28539,plain,
% 3.90/4.28 (b(elem!1, s(s(elem!1)))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[2522, 28538, 22705])).
% 3.90/4.28 tff(28540,plain,
% 3.90/4.28 (b(elem!1, s(s(z)))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28539, 22760])).
% 3.90/4.28 tff(28541,plain,
% 3.90/4.28 (((~![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(z)), elem!1)) | (~r(elem!1, 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(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28542,plain,
% 3.90/4.28 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28543,plain,
% 3.90/4.28 (((~![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(s(s(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(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28542])).
% 3.90/4.28 tff(28544,plain,
% 3.90/4.28 (((~![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(s(s(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(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28543, 28541])).
% 3.90/4.28 tff(28545,plain,
% 3.90/4.28 ((~![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(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28546,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28545, 28544])).
% 3.90/4.28 tff(28547,plain,
% 3.90/4.28 ($false),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28546, 333, 409, 2323, 7155, 9770])).
% 3.90/4.28 tff(28548,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.28 tff(28549,plain,
% 3.90/4.28 (~r(s(s(z)), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28548, 28536, 2323, 409])).
% 3.90/4.28 tff(28550,plain,
% 3.90/4.28 (b(s(s(z)), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[7970, 28549, 22830])).
% 3.90/4.28 tff(28551,plain,
% 3.90/4.28 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28552,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28551])).
% 3.90/4.28 tff(28553,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28552, 26863])).
% 3.90/4.28 tff(28554,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28555,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28554, 28553])).
% 3.90/4.28 tff(28556,plain,
% 3.90/4.28 ($false),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28555, 144, 133, 28550, 9739, 28540])).
% 3.90/4.28 tff(28557,plain,((~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.28 tff(28558,plain,
% 3.90/4.28 (~r(s(z), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28557, 28510, 27421, 28111, 28129, 28494, 56, 28505, 28502])).
% 3.90/4.28 tff(28559,plain,
% 3.90/4.28 (b(s(z), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[406, 28558, 28500])).
% 3.90/4.28 tff(28560,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28561,plain,
% 3.90/4.28 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28562,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28561])).
% 3.90/4.28 tff(28563,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28562, 28560])).
% 3.90/4.28 tff(28564,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28565,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28564, 28563])).
% 3.90/4.28 tff(28566,plain,
% 3.90/4.28 ($false),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28565, 144, 28559, 56, 27421, 17795, 28498])).
% 3.90/4.28 tff(28567,plain,(b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.28 tff(28568,plain,
% 3.90/4.28 (b(elem!1, s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28567, 7926, 11546, 54, 56])).
% 3.90/4.28 tff(28569,plain,
% 3.90/4.28 (b(z, s(z))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[305, 18025])).
% 3.90/4.28 tff(28570,plain,
% 3.90/4.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[22687, 18019, 54])).
% 3.90/4.28 tff(28571,plain,
% 3.90/4.28 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[302, 28570])).
% 3.90/4.28 tff(28572,plain,
% 3.90/4.28 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 3.90/4.28 inference(symmetry,[status(thm)],[22983])).
% 3.90/4.28 tff(28573,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28574,plain,
% 3.90/4.28 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(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(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28575,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28574])).
% 3.90/4.28 tff(28576,plain,
% 3.90/4.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28575, 28573])).
% 3.90/4.28 tff(28577,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28578,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28577, 28576])).
% 3.90/4.28 tff(28579,plain,
% 3.90/4.28 ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28578, 144, 305, 56, 283])).
% 3.90/4.28 tff(28580,plain,
% 3.90/4.28 (~b(elem!1, s(s(s(z))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28579, 28246])).
% 3.90/4.28 tff(28581,plain,
% 3.90/4.28 (r(elem!1, s(s(s(z))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[1538, 28580, 22768])).
% 3.90/4.28 tff(28582,plain,
% 3.90/4.28 (r(z, s(s(s(z))))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28581, 28572])).
% 3.90/4.28 tff(28583,plain,
% 3.90/4.28 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[846, 28440, 56, 283])).
% 3.90/4.28 tff(28584,plain,
% 3.90/4.28 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[319, 28583])).
% 3.90/4.28 tff(28585,plain,
% 3.90/4.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[27273, 155, 8677])).
% 3.90/4.28 tff(28586,plain,
% 3.90/4.28 (b(s(elem!1), s(s(s(elem!1))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[1067, 28585, 27261])).
% 3.90/4.28 tff(28587,plain,
% 3.90/4.28 (r(s(s(z)), s(z))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[22871, 2737, 8677])).
% 3.90/4.28 tff(28588,plain,
% 3.90/4.28 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[23385, 333, 11546, 322, 28587])).
% 3.90/4.28 tff(28589,plain,
% 3.90/4.28 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[1451, 28588])).
% 3.90/4.28 tff(28590,plain,
% 3.90/4.28 (~b(s(s(z)), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[11650, 144, 28589, 133, 132])).
% 3.90/4.28 tff(28591,plain,
% 3.90/4.28 (r(s(s(z)), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[7970, 28590, 22830])).
% 3.90/4.28 tff(28592,plain,
% 3.90/4.28 (~b(elem!1, s(s(s(z))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28579, 132])).
% 3.90/4.28 tff(28593,plain,
% 3.90/4.28 (r(elem!1, s(s(s(z))))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[1538, 28592, 22768])).
% 3.90/4.28 tff(28594,plain,
% 3.90/4.28 (((~![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(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), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28595,plain,
% 3.90/4.28 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.90/4.28 inference(rewrite,[status(thm)],[])).
% 3.90/4.28 tff(28596,plain,
% 3.90/4.28 (((~![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(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(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 3.90/4.28 inference(monotonicity,[status(thm)],[28595])).
% 3.90/4.28 tff(28597,plain,
% 3.90/4.28 (((~![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(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(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 3.90/4.28 inference(transitivity,[status(thm)],[28596, 28594])).
% 3.90/4.28 tff(28598,plain,
% 3.90/4.28 ((~![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(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 3.90/4.28 inference(quant_inst,[status(thm)],[])).
% 3.90/4.28 tff(28599,plain,
% 3.90/4.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 3.90/4.28 inference(modus_ponens,[status(thm)],[28598, 28597])).
% 3.90/4.28 tff(28600,plain,
% 3.90/4.28 ($false),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28599, 333, 409, 1525, 7155, 9770])).
% 3.90/4.28 tff(28601,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.28 tff(28602,plain,
% 3.90/4.28 (~r(s(z), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[28601, 28591, 28593, 28587])).
% 3.90/4.28 tff(28603,plain,
% 3.90/4.28 (b(s(z), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[406, 28602, 26622])).
% 3.90/4.28 tff(28604,plain,
% 3.90/4.28 (~b(s(s(s(z))), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[4375, 28603, 56, 305])).
% 3.90/4.28 tff(28605,plain,
% 3.90/4.28 (r(s(s(s(z))), elem!1)),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[704, 28604, 22766])).
% 3.90/4.28 tff(28606,plain,
% 3.90/4.28 (~r(s(s(s(z))), s(s(z)))),
% 3.90/4.28 inference(unit_resolution,[status(thm)],[8852, 333, 28593, 28605, 28591])).
% 3.90/4.28 tff(28607,plain,
% 3.90/4.28 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28606, 25412])).
% 3.90/4.29 tff(28608,plain,
% 3.90/4.29 (b(s(s(s(z))), s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1301, 28607, 26805])).
% 3.90/4.29 tff(28609,plain,
% 3.90/4.29 (b(s(s(s(z))), s(s(z)))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28608, 22810])).
% 3.90/4.29 tff(28610,plain,
% 3.90/4.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[3662, 2737, 22728, 27205])).
% 3.90/4.29 tff(28611,plain,
% 3.90/4.29 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[2758, 28610, 23135])).
% 3.90/4.29 tff(28612,plain,
% 3.90/4.29 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28611, 23136])).
% 3.90/4.29 tff(28613,plain,
% 3.90/4.29 (~r(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[7445, 333, 28593, 28605, 28591])).
% 3.90/4.29 tff(28614,plain,
% 3.90/4.29 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18132, 28613, 8677])).
% 3.90/4.29 tff(28615,plain,
% 3.90/4.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[4311, 28614, 22826])).
% 3.90/4.29 tff(28616,plain,
% 3.90/4.29 (b(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18122, 28615, 8677])).
% 3.90/4.29 tff(28617,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[9592, 144, 28616, 283, 28612, 28609])).
% 3.90/4.29 tff(28618,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28619,plain,
% 3.90/4.29 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28618, 28584, 8677, 56, 305, 27421, 28246, 11546, 283])).
% 3.90/4.29 tff(28620,plain,
% 3.90/4.29 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1283, 28619, 22759])).
% 3.90/4.29 tff(28621,plain,
% 3.90/4.29 (b(s(s(z)), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18895, 28620, 8677])).
% 3.90/4.29 tff(28622,plain,
% 3.90/4.29 (~b(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18116, 28621, 8677, 56, 28586])).
% 3.90/4.29 tff(28623,plain,
% 3.90/4.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18122, 28622, 8677])).
% 3.90/4.29 tff(28624,plain,
% 3.90/4.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[4311, 28623, 22826])).
% 3.90/4.29 tff(28625,plain,
% 3.90/4.29 (r(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18132, 28624, 8677])).
% 3.90/4.29 tff(28626,plain,
% 3.90/4.29 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27297, 28621, 27421, 8677, 305, 28581, 28584, 28586, 56])).
% 3.90/4.29 tff(28627,plain,
% 3.90/4.29 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1137, 28626])).
% 3.90/4.29 tff(28628,plain,
% 3.90/4.29 (~b(s(s(s(z))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[10110, 28627, 54, 28235, 3])).
% 3.90/4.29 tff(28629,plain,
% 3.90/4.29 (r(s(s(s(z))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[704, 28628, 22766])).
% 3.90/4.29 tff(28630,plain,
% 3.90/4.29 (~r(s(s(z)), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[23225, 333, 28581, 28629, 28625])).
% 3.90/4.29 tff(28631,plain,
% 3.90/4.29 (b(s(s(z)), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[7970, 28630, 22830])).
% 3.90/4.29 tff(28632,plain,
% 3.90/4.29 ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27287, 144, 305, 28621, 27421])).
% 3.90/4.29 tff(28633,plain,
% 3.90/4.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28632, 28631])).
% 3.90/4.29 tff(28634,plain,
% 3.90/4.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1451, 28633])).
% 3.90/4.29 tff(28635,plain,
% 3.90/4.29 (~r(s(z), s(s(z)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28260, 333, 28634, 11546, 28584])).
% 3.90/4.29 tff(28636,plain,
% 3.90/4.29 (~r(s(z), s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[22807, 28635, 8677])).
% 3.90/4.29 tff(28637,plain,
% 3.90/4.29 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 3.90/4.29 inference(symmetry,[status(thm)],[18026])).
% 3.90/4.29 tff(28638,plain,
% 3.90/4.29 (b(elem!1, s(elem!1))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[305, 28637])).
% 3.90/4.29 tff(28639,plain,
% 3.90/4.29 (~r(elem!1, s(s(z)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[23084, 333, 28581, 28629, 28625])).
% 3.90/4.29 tff(28640,plain,
% 3.90/4.29 (~r(elem!1, s(s(elem!1)))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28639, 28273])).
% 3.90/4.29 tff(28641,plain,
% 3.90/4.29 (b(elem!1, s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[2522, 28640, 22705])).
% 3.90/4.29 tff(28642,plain,
% 3.90/4.29 (~b(s(z), s(s(elem!1)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[5494, 28641, 305, 28638, 28620])).
% 3.90/4.29 tff(28643,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[5484, 28642, 28636])).
% 3.90/4.29 tff(28644,plain,(r(s(z), s(s(s(z)))) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28645,plain,
% 3.90/4.29 (r(s(z), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28644, 3, 8677, 11546, 54, 305, 56, 283])).
% 3.90/4.29 tff(28646,plain,
% 3.90/4.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28246, 22724])).
% 3.90/4.29 tff(28647,plain,
% 3.90/4.29 (~b(s(z), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[7093, 304, 286, 490])).
% 3.90/4.29 tff(28648,plain,
% 3.90/4.29 (~r(s(z), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27739, 304, 259, 56, 353, 623])).
% 3.90/4.29 tff(28649,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[348, 28648, 28647])).
% 3.90/4.29 tff(28650,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28651,plain,
% 3.90/4.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28650, 28646, 56, 28645, 28582, 28571, 28569])).
% 3.90/4.29 tff(28652,plain,
% 3.90/4.29 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[319, 28651])).
% 3.90/4.29 tff(28653,plain,
% 3.90/4.29 (~r(s(s(elem!1)), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28618, 28652, 8677, 56, 305, 27421, 28246, 11546, 283])).
% 3.90/4.29 tff(28654,plain,
% 3.90/4.29 (b(s(s(elem!1)), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1283, 28653, 22759])).
% 3.90/4.29 tff(28655,plain,
% 3.90/4.29 (b(s(s(z)), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18895, 28654, 8677])).
% 3.90/4.29 tff(28656,plain,
% 3.90/4.29 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[16388, 28652, 11546, 28645])).
% 3.90/4.29 tff(28657,plain,
% 3.90/4.29 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[1137, 28656])).
% 3.90/4.29 tff(28658,plain,
% 3.90/4.29 (~b(s(s(s(z))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[10110, 28657, 54, 28235, 3])).
% 3.90/4.29 tff(28659,plain,
% 3.90/4.29 (~b(s(s(s(z))), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[26887, 28658, 18019])).
% 3.90/4.29 tff(28660,plain,
% 3.90/4.29 (r(s(s(s(z))), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[396, 28659])).
% 3.90/4.29 tff(28661,plain,
% 3.90/4.29 (~r(s(z), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27726, 28660, 28582, 28645])).
% 3.90/4.29 tff(28662,plain,
% 3.90/4.29 (b(s(z), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[348, 28661])).
% 3.90/4.29 tff(28663,plain,
% 3.90/4.29 (b(s(z), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[22716, 28662, 22711])).
% 3.90/4.29 tff(28664,plain,
% 3.90/4.29 (~b(s(s(z)), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[23000, 144, 28663, 305, 28655])).
% 3.90/4.29 tff(28665,plain,
% 3.90/4.29 (r(s(s(z)), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[7970, 28664, 22830])).
% 3.90/4.29 tff(28666,plain,
% 3.90/4.29 (b(s(elem!1), z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18064, 28662, 18019])).
% 3.90/4.29 tff(28667,plain,
% 3.90/4.29 (b(s(elem!1), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[25335, 28666, 18019])).
% 3.90/4.29 tff(28668,plain,
% 3.90/4.29 (r(s(s(s(z))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[704, 28658, 22766])).
% 3.90/4.29 tff(28669,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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(s(s(z))), elem!1)) | (~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))))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28670,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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))))),
% 3.90/4.29 inference(quant_inst,[status(thm)],[])).
% 3.90/4.29 tff(28671,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~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)))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28670, 28669])).
% 3.90/4.29 tff(28672,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28671, 333, 707, 353, 27463])).
% 3.90/4.29 tff(28673,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28672, 25520])).
% 3.90/4.29 tff(28674,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28675,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.90/4.29 inference(quant_inst,[status(thm)],[])).
% 3.90/4.29 tff(28676,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28675, 28674])).
% 3.90/4.29 tff(28677,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28676, 333, 1525, 707, 27463])).
% 3.90/4.29 tff(28678,plain,
% 3.90/4.29 (b(s(s(s(s(z)))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24301, 28677, 24296])).
% 3.90/4.29 tff(28679,plain,
% 3.90/4.29 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24997, 28678, 547, 451])).
% 3.90/4.29 tff(28680,plain,
% 3.90/4.29 (r(s(s(s(s(z)))), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24448, 28679, 25190])).
% 3.90/4.29 tff(28681,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28680, 28673])).
% 3.90/4.29 tff(28682,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28683,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28682, 28667, 28638, 26568, 28581, 26567, 8677, 28668, 28645])).
% 3.90/4.29 tff(28684,plain,
% 3.90/4.29 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27512, 28683])).
% 3.90/4.29 tff(28685,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18464, 144, 283, 2254, 9725, 20266])).
% 3.90/4.29 tff(28686,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28687,plain,
% 3.90/4.29 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28686, 28684, 28657, 283])).
% 3.90/4.29 tff(28688,plain,
% 3.90/4.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[9761, 28687])).
% 3.90/4.29 tff(28689,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[23693, 333, 25527, 353, 322, 3559])).
% 3.90/4.29 tff(28690,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28691,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28690, 28688, 28645, 28652])).
% 3.90/4.29 tff(28692,plain,
% 3.90/4.29 (r(s(s(s(s(z)))), s(z))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[24678, 25518])).
% 3.90/4.29 tff(28693,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24597, 28692])).
% 3.90/4.29 tff(28694,plain,((~r(s(s(s(s(z)))), s(elem!1))) | r(s(s(s(s(z)))), s(z)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28695,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28694, 28691, 8677])).
% 3.90/4.29 tff(28696,plain,
% 3.90/4.29 (b(s(s(s(s(z)))), s(elem!1))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24448, 28695, 26568])).
% 3.90/4.29 tff(28697,plain,
% 3.90/4.29 (~b(s(s(s(s(z)))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24997, 28696, 28638, 28667])).
% 3.90/4.29 tff(28698,plain,
% 3.90/4.29 (r(s(s(s(s(z)))), elem!1)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[24301, 28697, 26567])).
% 3.90/4.29 tff(28699,plain,
% 3.90/4.29 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(z)))))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28700,plain,
% 3.90/4.29 (((~r(elem!1, s(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))))) <=> ((~r(s(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(s(z)))))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28701,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(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(s(z))))))),
% 3.90/4.29 inference(monotonicity,[status(thm)],[28700])).
% 3.90/4.29 tff(28702,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(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(s(z)))))),
% 3.90/4.29 inference(transitivity,[status(thm)],[28701, 28699])).
% 3.90/4.29 tff(28703,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))))),
% 3.90/4.29 inference(quant_inst,[status(thm)],[])).
% 3.90/4.29 tff(28704,plain,
% 3.90/4.29 ((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28703, 28702])).
% 3.90/4.29 tff(28705,plain,
% 3.90/4.29 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28704, 333, 28581, 28698, 28665])).
% 3.90/4.29 tff(28706,plain,
% 3.90/4.29 (b(s(s(s(s(z)))), s(s(z)))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 28705])).
% 3.90/4.29 tff(28707,plain,
% 3.90/4.29 (b(s(s(s(s(z)))), s(z))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[27538, 28691])).
% 3.90/4.29 tff(28708,plain,
% 3.90/4.29 (~r(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[7445, 333, 28581, 28668, 28665])).
% 3.90/4.29 tff(28709,plain,
% 3.90/4.29 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18132, 28708, 8677])).
% 3.90/4.29 tff(28710,plain,
% 3.90/4.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[4311, 28709, 22826])).
% 3.90/4.29 tff(28711,plain,
% 3.90/4.29 (b(s(s(z)), s(s(s(z))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[18122, 28710, 8677])).
% 3.90/4.29 tff(28712,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28713,plain,
% 3.90/4.29 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.90/4.29 inference(rewrite,[status(thm)],[])).
% 3.90/4.29 tff(28714,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.90/4.29 inference(monotonicity,[status(thm)],[28713])).
% 3.90/4.29 tff(28715,plain,
% 3.90/4.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.90/4.29 inference(transitivity,[status(thm)],[28714, 28712])).
% 3.90/4.29 tff(28716,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.90/4.29 inference(quant_inst,[status(thm)],[])).
% 3.90/4.29 tff(28717,plain,
% 3.90/4.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.90/4.29 inference(modus_ponens,[status(thm)],[28716, 28715])).
% 3.90/4.29 tff(28718,plain,
% 3.90/4.29 ($false),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28717, 144, 56, 28711, 28707, 28684, 28706])).
% 3.90/4.29 tff(28719,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.90/4.29 tff(28720,plain,
% 3.90/4.29 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28719, 28111, 56, 28568, 17795, 54, 11546])).
% 3.90/4.29 tff(28721,plain,
% 3.90/4.29 (s(elem!1) = s(z)),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[28110, 7926, 56, 11546, 133])).
% 3.90/4.29 tff(28722,plain,
% 3.90/4.29 (z = elem!1),
% 3.90/4.29 inference(unit_resolution,[status(thm)],[8683, 28721])).
% 3.90/4.29 tff(28723,plain,
% 3.90/4.29 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.90/4.29 inference(monotonicity,[status(thm)],[28722])).
% 3.90/4.29 tff(28724,plain,
% 3.90/4.29 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.99/4.30 inference(transitivity,[status(thm)],[28723, 203])).
% 3.99/4.30 tff(28725,plain,
% 3.99/4.30 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.99/4.30 inference(transitivity,[status(thm)],[28724, 24285])).
% 3.99/4.30 tff(28726,plain,
% 3.99/4.30 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28725])).
% 3.99/4.30 tff(28727,plain,
% 3.99/4.30 (~(s(s(s(s(z)))) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[242, 28726])).
% 3.99/4.30 tff(28728,plain,
% 3.99/4.30 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28721])).
% 3.99/4.30 tff(28729,plain,
% 3.99/4.30 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 3.99/4.30 inference(transitivity,[status(thm)],[28728, 52])).
% 3.99/4.30 tff(28730,plain,
% 3.99/4.30 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28729])).
% 3.99/4.30 tff(28731,plain,
% 3.99/4.30 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28722])).
% 3.99/4.30 tff(28732,plain,
% 3.99/4.30 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 3.99/4.30 inference(transitivity,[status(thm)],[28731, 28730, 199])).
% 3.99/4.30 tff(28733,plain,
% 3.99/4.30 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28732])).
% 3.99/4.30 tff(28734,plain,
% 3.99/4.30 (~(s(elem!1) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[344, 28733])).
% 3.99/4.30 tff(28735,plain,
% 3.99/4.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[846, 838, 56, 17795])).
% 3.99/4.30 tff(28736,plain,
% 3.99/4.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[319, 28735])).
% 3.99/4.30 tff(28737,plain,
% 3.99/4.30 (~r(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18406, 28736, 11546, 2323])).
% 3.99/4.30 tff(28738,plain,
% 3.99/4.30 (~r(s(elem!1), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18039, 28737, 28721])).
% 3.99/4.30 tff(28739,plain,
% 3.99/4.30 (b(s(elem!1), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[448, 28738, 28734])).
% 3.99/4.30 tff(28740,plain,
% 3.99/4.30 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28721])).
% 3.99/4.30 tff(28741,plain,
% 3.99/4.30 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28740])).
% 3.99/4.30 tff(28742,plain,
% 3.99/4.30 (b(elem!1, s(elem!1))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[305, 28741])).
% 3.99/4.30 tff(28743,plain,
% 3.99/4.30 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[25349, 28722])).
% 3.99/4.30 tff(28744,plain,
% 3.99/4.30 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28722])).
% 3.99/4.30 tff(28745,plain,
% 3.99/4.30 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.99/4.30 inference(transitivity,[status(thm)],[28744, 2])).
% 3.99/4.30 tff(28746,plain,
% 3.99/4.30 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.99/4.30 inference(transitivity,[status(thm)],[28745, 4795])).
% 3.99/4.30 tff(28747,plain,
% 3.99/4.30 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28746])).
% 3.99/4.30 tff(28748,plain,
% 3.99/4.30 (~(s(s(s(z))) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[392, 28747])).
% 3.99/4.30 tff(28749,plain,
% 3.99/4.30 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28731])).
% 3.99/4.30 tff(28750,plain,
% 3.99/4.30 (~(s(z) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[344, 28749])).
% 3.99/4.30 tff(28751,plain,
% 3.99/4.30 (b(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[406, 28737, 28750])).
% 3.99/4.30 tff(28752,plain,
% 3.99/4.30 (~b(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[4375, 28751, 56, 305])).
% 3.99/4.30 tff(28753,plain,
% 3.99/4.30 (r(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[704, 28752, 28748])).
% 3.99/4.30 tff(28754,plain,
% 3.99/4.30 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28722])).
% 3.99/4.30 tff(28755,plain,
% 3.99/4.30 (b(elem!1, s(z)) <=> b(z, s(z))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28754])).
% 3.99/4.30 tff(28756,plain,
% 3.99/4.30 (b(z, s(z))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[305, 28755])).
% 3.99/4.30 tff(28757,plain,
% 3.99/4.30 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28722])).
% 3.99/4.30 tff(28758,plain,
% 3.99/4.30 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28757])).
% 3.99/4.30 tff(28759,plain,
% 3.99/4.30 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[2323, 28758])).
% 3.99/4.30 tff(28760,plain,
% 3.99/4.30 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18624, 28736, 11546, 28759, 28756])).
% 3.99/4.30 tff(28761,plain,
% 3.99/4.30 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[18101])).
% 3.99/4.30 tff(28762,plain,
% 3.99/4.30 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28761])).
% 3.99/4.30 tff(28763,plain,
% 3.99/4.30 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[2671, 28762])).
% 3.99/4.30 tff(28764,plain,
% 3.99/4.30 ($false),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[22031, 28763])).
% 3.99/4.30 tff(28765,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.30 tff(28766,plain,
% 3.99/4.30 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28765, 28760, 28721])).
% 3.99/4.30 tff(28767,plain,
% 3.99/4.30 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1451, 28766])).
% 3.99/4.30 tff(28768,plain,
% 3.99/4.30 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[23169, 28736, 28721])).
% 3.99/4.30 tff(28769,plain,
% 3.99/4.30 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[66])).
% 3.99/4.30 tff(28770,plain,
% 3.99/4.30 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28769])).
% 3.99/4.30 tff(28771,plain,
% 3.99/4.30 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[2323, 28770])).
% 3.99/4.30 tff(28772,plain,
% 3.99/4.30 (~r(s(s(s(z))), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[13763, 6107, 28771, 524])).
% 3.99/4.30 tff(28773,plain,
% 3.99/4.30 (b(s(s(s(z))), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[396, 28772])).
% 3.99/4.30 tff(28774,plain,
% 3.99/4.30 (b(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[26887, 28773, 66])).
% 3.99/4.30 tff(28775,plain,
% 3.99/4.30 (~r(elem!1, s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27620, 333, 2323, 6107, 322])).
% 3.99/4.30 tff(28776,plain,
% 3.99/4.30 (b(elem!1, s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1538, 28775, 25347])).
% 3.99/4.30 tff(28777,plain,
% 3.99/4.30 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[11026, 144, 28776, 133, 28774])).
% 3.99/4.30 tff(28778,plain,
% 3.99/4.30 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[249, 28777])).
% 3.99/4.30 tff(28779,plain,
% 3.99/4.30 (~b(s(z), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[10692, 144, 134, 28776, 28774])).
% 3.99/4.30 tff(28780,plain,
% 3.99/4.30 (r(s(z), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[172, 28779])).
% 3.99/4.30 tff(28781,plain,
% 3.99/4.30 ($false),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27413, 333, 28780, 28778, 6107, 322])).
% 3.99/4.30 tff(28782,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.30 tff(28783,plain,
% 3.99/4.30 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28782, 28751, 133, 28722, 2323, 28736, 28768])).
% 3.99/4.30 tff(28784,plain,
% 3.99/4.30 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1137, 28783])).
% 3.99/4.30 tff(28785,plain,
% 3.99/4.30 (s(s(elem!1)) = s(s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28721])).
% 3.99/4.30 tff(28786,plain,
% 3.99/4.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28785])).
% 3.99/4.30 tff(28787,plain,
% 3.99/4.30 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28785, 28786])).
% 3.99/4.30 tff(28788,plain,
% 3.99/4.30 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28787])).
% 3.99/4.30 tff(28789,plain,
% 3.99/4.30 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28788])).
% 3.99/4.30 tff(28790,plain,
% 3.99/4.30 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[217, 28789])).
% 3.99/4.30 tff(28791,plain,
% 3.99/4.30 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[7952, 28767, 7926, 28783])).
% 3.99/4.30 tff(28792,plain,
% 3.99/4.30 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18122, 28791, 28721])).
% 3.99/4.30 tff(28793,plain,
% 3.99/4.30 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[4311, 28792, 28790])).
% 3.99/4.30 tff(28794,plain,
% 3.99/4.30 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18132, 28793, 28721])).
% 3.99/4.30 tff(28795,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[25545, 28794, 28784, 17795, 28767, 28753, 11546, 28736])).
% 3.99/4.30 tff(28796,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28694, 28795, 28721])).
% 3.99/4.30 tff(28797,plain,
% 3.99/4.30 (b(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24448, 28796, 28743])).
% 3.99/4.30 tff(28798,plain,
% 3.99/4.30 (~b(s(s(s(s(z)))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24997, 28797, 28742, 28739])).
% 3.99/4.30 tff(28799,plain,
% 3.99/4.30 (b(s(s(s(s(z)))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27538, 28795])).
% 3.99/4.30 tff(28800,plain,
% 3.99/4.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27536, 28799, 838, 56])).
% 3.99/4.30 tff(28801,plain,
% 3.99/4.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27512, 28800])).
% 3.99/4.30 tff(28802,plain,
% 3.99/4.30 ($false),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[25556, 333, 707, 9507, 2323, 27463])).
% 3.99/4.30 tff(28803,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.30 tff(28804,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28803, 28801, 2323, 28753])).
% 3.99/4.30 tff(28805,plain,
% 3.99/4.30 ($false),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24301, 28804, 28798, 28727])).
% 3.99/4.30 tff(28806,plain,((~b(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.30 tff(28807,plain,
% 3.99/4.30 (~b(s(z), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28806, 28720, 56, 11546, 7926, 28568, 27421])).
% 3.99/4.30 tff(28808,plain,
% 3.99/4.30 (r(s(z), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[172, 28807])).
% 3.99/4.30 tff(28809,plain,
% 3.99/4.30 (~b(z, s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[21533, 304, 56, 286, 283])).
% 3.99/4.30 tff(28810,plain,
% 3.99/4.30 (r(z, s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[619, 28809])).
% 3.99/4.30 tff(28811,plain,
% 3.99/4.30 (r(elem!1, s(s(s(z))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[28810, 22906])).
% 3.99/4.30 tff(28812,plain,
% 3.99/4.30 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.99/4.30 inference(monotonicity,[status(thm)],[66])).
% 3.99/4.30 tff(28813,plain,
% 3.99/4.30 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28812])).
% 3.99/4.30 tff(28814,plain,
% 3.99/4.30 (~(s(z) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[344, 28813])).
% 3.99/4.30 tff(28815,plain,
% 3.99/4.30 (~b(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[3955, 304, 133, 305])).
% 3.99/4.30 tff(28816,plain,
% 3.99/4.30 (r(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[406, 28815, 28814])).
% 3.99/4.30 tff(28817,plain,
% 3.99/4.30 (b(elem!1, s(z)) <=> b(z, s(z))),
% 3.99/4.30 inference(symmetry,[status(thm)],[26728])).
% 3.99/4.30 tff(28818,plain,
% 3.99/4.30 (b(z, s(z))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[305, 28817])).
% 3.99/4.30 tff(28819,plain,
% 3.99/4.30 (~b(s(z), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[7093, 304, 286, 28818])).
% 3.99/4.30 tff(28820,plain,
% 3.99/4.30 (r(s(z), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[348, 28819])).
% 3.99/4.30 tff(28821,plain,
% 3.99/4.30 (~r(s(s(s(z))), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27726, 28820, 28810, 353])).
% 3.99/4.30 tff(28822,plain,
% 3.99/4.30 (b(s(s(s(z))), z)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[396, 28821])).
% 3.99/4.30 tff(28823,plain,
% 3.99/4.30 (b(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[26887, 28822, 66])).
% 3.99/4.30 tff(28824,plain,
% 3.99/4.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.30 inference(rewrite,[status(thm)],[])).
% 3.99/4.30 tff(28825,plain,
% 3.99/4.30 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.30 inference(rewrite,[status(thm)],[])).
% 3.99/4.30 tff(28826,plain,
% 3.99/4.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28825])).
% 3.99/4.30 tff(28827,plain,
% 3.99/4.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.30 inference(transitivity,[status(thm)],[28826, 28824])).
% 3.99/4.30 tff(28828,plain,
% 3.99/4.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.30 inference(quant_inst,[status(thm)],[])).
% 3.99/4.30 tff(28829,plain,
% 3.99/4.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[28828, 28827])).
% 3.99/4.30 tff(28830,plain,
% 3.99/4.30 ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28829, 144, 305, 56, 133])).
% 3.99/4.30 tff(28831,plain,
% 3.99/4.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28830, 28823])).
% 3.99/4.30 tff(28832,plain,
% 3.99/4.30 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1137, 28831])).
% 3.99/4.30 tff(28833,plain,
% 3.99/4.30 (~r(elem!1, s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27266, 28832, 353, 28816])).
% 3.99/4.30 tff(28834,plain,
% 3.99/4.30 ($false),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28833, 28811])).
% 3.99/4.30 tff(28835,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(z = elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.30 tff(28836,plain,
% 3.99/4.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28835, 28112, 28808, 28568, 56, 27421, 28132, 17795])).
% 3.99/4.30 tff(28837,plain,
% 3.99/4.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[319, 28836])).
% 3.99/4.30 tff(28838,plain,
% 3.99/4.30 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[16388, 28837, 11546, 28808])).
% 3.99/4.30 tff(28839,plain,
% 3.99/4.30 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1137, 28838])).
% 3.99/4.30 tff(28840,plain,
% 3.99/4.30 (~r(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18406, 28837, 11546, 28720])).
% 3.99/4.30 tff(28841,plain,
% 3.99/4.30 (b(s(z), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[406, 28840, 28500])).
% 3.99/4.30 tff(28842,plain,
% 3.99/4.30 (~b(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[4375, 28841, 56, 28568])).
% 3.99/4.30 tff(28843,plain,
% 3.99/4.30 (r(s(s(s(z))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[704, 28842, 28465])).
% 3.99/4.30 tff(28844,plain,
% 3.99/4.30 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 3.99/4.30 inference(transitivity,[status(thm)],[28125, 28175, 199])).
% 3.99/4.30 tff(28845,plain,
% 3.99/4.30 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28844])).
% 3.99/4.30 tff(28846,plain,
% 3.99/4.30 (~(s(elem!1) = elem!1)),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[344, 28845])).
% 3.99/4.30 tff(28847,plain,
% 3.99/4.30 (~r(s(elem!1), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18039, 28840, 28111])).
% 3.99/4.30 tff(28848,plain,
% 3.99/4.30 (b(s(elem!1), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[448, 28847, 28846])).
% 3.99/4.30 tff(28849,plain,
% 3.99/4.30 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28111])).
% 3.99/4.30 tff(28850,plain,
% 3.99/4.30 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28849])).
% 3.99/4.30 tff(28851,plain,
% 3.99/4.30 (b(elem!1, s(elem!1))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[28568, 28850])).
% 3.99/4.30 tff(28852,plain,
% 3.99/4.30 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[25349, 28112])).
% 3.99/4.30 tff(28853,plain,
% 3.99/4.30 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.99/4.30 inference(monotonicity,[status(thm)],[28112])).
% 3.99/4.30 tff(28854,plain,
% 3.99/4.30 (b(elem!1, s(z)) <=> b(z, s(z))),
% 3.99/4.30 inference(symmetry,[status(thm)],[28853])).
% 3.99/4.30 tff(28855,plain,
% 3.99/4.30 (b(z, s(z))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[28568, 28854])).
% 3.99/4.30 tff(28856,plain,
% 3.99/4.30 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(modus_ponens,[status(thm)],[28720, 28124])).
% 3.99/4.30 tff(28857,plain,
% 3.99/4.30 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18624, 28837, 11546, 28856, 28855])).
% 3.99/4.30 tff(28858,plain,
% 3.99/4.30 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28765, 28857, 28111])).
% 3.99/4.30 tff(28859,plain,
% 3.99/4.30 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[1451, 28858])).
% 3.99/4.30 tff(28860,plain,
% 3.99/4.30 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[7952, 28859, 7926, 28838])).
% 3.99/4.30 tff(28861,plain,
% 3.99/4.30 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18122, 28860, 28111])).
% 3.99/4.30 tff(28862,plain,
% 3.99/4.30 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[4311, 28861, 28152])).
% 3.99/4.30 tff(28863,plain,
% 3.99/4.30 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[18132, 28862, 28111])).
% 3.99/4.30 tff(28864,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[25545, 28863, 28839, 17795, 28859, 28843, 11546, 28837])).
% 3.99/4.30 tff(28865,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28694, 28864, 28111])).
% 3.99/4.30 tff(28866,plain,
% 3.99/4.30 (b(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24448, 28865, 28852])).
% 3.99/4.30 tff(28867,plain,
% 3.99/4.30 (~b(s(s(s(s(z)))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24997, 28866, 28851, 28848])).
% 3.99/4.30 tff(28868,plain,
% 3.99/4.30 (r(s(s(s(s(z)))), elem!1)),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[24301, 28867, 28439])).
% 3.99/4.30 tff(28869,plain,
% 3.99/4.30 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28803, 28868, 28720, 28843])).
% 3.99/4.30 tff(28870,plain,
% 3.99/4.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[27512, 28869])).
% 3.99/4.30 tff(28871,plain,
% 3.99/4.30 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[28686, 28870, 28839, 17795])).
% 3.99/4.30 tff(28872,plain,
% 3.99/4.30 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.30 inference(unit_resolution,[status(thm)],[9761, 28871])).
% 3.99/4.31 tff(28873,plain,
% 3.99/4.31 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(rewrite,[status(thm)],[])).
% 3.99/4.31 tff(28874,plain,
% 3.99/4.31 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(rewrite,[status(thm)],[])).
% 3.99/4.31 tff(28875,plain,
% 3.99/4.31 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28874])).
% 3.99/4.31 tff(28876,plain,
% 3.99/4.31 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(transitivity,[status(thm)],[28875, 28873])).
% 3.99/4.31 tff(28877,plain,
% 3.99/4.31 ((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.99/4.31 inference(quant_inst,[status(thm)],[])).
% 3.99/4.31 tff(28878,plain,
% 3.99/4.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[28877, 28876])).
% 3.99/4.31 tff(28879,plain,
% 3.99/4.31 ($false),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28878, 333, 28868, 28720, 28837, 28872])).
% 3.99/4.31 tff(28880,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.31 tff(28881,plain,
% 3.99/4.31 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28880, 56, 11546, 54])).
% 3.99/4.31 tff(28882,plain,
% 3.99/4.31 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[27273, 155, 22669])).
% 3.99/4.31 tff(28883,plain,
% 3.99/4.31 (b(s(elem!1), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1067, 28882, 27254])).
% 3.99/4.31 tff(28884,plain,
% 3.99/4.31 (~(s(s(s(z))) = elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[227, 28881, 54])).
% 3.99/4.31 tff(28885,plain,
% 3.99/4.31 (~(elem!1 = s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[10997, 28884])).
% 3.99/4.31 tff(28886,plain,
% 3.99/4.31 (elem!1 = z),
% 3.99/4.31 inference(symmetry,[status(thm)],[22670])).
% 3.99/4.31 tff(28887,plain,
% 3.99/4.31 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28886])).
% 3.99/4.31 tff(28888,plain,
% 3.99/4.31 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.99/4.31 inference(symmetry,[status(thm)],[28887])).
% 3.99/4.31 tff(28889,plain,
% 3.99/4.31 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28888])).
% 3.99/4.31 tff(28890,plain,
% 3.99/4.31 (~(s(s(z)) = elem!1)),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[164, 28889])).
% 3.99/4.31 tff(28891,plain,
% 3.99/4.31 (~b(elem!1, s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18030, 9362, 22669])).
% 3.99/4.31 tff(28892,plain,
% 3.99/4.31 (r(elem!1, s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[560, 28891, 22695])).
% 3.99/4.31 tff(28893,plain,
% 3.99/4.31 (~b(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[26887, 55, 18019])).
% 3.99/4.31 tff(28894,plain,
% 3.99/4.31 (r(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[396, 28893])).
% 3.99/4.31 tff(28895,plain,
% 3.99/4.31 ((s(z) = elem!1) <=> (s(elem!1) = elem!1)),
% 3.99/4.31 inference(transitivity,[status(thm)],[22748, 199])).
% 3.99/4.31 tff(28896,plain,
% 3.99/4.31 ((~(s(z) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28895])).
% 3.99/4.31 tff(28897,plain,
% 3.99/4.31 (~(s(elem!1) = elem!1)),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[706, 28896])).
% 3.99/4.31 tff(28898,plain,
% 3.99/4.31 (~r(s(z), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28408, 8303, 133, 11546, 224, 26567, 132, 838, 56, 28304])).
% 3.99/4.31 tff(28899,plain,
% 3.99/4.31 (~r(s(elem!1), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18039, 28898, 8677])).
% 3.99/4.31 tff(28900,plain,
% 3.99/4.31 (b(s(elem!1), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[448, 28899, 28897])).
% 3.99/4.31 tff(28901,plain,
% 3.99/4.31 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[8472, 28900, 133, 22728, 23135, 28207, 28204, 22705, 563])).
% 3.99/4.31 tff(28902,plain,
% 3.99/4.31 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1283, 28901, 22759])).
% 3.99/4.31 tff(28903,plain,
% 3.99/4.31 (b(s(s(z)), s(z))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18895, 28902, 8677])).
% 3.99/4.31 tff(28904,plain,
% 3.99/4.31 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18116, 28903, 8677, 56, 10356])).
% 3.99/4.31 tff(28905,plain,
% 3.99/4.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18122, 28904, 8677])).
% 3.99/4.31 tff(28906,plain,
% 3.99/4.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[4311, 28905, 22826])).
% 3.99/4.31 tff(28907,plain,
% 3.99/4.31 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18132, 28906, 8677])).
% 3.99/4.31 tff(28908,plain,
% 3.99/4.31 (~r(s(s(z)), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18145, 28907, 354, 28894])).
% 3.99/4.31 tff(28909,plain,
% 3.99/4.31 (~r(s(s(z)), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28223, 28908, 18019])).
% 3.99/4.31 tff(28910,plain,
% 3.99/4.31 (b(s(s(z)), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[7970, 28909, 22830])).
% 3.99/4.31 tff(28911,plain,
% 3.99/4.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[7412, 28907, 224, 28894])).
% 3.99/4.31 tff(28912,plain,
% 3.99/4.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1451, 28911])).
% 3.99/4.31 tff(28913,plain,
% 3.99/4.31 (b(s(z), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[406, 28898, 706])).
% 3.99/4.31 tff(28914,plain,
% 3.99/4.31 ($false),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[23209, 144, 28913, 28903, 28912, 132, 28910])).
% 3.99/4.31 tff(28915,plain,(b(s(s(s(z))), elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.31 tff(28916,plain,
% 3.99/4.31 (b(s(s(s(z))), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28915, 9363, 28881, 26557, 22669, 56, 10356, 27421, 28892, 22694, 11546, 838, 28884])).
% 3.99/4.31 tff(28917,plain,
% 3.99/4.31 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[10110, 28916, 54, 26551, 3])).
% 3.99/4.31 tff(28918,plain,
% 3.99/4.31 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1137, 28917])).
% 3.99/4.31 tff(28919,plain,
% 3.99/4.31 (~b(z, s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18176, 28891, 22679])).
% 3.99/4.31 tff(28920,plain,
% 3.99/4.31 (r(z, s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[583, 28919])).
% 3.99/4.31 tff(28921,plain,
% 3.99/4.31 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28384, 409, 133, 11546, 224, 26567, 132, 722])).
% 3.99/4.31 tff(28922,plain,
% 3.99/4.31 (b(s(s(s(s(z)))), s(z))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[27538, 28921])).
% 3.99/4.31 tff(28923,plain,
% 3.99/4.31 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[27536, 28922, 838, 56])).
% 3.99/4.31 tff(28924,plain,
% 3.99/4.31 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[27512, 28923])).
% 3.99/4.31 tff(28925,plain,
% 3.99/4.31 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[21343, 333, 224, 6107, 28924])).
% 3.99/4.31 tff(28926,plain,
% 3.99/4.31 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[9761, 28925])).
% 3.99/4.31 tff(28927,plain,
% 3.99/4.31 (~r(s(s(s(z))), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28408, 409, 133, 11546, 224, 26567, 132, 838, 56, 722])).
% 3.99/4.31 tff(28928,plain,
% 3.99/4.31 (~r(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[22912, 28927, 18019])).
% 3.99/4.31 tff(28929,plain,
% 3.99/4.31 (b(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[396, 28928])).
% 3.99/4.31 tff(28930,plain,
% 3.99/4.31 (r(s(elem!1), elem!1)),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[409, 18035])).
% 3.99/4.31 tff(28931,plain,
% 3.99/4.31 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[27363, 28930, 8677, 56, 10356, 562, 28929, 284])).
% 3.99/4.31 tff(28932,plain,
% 3.99/4.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18122, 28931, 8677])).
% 3.99/4.31 tff(28933,plain,
% 3.99/4.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[4311, 28932, 22826])).
% 3.99/4.31 tff(28934,plain,
% 3.99/4.31 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18132, 28933, 8677])).
% 3.99/4.31 tff(28935,plain,
% 3.99/4.31 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(rewrite,[status(thm)],[])).
% 3.99/4.31 tff(28936,plain,
% 3.99/4.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28935])).
% 3.99/4.31 tff(28937,plain,
% 3.99/4.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(transitivity,[status(thm)],[28936, 1464])).
% 3.99/4.31 tff(28938,plain,
% 3.99/4.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.31 inference(quant_inst,[status(thm)],[])).
% 3.99/4.31 tff(28939,plain,
% 3.99/4.31 ((~![X0: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[28938, 28937])).
% 3.99/4.31 tff(28940,plain,
% 3.99/4.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28939, 333, 224, 6107, 28934])).
% 3.99/4.31 tff(28941,plain,
% 3.99/4.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1451, 28940])).
% 3.99/4.31 tff(28942,plain,
% 3.99/4.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.31 inference(rewrite,[status(thm)],[])).
% 3.99/4.31 tff(28943,plain,
% 3.99/4.31 (((~b(s(s(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(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.31 inference(rewrite,[status(thm)],[])).
% 3.99/4.31 tff(28944,plain,
% 3.99/4.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.99/4.31 inference(monotonicity,[status(thm)],[28943])).
% 3.99/4.31 tff(28945,plain,
% 3.99/4.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.31 inference(transitivity,[status(thm)],[28944, 28942])).
% 3.99/4.31 tff(28946,plain,
% 3.99/4.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.31 inference(quant_inst,[status(thm)],[])).
% 3.99/4.31 tff(28947,plain,
% 3.99/4.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[28946, 28945])).
% 3.99/4.31 tff(28948,plain,
% 3.99/4.31 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28947, 144, 28922, 28941, 304])).
% 3.99/4.31 tff(28949,plain,
% 3.99/4.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28948, 28926])).
% 3.99/4.31 tff(28950,plain,
% 3.99/4.31 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[21381, 333, 6107, 28934, 28924])).
% 3.99/4.31 tff(28951,plain,
% 3.99/4.31 ($false),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 28950, 28949])).
% 3.99/4.31 tff(28952,plain,((~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.31 tff(28953,plain,
% 3.99/4.31 (~r(s(z), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28952, 284, 6107, 224, 8677, 56, 10356, 562, 304, 838, 133, 11546, 132, 28304])).
% 3.99/4.31 tff(28954,plain,
% 3.99/4.31 (~r(s(z), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[25327, 28953, 18019])).
% 3.99/4.31 tff(28955,plain,
% 3.99/4.31 (b(s(z), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[348, 28954])).
% 3.99/4.31 tff(28956,plain,
% 3.99/4.31 (~b(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[2156, 28955, 284, 838])).
% 3.99/4.31 tff(28957,plain,
% 3.99/4.31 (r(s(s(s(z))), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[396, 28956])).
% 3.99/4.31 tff(28958,plain,
% 3.99/4.31 (~r(s(elem!1), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18039, 28953, 8677])).
% 3.99/4.31 tff(28959,plain,
% 3.99/4.31 (b(s(elem!1), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[448, 28958, 28897])).
% 3.99/4.31 tff(28960,plain,
% 3.99/4.31 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[8472, 28959, 133, 22728, 23135, 28207, 28204, 22705, 563])).
% 3.99/4.31 tff(28961,plain,
% 3.99/4.31 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1283, 28960, 22759])).
% 3.99/4.31 tff(28962,plain,
% 3.99/4.31 (b(s(s(z)), s(z))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18895, 28961, 8677])).
% 3.99/4.31 tff(28963,plain,
% 3.99/4.31 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18116, 28962, 8677, 56, 10356])).
% 3.99/4.31 tff(28964,plain,
% 3.99/4.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18122, 28963, 8677])).
% 3.99/4.31 tff(28965,plain,
% 3.99/4.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[4311, 28964, 22826])).
% 3.99/4.31 tff(28966,plain,
% 3.99/4.31 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18132, 28965, 8677])).
% 3.99/4.31 tff(28967,plain,
% 3.99/4.31 (~r(s(s(z)), z)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18145, 28966, 354, 28957])).
% 3.99/4.31 tff(28968,plain,
% 3.99/4.31 (~r(s(s(z)), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28223, 28967, 18019])).
% 3.99/4.31 tff(28969,plain,
% 3.99/4.31 (b(s(s(z)), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[7970, 28968, 22830])).
% 3.99/4.31 tff(28970,plain,
% 3.99/4.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[7412, 28966, 224, 28957])).
% 3.99/4.31 tff(28971,plain,
% 3.99/4.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[1451, 28970])).
% 3.99/4.31 tff(28972,plain,
% 3.99/4.31 (b(s(z), elem!1)),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[406, 28953, 706])).
% 3.99/4.31 tff(28973,plain,
% 3.99/4.31 ($false),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[23209, 144, 28972, 28962, 28971, 132, 28969])).
% 3.99/4.31 tff(28974,plain,((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (s(z) = elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.31 tff(28975,plain,
% 3.99/4.31 (~b(z, s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[28974, 6107, 224, 354, 8677, 56, 10356, 838, 133, 563, 706, 132, 562, 304, 11546])).
% 3.99/4.31 tff(28976,plain,
% 3.99/4.31 (r(z, s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[619, 28975])).
% 3.99/4.31 tff(28977,plain,
% 3.99/4.31 (r(elem!1, s(s(s(z))))),
% 3.99/4.31 inference(modus_ponens,[status(thm)],[28976, 22983])).
% 3.99/4.31 tff(28978,plain,
% 3.99/4.31 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18116, 1417, 8677, 56, 10356])).
% 3.99/4.31 tff(28979,plain,
% 3.99/4.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[18122, 28978, 8677])).
% 3.99/4.31 tff(28980,plain,
% 3.99/4.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.31 inference(unit_resolution,[status(thm)],[4311, 28979, 22826])).
% 3.99/4.31 tff(28981,plain,
% 3.99/4.31 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18132, 28980, 8677])).
% 3.99/4.32 tff(28982,plain,
% 3.99/4.32 (~r(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27294, 333, 1525, 6107, 28981])).
% 3.99/4.32 tff(28983,plain,
% 3.99/4.32 (b(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[7970, 28982, 22830])).
% 3.99/4.32 tff(28984,plain,
% 3.99/4.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28939, 333, 224, 6107, 28981])).
% 3.99/4.32 tff(28985,plain,
% 3.99/4.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1451, 28984])).
% 3.99/4.32 tff(28986,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.32 inference(rewrite,[status(thm)],[])).
% 3.99/4.32 tff(28987,plain,
% 3.99/4.32 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.32 inference(rewrite,[status(thm)],[])).
% 3.99/4.32 tff(28988,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.32 inference(monotonicity,[status(thm)],[28987])).
% 3.99/4.32 tff(28989,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.32 inference(transitivity,[status(thm)],[28988, 28986])).
% 3.99/4.32 tff(28990,plain,
% 3.99/4.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))),
% 3.99/4.32 inference(quant_inst,[status(thm)],[])).
% 3.99/4.32 tff(28991,plain,
% 3.99/4.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[28990, 28989])).
% 3.99/4.32 tff(28992,plain,
% 3.99/4.32 ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28991, 144, 1417, 132, 304])).
% 3.99/4.32 tff(28993,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28992, 28985, 28983])).
% 3.99/4.32 tff(28994,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(28995,plain,
% 3.99/4.32 (~b(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28994, 6107, 304, 224, 132, 28977, 8677, 56, 10356])).
% 3.99/4.32 tff(28996,plain,
% 3.99/4.32 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18895, 28995, 8677])).
% 3.99/4.32 tff(28997,plain,
% 3.99/4.32 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1283, 28996, 22759])).
% 3.99/4.32 tff(28998,plain,
% 3.99/4.32 (~b(s(elem!1), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[8472, 28997, 133, 22728, 23135, 28207, 28204, 22705, 563])).
% 3.99/4.32 tff(28999,plain,
% 3.99/4.32 (r(s(elem!1), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[448, 28998, 28897])).
% 3.99/4.32 tff(29000,plain,
% 3.99/4.32 (r(s(z), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18039, 28999, 8677])).
% 3.99/4.32 tff(29001,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28384, 29000, 133, 11546, 224, 26567, 132, 28304])).
% 3.99/4.32 tff(29002,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27538, 29001])).
% 3.99/4.32 tff(29003,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27536, 29002, 838, 56])).
% 3.99/4.32 tff(29004,plain,
% 3.99/4.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27512, 29003])).
% 3.99/4.32 tff(29005,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28456, 29004, 28977, 6107])).
% 3.99/4.32 tff(29006,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[24301, 29005, 26567])).
% 3.99/4.32 tff(29007,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28416, 29006, 133, 132])).
% 3.99/4.32 tff(29008,plain,
% 3.99/4.32 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[9761, 29007])).
% 3.99/4.32 tff(29009,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[21343, 333, 224, 6107, 29008, 29004])).
% 3.99/4.32 tff(29010,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(z))) | (s(z) = elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29011,plain,
% 3.99/4.32 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29010, 28918, 27421, 26557, 838, 56, 11546, 22669, 28892, 28881, 10356, 9363, 22694, 28920])).
% 3.99/4.32 tff(29012,plain,
% 3.99/4.32 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[319, 29011])).
% 3.99/4.32 tff(29013,plain,
% 3.99/4.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[19960, 29012, 11546, 28881, 28918, 56])).
% 3.99/4.32 tff(29014,plain,
% 3.99/4.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1451, 29013])).
% 3.99/4.32 tff(29015,plain,
% 3.99/4.32 (~b(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[11650, 144, 29014, 27421, 26557])).
% 3.99/4.32 tff(29016,plain,
% 3.99/4.32 (r(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[7970, 29015, 28890])).
% 3.99/4.32 tff(29017,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[26043, 29012, 11546, 56, 28918, 838])).
% 3.99/4.32 tff(29018,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[9761, 29017])).
% 3.99/4.32 tff(29019,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28416, 29018, 27421, 26557])).
% 3.99/4.32 tff(29020,plain,
% 3.99/4.32 (r(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[24301, 29019, 26922])).
% 3.99/4.32 tff(29021,plain,
% 3.99/4.32 (r(z, s(z)) <=> r(elem!1, s(z))),
% 3.99/4.32 inference(monotonicity,[status(thm)],[22670])).
% 3.99/4.32 tff(29022,plain,
% 3.99/4.32 (r(elem!1, s(z))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[9363, 29021])).
% 3.99/4.32 tff(29023,plain,
% 3.99/4.32 (((~![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(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(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.32 inference(rewrite,[status(thm)],[])).
% 3.99/4.32 tff(29024,plain,
% 3.99/4.32 ((~![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(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.32 inference(quant_inst,[status(thm)],[])).
% 3.99/4.32 tff(29025,plain,
% 3.99/4.32 ((~![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(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29024, 29023])).
% 3.99/4.32 tff(29026,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29025, 333, 29022, 29020, 29016])).
% 3.99/4.32 tff(29027,plain,
% 3.99/4.32 ((s(z) = elem!1) <=> (s(elem!1) = elem!1)),
% 3.99/4.32 inference(transitivity,[status(thm)],[22692, 199])).
% 3.99/4.32 tff(29028,plain,
% 3.99/4.32 ((~(s(z) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 3.99/4.32 inference(monotonicity,[status(thm)],[29027])).
% 3.99/4.32 tff(29029,plain,
% 3.99/4.32 (~(s(elem!1) = elem!1)),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[22694, 29028])).
% 3.99/4.32 tff(29030,plain,
% 3.99/4.32 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 3.99/4.32 inference(monotonicity,[status(thm)],[22670])).
% 3.99/4.32 tff(29031,plain,
% 3.99/4.32 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 3.99/4.32 inference(symmetry,[status(thm)],[29030])).
% 3.99/4.32 tff(29032,plain,
% 3.99/4.32 (b(s(s(s(z))), z)),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[28916, 29031])).
% 3.99/4.32 tff(29033,plain,
% 3.99/4.32 (~r(s(elem!1), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18039, 2310, 8677])).
% 3.99/4.32 tff(29034,plain,
% 3.99/4.32 (b(s(elem!1), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[448, 29033, 433])).
% 3.99/4.32 tff(29035,plain,
% 3.99/4.32 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[8472, 29034, 133, 525, 23135, 28207, 28204, 22705, 563])).
% 3.99/4.32 tff(29036,plain,
% 3.99/4.32 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1283, 29035, 22759])).
% 3.99/4.32 tff(29037,plain,
% 3.99/4.32 (b(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18895, 29036, 8677])).
% 3.99/4.32 tff(29038,plain,
% 3.99/4.32 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18116, 29037, 8677, 56, 10356])).
% 3.99/4.32 tff(29039,plain,
% 3.99/4.32 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18122, 29038, 8677])).
% 3.99/4.32 tff(29040,plain,
% 3.99/4.32 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[4311, 29039, 22826])).
% 3.99/4.32 tff(29041,plain,
% 3.99/4.32 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18132, 29040, 8677])).
% 3.99/4.32 tff(29042,plain,
% 3.99/4.32 (~r(s(z), z)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[25327, 2310, 18019])).
% 3.99/4.32 tff(29043,plain,
% 3.99/4.32 (b(s(z), z)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[348, 29042])).
% 3.99/4.32 tff(29044,plain,
% 3.99/4.32 (~b(z, s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[2156, 29043, 285, 838])).
% 3.99/4.32 tff(29045,plain,
% 3.99/4.32 (r(z, s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[619, 29044])).
% 3.99/4.32 tff(29046,plain,
% 3.99/4.32 (r(elem!1, s(s(s(z))))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29045, 22983])).
% 3.99/4.32 tff(29047,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27294, 333, 29046, 6107, 7155, 29041])).
% 3.99/4.32 tff(29048,plain,(r(s(z), elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29049,plain,
% 3.99/4.32 (r(s(z), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29048, 28918, 29016, 22669, 56, 10356, 29032, 838, 27421, 22698, 28892, 29029])).
% 3.99/4.32 tff(29050,plain,
% 3.99/4.32 (~r(s(z), s(s(z)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27377, 333, 29049, 29022, 29016])).
% 3.99/4.32 tff(29051,plain,
% 3.99/4.32 (~r(s(z), s(s(elem!1)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[22807, 29050, 22669])).
% 3.99/4.32 tff(29052,plain,
% 3.99/4.32 (b(s(z), s(s(elem!1)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[5484, 29051])).
% 3.99/4.32 tff(29053,plain,
% 3.99/4.32 (b(s(z), s(s(z)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[22799, 29052, 22669])).
% 3.99/4.32 tff(29054,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28384, 29049, 27421, 11546, 28881, 26922, 26557, 29022])).
% 3.99/4.32 tff(29055,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27538, 29054])).
% 3.99/4.32 tff(29056,plain,
% 3.99/4.32 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 3.99/4.32 inference(monotonicity,[status(thm)],[22670])).
% 3.99/4.32 tff(29057,plain,
% 3.99/4.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.99/4.32 inference(symmetry,[status(thm)],[29056])).
% 3.99/4.32 tff(29058,plain,
% 3.99/4.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 3.99/4.32 inference(monotonicity,[status(thm)],[27082])).
% 3.99/4.32 tff(29059,plain,
% 3.99/4.32 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.99/4.32 inference(symmetry,[status(thm)],[29058])).
% 3.99/4.32 tff(29060,plain,
% 3.99/4.32 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.99/4.32 inference(transitivity,[status(thm)],[29059, 29057])).
% 3.99/4.32 tff(29061,plain,
% 3.99/4.32 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 3.99/4.32 inference(monotonicity,[status(thm)],[29060])).
% 3.99/4.32 tff(29062,plain,
% 3.99/4.32 (~b(s(s(elem!1)), z)),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29015, 29061])).
% 3.99/4.32 tff(29063,plain,
% 3.99/4.32 (r(s(s(elem!1)), z)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[5509, 29062])).
% 3.99/4.32 tff(29064,plain,
% 3.99/4.32 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 3.99/4.32 inference(monotonicity,[status(thm)],[22669])).
% 3.99/4.32 tff(29065,plain,
% 3.99/4.32 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 3.99/4.32 inference(symmetry,[status(thm)],[29064])).
% 3.99/4.32 tff(29066,plain,
% 3.99/4.32 (r(s(elem!1), elem!1)),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29049, 29065])).
% 3.99/4.32 tff(29067,plain,
% 3.99/4.32 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[5505, 29066, 28920, 29063])).
% 3.99/4.32 tff(29068,plain,
% 3.99/4.32 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1283, 29067, 27098])).
% 3.99/4.32 tff(29069,plain,
% 3.99/4.32 (b(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18895, 29068, 22669])).
% 3.99/4.32 tff(29070,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))),
% 3.99/4.32 inference(rewrite,[status(thm)],[])).
% 3.99/4.32 tff(29071,plain,
% 3.99/4.32 (((~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(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~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(s(z)))))),
% 3.99/4.32 inference(rewrite,[status(thm)],[])).
% 3.99/4.32 tff(29072,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z))))))),
% 3.99/4.32 inference(monotonicity,[status(thm)],[29071])).
% 3.99/4.32 tff(29073,plain,
% 3.99/4.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))))),
% 3.99/4.32 inference(transitivity,[status(thm)],[29072, 29070])).
% 3.99/4.32 tff(29074,plain,
% 3.99/4.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.99/4.32 inference(quant_inst,[status(thm)],[])).
% 3.99/4.32 tff(29075,plain,
% 3.99/4.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29074, 29073])).
% 3.99/4.32 tff(29076,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29075, 144, 29069, 29055, 29053])).
% 3.99/4.32 tff(29077,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 29076, 29026])).
% 3.99/4.32 tff(29078,plain,(b(z, s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29079,plain,
% 3.99/4.32 (b(z, s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29078, 28883, 56, 11546, 28440, 54, 3])).
% 3.99/4.32 tff(29080,plain,
% 3.99/4.32 (b(elem!1, s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28115, 29079, 22670])).
% 3.99/4.32 tff(29081,plain,
% 3.99/4.32 (~b(elem!1, s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[22776, 29080, 28440, 56])).
% 3.99/4.32 tff(29082,plain,
% 3.99/4.32 (r(elem!1, s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1538, 29081, 28885])).
% 3.99/4.32 tff(29083,plain,
% 3.99/4.32 (~b(s(s(s(z))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[10110, 2254, 54, 26551, 3])).
% 3.99/4.32 tff(29084,plain,
% 3.99/4.32 (~b(s(s(s(z))), z)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[26887, 29083, 22670])).
% 3.99/4.32 tff(29085,plain,
% 3.99/4.32 (r(s(s(s(z))), z)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[396, 29084])).
% 3.99/4.32 tff(29086,plain,
% 3.99/4.32 (r(s(s(s(z))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[704, 29083, 28884])).
% 3.99/4.32 tff(29087,plain,
% 3.99/4.32 (~r(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[23225, 333, 1525, 707, 28981])).
% 3.99/4.32 tff(29088,plain,
% 3.99/4.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[7412, 28981, 224, 1699])).
% 3.99/4.32 tff(29089,plain,
% 3.99/4.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1451, 29088])).
% 3.99/4.32 tff(29090,plain,
% 3.99/4.32 (~b(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27287, 144, 305, 1417, 29089, 133])).
% 3.99/4.32 tff(29091,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[7970, 29090, 29087, 22830])).
% 3.99/4.32 tff(29092,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29093,plain,
% 3.99/4.32 (~b(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29092, 29086, 27421, 1525, 305, 28881, 29085, 22669, 56, 10356])).
% 3.99/4.32 tff(29094,plain,
% 3.99/4.32 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18895, 29093, 22669])).
% 3.99/4.32 tff(29095,plain,
% 3.99/4.32 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1283, 29094, 27098])).
% 3.99/4.32 tff(29096,plain,
% 3.99/4.32 (r(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[22871, 29095, 22669])).
% 3.99/4.32 tff(29097,plain,
% 3.99/4.32 (~(s(s(z)) = s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[855, 22694])).
% 3.99/4.32 tff(29098,plain,
% 3.99/4.32 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[862, 29097])).
% 3.99/4.32 tff(29099,plain,
% 3.99/4.32 (~b(s(s(s(z))), s(s(z)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[23595, 144, 28589, 2254, 28612])).
% 3.99/4.32 tff(29100,plain,
% 3.99/4.32 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29099, 22812])).
% 3.99/4.32 tff(29101,plain,
% 3.99/4.32 (r(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1301, 29100, 1184])).
% 3.99/4.32 tff(29102,plain,
% 3.99/4.32 (r(s(s(s(z))), s(s(z)))),
% 3.99/4.32 inference(modus_ponens,[status(thm)],[29101, 22809])).
% 3.99/4.32 tff(29103,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[8852, 333, 1525, 707, 28591, 29102])).
% 3.99/4.32 tff(29104,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29105,plain,
% 3.99/4.32 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29104, 29095, 29086, 22669, 29098, 2254, 27421, 26557, 11546, 1525])).
% 3.99/4.32 tff(29106,plain,
% 3.99/4.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[319, 29105])).
% 3.99/4.32 tff(29107,plain,
% 3.99/4.32 (~b(s(z), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[3955, 29106, 27421, 305])).
% 3.99/4.32 tff(29108,plain,
% 3.99/4.32 (r(s(z), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[406, 29107, 22694])).
% 3.99/4.32 tff(29109,plain,
% 3.99/4.32 (~r(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28601, 29108, 1525, 29096])).
% 3.99/4.32 tff(29110,plain,
% 3.99/4.32 (b(s(s(z)), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[7970, 29109, 28890])).
% 3.99/4.32 tff(29111,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[11650, 144, 1398, 133, 132, 7928])).
% 3.99/4.32 tff(29112,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29113,plain,
% 3.99/4.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29112, 29110, 26557, 27421])).
% 3.99/4.32 tff(29114,plain,
% 3.99/4.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1451, 29113])).
% 3.99/4.32 tff(29115,plain,
% 3.99/4.32 ($false),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[19954, 333, 29114, 11546, 28881, 29096])).
% 3.99/4.32 tff(29116,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.32 tff(29117,plain,
% 3.99/4.32 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[29116, 29082, 11546, 29080, 56, 28883, 54, 3])).
% 3.99/4.32 tff(29118,plain,
% 3.99/4.32 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1137, 29117])).
% 3.99/4.32 tff(29119,plain,
% 3.99/4.32 (~b(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27297, 322, 133, 8677, 305, 1525, 6107, 10356, 56])).
% 3.99/4.32 tff(29120,plain,
% 3.99/4.32 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[18895, 29119, 8677])).
% 3.99/4.32 tff(29121,plain,
% 3.99/4.32 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[1283, 29120, 22759])).
% 3.99/4.32 tff(29122,plain,
% 3.99/4.32 (r(s(s(z)), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[22871, 29121, 8677])).
% 3.99/4.32 tff(29123,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[26043, 322, 11546, 56, 6107, 838])).
% 3.99/4.32 tff(29124,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[9761, 29123])).
% 3.99/4.32 tff(29125,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28416, 29124, 133, 132])).
% 3.99/4.32 tff(29126,plain,
% 3.99/4.32 (r(s(s(s(s(z)))), elem!1)),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[24301, 29125, 26567])).
% 3.99/4.32 tff(29127,plain,
% 3.99/4.32 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[28456, 29126, 1525, 6107])).
% 3.99/4.32 tff(29128,plain,
% 3.99/4.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27512, 29127])).
% 3.99/4.32 tff(29129,plain,
% 3.99/4.32 (~b(s(s(s(s(z)))), s(z))),
% 3.99/4.32 inference(unit_resolution,[status(thm)],[27536, 29128, 838, 56])).
% 3.99/4.33 tff(29130,plain,
% 3.99/4.33 (r(s(s(s(s(z)))), s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[27538, 29129])).
% 3.99/4.33 tff(29131,plain,
% 3.99/4.33 (((~![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(z)))), s(z))) | (~r(s(z), s(s(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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29132,plain,
% 3.99/4.33 (((~r(s(z), s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29133,plain,
% 3.99/4.33 (((~![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(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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.99/4.33 inference(monotonicity,[status(thm)],[29132])).
% 3.99/4.33 tff(29134,plain,
% 3.99/4.33 (((~![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(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(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.99/4.33 inference(transitivity,[status(thm)],[29133, 29131])).
% 3.99/4.33 tff(29135,plain,
% 3.99/4.33 ((~![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(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)))))),
% 3.99/4.33 inference(quant_inst,[status(thm)],[])).
% 3.99/4.33 tff(29136,plain,
% 3.99/4.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.99/4.33 inference(modus_ponens,[status(thm)],[29135, 29134])).
% 3.99/4.33 tff(29137,plain,
% 3.99/4.33 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29136, 333, 29130, 11546, 29122])).
% 3.99/4.33 tff(29138,plain,
% 3.99/4.33 (b(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 29137])).
% 3.99/4.33 tff(29139,plain,
% 3.99/4.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[3662, 29121, 22728, 27205])).
% 3.99/4.33 tff(29140,plain,
% 3.99/4.33 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[2758, 29139, 23135])).
% 3.99/4.33 tff(29141,plain,
% 3.99/4.33 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.99/4.33 inference(modus_ponens,[status(thm)],[29140, 23136])).
% 3.99/4.33 tff(29142,plain,
% 3.99/4.33 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[19960, 322, 11546, 224, 6107, 56])).
% 3.99/4.33 tff(29143,plain,
% 3.99/4.33 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[1451, 29142])).
% 3.99/4.33 tff(29144,plain,
% 3.99/4.33 ($false),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[9745, 144, 29143, 29141, 29124, 29138])).
% 3.99/4.33 tff(29145,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.33 tff(29146,plain,
% 3.99/4.33 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29145, 28440, 22669, 11546, 56, 29082, 29118, 27421, 26557, 28881, 29080, 28883])).
% 3.99/4.33 tff(29147,plain,
% 3.99/4.33 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[319, 29146])).
% 3.99/4.33 tff(29148,plain,
% 3.99/4.33 (~b(s(s(z)), s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[28994, 29147, 29118, 28881, 26557, 29082, 22669, 56, 28883])).
% 3.99/4.33 tff(29149,plain,
% 3.99/4.33 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[18895, 29148, 22669])).
% 3.99/4.33 tff(29150,plain,
% 3.99/4.33 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[1283, 29149, 27098])).
% 3.99/4.33 tff(29151,plain,
% 3.99/4.33 (r(s(s(z)), s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[22871, 29150, 22669])).
% 3.99/4.33 tff(29152,plain,
% 3.99/4.33 (~b(s(z), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[3955, 29147, 27421, 29080])).
% 3.99/4.33 tff(29153,plain,
% 3.99/4.33 (r(s(z), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[406, 29152, 22694])).
% 3.99/4.33 tff(29154,plain,
% 3.99/4.33 (~r(s(s(z)), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[28601, 29151, 29082, 29153])).
% 3.99/4.33 tff(29155,plain,
% 3.99/4.33 (b(s(s(z)), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[7970, 29154, 28890])).
% 3.99/4.33 tff(29156,plain,
% 3.99/4.33 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29112, 29155, 26557, 27421])).
% 3.99/4.33 tff(29157,plain,
% 3.99/4.33 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[1451, 29156])).
% 3.99/4.33 tff(29158,plain,
% 3.99/4.33 ($false),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[19954, 333, 29157, 11546, 28881, 29151])).
% 3.99/4.33 tff(29159,plain,(r(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.33 tff(29160,plain,
% 3.99/4.33 (r(s(z), s(s(s(z))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29159, 3, 56, 54, 11546])).
% 3.99/4.33 tff(29161,plain,
% 3.99/4.33 ($false),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[16042, 333, 353, 11546, 224, 6107])).
% 3.99/4.33 tff(29162,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.33 tff(29163,plain,
% 3.99/4.33 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29162, 29160, 11546, 28881])).
% 3.99/4.33 tff(29164,plain,
% 3.99/4.33 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[1137, 29163])).
% 3.99/4.33 tff(29165,plain,
% 3.99/4.33 (~b(s(s(s(z))), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[10110, 29164, 54, 26551, 3])).
% 3.99/4.33 tff(29166,plain,
% 3.99/4.33 (r(s(s(s(z))), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[704, 29165, 28884])).
% 3.99/4.33 tff(29167,plain,
% 3.99/4.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29168,plain,
% 3.99/4.33 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29169,plain,
% 3.99/4.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.33 inference(monotonicity,[status(thm)],[29168])).
% 3.99/4.33 tff(29170,plain,
% 3.99/4.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(transitivity,[status(thm)],[29169, 29167])).
% 3.99/4.33 tff(29171,plain,
% 3.99/4.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(quant_inst,[status(thm)],[])).
% 3.99/4.33 tff(29172,plain,
% 3.99/4.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.33 inference(modus_ponens,[status(thm)],[29171, 29170])).
% 3.99/4.33 tff(29173,plain,
% 3.99/4.33 ($false),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29172, 333, 29166, 29160, 11546, 28881])).
% 3.99/4.33 tff(29174,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.33 tff(29175,plain,
% 3.99/4.33 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29174, 22678, 54, 11546])).
% 3.99/4.33 tff(29176,plain,
% 3.99/4.33 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[28880, 22678, 11546, 54])).
% 3.99/4.33 tff(29177,plain,
% 3.99/4.33 (((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29178,plain,
% 3.99/4.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29179,plain,
% 3.99/4.33 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.33 inference(monotonicity,[status(thm)],[29178])).
% 3.99/4.33 tff(29180,plain,
% 3.99/4.33 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(transitivity,[status(thm)],[29179, 29177])).
% 3.99/4.33 tff(29181,plain,
% 3.99/4.33 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))),
% 3.99/4.33 inference(quant_inst,[status(thm)],[])).
% 3.99/4.33 tff(29182,plain,
% 3.99/4.33 ((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.33 inference(modus_ponens,[status(thm)],[29181, 29180])).
% 3.99/4.33 tff(29183,plain,
% 3.99/4.33 (~r(s(z), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29182, 333, 11546, 29175, 29176])).
% 3.99/4.33 tff(29184,plain,
% 3.99/4.33 (~(s(s(s(z))) = elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[227, 29176, 54])).
% 3.99/4.33 tff(29185,plain,
% 3.99/4.33 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29186,plain,
% 3.99/4.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(rewrite,[status(thm)],[])).
% 3.99/4.33 tff(29187,plain,
% 3.99/4.33 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.33 inference(monotonicity,[status(thm)],[29186])).
% 3.99/4.33 tff(29188,plain,
% 3.99/4.33 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.33 inference(transitivity,[status(thm)],[29187, 29185])).
% 3.99/4.33 tff(29189,plain,
% 3.99/4.33 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 3.99/4.33 inference(quant_inst,[status(thm)],[])).
% 3.99/4.33 tff(29190,plain,
% 3.99/4.33 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.33 inference(modus_ponens,[status(thm)],[29189, 29188])).
% 3.99/4.33 tff(29191,plain,
% 3.99/4.33 (~r(elem!1, s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29190, 333, 11546, 29175, 29176])).
% 3.99/4.33 tff(29192,plain,
% 3.99/4.33 (~r(elem!1, s(z))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29190, 333, 11546, 2323, 224])).
% 3.99/4.33 tff(29193,plain,
% 3.99/4.33 (~r(s(z), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[29182, 333, 11546, 2323, 224])).
% 3.99/4.33 tff(29194,plain,
% 3.99/4.33 (~b(s(s(s(z))), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[4375, 6530, 56, 305])).
% 3.99/4.33 tff(29195,plain,
% 3.99/4.33 (r(s(s(s(z))), elem!1)),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[704, 29194, 698])).
% 3.99/4.33 tff(29196,plain,
% 3.99/4.33 (~b(elem!1, s(s(s(z))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[22776, 305, 838, 56])).
% 3.99/4.33 tff(29197,plain,
% 3.99/4.33 (r(elem!1, s(s(s(z))))),
% 3.99/4.33 inference(unit_resolution,[status(thm)],[1538, 29196, 12398])).
% 3.99/4.34 tff(29198,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29199,plain,
% 3.99/4.34 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(z)))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29200,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29199])).
% 3.99/4.34 tff(29201,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(transitivity,[status(thm)],[29200, 29198])).
% 3.99/4.34 tff(29202,plain,
% 3.99/4.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(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(s(s(z))))))))))),
% 3.99/4.34 inference(quant_inst,[status(thm)],[])).
% 3.99/4.34 tff(29203,plain,
% 3.99/4.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29202, 29201])).
% 3.99/4.34 tff(29204,plain,
% 3.99/4.34 ($false),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29203, 333, 29197, 29195, 2323, 224])).
% 3.99/4.34 tff(29205,plain,((~b(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(z))) | r(s(z), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.34 tff(29206,plain,
% 3.99/4.34 (~b(elem!1, s(z))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29205, 28440, 224, 698, 22678, 29193, 2323])).
% 3.99/4.34 tff(29207,plain,
% 3.99/4.34 (elem!1 = s(z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[720, 29206, 29192])).
% 3.99/4.34 tff(29208,plain,
% 3.99/4.34 (s(elem!1) = s(s(z))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29207])).
% 3.99/4.34 tff(29209,plain,
% 3.99/4.34 (s(s(z)) = s(elem!1)),
% 3.99/4.34 inference(symmetry,[status(thm)],[29208])).
% 3.99/4.34 tff(29210,plain,
% 3.99/4.34 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29209])).
% 3.99/4.34 tff(29211,plain,
% 3.99/4.34 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.99/4.34 inference(transitivity,[status(thm)],[29210, 174])).
% 3.99/4.34 tff(29212,plain,
% 3.99/4.34 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29211])).
% 3.99/4.34 tff(29213,plain,
% 3.99/4.34 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[1446, 29212])).
% 3.99/4.34 tff(29214,plain,
% 3.99/4.34 (s(z) = elem!1),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[712, 29207])).
% 3.99/4.34 tff(29215,plain,
% 3.99/4.34 (~(s(s(s(elem!1))) = elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[2468, 29214])).
% 3.99/4.34 tff(29216,plain,
% 3.99/4.34 (~(elem!1 = s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[2482, 29215])).
% 3.99/4.34 tff(29217,plain,
% 3.99/4.34 (~(s(s(elem!1)) = s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[1196, 29216])).
% 3.99/4.34 tff(29218,plain,
% 3.99/4.34 (s(s(elem!1)) = s(s(s(z)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29208])).
% 3.99/4.34 tff(29219,plain,
% 3.99/4.34 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29218])).
% 3.99/4.34 tff(29220,plain,
% 3.99/4.34 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29219])).
% 3.99/4.34 tff(29221,plain,
% 3.99/4.34 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[2254, 29220])).
% 3.99/4.34 tff(29222,plain,
% 3.99/4.34 (b(s(s(elem!1)), elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[24878, 29214, 22678])).
% 3.99/4.34 tff(29223,plain,
% 3.99/4.34 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[9386])).
% 3.99/4.34 tff(29224,plain,
% 3.99/4.34 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 3.99/4.34 inference(transitivity,[status(thm)],[9717, 29223])).
% 3.99/4.34 tff(29225,plain,
% 3.99/4.34 (~b(elem!1, s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[14987, 1249, 133, 4972, 6147])).
% 3.99/4.34 tff(29226,plain,
% 3.99/4.34 (r(elem!1, s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[560, 29225, 9430])).
% 3.99/4.34 tff(29227,plain,
% 3.99/4.34 (r(s(z), s(s(z)))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29226, 29224])).
% 3.99/4.34 tff(29228,plain,
% 3.99/4.34 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[27836, 1249, 133, 4972, 6147])).
% 3.99/4.34 tff(29229,plain,
% 3.99/4.34 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[2689, 29228, 9383])).
% 3.99/4.34 tff(29230,plain,
% 3.99/4.34 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[1451, 29229])).
% 3.99/4.34 tff(29231,plain,
% 3.99/4.34 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29232,plain,
% 3.99/4.34 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29233,plain,
% 3.99/4.34 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29232])).
% 3.99/4.34 tff(29234,plain,
% 3.99/4.34 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(transitivity,[status(thm)],[29233, 29231])).
% 3.99/4.34 tff(29235,plain,
% 3.99/4.34 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 3.99/4.34 inference(quant_inst,[status(thm)],[])).
% 3.99/4.34 tff(29236,plain,
% 3.99/4.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29235, 29234])).
% 3.99/4.34 tff(29237,plain,
% 3.99/4.34 ($false),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29236, 333, 29230, 11546, 224, 29227])).
% 3.99/4.34 tff(29238,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.34 tff(29239,plain,
% 3.99/4.34 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29238, 29207, 224, 11546, 133, 29222, 29221])).
% 3.99/4.34 tff(29240,plain,
% 3.99/4.34 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[1283, 29239, 29217])).
% 3.99/4.34 tff(29241,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29218])).
% 3.99/4.34 tff(29242,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29241])).
% 3.99/4.34 tff(29243,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[224, 29242])).
% 3.99/4.34 tff(29244,plain,
% 3.99/4.34 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29207])).
% 3.99/4.34 tff(29245,plain,
% 3.99/4.34 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 3.99/4.34 inference(symmetry,[status(thm)],[29244])).
% 3.99/4.34 tff(29246,plain,
% 3.99/4.34 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29245])).
% 3.99/4.34 tff(29247,plain,
% 3.99/4.34 (~r(s(s(s(z))), elem!1)),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[2788, 29246])).
% 3.99/4.34 tff(29248,plain,
% 3.99/4.34 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29207])).
% 3.99/4.34 tff(29249,plain,
% 3.99/4.34 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29248])).
% 3.99/4.34 tff(29250,plain,
% 3.99/4.34 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29249])).
% 3.99/4.34 tff(29251,plain,
% 3.99/4.34 (~r(elem!1, s(s(s(z))))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[155, 29250])).
% 3.99/4.34 tff(29252,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[9387])).
% 3.99/4.34 tff(29253,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29252])).
% 3.99/4.34 tff(29254,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[224, 29253])).
% 3.99/4.34 tff(29255,plain,
% 3.99/4.34 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[9386])).
% 3.99/4.34 tff(29256,plain,
% 3.99/4.34 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29255])).
% 3.99/4.34 tff(29257,plain,
% 3.99/4.34 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(transitivity,[status(thm)],[9763, 29256])).
% 3.99/4.34 tff(29258,plain,
% 3.99/4.34 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[2254, 23366])).
% 3.99/4.34 tff(29259,plain,
% 3.99/4.34 (b(s(s(elem!1)), elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[24878, 9383, 56])).
% 3.99/4.34 tff(29260,plain,
% 3.99/4.34 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29238, 709, 224, 11546, 133, 29259, 29258])).
% 3.99/4.34 tff(29261,plain,
% 3.99/4.34 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[1283, 29260, 9481])).
% 3.99/4.34 tff(29262,plain,
% 3.99/4.34 (r(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29261, 29257])).
% 3.99/4.34 tff(29263,plain,
% 3.99/4.34 (r(s(s(s(z))), s(s(z)))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29261, 9763])).
% 3.99/4.34 tff(29264,plain,
% 3.99/4.34 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[27431, 709, 133])).
% 3.99/4.34 tff(29265,plain,
% 3.99/4.34 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[9386])).
% 3.99/4.34 tff(29266,plain,
% 3.99/4.34 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(symmetry,[status(thm)],[29265])).
% 3.99/4.34 tff(29267,plain,
% 3.99/4.34 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(transitivity,[status(thm)],[9582, 29266])).
% 3.99/4.34 tff(29268,plain,
% 3.99/4.34 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29267])).
% 3.99/4.34 tff(29269,plain,
% 3.99/4.34 (~b(s(s(s(z))), s(elem!1))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29260, 29268])).
% 3.99/4.34 tff(29270,plain,
% 3.99/4.34 (~b(z, elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[9366, 9362, 57])).
% 3.99/4.34 tff(29271,plain,
% 3.99/4.34 (r(z, elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[658, 29270, 74])).
% 3.99/4.34 tff(29272,plain,
% 3.99/4.34 (~r(s(elem!1), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[24919, 29271, 435, 2323])).
% 3.99/4.34 tff(29273,plain,
% 3.99/4.34 (b(s(elem!1), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[507, 29272])).
% 3.99/4.34 tff(29274,plain,
% 3.99/4.34 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[15576, 9363, 11546, 224])).
% 3.99/4.34 tff(29275,plain,
% 3.99/4.34 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[279, 29274])).
% 3.99/4.34 tff(29276,plain,
% 3.99/4.34 (~b(s(s(s(z))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[24118, 144, 56, 2254, 304, 29275])).
% 3.99/4.34 tff(29277,plain,
% 3.99/4.34 (r(s(s(s(z))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[396, 29276])).
% 3.99/4.34 tff(29278,plain,
% 3.99/4.34 ($false),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[12304, 333, 354, 1699, 224, 321])).
% 3.99/4.34 tff(29279,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.34 tff(29280,plain,
% 3.99/4.34 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29279, 9363, 29277, 224])).
% 3.99/4.34 tff(29281,plain,
% 3.99/4.34 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[302, 29280])).
% 3.99/4.34 tff(29282,plain,
% 3.99/4.34 (~b(s(elem!1), s(s(s(z))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[15601, 29281, 450, 29273, 2254])).
% 3.99/4.34 tff(29283,plain,
% 3.99/4.34 (r(s(elem!1), s(s(s(z))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[965, 29282, 960])).
% 3.99/4.34 tff(29284,plain,
% 3.99/4.34 (~r(z, s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[12891, 29277, 3003, 435])).
% 3.99/4.34 tff(29285,plain,
% 3.99/4.34 (b(z, s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[583, 29284])).
% 3.99/4.34 tff(29286,plain,
% 3.99/4.34 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[12069, 29281, 29273, 29285])).
% 3.99/4.34 tff(29287,plain,
% 3.99/4.34 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[542, 29286, 537])).
% 3.99/4.34 tff(29288,plain,
% 3.99/4.34 ($false),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[5258, 29287, 29283, 3654, 2737])).
% 3.99/4.34 tff(29289,plain,(b(z, s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.34 tff(29290,plain,
% 3.99/4.34 (b(z, s(z))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29289, 435, 2737, 537, 960, 450, 2254, 224, 3003, 3654, 56, 304, 2323, 74, 11546, 57])).
% 3.99/4.34 tff(29291,plain,
% 3.99/4.34 (b(z, elem!1)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[8102, 29290, 57])).
% 3.99/4.34 tff(29292,plain,
% 3.99/4.34 (~b(z, s(s(s(z))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[21799, 29291, 698, 21019, 699])).
% 3.99/4.34 tff(29293,plain,
% 3.99/4.34 (r(z, s(s(s(z))))),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[619, 29292])).
% 3.99/4.34 tff(29294,plain,
% 3.99/4.34 (((~![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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29295,plain,
% 3.99/4.34 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29296,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.99/4.34 inference(monotonicity,[status(thm)],[29295])).
% 3.99/4.34 tff(29297,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.99/4.34 inference(transitivity,[status(thm)],[29296, 29294])).
% 3.99/4.34 tff(29298,plain,
% 3.99/4.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.99/4.34 inference(quant_inst,[status(thm)],[])).
% 3.99/4.34 tff(29299,plain,
% 3.99/4.34 ((~![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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.99/4.34 inference(modus_ponens,[status(thm)],[29298, 29297])).
% 3.99/4.34 tff(29300,plain,
% 3.99/4.34 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[29299, 333, 29293, 224, 19432])).
% 3.99/4.34 tff(29301,plain,
% 3.99/4.34 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[302, 29300])).
% 3.99/4.34 tff(29302,plain,
% 3.99/4.34 (~b(elem!1, z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[880, 29301, 133, 29291])).
% 3.99/4.34 tff(29303,plain,
% 3.99/4.34 (r(elem!1, z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[653, 29302, 730])).
% 3.99/4.34 tff(29304,plain,
% 3.99/4.34 (~r(s(elem!1), z)),
% 3.99/4.34 inference(unit_resolution,[status(thm)],[10865, 29303, 435, 29293])).
% 3.99/4.34 tff(29305,plain,
% 3.99/4.34 (((~![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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29306,plain,
% 3.99/4.34 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.34 inference(rewrite,[status(thm)],[])).
% 3.99/4.34 tff(29307,plain,
% 3.99/4.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29306])).
% 3.99/4.35 tff(29308,plain,
% 3.99/4.35 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(transitivity,[status(thm)],[29307, 29305])).
% 3.99/4.35 tff(29309,plain,
% 3.99/4.35 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(quant_inst,[status(thm)],[])).
% 3.99/4.35 tff(29310,plain,
% 3.99/4.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29309, 29308])).
% 3.99/4.35 tff(29311,plain,
% 3.99/4.35 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29310, 333, 29293, 224, 19432])).
% 3.99/4.35 tff(29312,plain,
% 3.99/4.35 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[279, 29311])).
% 3.99/4.35 tff(29313,plain,
% 3.99/4.35 (~b(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[15996, 29312, 304, 450, 29290])).
% 3.99/4.35 tff(29314,plain,
% 3.99/4.35 (r(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[583, 29313])).
% 3.99/4.35 tff(29315,plain,
% 3.99/4.35 (b(s(elem!1), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[4807, 29314, 3296, 960, 29293])).
% 3.99/4.35 tff(29316,plain,
% 3.99/4.35 (~b(s(elem!1), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[15601, 29315, 450, 29301, 2254])).
% 3.99/4.35 tff(29317,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[507, 29316, 29304])).
% 3.99/4.35 tff(29318,plain,((~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29319,plain,
% 3.99/4.35 (~r(s(elem!1), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29318, 450, 2254, 29269, 9448, 133, 29264, 224, 29263, 698, 21019, 699, 9383, 29261, 9578, 29262, 29254, 56, 2323, 74, 11546])).
% 3.99/4.35 tff(29320,plain,
% 3.99/4.35 (b(s(elem!1), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[448, 29319, 9469])).
% 3.99/4.35 tff(29321,plain,
% 3.99/4.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(rewrite,[status(thm)],[])).
% 3.99/4.35 tff(29322,plain,
% 3.99/4.35 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(rewrite,[status(thm)],[])).
% 3.99/4.35 tff(29323,plain,
% 3.99/4.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29322])).
% 3.99/4.35 tff(29324,plain,
% 3.99/4.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(transitivity,[status(thm)],[29323, 29321])).
% 3.99/4.35 tff(29325,plain,
% 3.99/4.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.99/4.35 inference(quant_inst,[status(thm)],[])).
% 3.99/4.35 tff(29326,plain,
% 3.99/4.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29325, 29324])).
% 3.99/4.35 tff(29327,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29326, 144, 451, 1794, 133, 2254, 450])).
% 3.99/4.35 tff(29328,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29329,plain,
% 3.99/4.35 (~b(s(elem!1), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29328, 29320, 133, 2254, 450])).
% 3.99/4.35 tff(29330,plain,
% 3.99/4.35 (r(s(elem!1), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[965, 29329, 9448])).
% 3.99/4.35 tff(29331,plain,
% 3.99/4.35 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[5258, 29330, 29254, 29261])).
% 3.99/4.35 tff(29332,plain,
% 3.99/4.35 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[542, 29331, 9578])).
% 3.99/4.35 tff(29333,plain,
% 3.99/4.35 (~b(elem!1, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[555, 29332, 133, 29320])).
% 3.99/4.35 tff(29334,plain,
% 3.99/4.35 (r(elem!1, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[560, 29333, 9430])).
% 3.99/4.35 tff(29335,plain,
% 3.99/4.35 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 3.99/4.35 inference(transitivity,[status(thm)],[9486, 4572])).
% 3.99/4.35 tff(29336,plain,
% 3.99/4.35 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29335])).
% 3.99/4.35 tff(29337,plain,
% 3.99/4.35 (~(s(s(elem!1)) = elem!1)),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[107, 29336])).
% 3.99/4.35 tff(29338,plain,
% 3.99/4.35 (~(s(elem!1) = s(s(elem!1)))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2856, 9481])).
% 3.99/4.35 tff(29339,plain,
% 3.99/4.35 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[8472, 29334, 133, 29261, 9402, 29338, 29337, 9488, 29320])).
% 3.99/4.35 tff(29340,plain,
% 3.99/4.35 (~r(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[5074, 29271, 563, 1686])).
% 3.99/4.35 tff(29341,plain,
% 3.99/4.35 (~b(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[8386, 29275, 535, 537, 466])).
% 3.99/4.35 tff(29342,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[583, 29341, 29340])).
% 3.99/4.35 tff(29343,plain,(b(z, s(z)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29344,plain,
% 3.99/4.35 (b(z, s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29343, 29331, 9578, 29339, 29334, 29330, 74, 11546, 224, 9383])).
% 3.99/4.35 tff(29345,plain,
% 3.99/4.35 (b(z, elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[8102, 29344, 9383])).
% 3.99/4.35 tff(29346,plain,
% 3.99/4.35 (~b(z, s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[21799, 29345, 698, 21019, 699])).
% 3.99/4.35 tff(29347,plain,
% 3.99/4.35 (r(z, s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[619, 29346])).
% 3.99/4.35 tff(29348,plain,
% 3.99/4.35 (~r(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[4807, 29347, 29269, 9448, 29329])).
% 3.99/4.35 tff(29349,plain,
% 3.99/4.35 (b(z, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[583, 29348])).
% 3.99/4.35 tff(29350,plain,
% 3.99/4.35 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[593, 29349, 133, 29320, 29332])).
% 3.99/4.35 tff(29351,plain,
% 3.99/4.35 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[302, 29350])).
% 3.99/4.35 tff(29352,plain,
% 3.99/4.35 (b(s(elem!1), s(z))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29320, 23559])).
% 3.99/4.35 tff(29353,plain,
% 3.99/4.35 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[9386, 9387])).
% 3.99/4.35 tff(29354,plain,
% 3.99/4.35 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29353])).
% 3.99/4.35 tff(29355,plain,
% 3.99/4.35 (r(s(s(z)), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[24894, 29330, 9383])).
% 3.99/4.35 tff(29356,plain,
% 3.99/4.35 (r(s(elem!1), s(s(elem!1)))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29355, 29354])).
% 3.99/4.35 tff(29357,plain,
% 3.99/4.35 (r(z, s(s(elem!1)))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2836, 29347, 9383])).
% 3.99/4.35 tff(29358,plain,
% 3.99/4.35 (~r(s(elem!1), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[23930, 29357, 29356, 29261])).
% 3.99/4.35 tff(29359,plain,
% 3.99/4.35 (b(s(elem!1), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[507, 29358])).
% 3.99/4.35 tff(29360,plain,
% 3.99/4.35 (~b(s(z), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[499, 29359, 29352, 29344])).
% 3.99/4.35 tff(29361,plain,
% 3.99/4.35 (r(s(z), z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[348, 29360])).
% 3.99/4.35 tff(29362,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[19065, 29361, 29351, 11546, 29347])).
% 3.99/4.35 tff(29363,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29364,plain,
% 3.99/4.35 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29363, 29251, 133, 698, 11546, 29247, 74, 224, 29207, 2254, 22678, 2323])).
% 3.99/4.35 tff(29365,plain,
% 3.99/4.35 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[21271, 29364, 29214])).
% 3.99/4.35 tff(29366,plain,
% 3.99/4.35 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[3662, 29365, 29243, 29240])).
% 3.99/4.35 tff(29367,plain,
% 3.99/4.35 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[542, 29366, 29213])).
% 3.99/4.35 tff(29368,plain,
% 3.99/4.35 (~(s(elem!1) = elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[906, 29216])).
% 3.99/4.35 tff(29369,plain,
% 3.99/4.35 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29207])).
% 3.99/4.35 tff(29370,plain,
% 3.99/4.35 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 3.99/4.35 inference(symmetry,[status(thm)],[29369])).
% 3.99/4.35 tff(29371,plain,
% 3.99/4.35 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29208])).
% 3.99/4.35 tff(29372,plain,
% 3.99/4.35 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29371])).
% 3.99/4.35 tff(29373,plain,
% 3.99/4.35 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 3.99/4.35 inference(transitivity,[status(thm)],[29372, 29370])).
% 3.99/4.35 tff(29374,plain,
% 3.99/4.35 ((~r(s(s(z)), s(z))) <=> (~r(s(elem!1), elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29373])).
% 3.99/4.35 tff(29375,plain,
% 3.99/4.35 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2689, 29364, 29214])).
% 3.99/4.35 tff(29376,plain,
% 3.99/4.35 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[1451, 29375])).
% 3.99/4.35 tff(29377,plain,
% 3.99/4.35 (~r(s(s(z)), s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[19954, 333, 29376, 11546, 224])).
% 3.99/4.35 tff(29378,plain,
% 3.99/4.35 (~r(s(elem!1), elem!1)),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29377, 29374])).
% 3.99/4.35 tff(29379,plain,
% 3.99/4.35 (b(s(elem!1), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[448, 29378, 29368])).
% 3.99/4.35 tff(29380,plain,
% 3.99/4.35 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29207])).
% 3.99/4.35 tff(29381,plain,
% 3.99/4.35 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29380])).
% 3.99/4.35 tff(29382,plain,
% 3.99/4.35 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29208])).
% 3.99/4.35 tff(29383,plain,
% 3.99/4.35 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29382])).
% 3.99/4.35 tff(29384,plain,
% 3.99/4.35 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 3.99/4.35 inference(transitivity,[status(thm)],[29383, 29381])).
% 3.99/4.35 tff(29385,plain,
% 3.99/4.35 ((~r(s(z), s(s(z)))) <=> (~r(elem!1, s(elem!1)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29384])).
% 3.99/4.35 tff(29386,plain,
% 3.99/4.35 (~r(s(z), s(s(z)))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29236, 333, 29376, 11546, 224])).
% 3.99/4.35 tff(29387,plain,
% 3.99/4.35 (~r(elem!1, s(elem!1))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29386, 29385])).
% 3.99/4.35 tff(29388,plain,
% 3.99/4.35 (b(elem!1, s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[560, 29387, 29216])).
% 3.99/4.35 tff(29389,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[555, 29388, 29379, 133, 29367])).
% 3.99/4.35 tff(29390,plain,(r(s(z), s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (z = elem!1) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29391,plain,
% 3.99/4.35 (r(s(z), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29390, 2254, 11546, 224, 698, 74, 133, 2323, 2788])).
% 3.99/4.35 tff(29392,plain,
% 3.99/4.35 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[3955, 14286, 133, 6060])).
% 3.99/4.35 tff(29393,plain,
% 3.99/4.35 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[319, 29392])).
% 3.99/4.35 tff(29394,plain,
% 3.99/4.35 (~b(s(s(s(z))), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[4375, 14286, 56, 6060])).
% 3.99/4.35 tff(29395,plain,
% 3.99/4.35 (r(s(s(s(z))), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[704, 29394, 698])).
% 3.99/4.35 tff(29396,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[22780, 29395, 29393, 224, 353])).
% 3.99/4.35 tff(29397,plain,((s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29398,plain,
% 3.99/4.35 (s(z) = elem!1),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29397, 29391, 224, 698, 22678, 133, 29192, 29193])).
% 3.99/4.35 tff(29399,plain,
% 3.99/4.35 (~(s(s(s(elem!1))) = elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2468, 29398])).
% 3.99/4.35 tff(29400,plain,
% 3.99/4.35 (~(elem!1 = s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2482, 29399])).
% 3.99/4.35 tff(29401,plain,
% 3.99/4.35 (~(s(s(elem!1)) = s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[1196, 29400])).
% 3.99/4.35 tff(29402,plain,
% 3.99/4.35 (s(s(z)) = s(elem!1)),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29398])).
% 3.99/4.35 tff(29403,plain,
% 3.99/4.35 (s(s(s(z))) = s(s(elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29402])).
% 3.99/4.35 tff(29404,plain,
% 3.99/4.35 (s(s(elem!1)) = s(s(s(z)))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29403])).
% 3.99/4.35 tff(29405,plain,
% 3.99/4.35 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29404])).
% 3.99/4.35 tff(29406,plain,
% 3.99/4.35 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29405])).
% 3.99/4.35 tff(29407,plain,
% 3.99/4.35 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29406])).
% 3.99/4.35 tff(29408,plain,
% 3.99/4.35 (((~![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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(rewrite,[status(thm)],[])).
% 3.99/4.35 tff(29409,plain,
% 3.99/4.35 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(rewrite,[status(thm)],[])).
% 3.99/4.35 tff(29410,plain,
% 3.99/4.35 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29409])).
% 3.99/4.35 tff(29411,plain,
% 3.99/4.35 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(transitivity,[status(thm)],[29410, 29408])).
% 3.99/4.35 tff(29412,plain,
% 3.99/4.35 ((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.35 inference(quant_inst,[status(thm)],[])).
% 3.99/4.35 tff(29413,plain,
% 3.99/4.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29412, 29411])).
% 3.99/4.35 tff(29414,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29413, 333, 353, 11546, 224, 19432])).
% 3.99/4.35 tff(29415,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29416,plain,
% 3.99/4.35 (~r(s(s(s(z))), s(s(z)))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29415, 29391, 11546, 224])).
% 3.99/4.35 tff(29417,plain,
% 3.99/4.35 (~b(elem!1, s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[6528, 29398])).
% 3.99/4.35 tff(29418,plain,
% 3.99/4.35 (elem!1 = s(z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[720, 29417, 29192])).
% 3.99/4.35 tff(29419,plain,
% 3.99/4.35 (~r(s(s(s(z))), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[13447, 29418, 29416])).
% 3.99/4.35 tff(29420,plain,
% 3.99/4.35 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29419, 29407])).
% 3.99/4.35 tff(29421,plain,
% 3.99/4.35 (b(s(s(elem!1)), elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[24878, 29398, 22678])).
% 3.99/4.35 tff(29422,plain,
% 3.99/4.35 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29403])).
% 3.99/4.35 tff(29423,plain,
% 3.99/4.35 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[2254, 29422])).
% 3.99/4.35 tff(29424,plain,
% 3.99/4.35 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29238, 29423, 224, 11546, 133, 29421, 29418])).
% 3.99/4.35 tff(29425,plain,
% 3.99/4.35 ($false),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[1283, 29424, 29420, 29401])).
% 3.99/4.35 tff(29426,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (z = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.35 tff(29427,plain,
% 3.99/4.35 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29426, 74, 11546, 133, 698, 224, 2323, 2788])).
% 3.99/4.35 tff(29428,plain,
% 3.99/4.35 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[1137, 29427])).
% 3.99/4.35 tff(29429,plain,
% 3.99/4.35 (~r(s(z), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29162, 29428, 11546, 224])).
% 3.99/4.35 tff(29430,plain,
% 3.99/4.35 (b(s(z), s(s(s(z))))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[172, 29429])).
% 3.99/4.35 tff(29431,plain,
% 3.99/4.35 (~b(elem!1, s(z))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[29205, 29430, 224, 698, 22678, 29193, 2323])).
% 3.99/4.35 tff(29432,plain,
% 3.99/4.35 (elem!1 = s(z)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[720, 29431, 29192])).
% 3.99/4.35 tff(29433,plain,
% 3.99/4.35 (s(z) = elem!1),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[712, 29432])).
% 3.99/4.35 tff(29434,plain,
% 3.99/4.35 (~(s(s(s(elem!1))) = elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2468, 29433])).
% 3.99/4.35 tff(29435,plain,
% 3.99/4.35 (~(elem!1 = s(elem!1))),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[2482, 29434])).
% 3.99/4.35 tff(29436,plain,
% 3.99/4.35 (~(s(elem!1) = elem!1)),
% 3.99/4.35 inference(unit_resolution,[status(thm)],[906, 29435])).
% 3.99/4.35 tff(29437,plain,
% 3.99/4.35 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29432])).
% 3.99/4.35 tff(29438,plain,
% 3.99/4.35 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 3.99/4.35 inference(symmetry,[status(thm)],[29437])).
% 3.99/4.35 tff(29439,plain,
% 3.99/4.35 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29438])).
% 3.99/4.35 tff(29440,plain,
% 3.99/4.35 (~r(s(s(s(z))), elem!1)),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[2788, 29439])).
% 3.99/4.35 tff(29441,plain,
% 3.99/4.35 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29432])).
% 3.99/4.35 tff(29442,plain,
% 3.99/4.35 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29441])).
% 3.99/4.35 tff(29443,plain,
% 3.99/4.35 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29442])).
% 3.99/4.35 tff(29444,plain,
% 3.99/4.35 (~r(elem!1, s(s(s(z))))),
% 3.99/4.35 inference(modus_ponens,[status(thm)],[29429, 29443])).
% 3.99/4.35 tff(29445,plain,
% 3.99/4.35 (s(elem!1) = s(s(z))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29432])).
% 3.99/4.35 tff(29446,plain,
% 3.99/4.35 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29445])).
% 3.99/4.35 tff(29447,plain,
% 3.99/4.35 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 3.99/4.35 inference(symmetry,[status(thm)],[29446])).
% 3.99/4.35 tff(29448,plain,
% 3.99/4.35 (s(s(elem!1)) = s(s(s(z)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29445])).
% 3.99/4.35 tff(29449,plain,
% 3.99/4.35 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.99/4.35 inference(monotonicity,[status(thm)],[29448, 29445])).
% 3.99/4.35 tff(29450,plain,
% 3.99/4.35 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.99/4.35 inference(transitivity,[status(thm)],[29449, 29447])).
% 3.99/4.36 tff(29451,plain,
% 3.99/4.36 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29450])).
% 3.99/4.36 tff(29452,plain,
% 3.99/4.36 (b(s(s(s(z))), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[63, 29433, 22678])).
% 3.99/4.36 tff(29453,plain,
% 3.99/4.36 (b(s(s(elem!1)), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24878, 29433, 22678])).
% 3.99/4.36 tff(29454,plain,
% 3.99/4.36 (~r(s(z), s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29162, 6107, 11546, 224])).
% 3.99/4.36 tff(29455,plain,
% 3.99/4.36 (b(s(z), s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[172, 29454])).
% 3.99/4.36 tff(29456,plain,
% 3.99/4.36 (~r(s(elem!1), s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24894, 11637, 9383])).
% 3.99/4.36 tff(29457,plain,
% 3.99/4.36 (b(s(elem!1), s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[965, 29456, 9448])).
% 3.99/4.36 tff(29458,plain,
% 3.99/4.36 (b(s(s(z)), s(s(s(z))))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29457, 9444])).
% 3.99/4.36 tff(29459,plain,
% 3.99/4.36 (((~b(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(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 3.99/4.36 inference(rewrite,[status(thm)],[])).
% 3.99/4.36 tff(29460,plain,
% 3.99/4.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29459])).
% 3.99/4.36 tff(29461,plain,
% 3.99/4.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 3.99/4.36 inference(transitivity,[status(thm)],[29460, 18108])).
% 3.99/4.36 tff(29462,plain,
% 3.99/4.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.99/4.36 inference(quant_inst,[status(thm)],[])).
% 3.99/4.36 tff(29463,plain,
% 3.99/4.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29462, 29461])).
% 3.99/4.36 tff(29464,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29463, 144, 56, 29458, 19956, 29455])).
% 3.99/4.36 tff(29465,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.36 tff(29466,plain,
% 3.99/4.36 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29465, 29432, 22678, 224, 29428, 11546])).
% 3.99/4.36 tff(29467,plain,
% 3.99/4.36 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[1451, 29466])).
% 3.99/4.36 tff(29468,plain,
% 3.99/4.36 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.99/4.36 inference(symmetry,[status(thm)],[23719])).
% 3.99/4.36 tff(29469,plain,
% 3.99/4.36 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29468])).
% 3.99/4.36 tff(29470,plain,
% 3.99/4.36 (~r(elem!1, s(s(s(z))))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29454, 29469])).
% 3.99/4.36 tff(29471,plain,
% 3.99/4.36 (b(s(s(s(z))), s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24791, 1249, 9383])).
% 3.99/4.36 tff(29472,plain,
% 3.99/4.36 (~b(z, s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[21799, 251, 698, 21019, 699])).
% 3.99/4.36 tff(29473,plain,
% 3.99/4.36 (r(z, s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[619, 29472])).
% 3.99/4.36 tff(29474,plain,
% 3.99/4.36 (r(z, s(s(elem!1)))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[2836, 29473, 9383])).
% 3.99/4.36 tff(29475,plain,
% 3.99/4.36 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[10435, 333, 29473, 224, 6107])).
% 3.99/4.36 tff(29476,plain,
% 3.99/4.36 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[302, 29475])).
% 3.99/4.36 tff(29477,plain,
% 3.99/4.36 (~b(elem!1, z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[880, 29476, 133, 251])).
% 3.99/4.36 tff(29478,plain,
% 3.99/4.36 (r(elem!1, z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[653, 29477, 1368])).
% 3.99/4.36 tff(29479,plain,
% 3.99/4.36 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 3.99/4.36 inference(monotonicity,[status(thm)],[9386])).
% 3.99/4.36 tff(29480,plain,
% 3.99/4.36 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 3.99/4.36 inference(symmetry,[status(thm)],[29479])).
% 3.99/4.36 tff(29481,plain,
% 3.99/4.36 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29480])).
% 3.99/4.36 tff(29482,plain,
% 3.99/4.36 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.36 inference(rewrite,[status(thm)],[])).
% 3.99/4.36 tff(29483,plain,
% 3.99/4.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29482])).
% 3.99/4.36 tff(29484,plain,
% 3.99/4.36 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.36 inference(transitivity,[status(thm)],[29483, 1475])).
% 3.99/4.36 tff(29485,plain,
% 3.99/4.36 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.36 inference(quant_inst,[status(thm)],[])).
% 3.99/4.36 tff(29486,plain,
% 3.99/4.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29485, 29484])).
% 3.99/4.36 tff(29487,plain,
% 3.99/4.36 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29486, 333, 29473, 224, 6107])).
% 3.99/4.36 tff(29488,plain,
% 3.99/4.36 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[279, 29487])).
% 3.99/4.36 tff(29489,plain,
% 3.99/4.36 (~b(s(s(z)), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[19968, 144, 1398, 29476, 29488])).
% 3.99/4.36 tff(29490,plain,
% 3.99/4.36 (~b(s(elem!1), z)),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29489, 29481])).
% 3.99/4.36 tff(29491,plain,
% 3.99/4.36 (r(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[507, 29490])).
% 3.99/4.36 tff(29492,plain,
% 3.99/4.36 (~r(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24407, 29491, 29478, 29474])).
% 3.99/4.36 tff(29493,plain,
% 3.99/4.36 (b(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[560, 29492, 9430])).
% 3.99/4.36 tff(29494,plain,
% 3.99/4.36 (~r(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[10865, 29491, 29478, 29473])).
% 3.99/4.36 tff(29495,plain,
% 3.99/4.36 (b(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[448, 29494, 9469])).
% 3.99/4.36 tff(29496,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[4819, 29495, 29493, 4367, 4811])).
% 3.99/4.36 tff(29497,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.36 tff(29498,plain,
% 3.99/4.36 (~b(z, elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29497, 29471, 4367, 709, 1398, 730, 133, 224, 6107, 698, 29470, 699])).
% 3.99/4.36 tff(29499,plain,
% 3.99/4.36 (~b(z, s(z))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[8102, 29498, 9383])).
% 3.99/4.36 tff(29500,plain,
% 3.99/4.36 (r(z, s(z))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[372, 29499])).
% 3.99/4.36 tff(29501,plain,
% 3.99/4.36 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[15576, 29500, 11546, 224])).
% 3.99/4.36 tff(29502,plain,
% 3.99/4.36 (r(z, elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[658, 29498, 74])).
% 3.99/4.36 tff(29503,plain,
% 3.99/4.36 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[6107, 23340])).
% 3.99/4.36 tff(29504,plain,
% 3.99/4.36 (~b(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[4819, 451, 4367, 4811])).
% 3.99/4.36 tff(29505,plain,
% 3.99/4.36 (r(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[560, 29504, 2483])).
% 3.99/4.36 tff(29506,plain,
% 3.99/4.36 (~b(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[27573, 451, 133, 259, 450])).
% 3.99/4.36 tff(29507,plain,
% 3.99/4.36 (r(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[507, 29506])).
% 3.99/4.36 tff(29508,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24950, 29507, 29505, 838, 57, 8162, 4972, 354, 670])).
% 3.99/4.36 tff(29509,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(z))))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.36 tff(29510,plain,
% 3.99/4.36 (~b(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29509, 9449, 9383, 8162, 4972, 354, 670, 133, 259, 838, 4367, 29471])).
% 3.99/4.36 tff(29511,plain,
% 3.99/4.36 (r(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[448, 29510, 9469])).
% 3.99/4.36 tff(29512,plain,
% 3.99/4.36 (~r(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24919, 29511, 670, 2323])).
% 3.99/4.36 tff(29513,plain,
% 3.99/4.36 (b(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[507, 29512])).
% 3.99/4.36 tff(29514,plain,
% 3.99/4.36 (b(s(s(z)), z)),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29513, 29479])).
% 3.99/4.36 tff(29515,plain,
% 3.99/4.36 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.99/4.36 inference(symmetry,[status(thm)],[23328])).
% 3.99/4.36 tff(29516,plain,
% 3.99/4.36 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29515])).
% 3.99/4.36 tff(29517,plain,
% 3.99/4.36 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 3.99/4.36 inference(transitivity,[status(thm)],[9843, 9688])).
% 3.99/4.36 tff(29518,plain,
% 3.99/4.36 (r(s(s(z)), s(z))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29511, 29517])).
% 3.99/4.36 tff(29519,plain,
% 3.99/4.36 (((~![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(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(s(s(z))))))))))),
% 3.99/4.36 inference(rewrite,[status(thm)],[])).
% 3.99/4.36 tff(29520,plain,
% 3.99/4.36 (((~r(s(z), s(s(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(s(s(z))))))))))),
% 3.99/4.36 inference(rewrite,[status(thm)],[])).
% 3.99/4.36 tff(29521,plain,
% 3.99/4.36 (((~![X0: $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(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(s(s(z)))))))))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29520])).
% 3.99/4.36 tff(29522,plain,
% 3.99/4.36 (((~![X0: $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(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(s(s(z))))))))))),
% 3.99/4.36 inference(transitivity,[status(thm)],[29521, 29519])).
% 3.99/4.36 tff(29523,plain,
% 3.99/4.36 ((~![X0: $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(z))))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 3.99/4.36 inference(quant_inst,[status(thm)],[])).
% 3.99/4.36 tff(29524,plain,
% 3.99/4.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29523, 29522])).
% 3.99/4.36 tff(29525,plain,
% 3.99/4.36 (~r(z, s(s(z)))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29524, 333, 354, 11546, 29518])).
% 3.99/4.36 tff(29526,plain,
% 3.99/4.36 (~r(z, s(elem!1))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29525, 29516])).
% 3.99/4.36 tff(29527,plain,
% 3.99/4.36 (b(z, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[583, 29526])).
% 3.99/4.36 tff(29528,plain,
% 3.99/4.36 (~b(s(s(elem!1)), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[5572, 29527, 1249, 29513])).
% 3.99/4.36 tff(29529,plain,
% 3.99/4.36 (r(s(s(elem!1)), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[5509, 29528])).
% 3.99/4.36 tff(29530,plain,
% 3.99/4.36 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[10243, 29529, 8162, 670])).
% 3.99/4.36 tff(29531,plain,
% 3.99/4.36 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[302, 29530])).
% 3.99/4.36 tff(29532,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[19968, 144, 1398, 29531, 259, 29514])).
% 3.99/4.36 tff(29533,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(elem!1 = s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.36 tff(29534,plain,
% 3.99/4.36 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29533, 29500, 29503, 1398, 1249, 709, 29502, 11546, 2323, 4972, 133, 29455, 4367])).
% 3.99/4.36 tff(29535,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[279, 29534, 29501])).
% 3.99/4.36 tff(29536,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (z = elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.36 tff(29537,plain,
% 3.99/4.36 (~b(s(s(elem!1)), s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[29536, 29467, 29432, 11546, 2323, 29453, 133, 29452, 224, 74, 29428, 698, 29440])).
% 3.99/4.36 tff(29538,plain,
% 3.99/4.36 (~b(s(s(s(z))), s(elem!1))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[29537, 29451])).
% 3.99/4.36 tff(29539,plain,
% 3.99/4.36 (b(elem!1, s(s(elem!1)))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[5343, 29433, 29430])).
% 3.99/4.36 tff(29540,plain,
% 3.99/4.36 (~(s(s(elem!1)) = s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[1196, 29435])).
% 3.99/4.36 tff(29541,plain,
% 3.99/4.36 (r(s(s(elem!1)), s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[1283, 29537, 29540])).
% 3.99/4.36 tff(29542,plain,
% 3.99/4.36 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29448])).
% 3.99/4.36 tff(29543,plain,
% 3.99/4.36 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.36 inference(symmetry,[status(thm)],[29542])).
% 3.99/4.36 tff(29544,plain,
% 3.99/4.36 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[224, 29543])).
% 3.99/4.36 tff(29545,plain,
% 3.99/4.36 (s(s(z)) = s(elem!1)),
% 3.99/4.36 inference(symmetry,[status(thm)],[29445])).
% 3.99/4.36 tff(29546,plain,
% 3.99/4.36 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29545])).
% 3.99/4.36 tff(29547,plain,
% 3.99/4.36 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.99/4.36 inference(transitivity,[status(thm)],[29546, 174])).
% 3.99/4.36 tff(29548,plain,
% 3.99/4.36 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.99/4.36 inference(monotonicity,[status(thm)],[29547])).
% 3.99/4.36 tff(29549,plain,
% 3.99/4.36 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.99/4.36 inference(modus_ponens,[status(thm)],[1446, 29548])).
% 3.99/4.36 tff(29550,plain,
% 3.99/4.36 (~r(z, s(z))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[15576, 51, 11546, 224])).
% 3.99/4.36 tff(29551,plain,
% 3.99/4.36 (b(z, s(z))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[372, 29550])).
% 3.99/4.36 tff(29552,plain,
% 3.99/4.36 (b(z, elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[8102, 29551, 57])).
% 3.99/4.36 tff(29553,plain,
% 3.99/4.36 (b(s(s(s(z))), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[63, 57, 56])).
% 3.99/4.36 tff(29554,plain,
% 3.99/4.36 (~b(z, s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[21648, 51, 11546, 56, 6107])).
% 3.99/4.36 tff(29555,plain,
% 3.99/4.36 (r(z, s(s(s(z))))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[619, 29554])).
% 3.99/4.36 tff(29556,plain,
% 3.99/4.36 (~r(s(s(s(z))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[15762, 29555, 224, 51])).
% 3.99/4.36 tff(29557,plain,
% 3.99/4.36 (b(s(s(s(z))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[396, 29556])).
% 3.99/4.36 tff(29558,plain,
% 3.99/4.36 (~b(elem!1, z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[10565, 29557, 29553, 29552])).
% 3.99/4.36 tff(29559,plain,
% 3.99/4.36 (r(elem!1, z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[653, 29558, 1368])).
% 3.99/4.36 tff(29560,plain,
% 3.99/4.36 (~b(s(z), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[2273, 29557, 56, 29551])).
% 3.99/4.36 tff(29561,plain,
% 3.99/4.36 (r(s(z), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[348, 29560])).
% 3.99/4.36 tff(29562,plain,
% 3.99/4.36 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[19065, 29561, 11546, 29555])).
% 3.99/4.36 tff(29563,plain,
% 3.99/4.36 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[302, 29562])).
% 3.99/4.36 tff(29564,plain,
% 3.99/4.36 (~b(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[11813, 29563, 133, 57, 2737, 51, 29552, 29557])).
% 3.99/4.36 tff(29565,plain,
% 3.99/4.36 (r(s(elem!1), z)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[507, 29564])).
% 3.99/4.36 tff(29566,plain,
% 3.99/4.36 (~r(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[517, 29565, 51, 29559])).
% 3.99/4.36 tff(29567,plain,
% 3.99/4.36 (b(s(elem!1), elem!1)),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[448, 29566, 2681])).
% 3.99/4.36 tff(29568,plain,
% 3.99/4.36 (r(z, s(s(elem!1)))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[2836, 29555, 57])).
% 3.99/4.36 tff(29569,plain,
% 3.99/4.36 (~r(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[24407, 29565, 29559, 29568])).
% 3.99/4.36 tff(29570,plain,
% 3.99/4.36 (b(elem!1, s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[560, 29569, 2483])).
% 3.99/4.36 tff(29571,plain,
% 3.99/4.36 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[8191, 29565, 3654, 2737])).
% 3.99/4.36 tff(29572,plain,
% 3.99/4.36 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[542, 29571, 537])).
% 3.99/4.36 tff(29573,plain,
% 3.99/4.36 ($false),
% 3.99/4.36 inference(unit_resolution,[status(thm)],[555, 29572, 29570, 133, 29567])).
% 3.99/4.36 tff(29574,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29575,plain,
% 3.99/4.37 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29574, 29549, 133, 29544, 29541, 29433, 11546, 730, 22678, 224, 29428])).
% 3.99/4.37 tff(29576,plain,
% 3.99/4.37 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[279, 29575])).
% 3.99/4.37 tff(29577,plain,
% 3.99/4.37 (b(z, elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[8102, 490, 9383])).
% 3.99/4.37 tff(29578,plain,
% 3.99/4.37 (~b(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[21799, 29577, 698, 21019, 699])).
% 3.99/4.37 tff(29579,plain,
% 3.99/4.37 (r(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[619, 29578])).
% 3.99/4.37 tff(29580,plain,
% 3.99/4.37 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[9386, 9387])).
% 3.99/4.37 tff(29581,plain,
% 3.99/4.37 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.99/4.37 inference(symmetry,[status(thm)],[29580])).
% 3.99/4.37 tff(29582,plain,
% 3.99/4.37 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.99/4.37 inference(transitivity,[status(thm)],[9444, 29581])).
% 3.99/4.37 tff(29583,plain,
% 3.99/4.37 (~b(z, s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[15996, 490, 29264, 259, 9449])).
% 3.99/4.37 tff(29584,plain,
% 3.99/4.37 (r(z, s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[583, 29583])).
% 3.99/4.37 tff(29585,plain,
% 3.99/4.37 (b(s(elem!1), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[4807, 29584, 3296, 9448, 29579])).
% 3.99/4.37 tff(29586,plain,
% 3.99/4.37 (b(s(elem!1), s(s(elem!1)))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29585, 29582])).
% 3.99/4.37 tff(29587,plain,
% 3.99/4.37 (~b(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24923, 29586, 4972, 2812])).
% 3.99/4.37 tff(29588,plain,
% 3.99/4.37 (r(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[448, 29587, 9469])).
% 3.99/4.37 tff(29589,plain,
% 3.99/4.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[10435, 333, 29579, 224, 6107])).
% 3.99/4.37 tff(29590,plain,
% 3.99/4.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[302, 29589])).
% 3.99/4.37 tff(29591,plain,
% 3.99/4.37 (~b(elem!1, z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[880, 29590, 133, 29577])).
% 3.99/4.37 tff(29592,plain,
% 3.99/4.37 (r(elem!1, z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[653, 29591, 1368])).
% 3.99/4.37 tff(29593,plain,
% 3.99/4.37 (~r(s(elem!1), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[10865, 29592, 29588, 29579])).
% 3.99/4.37 tff(29594,plain,
% 3.99/4.37 (b(s(elem!1), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[507, 29593])).
% 3.99/4.37 tff(29595,plain,
% 3.99/4.37 (b(s(s(z)), z)),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29594, 29479])).
% 3.99/4.37 tff(29596,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[19968, 144, 1398, 29590, 259, 29595])).
% 3.99/4.37 tff(29597,plain,((~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z))) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(elem!1)) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29598,plain,
% 3.99/4.37 (~b(z, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29597, 29467, 29576, 29432, 730, 133, 29453, 29539, 224, 29428, 29538, 698, 29444, 29440])).
% 3.99/4.37 tff(29599,plain,
% 3.99/4.37 (~b(z, elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[9366, 29598, 29433])).
% 3.99/4.37 tff(29600,plain,
% 3.99/4.37 (r(z, elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[658, 29599, 74])).
% 3.99/4.37 tff(29601,plain,
% 3.99/4.37 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29445])).
% 3.99/4.37 tff(29602,plain,
% 3.99/4.37 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 3.99/4.37 inference(symmetry,[status(thm)],[29601])).
% 3.99/4.37 tff(29603,plain,
% 3.99/4.37 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29602])).
% 3.99/4.37 tff(29604,plain,
% 3.99/4.37 (~b(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[21591, 321, 11546, 6107])).
% 3.99/4.37 tff(29605,plain,
% 3.99/4.37 (r(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[619, 29604])).
% 3.99/4.37 tff(29606,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[10435, 333, 29605, 224, 6107, 321])).
% 3.99/4.37 tff(29607,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29608,plain,
% 3.99/4.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29607, 29428, 224, 11546])).
% 3.99/4.37 tff(29609,plain,
% 3.99/4.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[302, 29608])).
% 3.99/4.37 tff(29610,plain,
% 3.99/4.37 (~b(s(s(z)), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[19968, 144, 29467, 29609, 29576])).
% 3.99/4.37 tff(29611,plain,
% 3.99/4.37 (~b(s(elem!1), z)),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29610, 29603])).
% 3.99/4.37 tff(29612,plain,
% 3.99/4.37 (r(s(elem!1), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[507, 29611])).
% 3.99/4.37 tff(29613,plain,
% 3.99/4.37 (~r(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24919, 29612, 29600, 2323])).
% 3.99/4.37 tff(29614,plain,
% 3.99/4.37 (b(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[448, 29613, 29436])).
% 3.99/4.37 tff(29615,plain,
% 3.99/4.37 (r(z, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[372, 29598])).
% 3.99/4.37 tff(29616,plain,
% 3.99/4.37 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29448])).
% 3.99/4.37 tff(29617,plain,
% 3.99/4.37 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(symmetry,[status(thm)],[29616])).
% 3.99/4.37 tff(29618,plain,
% 3.99/4.37 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29428, 29617])).
% 3.99/4.37 tff(29619,plain,
% 3.99/4.37 (~r(elem!1, s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24950, 29612, 29430, 29433, 29618, 29453, 29615, 29600])).
% 3.99/4.37 tff(29620,plain,
% 3.99/4.37 (b(elem!1, s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[560, 29619, 29435])).
% 3.99/4.37 tff(29621,plain,
% 3.99/4.37 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[8191, 29612, 29544, 29541])).
% 3.99/4.37 tff(29622,plain,
% 3.99/4.37 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[542, 29621, 29549])).
% 3.99/4.37 tff(29623,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[555, 29622, 29620, 133, 29614])).
% 3.99/4.37 tff(29624,plain,((z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29625,plain,
% 3.99/4.37 (z = elem!1),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29624, 29175, 27421, 29176, 11546, 29184, 2788])).
% 3.99/4.37 tff(29626,plain,
% 3.99/4.37 ((s(z) = z) <=> (s(z) = elem!1)),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29625])).
% 3.99/4.37 tff(29627,plain,
% 3.99/4.37 ((s(z) = z) <=> (elem!1 = s(z))),
% 3.99/4.37 inference(transitivity,[status(thm)],[29626, 53])).
% 3.99/4.37 tff(29628,plain,
% 3.99/4.37 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29627])).
% 3.99/4.37 tff(29629,plain,
% 3.99/4.37 (~(elem!1 = s(z))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[344, 29628])).
% 3.99/4.37 tff(29630,plain,
% 3.99/4.37 (b(elem!1, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[720, 29629, 29191])).
% 3.99/4.37 tff(29631,plain,
% 3.99/4.37 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29626])).
% 3.99/4.37 tff(29632,plain,
% 3.99/4.37 (~(s(z) = elem!1)),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[344, 29631])).
% 3.99/4.37 tff(29633,plain,
% 3.99/4.37 (~r(s(z), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29397, 29632, 29176, 29184, 22678, 27421, 29191, 29183])).
% 3.99/4.37 tff(29634,plain,
% 3.99/4.37 (b(s(z), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[172, 29633])).
% 3.99/4.37 tff(29635,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29205, 29634, 29630, 29176, 29184, 22678, 29183, 29175])).
% 3.99/4.37 tff(29636,plain,(r(s(s(s(z))), s(z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29637,plain,
% 3.99/4.37 (r(s(s(s(z))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29636, 11546, 54])).
% 3.99/4.37 tff(29638,plain,
% 3.99/4.37 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[27082])).
% 3.99/4.37 tff(29639,plain,
% 3.99/4.37 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[27082, 29638])).
% 3.99/4.37 tff(29640,plain,
% 3.99/4.37 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.99/4.37 inference(symmetry,[status(thm)],[29639])).
% 3.99/4.37 tff(29641,plain,
% 3.99/4.37 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29640])).
% 3.99/4.37 tff(29642,plain,
% 3.99/4.37 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[217, 29641])).
% 3.99/4.37 tff(29643,plain,
% 3.99/4.37 (~b(s(s(s(z))), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[10110, 23185, 54, 3, 26551])).
% 3.99/4.37 tff(29644,plain,
% 3.99/4.37 (r(s(s(s(z))), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[704, 29643, 698])).
% 3.99/4.37 tff(29645,plain,
% 3.99/4.37 (~b(elem!1, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18960, 23185, 17795, 26557])).
% 3.99/4.37 tff(29646,plain,
% 3.99/4.37 (r(elem!1, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[1538, 29645, 12398])).
% 3.99/4.37 tff(29647,plain,
% 3.99/4.37 (~b(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[16228, 23185, 17795, 26597])).
% 3.99/4.37 tff(29648,plain,
% 3.99/4.37 (r(z, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[619, 29647])).
% 3.99/4.37 tff(29649,plain,
% 3.99/4.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[22687, 22670, 54])).
% 3.99/4.37 tff(29650,plain,
% 3.99/4.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[302, 29649])).
% 3.99/4.37 tff(29651,plain,
% 3.99/4.37 (~b(elem!1, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18960, 23185, 17795, 132])).
% 3.99/4.37 tff(29652,plain,
% 3.99/4.37 (r(elem!1, s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[1538, 29651, 12398])).
% 3.99/4.37 tff(29653,plain,
% 3.99/4.37 (~r(s(z), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[27726, 353, 623, 28894])).
% 3.99/4.37 tff(29654,plain,
% 3.99/4.37 (b(s(z), z)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[348, 29653])).
% 3.99/4.37 tff(29655,plain,
% 3.99/4.37 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 3.99/4.37 inference(symmetry,[status(thm)],[22950])).
% 3.99/4.37 tff(29656,plain,
% 3.99/4.37 (r(s(s(s(z))), s(elem!1))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[3193, 29655])).
% 3.99/4.37 tff(29657,plain,
% 3.99/4.37 (~r(z, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[3011, 353, 29656, 623])).
% 3.99/4.37 tff(29658,plain,
% 3.99/4.37 (b(z, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[372, 29657])).
% 3.99/4.37 tff(29659,plain,
% 3.99/4.37 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[7093, 29658, 286, 29654])).
% 3.99/4.37 tff(29660,plain,
% 3.99/4.37 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[319, 29659])).
% 3.99/4.37 tff(29661,plain,
% 3.99/4.37 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29104, 29660, 8677, 23185, 863, 29652, 133, 132, 11546, 8303])).
% 3.99/4.37 tff(29662,plain,
% 3.99/4.37 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[1283, 29661, 22759])).
% 3.99/4.37 tff(29663,plain,
% 3.99/4.37 (b(s(s(z)), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18895, 29662, 8677])).
% 3.99/4.37 tff(29664,plain,
% 3.99/4.37 (~r(elem!1, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[12402, 353, 698, 29651, 55])).
% 3.99/4.37 tff(29665,plain,
% 3.99/4.37 (b(elem!1, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[720, 29664, 713])).
% 3.99/4.37 tff(29666,plain,
% 3.99/4.37 (~r(s(z), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[11876, 353, 3193, 29652])).
% 3.99/4.37 tff(29667,plain,
% 3.99/4.37 (b(s(z), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[406, 29666, 706])).
% 3.99/4.37 tff(29668,plain,
% 3.99/4.37 (~b(s(s(z)), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[23000, 144, 29667, 29665, 29663])).
% 3.99/4.37 tff(29669,plain,
% 3.99/4.37 (r(s(s(z)), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[7970, 29668, 22830])).
% 3.99/4.37 tff(29670,plain,
% 3.99/4.37 (~r(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18039, 29666, 8677])).
% 3.99/4.37 tff(29671,plain,
% 3.99/4.37 (b(s(elem!1), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[448, 29670, 28897])).
% 3.99/4.37 tff(29672,plain,
% 3.99/4.37 (b(elem!1, s(elem!1))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29665, 28637])).
% 3.99/4.37 tff(29673,plain,
% 3.99/4.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28682, 29672, 353, 26568, 29652, 26567, 8677, 8303, 29671])).
% 3.99/4.37 tff(29674,plain,
% 3.99/4.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[27512, 29673])).
% 3.99/4.37 tff(29675,plain,
% 3.99/4.37 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28686, 29674, 17795, 23185])).
% 3.99/4.37 tff(29676,plain,
% 3.99/4.37 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[9761, 29675])).
% 3.99/4.37 tff(29677,plain,
% 3.99/4.37 (~r(s(s(s(s(z)))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28690, 29676, 353, 29660])).
% 3.99/4.37 tff(29678,plain,
% 3.99/4.37 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28694, 29677, 8677])).
% 3.99/4.37 tff(29679,plain,
% 3.99/4.37 (b(s(s(s(s(z)))), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24448, 29678, 26568])).
% 3.99/4.37 tff(29680,plain,
% 3.99/4.37 (~b(s(s(s(s(z)))), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24997, 29679, 29672, 29671])).
% 3.99/4.37 tff(29681,plain,
% 3.99/4.37 (r(s(s(s(s(z)))), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[24301, 29680, 26567])).
% 3.99/4.37 tff(29682,plain,
% 3.99/4.37 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28704, 333, 29652, 29681, 29669])).
% 3.99/4.37 tff(29683,plain,
% 3.99/4.37 (~r(s(s(z)), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[23201, 29669, 3193, 29652])).
% 3.99/4.37 tff(29684,plain,
% 3.99/4.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18132, 29683, 8677])).
% 3.99/4.37 tff(29685,plain,
% 3.99/4.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[4311, 29684, 22826])).
% 3.99/4.37 tff(29686,plain,
% 3.99/4.37 (b(s(s(z)), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18122, 29685, 8677])).
% 3.99/4.37 tff(29687,plain,
% 3.99/4.37 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[7952, 29686, 7926, 7927])).
% 3.99/4.37 tff(29688,plain,
% 3.99/4.37 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[1451, 29687])).
% 3.99/4.37 tff(29689,plain,
% 3.99/4.37 (~r(s(z), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[28260, 333, 29688, 11546, 29660])).
% 3.99/4.37 tff(29690,plain,
% 3.99/4.37 (~r(s(z), s(s(elem!1)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[22807, 29689, 8677])).
% 3.99/4.37 tff(29691,plain,
% 3.99/4.37 (b(s(z), s(s(elem!1)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[5484, 29690])).
% 3.99/4.37 tff(29692,plain,
% 3.99/4.37 (b(s(z), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[22799, 29691, 8677])).
% 3.99/4.37 tff(29693,plain,
% 3.99/4.37 (b(s(s(s(s(z)))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[27538, 29677])).
% 3.99/4.37 tff(29694,plain,
% 3.99/4.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29075, 144, 29663, 29693, 29692])).
% 3.99/4.37 tff(29695,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 29694, 29682])).
% 3.99/4.37 tff(29696,plain,((~r(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29697,plain,
% 3.99/4.37 (~r(s(z), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29696, 7927, 11546, 7926, 22669, 29637, 27421, 26557, 29650, 706, 698, 29643, 29648])).
% 3.99/4.37 tff(29698,plain,
% 3.99/4.37 (b(s(z), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[172, 29697])).
% 3.99/4.37 tff(29699,plain,
% 3.99/4.37 ($false),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[22923, 333, 1525, 722, 3193, 11546])).
% 3.99/4.37 tff(29700,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.37 tff(29701,plain,
% 3.99/4.37 (~r(elem!1, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29700, 29646, 29637, 11546])).
% 3.99/4.37 tff(29702,plain,
% 3.99/4.37 (b(elem!1, s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[720, 29701, 713])).
% 3.99/4.37 tff(29703,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.37 inference(rewrite,[status(thm)],[])).
% 3.99/4.37 tff(29704,plain,
% 3.99/4.37 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.37 inference(rewrite,[status(thm)],[])).
% 3.99/4.37 tff(29705,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29704])).
% 3.99/4.37 tff(29706,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.37 inference(transitivity,[status(thm)],[29705, 29703])).
% 3.99/4.37 tff(29707,plain,
% 3.99/4.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.99/4.37 inference(quant_inst,[status(thm)],[])).
% 3.99/4.37 tff(29708,plain,
% 3.99/4.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29707, 29706])).
% 3.99/4.37 tff(29709,plain,
% 3.99/4.37 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29708, 144, 29702, 29698, 27421, 17795])).
% 3.99/4.37 tff(29710,plain,
% 3.99/4.37 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[319, 29709])).
% 3.99/4.37 tff(29711,plain,
% 3.99/4.37 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29104, 29710, 22669, 23185, 863, 29646, 27421, 26557, 11546, 29644])).
% 3.99/4.37 tff(29712,plain,
% 3.99/4.37 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[1283, 29711, 27098])).
% 3.99/4.37 tff(29713,plain,
% 3.99/4.37 (~(elem!1 = s(elem!1))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[706, 22693])).
% 3.99/4.37 tff(29714,plain,
% 3.99/4.37 (~r(elem!1, s(elem!1))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29701, 27180])).
% 3.99/4.37 tff(29715,plain,
% 3.99/4.37 (b(elem!1, s(elem!1))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[560, 29714, 29713])).
% 3.99/4.37 tff(29716,plain,
% 3.99/4.37 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29638])).
% 3.99/4.37 tff(29717,plain,
% 3.99/4.37 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 3.99/4.37 inference(symmetry,[status(thm)],[29716])).
% 3.99/4.37 tff(29718,plain,
% 3.99/4.37 (r(s(s(s(elem!1))), s(z))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29637, 29717])).
% 3.99/4.37 tff(29719,plain,
% 3.99/4.37 (b(s(z), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[22799, 5486, 8677])).
% 3.99/4.37 tff(29720,plain,
% 3.99/4.37 (b(s(s(z)), s(z))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18895, 1249, 8677])).
% 3.99/4.37 tff(29721,plain,
% 3.99/4.37 (r(elem!1, s(s(s(elem!1))))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[1525, 23014])).
% 3.99/4.37 tff(29722,plain,
% 3.99/4.37 (~b(elem!1, s(s(elem!1)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[5494, 5486, 305, 547, 1249])).
% 3.99/4.37 tff(29723,plain,
% 3.99/4.37 (r(elem!1, s(s(elem!1)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[2522, 29722, 22705])).
% 3.99/4.37 tff(29724,plain,
% 3.99/4.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[23051, 29723, 1024, 29721])).
% 3.99/4.37 tff(29725,plain,
% 3.99/4.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[4311, 29724, 22826])).
% 3.99/4.37 tff(29726,plain,
% 3.99/4.37 (b(s(s(z)), s(s(s(z))))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[18122, 29725, 8677])).
% 3.99/4.37 tff(29727,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 3.99/4.37 inference(rewrite,[status(thm)],[])).
% 3.99/4.37 tff(29728,plain,
% 3.99/4.37 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 3.99/4.37 inference(rewrite,[status(thm)],[])).
% 3.99/4.37 tff(29729,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 3.99/4.37 inference(monotonicity,[status(thm)],[29728])).
% 3.99/4.37 tff(29730,plain,
% 3.99/4.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 3.99/4.37 inference(transitivity,[status(thm)],[29729, 29727])).
% 3.99/4.37 tff(29731,plain,
% 3.99/4.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 3.99/4.37 inference(quant_inst,[status(thm)],[])).
% 3.99/4.37 tff(29732,plain,
% 3.99/4.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 3.99/4.37 inference(modus_ponens,[status(thm)],[29731, 29730])).
% 3.99/4.37 tff(29733,plain,
% 3.99/4.37 (~b(s(s(z)), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[29732, 144, 305, 29726, 29720, 838])).
% 3.99/4.37 tff(29734,plain,
% 3.99/4.37 (r(s(s(z)), elem!1)),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[7970, 29733, 22830])).
% 3.99/4.37 tff(29735,plain,
% 3.99/4.37 (~r(s(s(s(z))), s(s(z)))),
% 3.99/4.37 inference(unit_resolution,[status(thm)],[8852, 333, 1525, 707, 29734])).
% 3.99/4.38 tff(29736,plain,
% 3.99/4.38 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29735, 25412])).
% 3.99/4.38 tff(29737,plain,
% 3.99/4.38 (b(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[1301, 29736, 1184])).
% 3.99/4.38 tff(29738,plain,
% 3.99/4.38 (b(s(s(s(z))), s(s(z)))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29737, 22810])).
% 3.99/4.38 tff(29739,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29740,plain,
% 3.99/4.38 (((~b(s(s(z)), s(s(s(z))))) | (~b(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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29741,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[29740])).
% 3.99/4.38 tff(29742,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.99/4.38 inference(transitivity,[status(thm)],[29741, 29739])).
% 3.99/4.38 tff(29743,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(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))))))),
% 3.99/4.38 inference(quant_inst,[status(thm)],[])).
% 3.99/4.38 tff(29744,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29743, 29742])).
% 3.99/4.38 tff(29745,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29744, 144, 29726, 838, 29738, 29719])).
% 3.99/4.38 tff(29746,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29747,plain,
% 3.99/4.38 (~b(s(z), s(s(elem!1)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29746, 29698, 22669, 863, 29646, 29644, 29702, 29718, 29715, 29712])).
% 3.99/4.38 tff(29748,plain,
% 3.99/4.38 (r(s(z), s(s(elem!1)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[5484, 29747])).
% 3.99/4.38 tff(29749,plain,
% 3.99/4.38 (r(s(z), s(s(z)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[22807, 29748, 22669])).
% 3.99/4.38 tff(29750,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[28260, 333, 2671, 11546, 322, 22831])).
% 3.99/4.38 tff(29751,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29752,plain,
% 3.99/4.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29751, 29710, 11546, 29749])).
% 3.99/4.38 tff(29753,plain,
% 3.99/4.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[1451, 29752])).
% 3.99/4.38 tff(29754,plain,
% 3.99/4.38 (~b(s(s(z)), s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[7952, 29753, 7926, 7927])).
% 3.99/4.38 tff(29755,plain,
% 3.99/4.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[18122, 29754, 22669])).
% 3.99/4.38 tff(29756,plain,
% 3.99/4.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[4311, 29755, 29642])).
% 3.99/4.38 tff(29757,plain,
% 3.99/4.38 (~b(s(s(z)), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29112, 29753, 26557, 27421])).
% 3.99/4.38 tff(29758,plain,
% 3.99/4.38 (r(s(s(z)), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[7970, 29757, 28890])).
% 3.99/4.38 tff(29759,plain,
% 3.99/4.38 (~r(s(s(z)), s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[23201, 29758, 29637, 29646])).
% 3.99/4.38 tff(29760,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[18132, 29759, 29756, 22669])).
% 3.99/4.38 tff(29761,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29762,plain,
% 3.99/4.38 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29761, 3, 11546, 706, 698, 54, 7926])).
% 3.99/4.38 tff(29763,plain,
% 3.99/4.38 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[15720, 29762, 11546, 29637])).
% 3.99/4.38 tff(29764,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[319, 29763])).
% 3.99/4.38 tff(29765,plain,
% 3.99/4.38 (b(s(s(s(z))), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[704, 699, 698])).
% 3.99/4.38 tff(29766,plain,
% 3.99/4.38 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[15720, 6107, 11546, 3193])).
% 3.99/4.38 tff(29767,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[319, 29766])).
% 3.99/4.38 tff(29768,plain,
% 3.99/4.38 (~r(s(s(s(z))), z)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[22912, 699, 66])).
% 3.99/4.38 tff(29769,plain,
% 3.99/4.38 (b(s(s(s(z))), z)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[396, 29768])).
% 3.99/4.38 tff(29770,plain,
% 3.99/4.38 (~b(z, s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[294, 29769, 283, 286])).
% 3.99/4.38 tff(29771,plain,
% 3.99/4.38 (r(z, s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[619, 29770])).
% 3.99/4.38 tff(29772,plain,
% 3.99/4.38 (r(elem!1, s(s(s(z))))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29771, 22906])).
% 3.99/4.38 tff(29773,plain,
% 3.99/4.38 (~r(elem!1, s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29700, 29772, 3193, 11546])).
% 3.99/4.38 tff(29774,plain,
% 3.99/4.38 (b(elem!1, s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[720, 29773, 713])).
% 3.99/4.38 tff(29775,plain,
% 3.99/4.38 (~b(s(z), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[3955, 29774, 133, 29767])).
% 3.99/4.38 tff(29776,plain,
% 3.99/4.38 (r(s(z), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[406, 29775, 706])).
% 3.99/4.38 tff(29777,plain,
% 3.99/4.38 (~r(s(z), s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[27266, 29776, 6107, 29772])).
% 3.99/4.38 tff(29778,plain,
% 3.99/4.38 (b(s(z), s(s(s(z))))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[172, 29777])).
% 3.99/4.38 tff(29779,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29780,plain,
% 3.99/4.38 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29781,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[29780])).
% 3.99/4.38 tff(29782,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.38 inference(transitivity,[status(thm)],[29781, 29779])).
% 3.99/4.38 tff(29783,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.99/4.38 inference(quant_inst,[status(thm)],[])).
% 3.99/4.38 tff(29784,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29783, 29782])).
% 3.99/4.38 tff(29785,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29784, 144, 29778, 133, 283, 29767, 29765])).
% 3.99/4.38 tff(29786,plain,(r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29787,plain,
% 3.99/4.38 (r(s(s(s(z))), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29786, 29762, 17795, 27421, 706, 29637, 11546, 22670, 29650, 698])).
% 3.99/4.38 tff(29788,plain,
% 3.99/4.38 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[18019])).
% 3.99/4.38 tff(29789,plain,
% 3.99/4.38 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.99/4.38 inference(symmetry,[status(thm)],[29788])).
% 3.99/4.38 tff(29790,plain,
% 3.99/4.38 (b(elem!1, s(s(z))) <=> b(z, s(s(elem!1)))),
% 3.99/4.38 inference(transitivity,[status(thm)],[23020, 29789])).
% 3.99/4.38 tff(29791,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 3.99/4.38 tff(29792,plain,
% 3.99/4.38 (s(s(z)) = elem!1),
% 3.99/4.38 inference(symmetry,[status(thm)],[29791])).
% 3.99/4.38 tff(29793,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[1506, 29792])).
% 3.99/4.38 tff(29794,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29795,plain,
% 3.99/4.38 (~(elem!1 = s(s(z)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29794, 22830])).
% 3.99/4.38 tff(29796,plain,
% 3.99/4.38 (~b(s(z), z)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[21435, 27352, 283, 286, 29767])).
% 3.99/4.38 tff(29797,plain,
% 3.99/4.38 (r(s(z), z)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[348, 29796])).
% 3.99/4.38 tff(29798,plain,
% 3.99/4.38 (r(s(z), elem!1)),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[25327, 29797, 18019])).
% 3.99/4.38 tff(29799,plain,
% 3.99/4.38 (((~![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))), elem!1)) | (~r(s(s(s(z))), 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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29800,plain,
% 3.99/4.38 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29801,plain,
% 3.99/4.38 (((~![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(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z))))))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[29800])).
% 3.99/4.38 tff(29802,plain,
% 3.99/4.38 (((~![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(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z)))))),
% 3.99/4.38 inference(transitivity,[status(thm)],[29801, 29799])).
% 3.99/4.38 tff(29803,plain,
% 3.99/4.38 ((~![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(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 3.99/4.38 inference(quant_inst,[status(thm)],[])).
% 3.99/4.38 tff(29804,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z))))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29803, 29802])).
% 3.99/4.38 tff(29805,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29804, 333, 409, 3193, 707, 22740])).
% 3.99/4.38 tff(29806,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29807,plain,
% 3.99/4.38 (~r(elem!1, s(s(z)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29806, 29798, 3193, 707])).
% 3.99/4.38 tff(29808,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 3.99/4.38 tff(29809,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 3.99/4.38 tff(29810,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 3.99/4.38 tff(29811,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[18919, 44, 29810, 29809, 29808])).
% 3.99/4.38 tff(29812,plain,(b(elem!1, s(s(z))) | r(elem!1, s(s(z))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29813,plain,
% 3.99/4.38 (b(elem!1, s(s(z)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29812, 29807, 29795])).
% 3.99/4.38 tff(29814,plain,
% 3.99/4.38 (b(z, s(s(elem!1)))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29813, 29790])).
% 3.99/4.38 tff(29815,plain,
% 3.99/4.38 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[3654, 26862])).
% 3.99/4.38 tff(29816,plain,
% 3.99/4.38 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29817,plain,
% 3.99/4.38 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29818,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[29817])).
% 3.99/4.38 tff(29819,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.38 inference(transitivity,[status(thm)],[29818, 29816])).
% 3.99/4.38 tff(29820,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 3.99/4.38 inference(quant_inst,[status(thm)],[])).
% 3.99/4.38 tff(29821,plain,
% 3.99/4.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29820, 29819])).
% 3.99/4.38 tff(29822,plain,
% 3.99/4.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29821, 333, 3193, 11546, 6107])).
% 3.99/4.38 tff(29823,plain,
% 3.99/4.38 ($false),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29822, 29815])).
% 3.99/4.38 tff(29824,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.38 tff(29825,plain,
% 3.99/4.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[29824, 8677, 3193, 11546, 6107])).
% 3.99/4.38 tff(29826,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[2758, 29825, 23135])).
% 3.99/4.38 tff(29827,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.38 inference(monotonicity,[status(thm)],[8677])).
% 3.99/4.38 tff(29828,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.38 inference(symmetry,[status(thm)],[29827])).
% 3.99/4.38 tff(29829,plain,
% 3.99/4.38 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.99/4.38 inference(modus_ponens,[status(thm)],[29767, 29828])).
% 3.99/4.38 tff(29830,plain,
% 3.99/4.38 (~r(elem!1, s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[8824, 29797, 3193, 707])).
% 3.99/4.38 tff(29831,plain,
% 3.99/4.38 (b(elem!1, s(z))),
% 3.99/4.38 inference(unit_resolution,[status(thm)],[720, 29830, 714])).
% 3.99/4.38 tff(29832,plain,
% 3.99/4.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.38 inference(rewrite,[status(thm)],[])).
% 3.99/4.38 tff(29833,plain,
% 3.99/4.38 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29834,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.99/4.39 inference(monotonicity,[status(thm)],[29833])).
% 3.99/4.39 tff(29835,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.39 inference(transitivity,[status(thm)],[29834, 29832])).
% 3.99/4.39 tff(29836,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.39 inference(quant_inst,[status(thm)],[])).
% 3.99/4.39 tff(29837,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29836, 29835])).
% 3.99/4.39 tff(29838,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29837, 144, 2082, 305, 838, 132, 304])).
% 3.99/4.39 tff(29839,plain,((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29840,plain,
% 3.99/4.39 (~b(s(z), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29839, 29831, 2082, 132, 29767])).
% 3.99/4.39 tff(29841,plain,
% 3.99/4.39 (r(s(z), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[172, 29840])).
% 3.99/4.39 tff(29842,plain,
% 3.99/4.39 (~r(s(s(s(z))), s(s(z)))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[19440, 9770, 11546, 3193])).
% 3.99/4.39 tff(29843,plain,
% 3.99/4.39 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29842, 25412])).
% 3.99/4.39 tff(29844,plain,
% 3.99/4.39 (b(s(s(s(z))), s(s(elem!1)))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[1301, 29843, 1184])).
% 3.99/4.39 tff(29845,plain,
% 3.99/4.39 (b(s(s(s(z))), s(s(z)))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29844, 22810])).
% 3.99/4.39 tff(29846,plain,
% 3.99/4.39 (((~![X0: $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(s(s(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(s(s(z))))))))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29847,plain,
% 3.99/4.39 (((~r(s(s(s(z))), s(s(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(s(s(z))))))))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29848,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(s(s(z)))))))))))),
% 3.99/4.39 inference(monotonicity,[status(thm)],[29847])).
% 3.99/4.39 tff(29849,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(s(s(z))))))))))),
% 3.99/4.39 inference(transitivity,[status(thm)],[29848, 29846])).
% 3.99/4.39 tff(29850,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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))))),
% 3.99/4.39 inference(quant_inst,[status(thm)],[])).
% 3.99/4.39 tff(29851,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29850, 29849])).
% 3.99/4.39 tff(29852,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29851, 333, 353, 6107, 6330, 9770])).
% 3.99/4.39 tff(29853,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29854,plain,
% 3.99/4.39 (~r(s(s(z)), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29853, 9770, 6107, 353])).
% 3.99/4.39 tff(29855,plain,
% 3.99/4.39 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[18132, 29854, 8677])).
% 3.99/4.39 tff(29856,plain,
% 3.99/4.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[4311, 29855, 22826])).
% 3.99/4.39 tff(29857,plain,
% 3.99/4.39 (b(s(s(z)), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[18122, 29856, 8677])).
% 3.99/4.39 tff(29858,plain,
% 3.99/4.39 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29859,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.99/4.39 inference(monotonicity,[status(thm)],[29858])).
% 3.99/4.39 tff(29860,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.99/4.39 inference(transitivity,[status(thm)],[29859, 26831])).
% 3.99/4.39 tff(29861,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 3.99/4.39 inference(quant_inst,[status(thm)],[])).
% 3.99/4.39 tff(29862,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29861, 29860])).
% 3.99/4.39 tff(29863,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29862, 144, 2082, 29857, 29845, 22783])).
% 3.99/4.39 tff(29864,plain,((~r(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29865,plain,
% 3.99/4.39 (~r(s(s(z)), s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29864, 29813, 29841, 8677, 1184, 6107, 2082, 11546, 3193])).
% 3.99/4.39 tff(29866,plain,
% 3.99/4.39 (~r(s(s(elem!1)), s(elem!1))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[22871, 29865, 8677])).
% 3.99/4.39 tff(29867,plain,
% 3.99/4.39 (b(s(s(elem!1)), s(elem!1))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[1283, 29866, 22759])).
% 3.99/4.39 tff(29868,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29869,plain,
% 3.99/4.39 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.99/4.39 inference(rewrite,[status(thm)],[])).
% 3.99/4.39 tff(29870,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.99/4.39 inference(monotonicity,[status(thm)],[29869])).
% 3.99/4.39 tff(29871,plain,
% 3.99/4.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.99/4.39 inference(transitivity,[status(thm)],[29870, 29868])).
% 3.99/4.39 tff(29872,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.99/4.39 inference(quant_inst,[status(thm)],[])).
% 3.99/4.39 tff(29873,plain,
% 3.99/4.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.99/4.39 inference(modus_ponens,[status(thm)],[29872, 29871])).
% 3.99/4.39 tff(29874,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29873, 144, 1249, 2811, 5659, 286, 546])).
% 3.99/4.39 tff(29875,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29876,plain,
% 3.99/4.39 (~b(z, s(s(elem!1)))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29875, 29867, 286, 29829, 29826])).
% 3.99/4.39 tff(29877,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29876, 29814])).
% 3.99/4.39 tff(29878,plain,((~b(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29879,plain,
% 3.99/4.39 (~b(elem!1, s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29878, 22669, 29650, 863, 29762, 11546, 29637, 26557, 713, 29787, 17795])).
% 3.99/4.39 tff(29880,plain,
% 3.99/4.39 (r(elem!1, s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[1538, 29879, 12398])).
% 3.99/4.39 tff(29881,plain,
% 3.99/4.39 (~r(elem!1, s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29700, 29880, 29637, 11546])).
% 3.99/4.39 tff(29882,plain,
% 3.99/4.39 (b(elem!1, s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[720, 29881, 713])).
% 3.99/4.39 tff(29883,plain,
% 3.99/4.39 (~b(s(z), elem!1)),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[3955, 29882, 27421, 29764])).
% 3.99/4.39 tff(29884,plain,
% 3.99/4.39 (r(s(z), elem!1)),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[406, 29883, 706])).
% 3.99/4.39 tff(29885,plain,
% 3.99/4.39 (~r(s(z), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[27266, 29884, 29762, 29880])).
% 3.99/4.39 tff(29886,plain,
% 3.99/4.39 (b(s(z), s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[172, 29885])).
% 3.99/4.39 tff(29887,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29708, 144, 29882, 29886, 27421, 17795, 29764])).
% 3.99/4.39 tff(29888,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29889,plain,
% 3.99/4.39 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29888, 698, 11546, 706, 54, 7926])).
% 3.99/4.39 tff(29890,plain,
% 3.99/4.39 ($false),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[21569, 144, 2082, 133, 283, 4367])).
% 3.99/4.39 tff(29891,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.99/4.39 tff(29892,plain,
% 3.99/4.39 (~b(elem!1, s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29891, 4367, 17795, 133])).
% 3.99/4.39 tff(29893,plain,
% 3.99/4.39 (r(elem!1, s(s(s(z))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[1538, 29892, 12398])).
% 3.99/4.39 tff(29894,plain,
% 3.99/4.39 (~r(elem!1, s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[29700, 1525, 3193, 11546])).
% 3.99/4.39 tff(29895,plain,
% 3.99/4.39 (b(elem!1, s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[720, 29894, 713])).
% 3.99/4.39 tff(29896,plain,
% 3.99/4.39 (~r(s(z), elem!1)),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[11876, 353, 3193, 1525])).
% 3.99/4.39 tff(29897,plain,
% 3.99/4.39 (b(s(z), elem!1)),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[406, 29896, 706])).
% 3.99/4.39 tff(29898,plain,
% 3.99/4.39 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[3955, 29897, 133, 29895])).
% 3.99/4.39 tff(29899,plain,
% 3.99/4.39 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[319, 29898])).
% 3.99/4.39 tff(29900,plain,
% 3.99/4.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[27441, 74, 29899, 11546, 29897, 2323])).
% 3.99/4.39 tff(29901,plain,
% 3.99/4.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[279, 29900])).
% 3.99/4.39 tff(29902,plain,
% 3.99/4.39 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.39 inference(unit_resolution,[status(thm)],[28001, 74, 29895, 133, 11546, 2323, 353])).
% 3.99/4.40 tff(29903,plain,
% 3.99/4.40 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[302, 29902])).
% 3.99/4.40 tff(29904,plain,
% 3.99/4.40 (~b(s(s(s(z))), z)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[27648, 29903, 133, 2323, 29895, 698, 29901, 29897])).
% 3.99/4.40 tff(29905,plain,
% 3.99/4.40 (r(s(s(s(z))), z)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[396, 29904])).
% 3.99/4.40 tff(29906,plain,
% 3.99/4.40 (~r(z, s(z))),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[26130, 29905, 3193, 353])).
% 3.99/4.40 tff(29907,plain,
% 3.99/4.40 (b(z, s(z))),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[372, 29906])).
% 3.99/4.40 tff(29908,plain,
% 3.99/4.40 (~b(z, s(s(s(z))))),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[16228, 29901, 283, 2254])).
% 3.99/4.40 tff(29909,plain,
% 3.99/4.40 (r(z, s(s(s(z))))),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[619, 29908])).
% 3.99/4.40 tff(29910,plain,
% 3.99/4.40 (~r(z, elem!1)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[3201, 29909, 3193, 1525])).
% 3.99/4.40 tff(29911,plain,
% 3.99/4.40 (b(z, elem!1)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[658, 29910, 74])).
% 3.99/4.40 tff(29912,plain,
% 3.99/4.40 ($false),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[18838, 29911, 29907, 11546, 706, 2323, 29899])).
% 3.99/4.40 tff(29913,plain,((z = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.99/4.40 tff(29914,plain,
% 3.99/4.40 (z = elem!1),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[29913, 353, 706, 2323, 3193, 1525, 11546, 17795, 23185, 133, 698])).
% 3.99/4.40 tff(29915,plain,
% 3.99/4.40 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29914])).
% 3.99/4.40 tff(29916,plain,
% 3.99/4.40 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.99/4.40 inference(transitivity,[status(thm)],[29915, 1218])).
% 3.99/4.40 tff(29917,plain,
% 3.99/4.40 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29916])).
% 3.99/4.40 tff(29918,plain,
% 3.99/4.40 (~(elem!1 = s(s(elem!1)))),
% 3.99/4.40 inference(modus_ponens,[status(thm)],[1094, 29917])).
% 3.99/4.40 tff(29919,plain,
% 3.99/4.40 (s(elem!1) = s(z)),
% 3.99/4.40 inference(unit_resolution,[status(thm)],[70, 29914])).
% 3.99/4.40 tff(29920,plain,
% 3.99/4.40 (s(s(elem!1)) = s(s(z))),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29919])).
% 3.99/4.40 tff(29921,plain,
% 3.99/4.40 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29920])).
% 3.99/4.40 tff(29922,plain,
% 3.99/4.40 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29921])).
% 3.99/4.40 tff(29923,plain,
% 3.99/4.40 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.99/4.40 inference(symmetry,[status(thm)],[29922])).
% 3.99/4.40 tff(29924,plain,
% 3.99/4.40 (r(elem!1, s(s(s(elem!1))))),
% 3.99/4.40 inference(modus_ponens,[status(thm)],[1525, 29923])).
% 3.99/4.40 tff(29925,plain,
% 3.99/4.40 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 3.99/4.40 inference(monotonicity,[status(thm)],[29921])).
% 3.99/4.40 tff(29926,plain,
% 3.99/4.40 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 3.99/4.40 inference(symmetry,[status(thm)],[29925])).
% 3.99/4.40 tff(29927,plain,
% 3.99/4.40 (r(s(s(s(elem!1))), s(z))),
% 3.99/4.40 inference(modus_ponens,[status(thm)],[3193, 29926])).
% 3.99/4.40 tff(29928,plain,
% 3.99/4.40 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.99/4.40 inference(rewrite,[status(thm)],[])).
% 3.99/4.40 tff(29929,plain,
% 3.99/4.40 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29930,plain,
% 4.09/4.40 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29929])).
% 4.09/4.40 tff(29931,plain,
% 4.09/4.40 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(transitivity,[status(thm)],[29930, 29928])).
% 4.09/4.40 tff(29932,plain,
% 4.09/4.40 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 4.09/4.40 inference(quant_inst,[status(thm)],[])).
% 4.09/4.40 tff(29933,plain,
% 4.09/4.40 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29932, 29931])).
% 4.09/4.40 tff(29934,plain,
% 4.09/4.40 (~r(elem!1, s(s(z)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29933, 333, 2671, 2323, 322])).
% 4.09/4.40 tff(29935,plain,
% 4.09/4.40 (~r(elem!1, s(s(elem!1)))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29934, 22710])).
% 4.09/4.40 tff(29936,plain,
% 4.09/4.40 (b(elem!1, s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[2522, 29935, 22705])).
% 4.09/4.40 tff(29937,plain,
% 4.09/4.40 (b(elem!1, s(s(z)))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29936, 22760])).
% 4.09/4.40 tff(29938,plain,
% 4.09/4.40 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29939,plain,
% 4.09/4.40 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29940,plain,
% 4.09/4.40 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29939])).
% 4.09/4.40 tff(29941,plain,
% 4.09/4.40 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(transitivity,[status(thm)],[29940, 29938])).
% 4.09/4.40 tff(29942,plain,
% 4.09/4.40 ((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 4.09/4.40 inference(quant_inst,[status(thm)],[])).
% 4.09/4.40 tff(29943,plain,
% 4.09/4.40 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29942, 29941])).
% 4.09/4.40 tff(29944,plain,
% 4.09/4.40 (~r(s(s(z)), elem!1)),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29943, 333, 2671, 2323, 322])).
% 4.09/4.40 tff(29945,plain,
% 4.09/4.40 (b(s(s(z)), elem!1)),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[7970, 29944, 26795])).
% 4.09/4.40 tff(29946,plain,
% 4.09/4.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[26868, 144, 133, 29945, 29937])).
% 4.09/4.40 tff(29947,plain,
% 4.09/4.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29946, 23138])).
% 4.09/4.40 tff(29948,plain,
% 4.09/4.40 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[2758, 29947, 23135])).
% 4.09/4.40 tff(29949,plain,
% 4.09/4.40 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29948, 26862])).
% 4.09/4.40 tff(29950,plain,
% 4.09/4.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29951,plain,
% 4.09/4.40 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29952,plain,
% 4.09/4.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29951])).
% 4.09/4.40 tff(29953,plain,
% 4.09/4.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.09/4.40 inference(transitivity,[status(thm)],[29952, 29950])).
% 4.09/4.40 tff(29954,plain,
% 4.09/4.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 4.09/4.40 inference(quant_inst,[status(thm)],[])).
% 4.09/4.40 tff(29955,plain,
% 4.09/4.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29954, 29953])).
% 4.09/4.40 tff(29956,plain,
% 4.09/4.40 (~b(s(z), s(s(z)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29955, 144, 134, 29945, 29937])).
% 4.09/4.40 tff(29957,plain,
% 4.09/4.40 (~b(s(z), s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[22799, 29956, 8677])).
% 4.09/4.40 tff(29958,plain,
% 4.09/4.40 (r(s(z), s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[5484, 29957])).
% 4.09/4.40 tff(29959,plain,
% 4.09/4.40 (r(s(z), s(s(z)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[22807, 29958, 8677])).
% 4.09/4.40 tff(29960,plain,
% 4.09/4.40 (((~![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(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29961,plain,
% 4.09/4.40 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29962,plain,
% 4.09/4.40 (((~![X0: $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(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29961])).
% 4.09/4.40 tff(29963,plain,
% 4.09/4.40 (((~![X0: $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(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.40 inference(transitivity,[status(thm)],[29962, 29960])).
% 4.09/4.40 tff(29964,plain,
% 4.09/4.40 ((~![X0: $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(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.09/4.40 inference(quant_inst,[status(thm)],[])).
% 4.09/4.40 tff(29965,plain,
% 4.09/4.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29964, 29963])).
% 4.09/4.40 tff(29966,plain,
% 4.09/4.40 ($false),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29965, 333, 2671, 322, 29959, 29949])).
% 4.09/4.40 tff(29967,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.40 tff(29968,plain,
% 4.09/4.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29967, 29919, 133, 2323, 29899, 29897])).
% 4.09/4.40 tff(29969,plain,
% 4.09/4.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[1451, 29968])).
% 4.09/4.40 tff(29970,plain,
% 4.09/4.40 (~b(s(s(z)), s(s(s(z))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[7952, 29969, 7926, 7927])).
% 4.09/4.40 tff(29971,plain,
% 4.09/4.40 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[18122, 29970, 29919])).
% 4.09/4.40 tff(29972,plain,
% 4.09/4.40 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29920, 29921])).
% 4.09/4.40 tff(29973,plain,
% 4.09/4.40 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.40 inference(symmetry,[status(thm)],[29972])).
% 4.09/4.40 tff(29974,plain,
% 4.09/4.40 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29973])).
% 4.09/4.40 tff(29975,plain,
% 4.09/4.40 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[217, 29974])).
% 4.09/4.40 tff(29976,plain,
% 4.09/4.40 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[4311, 29975, 29971])).
% 4.09/4.40 tff(29977,plain,
% 4.09/4.40 (~r(elem!1, s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[23051, 29976, 29927, 29924])).
% 4.09/4.40 tff(29978,plain,
% 4.09/4.40 (b(elem!1, s(s(elem!1)))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[2522, 29977, 29918])).
% 4.09/4.40 tff(29979,plain,
% 4.09/4.40 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29919])).
% 4.09/4.40 tff(29980,plain,
% 4.09/4.40 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.09/4.40 inference(symmetry,[status(thm)],[29979])).
% 4.09/4.40 tff(29981,plain,
% 4.09/4.40 (b(elem!1, s(elem!1))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29895, 29980])).
% 4.09/4.40 tff(29982,plain,
% 4.09/4.40 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29919])).
% 4.09/4.40 tff(29983,plain,
% 4.09/4.40 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.09/4.40 inference(symmetry,[status(thm)],[29982])).
% 4.09/4.40 tff(29984,plain,
% 4.09/4.40 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29983])).
% 4.09/4.40 tff(29985,plain,
% 4.09/4.40 (~(s(s(elem!1)) = s(elem!1))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[107, 29984])).
% 4.09/4.40 tff(29986,plain,
% 4.09/4.40 (r(s(s(z)), s(s(s(z))))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[18132, 29976, 29919])).
% 4.09/4.40 tff(29987,plain,
% 4.09/4.40 (((~![X0: $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(z))) | (~r(s(z), 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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29988,plain,
% 4.09/4.40 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.09/4.40 inference(rewrite,[status(thm)],[])).
% 4.09/4.40 tff(29989,plain,
% 4.09/4.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.09/4.40 inference(monotonicity,[status(thm)],[29988])).
% 4.09/4.40 tff(29990,plain,
% 4.09/4.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.09/4.40 inference(transitivity,[status(thm)],[29989, 29987])).
% 4.09/4.40 tff(29991,plain,
% 4.09/4.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 4.09/4.40 inference(quant_inst,[status(thm)],[])).
% 4.09/4.40 tff(29992,plain,
% 4.09/4.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 4.09/4.40 inference(modus_ponens,[status(thm)],[29991, 29990])).
% 4.09/4.40 tff(29993,plain,
% 4.09/4.40 (~r(s(s(z)), s(z))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[29992, 333, 3193, 353, 29986])).
% 4.09/4.40 tff(29994,plain,
% 4.09/4.40 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.40 inference(unit_resolution,[status(thm)],[22871, 29993, 29919])).
% 4.09/4.41 tff(29995,plain,
% 4.09/4.41 (b(s(s(elem!1)), s(elem!1))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[1283, 29994, 29985])).
% 4.09/4.41 tff(29996,plain,
% 4.09/4.41 (~r(s(z), s(s(z)))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[23647, 333, 3193, 353, 29986])).
% 4.09/4.41 tff(29997,plain,
% 4.09/4.41 (~r(s(z), s(s(elem!1)))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[22807, 29996, 29919])).
% 4.09/4.41 tff(29998,plain,
% 4.09/4.41 (b(s(z), s(s(elem!1)))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[5484, 29997])).
% 4.09/4.41 tff(29999,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[5494, 29998, 29995, 29895, 29981, 29978])).
% 4.09/4.41 tff(30000,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30001,plain,
% 4.09/4.41 (~r(s(z), s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30000, 29893, 3193, 7926, 7927, 133, 2323, 706, 11546, 698])).
% 4.09/4.41 tff(30002,plain,
% 4.09/4.41 (b(s(z), s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[172, 30001])).
% 4.09/4.41 tff(30003,plain,
% 4.09/4.41 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[29784, 144, 30002, 133, 17795, 4367])).
% 4.09/4.41 tff(30004,plain,
% 4.09/4.41 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[319, 30003])).
% 4.09/4.41 tff(30005,plain,
% 4.09/4.41 (~r(s(z), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[18406, 30004, 11546, 2323])).
% 4.09/4.41 tff(30006,plain,
% 4.09/4.41 (b(s(z), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[406, 30005, 706])).
% 4.09/4.41 tff(30007,plain,
% 4.09/4.41 (~r(elem!1, s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[29700, 29893, 3193, 11546])).
% 4.09/4.41 tff(30008,plain,
% 4.09/4.41 (b(elem!1, s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[720, 30007, 713])).
% 4.09/4.41 tff(30009,plain,
% 4.09/4.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[27441, 74, 322, 11546, 134, 2323])).
% 4.09/4.41 tff(30010,plain,
% 4.09/4.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[279, 30009])).
% 4.09/4.41 tff(30011,plain,
% 4.09/4.41 (~b(z, s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[16228, 30010, 283, 2254])).
% 4.09/4.41 tff(30012,plain,
% 4.09/4.41 (r(z, s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[619, 30011])).
% 4.09/4.41 tff(30013,plain,
% 4.09/4.41 (~r(z, elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[3201, 30012, 3193, 1525])).
% 4.09/4.41 tff(30014,plain,
% 4.09/4.41 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[24033, 30013, 11546, 2323, 74, 305])).
% 4.09/4.41 tff(30015,plain,
% 4.09/4.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[302, 30014])).
% 4.09/4.41 tff(30016,plain,
% 4.09/4.41 (~b(s(s(s(z))), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[27648, 30015, 133, 2323, 305, 698, 30010, 134])).
% 4.09/4.41 tff(30017,plain,
% 4.09/4.41 (r(s(s(s(z))), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[396, 30016])).
% 4.09/4.41 tff(30018,plain,
% 4.09/4.41 (~b(elem!1, z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[27496, 30013, 133, 74, 11546, 2323, 305])).
% 4.09/4.41 tff(30019,plain,
% 4.09/4.41 (r(elem!1, z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[653, 30018, 730])).
% 4.09/4.41 tff(30020,plain,
% 4.09/4.41 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 4.09/4.41 inference(rewrite,[status(thm)],[])).
% 4.09/4.41 tff(30021,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30020])).
% 4.09/4.41 tff(30022,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 4.09/4.41 inference(transitivity,[status(thm)],[30021, 10815])).
% 4.09/4.41 tff(30023,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 4.09/4.41 inference(quant_inst,[status(thm)],[])).
% 4.09/4.41 tff(30024,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30023, 30022])).
% 4.09/4.41 tff(30025,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30024, 333, 30019, 1525, 30017, 30012])).
% 4.09/4.41 tff(30026,plain,((z = elem!1) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30027,plain,
% 4.09/4.41 (z = elem!1),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30026, 29893, 133, 2323, 30008, 698, 30006, 11546, 3193, 17795, 23185, 30004])).
% 4.09/4.41 tff(30028,plain,
% 4.09/4.41 (s(elem!1) = s(z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[70, 30027])).
% 4.09/4.41 tff(30029,plain,
% 4.09/4.41 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30028])).
% 4.09/4.41 tff(30030,plain,
% 4.09/4.41 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.09/4.41 inference(symmetry,[status(thm)],[30029])).
% 4.09/4.41 tff(30031,plain,
% 4.09/4.41 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30030])).
% 4.09/4.41 tff(30032,plain,
% 4.09/4.41 (~(s(s(elem!1)) = s(elem!1))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[107, 30031])).
% 4.09/4.41 tff(30033,plain,
% 4.09/4.41 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30027])).
% 4.09/4.41 tff(30034,plain,
% 4.09/4.41 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 4.09/4.41 inference(symmetry,[status(thm)],[30033])).
% 4.09/4.41 tff(30035,plain,
% 4.09/4.41 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30028])).
% 4.09/4.41 tff(30036,plain,
% 4.09/4.41 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.09/4.41 inference(symmetry,[status(thm)],[30035])).
% 4.09/4.41 tff(30037,plain,
% 4.09/4.41 (b(elem!1, s(z)) <=> b(z, s(elem!1))),
% 4.09/4.41 inference(transitivity,[status(thm)],[30036, 30034])).
% 4.09/4.41 tff(30038,plain,
% 4.09/4.41 (b(z, s(elem!1))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30008, 30037])).
% 4.09/4.41 tff(30039,plain,
% 4.09/4.41 (~r(s(z), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[25327, 30027, 30005])).
% 4.09/4.41 tff(30040,plain,
% 4.09/4.41 (b(s(z), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[348, 30039])).
% 4.09/4.41 tff(30041,plain,
% 4.09/4.41 (b(s(elem!1), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[18064, 30040, 30027])).
% 4.09/4.41 tff(30042,plain,
% 4.09/4.41 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30027])).
% 4.09/4.41 tff(30043,plain,
% 4.09/4.41 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.09/4.41 inference(symmetry,[status(thm)],[30042])).
% 4.09/4.41 tff(30044,plain,
% 4.09/4.41 (s(s(elem!1)) = s(s(z))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30028])).
% 4.09/4.41 tff(30045,plain,
% 4.09/4.41 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30044])).
% 4.09/4.41 tff(30046,plain,
% 4.09/4.41 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.09/4.41 inference(symmetry,[status(thm)],[30045])).
% 4.09/4.41 tff(30047,plain,
% 4.09/4.41 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.09/4.41 inference(transitivity,[status(thm)],[30046, 30043])).
% 4.09/4.41 tff(30048,plain,
% 4.09/4.41 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30047])).
% 4.09/4.41 tff(30049,plain,
% 4.09/4.41 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[29967, 30028, 133, 2323, 30004, 30006])).
% 4.09/4.41 tff(30050,plain,
% 4.09/4.41 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[1451, 30049])).
% 4.09/4.41 tff(30051,plain,
% 4.09/4.41 (~b(s(s(z)), s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[7952, 30050, 7926, 7927])).
% 4.09/4.41 tff(30052,plain,
% 4.09/4.41 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[18122, 30051, 30028])).
% 4.09/4.41 tff(30053,plain,
% 4.09/4.41 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30044])).
% 4.09/4.41 tff(30054,plain,
% 4.09/4.41 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30044, 30053])).
% 4.09/4.41 tff(30055,plain,
% 4.09/4.41 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.41 inference(symmetry,[status(thm)],[30054])).
% 4.09/4.41 tff(30056,plain,
% 4.09/4.41 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30055])).
% 4.09/4.41 tff(30057,plain,
% 4.09/4.41 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[217, 30056])).
% 4.09/4.41 tff(30058,plain,
% 4.09/4.41 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[4311, 30057, 30052])).
% 4.09/4.41 tff(30059,plain,
% 4.09/4.41 (r(s(s(z)), s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[18132, 30058, 30028])).
% 4.09/4.41 tff(30060,plain,
% 4.09/4.41 (~r(s(s(z)), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[23201, 30059, 3193, 29893])).
% 4.09/4.41 tff(30061,plain,
% 4.09/4.41 (~r(s(s(elem!1)), z)),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30060, 30048])).
% 4.09/4.41 tff(30062,plain,
% 4.09/4.41 (b(s(s(elem!1)), z)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[5509, 30061])).
% 4.09/4.41 tff(30063,plain,
% 4.09/4.41 (~b(s(s(elem!1)), s(elem!1))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[5572, 30062, 30041, 30038])).
% 4.09/4.41 tff(30064,plain,
% 4.09/4.41 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30044])).
% 4.09/4.41 tff(30065,plain,
% 4.09/4.41 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30044])).
% 4.09/4.41 tff(30066,plain,
% 4.09/4.41 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 4.09/4.41 inference(symmetry,[status(thm)],[30065])).
% 4.09/4.41 tff(30067,plain,
% 4.09/4.41 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30066])).
% 4.09/4.41 tff(30068,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.41 inference(rewrite,[status(thm)],[])).
% 4.09/4.41 tff(30069,plain,
% 4.09/4.41 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.41 inference(rewrite,[status(thm)],[])).
% 4.09/4.41 tff(30070,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30069])).
% 4.09/4.41 tff(30071,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.41 inference(transitivity,[status(thm)],[30070, 30068])).
% 4.09/4.41 tff(30072,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.09/4.41 inference(quant_inst,[status(thm)],[])).
% 4.09/4.41 tff(30073,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30072, 30071])).
% 4.09/4.41 tff(30074,plain,
% 4.09/4.41 (~b(s(s(s(z))), s(s(z)))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30073, 144, 30050, 133, 23185, 4367])).
% 4.09/4.41 tff(30075,plain,
% 4.09/4.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30074, 30067])).
% 4.09/4.41 tff(30076,plain,
% 4.09/4.41 (r(s(s(s(z))), s(s(elem!1)))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[1301, 30075, 863])).
% 4.09/4.41 tff(30077,plain,
% 4.09/4.41 (r(s(s(s(z))), s(s(z)))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30076, 30064])).
% 4.09/4.41 tff(30078,plain,
% 4.09/4.41 (~r(s(s(z)), s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[19440, 30077, 11546, 3193])).
% 4.09/4.41 tff(30079,plain,
% 4.09/4.41 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[22871, 30078, 30028])).
% 4.09/4.41 tff(30080,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[1283, 30079, 30063, 30032])).
% 4.09/4.41 tff(30081,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30082,plain,
% 4.09/4.41 (~b(s(s(s(z))), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30081, 7927, 3193, 133, 7926, 11546, 2323, 698, 706])).
% 4.09/4.41 tff(30083,plain,
% 4.09/4.41 (r(s(s(s(z))), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[704, 30082, 698])).
% 4.09/4.41 tff(30084,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[18836, 333, 722, 11546, 2323, 322])).
% 4.09/4.41 tff(30085,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30086,plain,
% 4.09/4.41 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30085, 722, 11546, 2323])).
% 4.09/4.41 tff(30087,plain,
% 4.09/4.41 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[319, 30086])).
% 4.09/4.41 tff(30088,plain,
% 4.09/4.41 (~r(elem!1, s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[29700, 722, 3193, 11546])).
% 4.09/4.41 tff(30089,plain,
% 4.09/4.41 (b(elem!1, s(s(s(z))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[1538, 30088, 1524])).
% 4.09/4.41 tff(30090,plain,
% 4.09/4.41 (~r(s(z), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[9910, 722, 3193, 707])).
% 4.09/4.41 tff(30091,plain,
% 4.09/4.41 (b(s(z), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[406, 30090, 706])).
% 4.09/4.41 tff(30092,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.09/4.41 inference(rewrite,[status(thm)],[])).
% 4.09/4.41 tff(30093,plain,
% 4.09/4.41 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.09/4.41 inference(rewrite,[status(thm)],[])).
% 4.09/4.41 tff(30094,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 4.09/4.41 inference(monotonicity,[status(thm)],[30093])).
% 4.09/4.41 tff(30095,plain,
% 4.09/4.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.09/4.41 inference(transitivity,[status(thm)],[30094, 30092])).
% 4.09/4.41 tff(30096,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.09/4.41 inference(quant_inst,[status(thm)],[])).
% 4.09/4.41 tff(30097,plain,
% 4.09/4.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 4.09/4.41 inference(modus_ponens,[status(thm)],[30096, 30095])).
% 4.09/4.41 tff(30098,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30097, 144, 134, 2082, 133, 283, 304])).
% 4.09/4.41 tff(30099,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30100,plain,
% 4.09/4.41 ($false),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30099, 30091, 30089, 133, 283, 30087])).
% 4.09/4.41 tff(30101,plain,((~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(z) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.41 tff(30102,plain,
% 4.09/4.41 (~r(elem!1, s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[30101, 30083, 17795, 706, 12398, 3193, 133, 11546, 2323])).
% 4.09/4.41 tff(30103,plain,
% 4.09/4.41 (b(elem!1, s(z))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[720, 30102, 713])).
% 4.09/4.41 tff(30104,plain,
% 4.09/4.41 (b(s(z), elem!1)),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[406, 28007, 706])).
% 4.09/4.41 tff(30105,plain,
% 4.09/4.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[27441, 74, 322, 11546, 30104, 2323])).
% 4.09/4.41 tff(30106,plain,
% 4.09/4.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.41 inference(unit_resolution,[status(thm)],[279, 30105])).
% 4.09/4.42 tff(30107,plain,
% 4.09/4.42 (~b(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[16228, 30106, 283, 2254])).
% 4.09/4.42 tff(30108,plain,
% 4.09/4.42 (r(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[619, 30107])).
% 4.09/4.42 tff(30109,plain,
% 4.09/4.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.42 inference(rewrite,[status(thm)],[])).
% 4.09/4.42 tff(30110,plain,
% 4.09/4.42 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.42 inference(rewrite,[status(thm)],[])).
% 4.09/4.42 tff(30111,plain,
% 4.09/4.42 (((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(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(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30110])).
% 4.09/4.42 tff(30112,plain,
% 4.09/4.42 (((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(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(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.42 inference(transitivity,[status(thm)],[30111, 30109])).
% 4.09/4.42 tff(30113,plain,
% 4.09/4.42 ((~![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(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 4.09/4.42 inference(quant_inst,[status(thm)],[])).
% 4.09/4.42 tff(30114,plain,
% 4.09/4.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[30113, 30112])).
% 4.09/4.42 tff(30115,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30114, 333, 670, 623, 707, 2323])).
% 4.09/4.42 tff(30116,plain,((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30117,plain,
% 4.09/4.42 (~r(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30116, 30108, 707, 2323])).
% 4.09/4.42 tff(30118,plain,
% 4.09/4.42 (~b(elem!1, z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[27496, 30117, 133, 74, 11546, 2323, 305])).
% 4.09/4.42 tff(30119,plain,
% 4.09/4.42 (r(elem!1, z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[653, 30118, 730])).
% 4.09/4.42 tff(30120,plain,
% 4.09/4.42 (b(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[658, 30117, 74])).
% 4.09/4.42 tff(30121,plain,
% 4.09/4.42 (~b(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[18838, 30120, 11546, 706, 2323, 322])).
% 4.09/4.42 tff(30122,plain,
% 4.09/4.42 (r(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[372, 30121])).
% 4.09/4.42 tff(30123,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[24033, 30117, 11546, 2323, 74, 305])).
% 4.09/4.42 tff(30124,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[302, 30123])).
% 4.09/4.42 tff(30125,plain,
% 4.09/4.42 (~b(s(s(s(z))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[27648, 30124, 133, 2323, 305, 698, 30106, 30104])).
% 4.09/4.42 tff(30126,plain,
% 4.09/4.42 (r(s(s(s(z))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[396, 30125])).
% 4.09/4.42 tff(30127,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[2122, 30126, 30122, 707, 30119])).
% 4.09/4.42 tff(30128,plain,((z = elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30129,plain,
% 4.09/4.42 (z = elem!1),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30128, 322, 133, 2323, 305, 698, 11546, 706, 707, 17795, 23185])).
% 4.09/4.42 tff(30130,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30129])).
% 4.09/4.42 tff(30131,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 4.09/4.42 inference(transitivity,[status(thm)],[30130, 203])).
% 4.09/4.42 tff(30132,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.09/4.42 inference(transitivity,[status(thm)],[30131, 24285])).
% 4.09/4.42 tff(30133,plain,
% 4.09/4.42 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30132])).
% 4.09/4.42 tff(30134,plain,
% 4.09/4.42 (~(s(s(s(s(z)))) = elem!1)),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[242, 30133])).
% 4.09/4.42 tff(30135,plain,
% 4.09/4.42 (~r(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[25327, 30129, 28007])).
% 4.09/4.42 tff(30136,plain,
% 4.09/4.42 (b(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[348, 30135])).
% 4.09/4.42 tff(30137,plain,
% 4.09/4.42 (b(s(elem!1), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[18064, 30136, 30129])).
% 4.09/4.42 tff(30138,plain,
% 4.09/4.42 (b(s(elem!1), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[25335, 30137, 30129])).
% 4.09/4.42 tff(30139,plain,
% 4.09/4.42 (s(elem!1) = s(z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[70, 30129])).
% 4.09/4.42 tff(30140,plain,
% 4.09/4.42 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30139])).
% 4.09/4.42 tff(30141,plain,
% 4.09/4.42 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.09/4.42 inference(symmetry,[status(thm)],[30140])).
% 4.09/4.42 tff(30142,plain,
% 4.09/4.42 (b(elem!1, s(elem!1))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[305, 30141])).
% 4.09/4.42 tff(30143,plain,
% 4.09/4.42 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[25349, 30129])).
% 4.09/4.42 tff(30144,plain,
% 4.09/4.42 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[29967, 30139, 133, 2323, 322, 30104])).
% 4.09/4.42 tff(30145,plain,
% 4.09/4.42 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[1451, 30144])).
% 4.09/4.42 tff(30146,plain,
% 4.09/4.42 (~b(s(s(z)), s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[7952, 30145, 7926, 7927])).
% 4.09/4.42 tff(30147,plain,
% 4.09/4.42 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[18122, 30146, 30139])).
% 4.09/4.42 tff(30148,plain,
% 4.09/4.42 (s(s(elem!1)) = s(s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30139])).
% 4.09/4.42 tff(30149,plain,
% 4.09/4.42 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30148])).
% 4.09/4.42 tff(30150,plain,
% 4.09/4.42 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30148, 30149])).
% 4.09/4.42 tff(30151,plain,
% 4.09/4.42 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.42 inference(symmetry,[status(thm)],[30150])).
% 4.09/4.42 tff(30152,plain,
% 4.09/4.42 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30151])).
% 4.09/4.42 tff(30153,plain,
% 4.09/4.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[217, 30152])).
% 4.09/4.42 tff(30154,plain,
% 4.09/4.42 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[4311, 30153, 30147])).
% 4.09/4.42 tff(30155,plain,
% 4.09/4.42 (r(s(s(z)), s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[18132, 30154, 30139])).
% 4.09/4.42 tff(30156,plain,
% 4.09/4.42 (~r(s(s(s(s(z)))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[25545, 30155, 17795, 23185, 707, 30145, 11546, 322])).
% 4.09/4.42 tff(30157,plain,
% 4.09/4.42 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28694, 30156, 30139])).
% 4.09/4.42 tff(30158,plain,
% 4.09/4.42 (b(s(s(s(s(z)))), s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[24448, 30157, 30143])).
% 4.09/4.42 tff(30159,plain,
% 4.09/4.42 (~b(s(s(s(s(z)))), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[24997, 30158, 30142, 30138])).
% 4.09/4.42 tff(30160,plain,
% 4.09/4.42 (r(s(s(s(s(z)))), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[24301, 30159, 30134])).
% 4.09/4.42 tff(30161,plain,
% 4.09/4.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28803, 30160, 2323, 707])).
% 4.09/4.42 tff(30162,plain,
% 4.09/4.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[27512, 30161])).
% 4.09/4.42 tff(30163,plain,
% 4.09/4.42 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28686, 30162, 17795, 23185])).
% 4.09/4.42 tff(30164,plain,
% 4.09/4.42 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[9761, 30163])).
% 4.09/4.42 tff(30165,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28878, 333, 30160, 2323, 322, 30164])).
% 4.09/4.42 tff(30166,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30167,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30166, 30083, 2323, 11546, 30103, 7926, 7927, 133, 698, 706])).
% 4.09/4.42 tff(30168,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[319, 30167])).
% 4.09/4.42 tff(30169,plain,
% 4.09/4.42 (~b(s(z), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[3955, 30168, 133, 30103])).
% 4.09/4.42 tff(30170,plain,
% 4.09/4.42 (r(s(z), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[406, 30169, 706])).
% 4.09/4.42 tff(30171,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[26742, 333, 30170, 3193, 30083, 2323])).
% 4.09/4.42 tff(30172,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30173,plain,
% 4.09/4.42 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30172, 29889, 29637, 706, 27421, 11546, 7926, 698])).
% 4.09/4.42 tff(30174,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[15720, 30173, 11546, 29637])).
% 4.09/4.42 tff(30175,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[319, 30174])).
% 4.09/4.42 tff(30176,plain,
% 4.09/4.42 (b(elem!1, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[1538, 30088, 12398])).
% 4.09/4.42 tff(30177,plain,
% 4.09/4.42 (~r(s(s(s(z))), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30101, 722, 283, 706, 12398, 3193, 133, 11546, 2323])).
% 4.09/4.42 tff(30178,plain,
% 4.09/4.42 (b(s(s(s(z))), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[704, 30177, 698])).
% 4.09/4.42 tff(30179,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[29891, 30178, 30176, 283, 133])).
% 4.09/4.42 tff(30180,plain,((~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (s(z) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30181,plain,
% 4.09/4.42 (~r(elem!1, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30180, 698, 27421, 17795, 706, 29637, 11546, 29889])).
% 4.09/4.42 tff(30182,plain,
% 4.09/4.42 (b(elem!1, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[720, 30181, 713])).
% 4.09/4.42 tff(30183,plain,
% 4.09/4.42 (~b(s(z), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[3955, 30182, 27421, 30175])).
% 4.09/4.42 tff(30184,plain,
% 4.09/4.42 (r(s(z), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[406, 30183, 706])).
% 4.09/4.42 tff(30185,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[19126, 30184, 11546, 29889])).
% 4.09/4.42 tff(30186,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[302, 30185])).
% 4.09/4.42 tff(30187,plain,
% 4.09/4.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.42 inference(rewrite,[status(thm)],[])).
% 4.09/4.42 tff(30188,plain,
% 4.09/4.42 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.42 inference(rewrite,[status(thm)],[])).
% 4.09/4.42 tff(30189,plain,
% 4.09/4.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30188])).
% 4.09/4.42 tff(30190,plain,
% 4.09/4.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.42 inference(transitivity,[status(thm)],[30189, 30187])).
% 4.09/4.42 tff(30191,plain,
% 4.09/4.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.42 inference(quant_inst,[status(thm)],[])).
% 4.09/4.42 tff(30192,plain,
% 4.09/4.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[30191, 30190])).
% 4.09/4.42 tff(30193,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30192, 144, 251, 305, 133, 304, 286])).
% 4.09/4.42 tff(30194,plain,((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30195,plain,
% 4.09/4.42 (~b(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30194, 30182, 27421, 30175, 30186])).
% 4.09/4.42 tff(30196,plain,
% 4.09/4.42 (~b(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28032, 30186, 27421, 30182, 30175])).
% 4.09/4.42 tff(30197,plain,
% 4.09/4.42 (r(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[348, 30196])).
% 4.09/4.42 tff(30198,plain,
% 4.09/4.42 (~b(elem!1, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[29891, 29765, 283, 133])).
% 4.09/4.42 tff(30199,plain,
% 4.09/4.42 (r(elem!1, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[1538, 30198, 12398])).
% 4.09/4.42 tff(30200,plain,
% 4.09/4.42 (~(z = elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[29786, 699, 283, 133, 706, 3193, 11546, 6107, 286, 698])).
% 4.09/4.42 tff(30201,plain,
% 4.09/4.42 (r(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[658, 30200, 606])).
% 4.09/4.42 tff(30202,plain,
% 4.09/4.42 (~r(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[3201, 30201, 3193, 30199])).
% 4.09/4.42 tff(30203,plain,
% 4.09/4.42 (b(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[619, 30202])).
% 4.09/4.42 tff(30204,plain,
% 4.09/4.42 (~r(s(s(s(z))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[11212, 30201, 3193, 323])).
% 4.09/4.42 tff(30205,plain,
% 4.09/4.42 (b(s(s(s(z))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[396, 30204])).
% 4.09/4.42 tff(30206,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[294, 30205, 30203, 283, 286])).
% 4.09/4.42 tff(30207,plain,(r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | b(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30208,plain,
% 4.09/4.42 (r(s(s(s(z))), elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30207, 30186, 17795, 29637, 30197, 30195, 27421, 706, 11546, 30173, 698])).
% 4.09/4.42 tff(30209,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[26742, 333, 30184, 29637, 30208, 29889])).
% 4.09/4.42 tff(30210,plain,((s(s(s(z))) = elem!1) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30211,plain,
% 4.09/4.42 (s(s(s(z))) = elem!1),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30210, 706, 11546, 7926, 54])).
% 4.09/4.42 tff(30212,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30211])).
% 4.09/4.42 tff(30213,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 4.09/4.42 inference(transitivity,[status(thm)],[30212, 18283])).
% 4.09/4.42 tff(30214,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.09/4.42 inference(transitivity,[status(thm)],[30213, 18284])).
% 4.09/4.42 tff(30215,plain,
% 4.09/4.42 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30214])).
% 4.09/4.42 tff(30216,plain,
% 4.09/4.42 (~(elem!1 = z)),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[392, 30215])).
% 4.09/4.42 tff(30217,plain,
% 4.09/4.42 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30211])).
% 4.09/4.42 tff(30218,plain,
% 4.09/4.42 (r(elem!1, s(z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[29637, 30217])).
% 4.09/4.42 tff(30219,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.09/4.42 inference(monotonicity,[status(thm)],[78])).
% 4.09/4.42 tff(30220,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 4.09/4.42 inference(transitivity,[status(thm)],[30219, 18283])).
% 4.09/4.42 tff(30221,plain,
% 4.09/4.42 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30220])).
% 4.09/4.42 tff(30222,plain,
% 4.09/4.42 (~(z = elem!1)),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[392, 30221])).
% 4.09/4.42 tff(30223,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[94])).
% 4.09/4.42 tff(30224,plain,
% 4.09/4.42 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30223])).
% 4.09/4.42 tff(30225,plain,
% 4.09/4.42 (~(s(elem!1) = s(z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[24294, 30224])).
% 4.09/4.42 tff(30226,plain,
% 4.09/4.42 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[22668, 30225])).
% 4.09/4.42 tff(30227,plain,
% 4.09/4.42 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[30226, 7852])).
% 4.09/4.42 tff(30228,plain,
% 4.09/4.42 (~b(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[21591, 321, 11546, 30227])).
% 4.09/4.42 tff(30229,plain,
% 4.09/4.42 (~b(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[257, 30228, 78])).
% 4.09/4.42 tff(30230,plain,
% 4.09/4.42 (r(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[658, 30229, 30222])).
% 4.09/4.42 tff(30231,plain,
% 4.09/4.42 (~r(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[19174, 30230, 11546, 722])).
% 4.09/4.42 tff(30232,plain,
% 4.09/4.42 (r(z, s(s(s(z))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[619, 30228])).
% 4.09/4.42 tff(30233,plain,
% 4.09/4.42 (~r(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[19065, 30232, 11546, 321])).
% 4.09/4.42 tff(30234,plain,
% 4.09/4.42 (b(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[348, 30233])).
% 4.09/4.42 tff(30235,plain,
% 4.09/4.42 (~b(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[19223, 30234, 11546, 30227, 30230, 321])).
% 4.09/4.42 tff(30236,plain,
% 4.09/4.42 ($false),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[372, 30235, 30231])).
% 4.09/4.42 tff(30237,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.42 tff(30238,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30237, 30218, 11546, 30211])).
% 4.09/4.42 tff(30239,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[302, 30238])).
% 4.09/4.42 tff(30240,plain,
% 4.09/4.42 (s(s(s(s(z)))) = s(elem!1)),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30211])).
% 4.09/4.42 tff(30241,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30240])).
% 4.09/4.42 tff(30242,plain,
% 4.09/4.42 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30241])).
% 4.09/4.42 tff(30243,plain,
% 4.09/4.42 (~(s(elem!1) = s(z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[24294, 30242])).
% 4.09/4.42 tff(30244,plain,
% 4.09/4.42 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[22668, 30243])).
% 4.09/4.42 tff(30245,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30085, 30244, 11546, 30218])).
% 4.09/4.42 tff(30246,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[319, 30245])).
% 4.09/4.42 tff(30247,plain,
% 4.09/4.42 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30211])).
% 4.09/4.42 tff(30248,plain,
% 4.09/4.42 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30247])).
% 4.09/4.42 tff(30249,plain,
% 4.09/4.42 (~b(s(s(s(z))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[28880, 7926, 11546, 54])).
% 4.09/4.42 tff(30250,plain,
% 4.09/4.42 (~b(elem!1, s(z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[30249, 30248])).
% 4.09/4.42 tff(30251,plain,
% 4.09/4.42 (r(elem!1, s(z))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[3193, 7585])).
% 4.09/4.42 tff(30252,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30237, 30251, 11546, 78])).
% 4.09/4.42 tff(30253,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[302, 30252])).
% 4.09/4.42 tff(30254,plain,
% 4.09/4.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[30085, 30226, 11546, 30251])).
% 4.09/4.42 tff(30255,plain,
% 4.09/4.42 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[319, 30254])).
% 4.09/4.42 tff(30256,plain,
% 4.09/4.42 (~b(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[21435, 284, 283, 304, 286])).
% 4.09/4.42 tff(30257,plain,
% 4.09/4.42 (r(s(z), z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[348, 30256])).
% 4.09/4.42 tff(30258,plain,
% 4.09/4.42 (~r(z, s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[8030, 28194, 3193, 30257])).
% 4.09/4.42 tff(30259,plain,
% 4.09/4.42 (b(z, s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[583, 30258])).
% 4.09/4.42 tff(30260,plain,
% 4.09/4.42 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.09/4.42 inference(transitivity,[status(thm)],[30220, 18284])).
% 4.09/4.42 tff(30261,plain,
% 4.09/4.42 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30260])).
% 4.09/4.42 tff(30262,plain,
% 4.09/4.42 (~(elem!1 = z)),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[392, 30261])).
% 4.09/4.42 tff(30263,plain,
% 4.09/4.42 (b(z, elem!1)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[609, 284, 78])).
% 4.09/4.42 tff(30264,plain,
% 4.09/4.42 (~b(elem!1, z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[880, 30263, 133, 286])).
% 4.09/4.42 tff(30265,plain,
% 4.09/4.42 (r(elem!1, z)),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[1380, 30264, 30262])).
% 4.09/4.42 tff(30266,plain,
% 4.09/4.42 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 4.09/4.42 inference(transitivity,[status(thm)],[30223, 1578])).
% 4.09/4.42 tff(30267,plain,
% 4.09/4.42 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 4.09/4.42 inference(monotonicity,[status(thm)],[30266])).
% 4.09/4.42 tff(30268,plain,
% 4.09/4.42 (~(s(z) = s(elem!1))),
% 4.09/4.42 inference(modus_ponens,[status(thm)],[24294, 30267])).
% 4.09/4.42 tff(30269,plain,
% 4.09/4.42 (~r(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[7314, 30257, 19237, 28194])).
% 4.09/4.42 tff(30270,plain,
% 4.09/4.42 (b(z, s(z))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[372, 30269])).
% 4.09/4.42 tff(30271,plain,
% 4.09/4.42 (~r(s(z), s(elem!1))),
% 4.09/4.42 inference(unit_resolution,[status(thm)],[7675, 435, 706, 708, 350])).
% 4.09/4.42 tff(30272,plain,
% 4.09/4.42 (b(s(z), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1244, 30271, 1237])).
% 4.09/4.43 tff(30273,plain,
% 4.09/4.43 (~r(s(elem!1), s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[443, 435, 2169, 408])).
% 4.09/4.43 tff(30274,plain,
% 4.09/4.43 (b(s(elem!1), s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[486, 30273, 1])).
% 4.09/4.43 tff(30275,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1853, 30274, 30272, 490, 585])).
% 4.09/4.43 tff(30276,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (s(z) = elem!1) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30277,plain,
% 4.09/4.43 (~r(s(elem!1), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30276, 30270, 30259, 30225, 30268, 30265, 706, 708, 350])).
% 4.09/4.43 tff(30278,plain,
% 4.09/4.43 (b(s(elem!1), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[448, 30277, 14076])).
% 4.09/4.43 tff(30279,plain,
% 4.09/4.43 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[593, 30278, 133, 286, 30259])).
% 4.09/4.43 tff(30280,plain,
% 4.09/4.43 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[542, 30279, 22256])).
% 4.09/4.43 tff(30281,plain,
% 4.09/4.43 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[417, 30265, 2169, 30257])).
% 4.09/4.43 tff(30282,plain,
% 4.09/4.43 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[279, 30281])).
% 4.09/4.43 tff(30283,plain,
% 4.09/4.43 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[15996, 30282, 304, 30270, 30259])).
% 4.09/4.43 tff(30284,plain,
% 4.09/4.43 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[472, 30283, 14872])).
% 4.09/4.43 tff(30285,plain,
% 4.09/4.43 (~b(elem!1, s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1642, 30278, 30263, 30259])).
% 4.09/4.43 tff(30286,plain,
% 4.09/4.43 (r(elem!1, s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[560, 30285, 14077])).
% 4.09/4.43 tff(30287,plain,
% 4.09/4.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(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(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30288,plain,
% 4.09/4.43 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30289,plain,
% 4.09/4.43 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30288])).
% 4.09/4.43 tff(30290,plain,
% 4.09/4.43 (((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(transitivity,[status(thm)],[30289, 30287])).
% 4.09/4.43 tff(30291,plain,
% 4.09/4.43 ((~![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(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 4.09/4.43 inference(quant_inst,[status(thm)],[])).
% 4.09/4.43 tff(30292,plain,
% 4.09/4.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[30291, 30290])).
% 4.09/4.43 tff(30293,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30292, 333, 30286, 30226, 30284, 30280])).
% 4.09/4.43 tff(30294,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1) | b(elem!1, s(z)) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30295,plain,
% 4.09/4.43 (~b(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30294, 350, 30253, 706, 708, 133, 30255, 3193, 283, 78])).
% 4.09/4.43 tff(30296,plain,
% 4.09/4.43 (~b(z, elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[257, 30295, 78])).
% 4.09/4.43 tff(30297,plain,
% 4.09/4.43 (r(z, elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[658, 30296, 30222])).
% 4.09/4.43 tff(30298,plain,
% 4.09/4.43 (~r(z, s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[19174, 30297, 11546, 30251])).
% 4.09/4.43 tff(30299,plain,
% 4.09/4.43 (b(z, s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[372, 30298])).
% 4.09/4.43 tff(30300,plain,
% 4.09/4.43 (r(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[619, 30295])).
% 4.09/4.43 tff(30301,plain,
% 4.09/4.43 (~b(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[7093, 30299, 30255, 30253])).
% 4.09/4.43 tff(30302,plain,
% 4.09/4.43 (r(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[348, 30301])).
% 4.09/4.43 tff(30303,plain,
% 4.09/4.43 (~r(s(s(s(z))), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[27726, 30302, 19237, 30300])).
% 4.09/4.43 tff(30304,plain,
% 4.09/4.43 (b(s(s(s(z))), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[396, 30303])).
% 4.09/4.43 tff(30305,plain,
% 4.09/4.43 (b(elem!1, z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[380, 30304, 78])).
% 4.09/4.43 tff(30306,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[19377, 144, 30305, 30299, 133, 30255, 30253])).
% 4.09/4.43 tff(30307,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | b(elem!1, s(z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30308,plain,
% 4.09/4.43 (b(s(z), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30307, 30211, 27421, 11546, 706, 30250, 29637, 17795])).
% 4.09/4.43 tff(30309,plain,
% 4.09/4.43 (~b(elem!1, z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[3988, 30308, 27421, 30246, 30239])).
% 4.09/4.43 tff(30310,plain,
% 4.09/4.43 (r(elem!1, z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1380, 30309, 30216])).
% 4.09/4.43 tff(30311,plain,
% 4.09/4.43 (~r(z, s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[20609, 30310, 11546, 30218])).
% 4.09/4.43 tff(30312,plain,
% 4.09/4.43 (b(z, s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[372, 30311])).
% 4.09/4.43 tff(30313,plain,
% 4.09/4.43 (~b(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[7093, 30312, 30246, 30239])).
% 4.09/4.43 tff(30314,plain,
% 4.09/4.43 (r(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[348, 30313])).
% 4.09/4.43 tff(30315,plain,
% 4.09/4.43 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[22285, 30314, 27421, 11546, 30308, 713, 30310])).
% 4.09/4.43 tff(30316,plain,
% 4.09/4.43 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[279, 30315])).
% 4.09/4.43 tff(30317,plain,
% 4.09/4.43 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30213])).
% 4.09/4.43 tff(30318,plain,
% 4.09/4.43 (~(z = elem!1)),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[392, 30317])).
% 4.09/4.43 tff(30319,plain,
% 4.09/4.43 (~b(s(s(s(z))), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[380, 30309, 30211])).
% 4.09/4.43 tff(30320,plain,
% 4.09/4.43 (r(s(s(s(z))), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[396, 30319])).
% 4.09/4.43 tff(30321,plain,
% 4.09/4.43 (~r(z, elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[11212, 30314, 29637, 30320])).
% 4.09/4.43 tff(30322,plain,
% 4.09/4.43 (b(z, elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[658, 30321, 30318])).
% 4.09/4.43 tff(30323,plain,
% 4.09/4.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30324,plain,
% 4.09/4.43 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30325,plain,
% 4.09/4.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30324])).
% 4.09/4.43 tff(30326,plain,
% 4.09/4.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(transitivity,[status(thm)],[30325, 30323])).
% 4.09/4.43 tff(30327,plain,
% 4.09/4.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.43 inference(quant_inst,[status(thm)],[])).
% 4.09/4.43 tff(30328,plain,
% 4.09/4.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[30327, 30326])).
% 4.09/4.43 tff(30329,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30328, 144, 30322, 30308, 30312, 30246, 30316])).
% 4.09/4.43 tff(30330,plain,((s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30331,plain,
% 4.09/4.43 (s(z) = elem!1),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30330, 7926, 11546, 54])).
% 4.09/4.43 tff(30332,plain,
% 4.09/4.43 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30331])).
% 4.09/4.43 tff(30333,plain,
% 4.09/4.43 (r(s(s(s(z))), elem!1)),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[29637, 30332])).
% 4.09/4.43 tff(30334,plain,
% 4.09/4.43 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[15132, 57, 11546])).
% 4.09/4.43 tff(30335,plain,
% 4.09/4.43 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 4.09/4.43 inference(monotonicity,[status(thm)],[57])).
% 4.09/4.43 tff(30336,plain,
% 4.09/4.43 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30335])).
% 4.09/4.43 tff(30337,plain,
% 4.09/4.43 (~(s(s(z)) = elem!1)),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[1416, 30336])).
% 4.09/4.43 tff(30338,plain,
% 4.09/4.43 (~r(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30116, 23297, 707, 30334])).
% 4.09/4.43 tff(30339,plain,
% 4.09/4.43 (b(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[619, 30338])).
% 4.09/4.43 tff(30340,plain,
% 4.09/4.43 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[15183, 23299, 11546, 321])).
% 4.09/4.43 tff(30341,plain,
% 4.09/4.43 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[279, 30340])).
% 4.09/4.43 tff(30342,plain,
% 4.09/4.43 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[21591, 30339, 11546, 321])).
% 4.09/4.43 tff(30343,plain,
% 4.09/4.43 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1137, 30342])).
% 4.09/4.43 tff(30344,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[16228, 30343, 30341, 283, 30339])).
% 4.09/4.43 tff(30345,plain,(b(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30346,plain,
% 4.09/4.43 (b(z, elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30345, 321, 11546, 283, 707, 57])).
% 4.09/4.43 tff(30347,plain,
% 4.09/4.43 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[27825, 30346, 133, 30337, 321, 30334])).
% 4.09/4.43 tff(30348,plain,
% 4.09/4.43 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1451, 30347])).
% 4.09/4.43 tff(30349,plain,
% 4.09/4.43 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[2689, 30348, 57])).
% 4.09/4.43 tff(30350,plain,
% 4.09/4.43 (~b(s(elem!1), s(s(elem!1)))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[15113, 144, 23322, 14453, 30349])).
% 4.09/4.43 tff(30351,plain,
% 4.09/4.43 (~b(s(elem!1), s(s(s(z))))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[30350, 24911])).
% 4.09/4.43 tff(30352,plain,
% 4.09/4.43 (r(s(elem!1), s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[965, 30351, 11786])).
% 4.09/4.43 tff(30353,plain,
% 4.09/4.43 (r(s(s(z)), s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[24894, 30352, 57])).
% 4.09/4.43 tff(30354,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[25384, 333, 707, 2323, 7155, 6330])).
% 4.09/4.43 tff(30355,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30356,plain,
% 4.09/4.43 (~r(s(s(z)), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30355, 30353, 30334, 707])).
% 4.09/4.43 tff(30357,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[7180, 12779])).
% 4.09/4.43 tff(30358,plain,((~r(s(elem!1), elem!1)) | r(s(s(z)), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30359,plain,
% 4.09/4.43 (~r(s(elem!1), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30358, 30356, 57])).
% 4.09/4.43 tff(30360,plain,
% 4.09/4.43 (b(s(elem!1), elem!1)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[448, 30359, 2681])).
% 4.09/4.43 tff(30361,plain,
% 4.09/4.43 (b(s(elem!1), s(z))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[30360, 2662])).
% 4.09/4.43 tff(30362,plain,
% 4.09/4.43 (b(z, s(z))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[9366, 30346, 57])).
% 4.09/4.43 tff(30363,plain,
% 4.09/4.43 (r(s(elem!1), s(s(elem!1)))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[2860, 44, 30350, 2857])).
% 4.09/4.43 tff(30364,plain,
% 4.09/4.43 (~r(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[19065, 623, 11546, 321])).
% 4.09/4.43 tff(30365,plain,
% 4.09/4.43 (b(s(z), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[348, 30364])).
% 4.09/4.43 tff(30366,plain,
% 4.09/4.43 (~b(s(elem!1), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[499, 30365, 490, 488])).
% 4.09/4.43 tff(30367,plain,
% 4.09/4.43 (r(s(elem!1), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[507, 30366])).
% 4.09/4.43 tff(30368,plain,
% 4.09/4.43 (((~![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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30369,plain,
% 4.09/4.43 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.43 inference(rewrite,[status(thm)],[])).
% 4.09/4.43 tff(30370,plain,
% 4.09/4.43 (((~![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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 4.09/4.43 inference(monotonicity,[status(thm)],[30369])).
% 4.09/4.43 tff(30371,plain,
% 4.09/4.43 (((~![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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.43 inference(transitivity,[status(thm)],[30370, 30368])).
% 4.09/4.43 tff(30372,plain,
% 4.09/4.43 ((~![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)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 4.09/4.43 inference(quant_inst,[status(thm)],[])).
% 4.09/4.43 tff(30373,plain,
% 4.09/4.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[30372, 30371])).
% 4.09/4.43 tff(30374,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30373, 333, 30367, 4627, 10049, 4571])).
% 4.09/4.43 tff(30375,plain,((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.43 tff(30376,plain,
% 4.09/4.43 (~r(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[30375, 30363, 10048, 30362, 30361, 11546, 321, 57])).
% 4.09/4.43 tff(30377,plain,
% 4.09/4.43 (b(z, s(s(s(z))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[619, 30376])).
% 4.09/4.43 tff(30378,plain,
% 4.09/4.43 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[16228, 30377, 283, 2254])).
% 4.09/4.43 tff(30379,plain,
% 4.09/4.43 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[279, 30378])).
% 4.09/4.43 tff(30380,plain,
% 4.09/4.43 (~r(elem!1, z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[27689, 333, 30334, 321, 30379])).
% 4.09/4.43 tff(30381,plain,
% 4.09/4.43 (b(elem!1, z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[653, 30380, 23320])).
% 4.09/4.43 tff(30382,plain,
% 4.09/4.43 (~b(s(elem!1), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[916, 30381, 30346, 30360])).
% 4.09/4.43 tff(30383,plain,
% 4.09/4.43 (r(s(elem!1), z)),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[507, 30382])).
% 4.09/4.43 tff(30384,plain,
% 4.09/4.43 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.43 inference(modus_ponens,[status(thm)],[133, 5278])).
% 4.09/4.43 tff(30385,plain,
% 4.09/4.43 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[7702, 333, 30383, 321, 30379])).
% 4.09/4.43 tff(30386,plain,
% 4.09/4.43 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[542, 30385, 2698])).
% 4.09/4.43 tff(30387,plain,
% 4.09/4.43 (~b(s(s(elem!1)), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[5667, 30386, 30384, 23322, 30361])).
% 4.09/4.43 tff(30388,plain,
% 4.09/4.43 (r(s(s(elem!1)), s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[1283, 30387, 2507])).
% 4.09/4.43 tff(30389,plain,
% 4.09/4.43 (~b(elem!1, s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[555, 30386, 133, 30360])).
% 4.09/4.43 tff(30390,plain,
% 4.09/4.43 (r(elem!1, s(elem!1))),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[560, 30389, 2483])).
% 4.09/4.43 tff(30391,plain,
% 4.09/4.43 ($false),
% 4.09/4.43 inference(unit_resolution,[status(thm)],[13677, 333, 30390, 30388, 30383, 10048])).
% 4.09/4.43 tff(30392,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30393,plain,
% 4.09/4.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30392, 321, 133, 283, 11546, 57, 707])).
% 4.09/4.44 tff(30394,plain,
% 4.09/4.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1137, 30393])).
% 4.09/4.44 tff(30395,plain,
% 4.09/4.44 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30394, 2767])).
% 4.09/4.44 tff(30396,plain,
% 4.09/4.44 (((~![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)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30397,plain,
% 4.09/4.44 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30398,plain,
% 4.09/4.44 (((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30397])).
% 4.09/4.44 tff(30399,plain,
% 4.09/4.44 (((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.44 inference(transitivity,[status(thm)],[30398, 30396])).
% 4.09/4.44 tff(30400,plain,
% 4.09/4.44 ((~![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(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))),
% 4.09/4.44 inference(quant_inst,[status(thm)],[])).
% 4.09/4.44 tff(30401,plain,
% 4.09/4.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30400, 30399])).
% 4.09/4.44 tff(30402,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30401, 333, 10048, 30334, 321, 30395])).
% 4.09/4.44 tff(30403,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30404,plain,
% 4.09/4.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30403, 30331, 27421, 17795, 11546, 30333])).
% 4.09/4.44 tff(30405,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[302, 30404])).
% 4.09/4.44 tff(30406,plain,
% 4.09/4.44 (s(s(z)) = s(elem!1)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30331])).
% 4.09/4.44 tff(30407,plain,
% 4.09/4.44 (s(s(s(z))) = s(s(elem!1))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30406])).
% 4.09/4.44 tff(30408,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30407])).
% 4.09/4.44 tff(30409,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[17795, 30408])).
% 4.09/4.44 tff(30410,plain,
% 4.09/4.44 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30331])).
% 4.09/4.44 tff(30411,plain,
% 4.09/4.44 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 4.09/4.44 inference(transitivity,[status(thm)],[30410, 2])).
% 4.09/4.44 tff(30412,plain,
% 4.09/4.44 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30411])).
% 4.09/4.44 tff(30413,plain,
% 4.09/4.44 (~(elem!1 = s(s(s(z))))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[166, 30412])).
% 4.09/4.44 tff(30414,plain,
% 4.09/4.44 ((s(z) = z) <=> (elem!1 = z)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30331])).
% 4.09/4.44 tff(30415,plain,
% 4.09/4.44 ((s(z) = z) <=> (z = elem!1)),
% 4.09/4.44 inference(transitivity,[status(thm)],[30414, 18283])).
% 4.09/4.44 tff(30416,plain,
% 4.09/4.44 ((s(z) = z) <=> (elem!1 = z)),
% 4.09/4.44 inference(transitivity,[status(thm)],[30415, 18284])).
% 4.09/4.44 tff(30417,plain,
% 4.09/4.44 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30416])).
% 4.09/4.44 tff(30418,plain,
% 4.09/4.44 (~(elem!1 = z)),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[344, 30417])).
% 4.09/4.44 tff(30419,plain,
% 4.09/4.44 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30415])).
% 4.09/4.44 tff(30420,plain,
% 4.09/4.44 (~(z = elem!1)),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[344, 30419])).
% 4.09/4.44 tff(30421,plain,
% 4.09/4.44 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[15132, 30331, 11546])).
% 4.09/4.44 tff(30422,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30331])).
% 4.09/4.44 tff(30423,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.44 inference(symmetry,[status(thm)],[30422])).
% 4.09/4.44 tff(30424,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[27421, 30423])).
% 4.09/4.44 tff(30425,plain,
% 4.09/4.44 (~r(z, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30116, 670, 707, 2323])).
% 4.09/4.44 tff(30426,plain,
% 4.09/4.44 (b(z, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[619, 30425])).
% 4.09/4.44 tff(30427,plain,
% 4.09/4.44 (~r(s(s(s(z))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[11212, 670, 3193, 323])).
% 4.09/4.44 tff(30428,plain,
% 4.09/4.44 (b(s(s(s(z))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[396, 30427])).
% 4.09/4.44 tff(30429,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[294, 30426, 30428, 283, 286])).
% 4.09/4.44 tff(30430,plain,((~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30431,plain,
% 4.09/4.44 (~r(s(z), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30430, 670, 283, 707, 2323, 3193, 286])).
% 4.09/4.44 tff(30432,plain,
% 4.09/4.44 (b(s(z), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[348, 30431])).
% 4.09/4.44 tff(30433,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[21435, 30432, 30426, 283, 304, 286])).
% 4.09/4.44 tff(30434,plain,((~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30435,plain,
% 4.09/4.44 (~r(z, elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30434, 17795, 30424, 30405, 30333, 30421, 29637])).
% 4.09/4.44 tff(30436,plain,
% 4.09/4.44 (b(z, elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[658, 30435, 30420])).
% 4.09/4.44 tff(30437,plain,
% 4.09/4.44 (~b(elem!1, z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[880, 30436, 27421, 30405])).
% 4.09/4.44 tff(30438,plain,
% 4.09/4.44 (r(elem!1, z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1380, 30437, 30418])).
% 4.09/4.44 tff(30439,plain,
% 4.09/4.44 (~b(elem!1, z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[880, 251, 133, 286])).
% 4.09/4.44 tff(30440,plain,
% 4.09/4.44 (r(elem!1, z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1380, 30439, 23320])).
% 4.09/4.44 tff(30441,plain,
% 4.09/4.44 (b(z, s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[9366, 251, 57])).
% 4.09/4.44 tff(30442,plain,
% 4.09/4.44 (~b(s(z), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[7093, 30441, 30384, 286])).
% 4.09/4.44 tff(30443,plain,
% 4.09/4.44 (r(s(z), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[348, 30442])).
% 4.09/4.44 tff(30444,plain,
% 4.09/4.44 (~r(z, s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[8030, 28194, 3193, 30443])).
% 4.09/4.44 tff(30445,plain,
% 4.09/4.44 (b(z, s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[583, 30444])).
% 4.09/4.44 tff(30446,plain,
% 4.09/4.44 (r(s(s(elem!1)), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[6447, 28194, 57])).
% 4.09/4.44 tff(30447,plain,
% 4.09/4.44 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[9984, 30446, 14389, 30440])).
% 4.09/4.44 tff(30448,plain,
% 4.09/4.44 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[279, 30447])).
% 4.09/4.44 tff(30449,plain,
% 4.09/4.44 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[15996, 30448, 30384, 30441, 30445])).
% 4.09/4.44 tff(30450,plain,
% 4.09/4.44 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[472, 30449, 4762])).
% 4.09/4.44 tff(30451,plain,
% 4.09/4.44 (~b(elem!1, s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1642, 451, 251, 585])).
% 4.09/4.44 tff(30452,plain,
% 4.09/4.44 (r(elem!1, s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[560, 30451, 902])).
% 4.09/4.44 tff(30453,plain,
% 4.09/4.44 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[8472, 30452, 133, 525, 2725, 4007, 1257, 1221, 451])).
% 4.09/4.44 tff(30454,plain,
% 4.09/4.44 (b(s(s(elem!1)), s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1283, 30453, 2727])).
% 4.09/4.44 tff(30455,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[13699, 144, 451, 251, 585, 30454, 2811])).
% 4.09/4.44 tff(30456,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30457,plain,
% 4.09/4.44 (~b(s(elem!1), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30456, 30445, 251, 14704, 133, 30450, 10047, 4575, 2462, 2483])).
% 4.09/4.44 tff(30458,plain,
% 4.09/4.44 (r(s(elem!1), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[448, 30457, 2681])).
% 4.09/4.44 tff(30459,plain,
% 4.09/4.44 (((~![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(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, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30460,plain,
% 4.09/4.44 ((~![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(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 4.09/4.44 inference(quant_inst,[status(thm)],[])).
% 4.09/4.44 tff(30461,plain,
% 4.09/4.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30460, 30459])).
% 4.09/4.44 tff(30462,plain,
% 4.09/4.44 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30461, 333, 30458, 30440, 14389])).
% 4.09/4.44 tff(30463,plain,
% 4.09/4.44 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[57])).
% 4.09/4.44 tff(30464,plain,
% 4.09/4.44 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 4.09/4.44 inference(symmetry,[status(thm)],[30463])).
% 4.09/4.44 tff(30465,plain,
% 4.09/4.44 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30464])).
% 4.09/4.44 tff(30466,plain,
% 4.09/4.44 (~b(s(z), elem!1)),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[5882, 30465])).
% 4.09/4.44 tff(30467,plain,
% 4.09/4.44 (b(s(elem!1), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[8646, 30458, 2789, 23292, 30466, 3516, 30440, 14388])).
% 4.09/4.44 tff(30468,plain,
% 4.09/4.44 (b(s(elem!1), s(s(elem!1)))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30467, 2501])).
% 4.09/4.44 tff(30469,plain,
% 4.09/4.44 (~b(s(s(elem!1)), s(elem!1))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[6781, 30468, 14704, 30445])).
% 4.09/4.44 tff(30470,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1283, 30469, 30462, 2507])).
% 4.09/4.44 tff(30471,plain,((~b(z, s(s(s(z))))) | (~(s(z) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30472,plain,
% 4.09/4.44 (~b(z, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30471, 30331, 30249, 30436, 27421, 29637, 17795, 30405])).
% 4.09/4.44 tff(30473,plain,
% 4.09/4.44 (r(z, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[619, 30472])).
% 4.09/4.44 tff(30474,plain,
% 4.09/4.44 (~r(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[7510, 30473, 30333, 30438])).
% 4.09/4.44 tff(30475,plain,
% 4.09/4.44 (b(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1538, 30474, 30413])).
% 4.09/4.44 tff(30476,plain,
% 4.09/4.44 (b(s(z), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[13482, 30475, 30331])).
% 4.09/4.44 tff(30477,plain,
% 4.09/4.44 (b(elem!1, s(s(elem!1)))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[5343, 30476, 30331])).
% 4.09/4.44 tff(30478,plain,
% 4.09/4.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30479,plain,
% 4.09/4.44 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30480,plain,
% 4.09/4.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30479])).
% 4.09/4.44 tff(30481,plain,
% 4.09/4.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.44 inference(transitivity,[status(thm)],[30480, 30478])).
% 4.09/4.44 tff(30482,plain,
% 4.09/4.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.44 inference(quant_inst,[status(thm)],[])).
% 4.09/4.44 tff(30483,plain,
% 4.09/4.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30482, 30481])).
% 4.09/4.44 tff(30484,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30483, 144, 30436, 30477, 30409, 27421, 30405])).
% 4.09/4.44 tff(30485,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30486,plain,
% 4.09/4.44 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30485, 11546, 54])).
% 4.09/4.44 tff(30487,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[15703, 333, 3193, 11546, 224, 322])).
% 4.09/4.44 tff(30488,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30489,plain,
% 4.09/4.44 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30488, 29637, 11546, 30486])).
% 4.09/4.44 tff(30490,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[319, 30489])).
% 4.09/4.44 tff(30491,plain,
% 4.09/4.44 (b(elem!1, s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[720, 29192, 713])).
% 4.09/4.44 tff(30492,plain,
% 4.09/4.44 (b(s(z), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[406, 29193, 706])).
% 4.09/4.44 tff(30493,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[3955, 30492, 30491, 133, 304])).
% 4.09/4.44 tff(30494,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30495,plain,
% 4.09/4.44 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30494, 706, 30490, 27421, 11546, 30486])).
% 4.09/4.44 tff(30496,plain,
% 4.09/4.44 (s(elem!1) = s(z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[22668, 30495])).
% 4.09/4.44 tff(30497,plain,
% 4.09/4.44 (z = elem!1),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[8683, 30496])).
% 4.09/4.44 tff(30498,plain,
% 4.09/4.44 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30497])).
% 4.09/4.44 tff(30499,plain,
% 4.09/4.44 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 4.09/4.44 inference(symmetry,[status(thm)],[30498])).
% 4.09/4.44 tff(30500,plain,
% 4.09/4.44 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30499])).
% 4.09/4.44 tff(30501,plain,
% 4.09/4.44 (~b(elem!1, z)),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[5882, 30500])).
% 4.09/4.44 tff(30502,plain,
% 4.09/4.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[22687, 30497, 54])).
% 4.09/4.44 tff(30503,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[302, 30502])).
% 4.09/4.44 tff(30504,plain,
% 4.09/4.44 (~(s(s(s(z))) = elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[227, 30486, 54])).
% 4.09/4.44 tff(30505,plain,
% 4.09/4.44 (~b(s(s(s(z))), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[10110, 26551, 54, 2254, 3])).
% 4.09/4.44 tff(30506,plain,
% 4.09/4.44 (r(s(s(s(z))), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[704, 30505, 30504])).
% 4.09/4.44 tff(30507,plain,
% 4.09/4.44 (~r(s(z), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[15519, 30486, 11546, 29637])).
% 4.09/4.44 tff(30508,plain,
% 4.09/4.44 (b(s(z), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[172, 30507])).
% 4.09/4.44 tff(30509,plain,
% 4.09/4.44 (~(elem!1 = s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[10997, 30504])).
% 4.09/4.44 tff(30510,plain,
% 4.09/4.44 (~b(s(z), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[3955, 29895, 133, 304])).
% 4.09/4.44 tff(30511,plain,
% 4.09/4.44 (r(s(z), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[406, 30510, 706])).
% 4.09/4.44 tff(30512,plain,
% 4.09/4.44 (((~![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))), 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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30513,plain,
% 4.09/4.44 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.09/4.44 inference(rewrite,[status(thm)],[])).
% 4.09/4.44 tff(30514,plain,
% 4.09/4.44 (((~![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(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 4.09/4.44 inference(monotonicity,[status(thm)],[30513])).
% 4.09/4.44 tff(30515,plain,
% 4.09/4.44 (((~![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(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(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.09/4.44 inference(transitivity,[status(thm)],[30514, 30512])).
% 4.09/4.44 tff(30516,plain,
% 4.09/4.44 ((~![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(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 4.09/4.44 inference(quant_inst,[status(thm)],[])).
% 4.09/4.44 tff(30517,plain,
% 4.09/4.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 4.09/4.44 inference(modus_ponens,[status(thm)],[30516, 30515])).
% 4.09/4.44 tff(30518,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30517, 333, 30511, 1525, 3193, 707])).
% 4.09/4.44 tff(30519,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30520,plain,
% 4.09/4.44 (~r(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30519, 30506, 29637, 706, 27421, 30490, 11546])).
% 4.09/4.44 tff(30521,plain,
% 4.09/4.44 (b(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1538, 30520, 30509])).
% 4.09/4.44 tff(30522,plain,
% 4.09/4.44 (~b(elem!1, s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[29839, 30521, 30508, 26557, 30490])).
% 4.09/4.44 tff(30523,plain,
% 4.09/4.44 (r(elem!1, s(z))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[720, 30522, 713])).
% 4.09/4.44 tff(30524,plain,
% 4.09/4.44 ($false),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[22899, 333, 30523, 29637, 30506, 11546])).
% 4.09/4.44 tff(30525,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.44 tff(30526,plain,
% 4.09/4.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30525, 30495, 706, 54, 11546])).
% 4.09/4.44 tff(30527,plain,
% 4.09/4.44 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[16045, 30526, 11546, 29637])).
% 4.09/4.44 tff(30528,plain,
% 4.09/4.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1137, 30526])).
% 4.09/4.44 tff(30529,plain,
% 4.09/4.44 (r(s(s(s(z))), elem!1)),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[29786, 30503, 30497, 27421, 706, 29637, 11546, 30528, 30527, 30504])).
% 4.09/4.44 tff(30530,plain,
% 4.09/4.44 (~r(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[30519, 30529, 29637, 706, 27421, 30490, 11546])).
% 4.09/4.44 tff(30531,plain,
% 4.09/4.44 (b(elem!1, s(s(s(z))))),
% 4.09/4.44 inference(unit_resolution,[status(thm)],[1538, 30530, 30509])).
% 4.09/4.45 tff(30532,plain,
% 4.09/4.45 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[29878, 30531, 30528, 863, 30527, 11546, 29637, 30496, 713, 30529, 30503])).
% 4.09/4.45 tff(30533,plain,
% 4.09/4.45 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[121, 30532, 30495])).
% 4.09/4.45 tff(30534,plain,
% 4.09/4.45 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[116, 30533])).
% 4.09/4.45 tff(30535,plain,
% 4.09/4.45 (b(elem!1, z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[787, 30534, 30503])).
% 4.09/4.45 tff(30536,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30535, 30501])).
% 4.09/4.45 tff(30537,plain,((s(z) = elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30538,plain,
% 4.09/4.45 (s(z) = elem!1),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30537, 11546, 54])).
% 4.09/4.45 tff(30539,plain,
% 4.09/4.45 (s(s(z)) = s(elem!1)),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30538])).
% 4.09/4.45 tff(30540,plain,
% 4.09/4.45 (s(s(s(z))) = s(s(elem!1))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30539])).
% 4.09/4.45 tff(30541,plain,
% 4.09/4.45 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30540])).
% 4.09/4.45 tff(30542,plain,
% 4.09/4.45 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30540])).
% 4.09/4.45 tff(30543,plain,
% 4.09/4.45 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30538])).
% 4.09/4.45 tff(30544,plain,
% 4.09/4.45 (r(s(s(s(z))), elem!1)),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[29637, 30543])).
% 4.09/4.45 tff(30545,plain,
% 4.09/4.45 (r(s(s(elem!1)), elem!1)),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30544, 30542])).
% 4.09/4.45 tff(30546,plain,
% 4.09/4.45 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[224, 8165])).
% 4.09/4.45 tff(30547,plain,
% 4.09/4.45 (~r(z, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[9411, 321, 4627, 30546])).
% 4.09/4.45 tff(30548,plain,
% 4.09/4.45 (~r(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2836, 30547, 57])).
% 4.09/4.45 tff(30549,plain,
% 4.09/4.45 (b(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[619, 30548])).
% 4.09/4.45 tff(30550,plain,
% 4.09/4.45 (~r(s(z), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[21949, 23297, 11546, 321])).
% 4.09/4.45 tff(30551,plain,
% 4.09/4.45 (b(s(z), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[348, 30550])).
% 4.09/4.45 tff(30552,plain,
% 4.09/4.45 (~r(s(s(s(z))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[29279, 23299, 224, 321])).
% 4.09/4.45 tff(30553,plain,
% 4.09/4.45 (b(s(s(s(z))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[396, 30552])).
% 4.09/4.45 tff(30554,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2156, 30553, 30551, 838, 284])).
% 4.09/4.45 tff(30555,plain,(b(z, elem!1) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30556,plain,
% 4.09/4.45 (b(z, elem!1)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30555, 30549, 838, 224, 321, 11546, 57])).
% 4.09/4.45 tff(30557,plain,
% 4.09/4.45 (b(z, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2828, 30549, 57])).
% 4.09/4.45 tff(30558,plain,
% 4.09/4.45 (b(elem!1, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[5343, 57, 838])).
% 4.09/4.45 tff(30559,plain,
% 4.09/4.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30560,plain,
% 4.09/4.45 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30561,plain,
% 4.09/4.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30560])).
% 4.09/4.45 tff(30562,plain,
% 4.09/4.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(transitivity,[status(thm)],[30561, 30559])).
% 4.09/4.45 tff(30563,plain,
% 4.09/4.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(quant_inst,[status(thm)],[])).
% 4.09/4.45 tff(30564,plain,
% 4.09/4.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30563, 30562])).
% 4.09/4.45 tff(30565,plain,
% 4.09/4.45 ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30564, 144, 30558, 30557, 133])).
% 4.09/4.45 tff(30566,plain,
% 4.09/4.45 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30565, 30556])).
% 4.09/4.45 tff(30567,plain,
% 4.09/4.45 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[279, 30566])).
% 4.09/4.45 tff(30568,plain,
% 4.09/4.45 (((~![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(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30569,plain,
% 4.09/4.45 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30570,plain,
% 4.09/4.45 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30569])).
% 4.09/4.45 tff(30571,plain,
% 4.09/4.45 (((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.45 inference(transitivity,[status(thm)],[30570, 30568])).
% 4.09/4.45 tff(30572,plain,
% 4.09/4.45 ((~![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(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))),
% 4.09/4.45 inference(quant_inst,[status(thm)],[])).
% 4.09/4.45 tff(30573,plain,
% 4.09/4.45 ((~![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(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30572, 30571])).
% 4.09/4.45 tff(30574,plain,
% 4.09/4.45 (~r(elem!1, z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30573, 333, 30546, 30334, 30567])).
% 4.09/4.45 tff(30575,plain,
% 4.09/4.45 (b(elem!1, z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[653, 30574, 23320])).
% 4.09/4.45 tff(30576,plain,
% 4.09/4.45 (~b(s(s(s(z))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2821, 30575, 57, 30558, 30557])).
% 4.09/4.45 tff(30577,plain,
% 4.09/4.45 (r(s(s(s(z))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[396, 30576])).
% 4.09/4.45 tff(30578,plain,
% 4.09/4.45 (b(elem!1, s(s(s(z))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[838, 5334])).
% 4.09/4.45 tff(30579,plain,
% 4.09/4.45 (~r(z, s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[6430, 30577, 57, 30546, 321])).
% 4.09/4.45 tff(30580,plain,
% 4.09/4.45 (b(z, s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[583, 30579])).
% 4.09/4.45 tff(30581,plain,
% 4.09/4.45 (~b(s(elem!1), elem!1)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[23731, 30580, 30556, 30578, 30549])).
% 4.09/4.45 tff(30582,plain,
% 4.09/4.45 (r(s(elem!1), elem!1)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[448, 30581, 2681])).
% 4.09/4.45 tff(30583,plain,
% 4.09/4.45 (elem!1 = s(z)),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 4.09/4.45 tff(30584,plain,
% 4.09/4.45 (((~![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)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30585,plain,
% 4.09/4.45 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30586,plain,
% 4.09/4.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30585])).
% 4.09/4.45 tff(30587,plain,
% 4.09/4.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.45 inference(transitivity,[status(thm)],[30586, 30584])).
% 4.09/4.45 tff(30588,plain,
% 4.09/4.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.09/4.45 inference(quant_inst,[status(thm)],[])).
% 4.09/4.45 tff(30589,plain,
% 4.09/4.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30588, 30587])).
% 4.09/4.45 tff(30590,plain,
% 4.09/4.45 (~r(s(elem!1), s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30589, 333, 563, 435, 4627])).
% 4.09/4.45 tff(30591,plain,
% 4.09/4.45 (~r(s(elem!1), s(s(s(z))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30590, 14970])).
% 4.09/4.45 tff(30592,plain,
% 4.09/4.45 (b(s(elem!1), s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[965, 30591, 14969])).
% 4.09/4.45 tff(30593,plain,
% 4.09/4.45 (b(s(elem!1), s(s(elem!1)))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30592, 2501])).
% 4.09/4.45 tff(30594,plain,
% 4.09/4.45 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[8792, 333, 563, 435, 4627])).
% 4.09/4.45 tff(30595,plain,
% 4.09/4.45 (b(s(s(elem!1)), s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[1283, 30594, 2507])).
% 4.09/4.45 tff(30596,plain,
% 4.09/4.45 (~b(z, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[6781, 30595, 585, 30593])).
% 4.09/4.45 tff(30597,plain,
% 4.09/4.45 (~b(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2828, 30596, 57])).
% 4.09/4.45 tff(30598,plain,
% 4.09/4.45 (r(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[619, 30597])).
% 4.09/4.45 tff(30599,plain,
% 4.09/4.45 (r(z, s(s(elem!1)))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30598, 2832])).
% 4.09/4.45 tff(30600,plain,
% 4.09/4.45 (~r(z, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[10019, 333, 4627, 3654, 51])).
% 4.09/4.45 tff(30601,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30600, 30599])).
% 4.09/4.45 tff(30602,plain,((~r(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30603,plain,
% 4.09/4.45 (~r(elem!1, s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30602, 30582, 57, 4627, 30546, 30567, 30580])).
% 4.09/4.45 tff(30604,plain,
% 4.09/4.45 (b(elem!1, s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[560, 30603, 2483])).
% 4.09/4.45 tff(30605,plain,
% 4.09/4.45 (~r(s(s(elem!1)), s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[13461, 30604, 30583, 30575, 30582, 30577, 30567])).
% 4.09/4.45 tff(30606,plain,
% 4.09/4.45 (~b(s(s(elem!1)), s(elem!1))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[6931, 30604, 30557, 30575, 30558])).
% 4.09/4.45 tff(30607,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[1283, 30606, 30605, 2507])).
% 4.09/4.45 tff(30608,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30609,plain,
% 4.09/4.45 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30608, 30538, 30545, 27421, 30508, 30486, 11546])).
% 4.09/4.45 tff(30610,plain,
% 4.09/4.45 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[302, 30609])).
% 4.09/4.45 tff(30611,plain,
% 4.09/4.45 (((~![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)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, 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(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30612,plain,
% 4.09/4.45 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(rewrite,[status(thm)],[])).
% 4.09/4.45 tff(30613,plain,
% 4.09/4.45 (((~![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(s(s(s(s(s(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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.45 inference(monotonicity,[status(thm)],[30612])).
% 4.09/4.45 tff(30614,plain,
% 4.09/4.45 (((~![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(s(s(s(s(s(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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.45 inference(transitivity,[status(thm)],[30613, 30611])).
% 4.09/4.45 tff(30615,plain,
% 4.09/4.45 ((~![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(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 4.09/4.45 inference(quant_inst,[status(thm)],[])).
% 4.09/4.45 tff(30616,plain,
% 4.09/4.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.45 inference(modus_ponens,[status(thm)],[30615, 30614])).
% 4.09/4.45 tff(30617,plain,
% 4.09/4.45 (~r(s(s(elem!1)), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30616, 333, 23297, 4627, 30334])).
% 4.09/4.45 tff(30618,plain,
% 4.09/4.45 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[15576, 23299, 11546, 224])).
% 4.09/4.45 tff(30619,plain,
% 4.09/4.45 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[279, 30618])).
% 4.09/4.45 tff(30620,plain,
% 4.09/4.45 (~b(s(s(elem!1)), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[24767, 144, 286, 6147, 30619])).
% 4.09/4.45 tff(30621,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[5509, 30620, 30617])).
% 4.09/4.45 tff(30622,plain,(b(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30623,plain,
% 4.09/4.45 (b(z, elem!1)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30622, 14453, 286, 4627, 11546, 224, 57])).
% 4.09/4.45 tff(30624,plain,
% 4.09/4.45 (b(z, s(z))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[9366, 30623, 57])).
% 4.09/4.45 tff(30625,plain,
% 4.09/4.45 (~b(elem!1, z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[880, 30623, 133, 286])).
% 4.09/4.45 tff(30626,plain,
% 4.09/4.45 (r(elem!1, z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[1380, 30625, 23320])).
% 4.09/4.45 tff(30627,plain,
% 4.09/4.45 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[10021, 4223, 4627, 3654])).
% 4.09/4.45 tff(30628,plain,
% 4.09/4.45 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[279, 30627])).
% 4.09/4.45 tff(30629,plain,
% 4.09/4.45 (~b(s(s(elem!1)), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[24767, 144, 286, 6147, 30628])).
% 4.09/4.45 tff(30630,plain,
% 4.09/4.45 (r(s(s(elem!1)), z)),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[5509, 30629])).
% 4.09/4.45 tff(30631,plain,
% 4.09/4.45 ($false),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[24340, 333, 408, 4627, 4223, 30630])).
% 4.09/4.45 tff(30632,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.45 tff(30633,plain,
% 4.09/4.45 (~r(z, s(s(elem!1)))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[30632, 30626, 4627, 286, 14453, 30546])).
% 4.09/4.45 tff(30634,plain,
% 4.09/4.45 (~r(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[2836, 30633, 57])).
% 4.09/4.45 tff(30635,plain,
% 4.09/4.45 (b(z, s(s(s(z))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[619, 30634])).
% 4.09/4.45 tff(30636,plain,
% 4.09/4.45 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[22484, 30635, 2254, 30624, 304])).
% 4.09/4.45 tff(30637,plain,
% 4.09/4.45 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.45 inference(unit_resolution,[status(thm)],[279, 30636])).
% 4.09/4.46 tff(30638,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30573, 333, 30626, 30546, 30334, 30637])).
% 4.09/4.46 tff(30639,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30640,plain,
% 4.09/4.46 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30639, 30490, 30538, 30545, 30610, 27421, 11546, 30486])).
% 4.09/4.46 tff(30641,plain,
% 4.09/4.46 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[1137, 30640])).
% 4.09/4.46 tff(30642,plain,
% 4.09/4.46 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[30641, 30541])).
% 4.09/4.46 tff(30643,plain,
% 4.09/4.46 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[15132, 30538, 11546])).
% 4.09/4.46 tff(30644,plain,
% 4.09/4.46 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.46 inference(monotonicity,[status(thm)],[30540])).
% 4.09/4.46 tff(30645,plain,
% 4.09/4.46 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[30486, 30644])).
% 4.09/4.46 tff(30646,plain,
% 4.09/4.46 (((~![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)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30647,plain,
% 4.09/4.46 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30648,plain,
% 4.09/4.46 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 4.09/4.46 inference(monotonicity,[status(thm)],[30647])).
% 4.09/4.46 tff(30649,plain,
% 4.09/4.46 (((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.09/4.46 inference(transitivity,[status(thm)],[30648, 30646])).
% 4.09/4.46 tff(30650,plain,
% 4.09/4.46 ((~![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(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))),
% 4.09/4.46 inference(quant_inst,[status(thm)],[])).
% 4.09/4.46 tff(30651,plain,
% 4.09/4.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[30650, 30649])).
% 4.09/4.46 tff(30652,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30651, 333, 30545, 30645, 30643, 30642])).
% 4.09/4.46 tff(30653,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30654,plain,
% 4.09/4.46 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30653, 54])).
% 4.09/4.46 tff(30655,plain,
% 4.09/4.46 (~(z = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[22687, 321, 54])).
% 4.09/4.46 tff(30656,plain,
% 4.09/4.46 (~(s(elem!1) = s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[8683, 30655])).
% 4.09/4.46 tff(30657,plain,
% 4.09/4.46 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[15125, 1, 4])).
% 4.09/4.46 tff(30658,plain,
% 4.09/4.46 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[2323, 15128])).
% 4.09/4.46 tff(30659,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[4, 30658])).
% 4.09/4.46 tff(30660,plain,((~(s(z) = elem!1)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30661,plain,
% 4.09/4.46 (~(s(z) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30660, 30657, 4])).
% 4.09/4.46 tff(30662,plain,
% 4.09/4.46 (~(elem!1 = s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[712, 30661])).
% 4.09/4.46 tff(30663,plain,
% 4.09/4.46 (r(s(z), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[406, 350, 30661])).
% 4.09/4.46 tff(30664,plain,
% 4.09/4.46 (r(s(z), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[9176, 51, 1, 4, 350, 606])).
% 4.09/4.46 tff(30665,plain,
% 4.09/4.46 (~r(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[28050, 333, 7265, 30664, 30657])).
% 4.09/4.46 tff(30666,plain,
% 4.09/4.46 (b(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[348, 30665])).
% 4.09/4.46 tff(30667,plain,
% 4.09/4.46 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2541, 51, 30657, 7265])).
% 4.09/4.46 tff(30668,plain,
% 4.09/4.46 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[319, 30667])).
% 4.09/4.46 tff(30669,plain,
% 4.09/4.46 (((~![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(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, 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(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30670,plain,
% 4.09/4.46 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30671,plain,
% 4.09/4.46 (((~![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(s(s(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(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.46 inference(monotonicity,[status(thm)],[30670])).
% 4.09/4.46 tff(30672,plain,
% 4.09/4.46 (((~![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(s(s(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(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(transitivity,[status(thm)],[30671, 30669])).
% 4.09/4.46 tff(30673,plain,
% 4.09/4.46 ((~![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(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 4.09/4.46 inference(quant_inst,[status(thm)],[])).
% 4.09/4.46 tff(30674,plain,
% 4.09/4.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[30673, 30672])).
% 4.09/4.46 tff(30675,plain,
% 4.09/4.46 (~r(z, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30674, 333, 7265, 30664, 30657])).
% 4.09/4.46 tff(30676,plain,
% 4.09/4.46 (b(z, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[372, 30675])).
% 4.09/4.46 tff(30677,plain,
% 4.09/4.46 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[7093, 30676, 30668, 30666])).
% 4.09/4.46 tff(30678,plain,
% 4.09/4.46 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[302, 30677])).
% 4.09/4.46 tff(30679,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[3996, 333, 7265, 30657, 30678, 51])).
% 4.09/4.46 tff(30680,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(s(z), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30681,plain,
% 4.09/4.46 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30680, 606, 4, 350, 1])).
% 4.09/4.46 tff(30682,plain,
% 4.09/4.46 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[279, 30681])).
% 4.09/4.46 tff(30683,plain,
% 4.09/4.46 (~r(z, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30674, 333, 7265, 409, 30657])).
% 4.09/4.46 tff(30684,plain,
% 4.09/4.46 (b(z, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[372, 30683])).
% 4.09/4.46 tff(30685,plain,
% 4.09/4.46 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[757, 30684, 30682, 50])).
% 4.09/4.46 tff(30686,plain,
% 4.09/4.46 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[319, 30685])).
% 4.09/4.46 tff(30687,plain,
% 4.09/4.46 (~r(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[28050, 333, 7265, 409, 30657])).
% 4.09/4.46 tff(30688,plain,
% 4.09/4.46 (b(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[348, 30687])).
% 4.09/4.46 tff(30689,plain,
% 4.09/4.46 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[7741, 30688, 30682, 50])).
% 4.09/4.46 tff(30690,plain,
% 4.09/4.46 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[302, 30689])).
% 4.09/4.46 tff(30691,plain,
% 4.09/4.46 (~r(elem!1, z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[3282, 30690, 30657, 7265])).
% 4.09/4.46 tff(30692,plain,
% 4.09/4.46 (b(elem!1, z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[1380, 30691, 77])).
% 4.09/4.46 tff(30693,plain,
% 4.09/4.46 (~b(elem!1, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[387, 144, 30692, 30684, 30688])).
% 4.09/4.46 tff(30694,plain,
% 4.09/4.46 (r(elem!1, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[720, 30693, 714])).
% 4.09/4.46 tff(30695,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[18811, 333, 409, 30694, 30657, 30686])).
% 4.09/4.46 tff(30696,plain,(b(z, elem!1) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(s(z), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30697,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30696, 30663, 350, 30662, 4, 606, 1])).
% 4.09/4.46 tff(30698,plain,(b(s(z), elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(z, elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30699,plain,
% 4.09/4.46 (b(s(z), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30698, 30656, 4, 606])).
% 4.09/4.46 tff(30700,plain,
% 4.09/4.46 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[22668, 30656])).
% 4.09/4.46 tff(30701,plain,
% 4.09/4.46 (~(s(z) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30660, 30700, 4])).
% 4.09/4.46 tff(30702,plain,
% 4.09/4.46 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2541, 7265, 2323, 322])).
% 4.09/4.46 tff(30703,plain,
% 4.09/4.46 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2305, 30702, 7265])).
% 4.09/4.46 tff(30704,plain,
% 4.09/4.46 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[130, 30703, 54])).
% 4.09/4.46 tff(30705,plain,
% 4.09/4.46 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[279, 30702])).
% 4.09/4.46 tff(30706,plain,
% 4.09/4.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30707,plain,
% 4.09/4.46 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30708,plain,
% 4.09/4.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.46 inference(monotonicity,[status(thm)],[30707])).
% 4.09/4.46 tff(30709,plain,
% 4.09/4.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(transitivity,[status(thm)],[30708, 30706])).
% 4.09/4.46 tff(30710,plain,
% 4.09/4.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))),
% 4.09/4.46 inference(quant_inst,[status(thm)],[])).
% 4.09/4.46 tff(30711,plain,
% 4.09/4.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.46 inference(modus_ponens,[status(thm)],[30710, 30709])).
% 4.09/4.46 tff(30712,plain,
% 4.09/4.46 (~b(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30711, 144, 134, 123, 133, 30705])).
% 4.09/4.46 tff(30713,plain,
% 4.09/4.46 (r(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[348, 30712])).
% 4.09/4.46 tff(30714,plain,
% 4.09/4.46 (~b(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30711, 144, 134, 123, 133, 24886])).
% 4.09/4.46 tff(30715,plain,
% 4.09/4.46 (r(s(z), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[348, 30714])).
% 4.09/4.46 tff(30716,plain,
% 4.09/4.46 (~r(elem!1, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[3944, 333, 670, 30715, 408])).
% 4.09/4.46 tff(30717,plain,
% 4.09/4.46 (b(elem!1, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[720, 30716, 713])).
% 4.09/4.46 tff(30718,plain,
% 4.09/4.46 (~b(s(s(s(z))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[27648, 698, 259, 2323, 134, 133, 305, 286])).
% 4.09/4.46 tff(30719,plain,
% 4.09/4.46 (r(s(s(s(z))), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[396, 30718])).
% 4.09/4.46 tff(30720,plain,
% 4.09/4.46 (~r(s(s(s(z))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[11212, 30719, 670, 323])).
% 4.09/4.46 tff(30721,plain,
% 4.09/4.46 (b(s(s(s(z))), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2794, 30720])).
% 4.09/4.46 tff(30722,plain,
% 4.09/4.46 (~r(s(s(s(z))), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2079, 30719, 408, 670])).
% 4.09/4.46 tff(30723,plain,
% 4.09/4.46 (b(s(s(s(z))), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[704, 30722, 698])).
% 4.09/4.46 tff(30724,plain,
% 4.09/4.46 ($false),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[4375, 30723, 30721, 134, 305])).
% 4.09/4.46 tff(30725,plain,((s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.46 tff(30726,plain,
% 4.09/4.46 (s(s(s(z))) = elem!1),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[30725, 30717, 134, 408, 670, 30715, 24886, 2323, 133, 286])).
% 4.09/4.46 tff(30727,plain,
% 4.09/4.46 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[12214, 30726])).
% 4.09/4.46 tff(30728,plain,
% 4.09/4.46 (~(s(s(elem!1)) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[7595, 30726, 863])).
% 4.09/4.46 tff(30729,plain,
% 4.09/4.46 (~(elem!1 = s(s(elem!1)))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[5603, 30728])).
% 4.09/4.46 tff(30730,plain,
% 4.09/4.46 (~(s(elem!1) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[5813, 30729])).
% 4.09/4.46 tff(30731,plain,
% 4.09/4.46 (~(elem!1 = s(elem!1))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[1569, 30730])).
% 4.09/4.46 tff(30732,plain,
% 4.09/4.46 (b(elem!1, s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[720, 3945, 713])).
% 4.09/4.46 tff(30733,plain,
% 4.09/4.46 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[2305, 24885, 670])).
% 4.09/4.46 tff(30734,plain,
% 4.09/4.46 (r(s(elem!1), elem!1)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[14240, 354, 123, 670, 30733, 408, 902, 706, 24886, 1, 134])).
% 4.09/4.46 tff(30735,plain,
% 4.09/4.46 (~r(s(elem!1), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[4411, 30734, 1, 670, 323, 30732, 902, 354])).
% 4.09/4.46 tff(30736,plain,
% 4.09/4.46 (b(s(elem!1), z)),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[507, 30735])).
% 4.09/4.46 tff(30737,plain,
% 4.09/4.46 (~r(s(elem!1), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[1670, 30736, 322, 323, 20735, 354])).
% 4.09/4.46 tff(30738,plain,
% 4.09/4.46 (b(s(elem!1), s(z))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[486, 30737, 1])).
% 4.09/4.46 tff(30739,plain,
% 4.09/4.46 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[4143, 144, 30736, 30738, 123, 286])).
% 4.09/4.46 tff(30740,plain,
% 4.09/4.46 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.46 inference(unit_resolution,[status(thm)],[472, 30739, 432])).
% 4.09/4.46 tff(30741,plain,
% 4.09/4.46 (((~![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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30742,plain,
% 4.09/4.46 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(rewrite,[status(thm)],[])).
% 4.09/4.46 tff(30743,plain,
% 4.09/4.46 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.46 inference(monotonicity,[status(thm)],[30742])).
% 4.09/4.46 tff(30744,plain,
% 4.09/4.46 (((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.46 inference(transitivity,[status(thm)],[30743, 30741])).
% 4.09/4.47 tff(30745,plain,
% 4.09/4.47 ((~![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(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))),
% 4.09/4.47 inference(quant_inst,[status(thm)],[])).
% 4.09/4.47 tff(30746,plain,
% 4.09/4.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30745, 30744])).
% 4.09/4.47 tff(30747,plain,
% 4.09/4.47 ($false),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30746, 333, 30734, 2323, 322, 30740])).
% 4.09/4.47 tff(30748,plain,((~r(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (s(z) = elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.47 tff(30749,plain,
% 4.09/4.47 (~r(z, s(z))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30748, 30727, 322, 2323, 123, 286, 1, 30715, 670, 30731, 408, 706, 134])).
% 4.09/4.47 tff(30750,plain,
% 4.09/4.47 (b(z, s(z))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[372, 30749])).
% 4.09/4.47 tff(30751,plain,
% 4.09/4.47 (~r(s(elem!1), z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[7112, 30750, 670, 30731, 30715, 1, 30717])).
% 4.09/4.47 tff(30752,plain,
% 4.09/4.47 (b(s(elem!1), z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[507, 30751])).
% 4.09/4.47 tff(30753,plain,
% 4.09/4.47 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[10345, 144, 30752, 286, 24886])).
% 4.09/4.47 tff(30754,plain,
% 4.09/4.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[472, 30753, 30727])).
% 4.09/4.47 tff(30755,plain,
% 4.09/4.47 (~r(s(elem!1), elem!1)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30746, 333, 2323, 322, 30754])).
% 4.09/4.47 tff(30756,plain,
% 4.09/4.47 (b(s(elem!1), elem!1)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[448, 30755, 30730])).
% 4.09/4.47 tff(30757,plain,
% 4.09/4.47 (~b(s(elem!1), s(z))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[1820, 30756, 134, 30750, 30752])).
% 4.09/4.47 tff(30758,plain,
% 4.09/4.47 (r(s(elem!1), s(z))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[486, 30757, 1])).
% 4.09/4.47 tff(30759,plain,
% 4.09/4.47 ($false),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[13998, 333, 30715, 30758, 322, 30754])).
% 4.09/4.47 tff(30760,plain,((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.47 tff(30761,plain,
% 4.09/4.47 (~r(elem!1, z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30760, 286, 1, 134, 2323, 322, 7265, 123, 706, 133])).
% 4.09/4.47 tff(30762,plain,
% 4.09/4.47 (b(elem!1, z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[1380, 30761, 77])).
% 4.09/4.47 tff(30763,plain,
% 4.09/4.47 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[927])).
% 4.09/4.47 tff(30764,plain,
% 4.09/4.47 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(elem!1))),
% 4.09/4.47 inference(symmetry,[status(thm)],[30763])).
% 4.09/4.47 tff(30765,plain,
% 4.09/4.47 (r(elem!1, s(elem!1))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[2323, 30764])).
% 4.09/4.47 tff(30766,plain,
% 4.09/4.47 (~r(s(s(s(z))), elem!1)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[6585, 1699, 670, 563])).
% 4.09/4.47 tff(30767,plain,
% 4.09/4.47 (b(s(s(s(z))), elem!1)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[704, 30766, 698])).
% 4.09/4.47 tff(30768,plain,
% 4.09/4.47 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30767, 20947])).
% 4.09/4.47 tff(30769,plain,
% 4.09/4.47 (r(z, s(s(s(s(s(s(z)))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[10398, 927, 670])).
% 4.09/4.47 tff(30770,plain,
% 4.09/4.47 (((~![X0: $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))), z)) | (~r(z, s(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), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30771,plain,
% 4.09/4.47 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30772,plain,
% 4.09/4.47 (((~![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(z)))))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[30771])).
% 4.09/4.47 tff(30773,plain,
% 4.09/4.47 (((~![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(z)))))))) | (~r(s(s(s(z))), z)) | (~r(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(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.47 inference(transitivity,[status(thm)],[30772, 30770])).
% 4.09/4.47 tff(30774,plain,
% 4.09/4.47 ((~![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(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.47 inference(quant_inst,[status(thm)],[])).
% 4.09/4.47 tff(30775,plain,
% 4.09/4.47 ((~![X0: $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))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30774, 30773])).
% 4.09/4.47 tff(30776,plain,
% 4.09/4.47 (~r(s(z), s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30775, 333, 323, 1699, 30769])).
% 4.09/4.47 tff(30777,plain,
% 4.09/4.47 (b(s(z), s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[172, 30776])).
% 4.09/4.47 tff(30778,plain,
% 4.09/4.47 (~b(elem!1, s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[26209, 30777, 927, 6169, 30768])).
% 4.09/4.47 tff(30779,plain,
% 4.09/4.47 (r(elem!1, s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[1538, 30778, 12398])).
% 4.09/4.47 tff(30780,plain,
% 4.09/4.47 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30779, 20773])).
% 4.09/4.47 tff(30781,plain,
% 4.09/4.47 (~b(z, s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[777, 144, 490, 19302, 123, 259])).
% 4.09/4.47 tff(30782,plain,
% 4.09/4.47 (r(z, s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[619, 30781])).
% 4.09/4.47 tff(30783,plain,
% 4.09/4.47 (((~![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(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30784,plain,
% 4.09/4.47 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30785,plain,
% 4.09/4.47 (((~![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))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(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(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[30784])).
% 4.09/4.47 tff(30786,plain,
% 4.09/4.47 (((~![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))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(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(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(transitivity,[status(thm)],[30785, 30783])).
% 4.09/4.47 tff(30787,plain,
% 4.09/4.47 ((~![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))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(quant_inst,[status(thm)],[])).
% 4.09/4.47 tff(30788,plain,
% 4.09/4.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30787, 30786])).
% 4.09/4.47 tff(30789,plain,
% 4.09/4.47 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30788, 333, 1699, 30782, 30769])).
% 4.09/4.47 tff(30790,plain,
% 4.09/4.47 ($false),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30789, 30780])).
% 4.09/4.47 tff(30791,plain,((~r(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.47 tff(30792,plain,
% 4.09/4.47 (~r(s(s(s(z))), z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30791, 927, 14200, 490, 123, 24886, 323, 698, 670, 30765])).
% 4.09/4.47 tff(30793,plain,
% 4.09/4.47 (b(s(s(s(z))), z)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[396, 30792])).
% 4.09/4.47 tff(30794,plain,
% 4.09/4.47 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[14138, 144, 30793, 286, 24886])).
% 4.09/4.47 tff(30795,plain,
% 4.09/4.47 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[1137, 30794])).
% 4.09/4.47 tff(30796,plain,
% 4.09/4.47 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[6165])).
% 4.09/4.47 tff(30797,plain,
% 4.09/4.47 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(symmetry,[status(thm)],[30796])).
% 4.09/4.47 tff(30798,plain,
% 4.09/4.47 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[2323, 30797])).
% 4.09/4.47 tff(30799,plain,
% 4.09/4.47 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30800,plain,
% 4.09/4.47 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30801,plain,
% 4.09/4.47 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[30800])).
% 4.09/4.47 tff(30802,plain,
% 4.09/4.47 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.47 inference(transitivity,[status(thm)],[30801, 30799])).
% 4.09/4.47 tff(30803,plain,
% 4.09/4.47 ((~![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(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 4.09/4.47 inference(quant_inst,[status(thm)],[])).
% 4.09/4.47 tff(30804,plain,
% 4.09/4.47 ((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30803, 30802])).
% 4.09/4.47 tff(30805,plain,
% 4.09/4.47 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30804, 333, 30795, 322])).
% 4.09/4.47 tff(30806,plain,
% 4.09/4.47 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[30805, 30798])).
% 4.09/4.47 tff(30807,plain,
% 4.09/4.47 (~r(elem!1, s(s(s(z))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30806, 20663])).
% 4.09/4.47 tff(30808,plain,
% 4.09/4.47 (b(elem!1, s(s(s(z))))),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[1538, 30807, 12398])).
% 4.09/4.47 tff(30809,plain,
% 4.09/4.47 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(z))) = elem!1)),
% 4.09/4.47 inference(monotonicity,[status(thm)],[6165])).
% 4.09/4.47 tff(30810,plain,
% 4.09/4.47 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(z))))),
% 4.09/4.47 inference(transitivity,[status(thm)],[30809, 2])).
% 4.09/4.47 tff(30811,plain,
% 4.09/4.47 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 4.09/4.47 inference(symmetry,[status(thm)],[30810])).
% 4.09/4.47 tff(30812,plain,
% 4.09/4.47 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[30811])).
% 4.09/4.47 tff(30813,plain,
% 4.09/4.47 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[12398, 30812])).
% 4.09/4.47 tff(30814,plain,
% 4.09/4.47 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 4.09/4.47 inference(monotonicity,[status(thm)],[17993])).
% 4.09/4.47 tff(30815,plain,
% 4.09/4.47 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(elem!1), s(z))),
% 4.09/4.47 inference(symmetry,[status(thm)],[14220])).
% 4.09/4.47 tff(30816,plain,
% 4.09/4.47 (r(s(elem!1), s(z))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[322, 30815])).
% 4.09/4.47 tff(30817,plain,
% 4.09/4.47 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(elem!1))),
% 4.09/4.47 inference(symmetry,[status(thm)],[5993])).
% 4.09/4.47 tff(30818,plain,
% 4.09/4.47 (r(s(s(s(z))), s(elem!1))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30795, 30817])).
% 4.09/4.47 tff(30819,plain,
% 4.09/4.47 (~r(s(s(s(z))), elem!1)),
% 4.09/4.47 inference(unit_resolution,[status(thm)],[3181, 30818, 30816, 30765])).
% 4.09/4.47 tff(30820,plain,
% 4.09/4.47 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.09/4.47 inference(modus_ponens,[status(thm)],[30819, 30814])).
% 4.09/4.47 tff(30821,plain,
% 4.09/4.47 (((~![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))))))))),
% 4.09/4.47 inference(rewrite,[status(thm)],[])).
% 4.09/4.47 tff(30822,plain,
% 4.09/4.47 ((~![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))))))))),
% 4.09/4.48 inference(quant_inst,[status(thm)],[])).
% 4.09/4.48 tff(30823,plain,
% 4.09/4.48 ((~![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)))))))),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[30822, 30821])).
% 4.09/4.48 tff(30824,plain,
% 4.09/4.48 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30823, 44, 30820])).
% 4.09/4.48 tff(30825,plain,
% 4.09/4.48 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30824, 30813])).
% 4.09/4.48 tff(30826,plain,
% 4.09/4.48 (~b(s(z), s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[26209, 30825, 30808, 14200, 927])).
% 4.09/4.48 tff(30827,plain,
% 4.09/4.48 (r(s(z), s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[172, 30826])).
% 4.09/4.48 tff(30828,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(z)))))), z)),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[624, 18532])).
% 4.09/4.48 tff(30829,plain,
% 4.09/4.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 4.09/4.48 inference(rewrite,[status(thm)],[])).
% 4.09/4.48 tff(30830,plain,
% 4.09/4.48 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 4.09/4.48 inference(rewrite,[status(thm)],[])).
% 4.09/4.48 tff(30831,plain,
% 4.09/4.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 4.09/4.48 inference(monotonicity,[status(thm)],[30830])).
% 4.09/4.48 tff(30832,plain,
% 4.09/4.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 4.09/4.48 inference(transitivity,[status(thm)],[30831, 30829])).
% 4.09/4.48 tff(30833,plain,
% 4.09/4.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))),
% 4.09/4.48 inference(quant_inst,[status(thm)],[])).
% 4.09/4.48 tff(30834,plain,
% 4.09/4.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[30833, 30832])).
% 4.09/4.48 tff(30835,plain,
% 4.09/4.48 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30834, 144, 30793, 14200])).
% 4.09/4.48 tff(30836,plain,
% 4.09/4.48 (~b(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30835, 30825, 30828])).
% 4.09/4.48 tff(30837,plain,
% 4.09/4.48 (r(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2794, 30836])).
% 4.09/4.48 tff(30838,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[10422, 30837, 30827, 322, 30795])).
% 4.09/4.48 tff(30839,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30840,plain,
% 4.09/4.48 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30839, 490, 2323, 624, 286, 322, 123, 30713, 698, 7265, 134])).
% 4.09/4.48 tff(30841,plain,
% 4.09/4.48 (b(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[448, 19818, 907])).
% 4.09/4.48 tff(30842,plain,
% 4.09/4.48 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[3930, 144, 30841, 123, 133])).
% 4.09/4.48 tff(30843,plain,
% 4.09/4.48 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30842, 7104])).
% 4.09/4.48 tff(30844,plain,
% 4.09/4.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[472, 30843, 432])).
% 4.09/4.48 tff(30845,plain,
% 4.09/4.48 (r(elem!1, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1732, 7106, 134, 19818, 902])).
% 4.09/4.48 tff(30846,plain,
% 4.09/4.48 (~b(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1853, 7104, 490, 7106])).
% 4.09/4.48 tff(30847,plain,
% 4.09/4.48 (r(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[583, 30846])).
% 4.09/4.48 tff(30848,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[4052, 30847, 30845, 670, 30844])).
% 4.09/4.48 tff(30849,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30850,plain,
% 4.09/4.48 (~r(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30849, 432, 670, 134, 902, 123, 133, 490, 1, 30715, 722])).
% 4.09/4.48 tff(30851,plain,
% 4.09/4.48 (b(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[507, 30850])).
% 4.09/4.48 tff(30852,plain,
% 4.09/4.48 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[10345, 144, 30851, 286, 24886])).
% 4.09/4.48 tff(30853,plain,
% 4.09/4.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[472, 30852, 432])).
% 4.09/4.48 tff(30854,plain,
% 4.09/4.48 (~r(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30746, 333, 2323, 322, 30853])).
% 4.09/4.48 tff(30855,plain,
% 4.09/4.48 (b(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[448, 30854, 907])).
% 4.09/4.48 tff(30856,plain,
% 4.09/4.48 (~b(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1820, 30855, 134, 490, 30851])).
% 4.09/4.48 tff(30857,plain,
% 4.09/4.48 (r(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[486, 30856, 1])).
% 4.09/4.48 tff(30858,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[13998, 333, 30715, 30857, 322, 30853])).
% 4.09/4.48 tff(30859,plain,((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30860,plain,
% 4.09/4.48 (~r(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30859, 902, 1, 134, 490, 2323, 286, 670, 322, 123, 133, 432])).
% 4.09/4.48 tff(30861,plain,
% 4.09/4.48 (b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[720, 30860, 714])).
% 4.09/4.48 tff(30862,plain,
% 4.09/4.48 (~b(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[27648, 30861, 24886, 2323, 134, 133, 698, 286])).
% 4.09/4.48 tff(30863,plain,
% 4.09/4.48 (r(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[396, 30862])).
% 4.09/4.48 tff(30864,plain,
% 4.09/4.48 (~r(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[11212, 30863, 670, 30715])).
% 4.09/4.48 tff(30865,plain,
% 4.09/4.48 (b(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2794, 30864])).
% 4.09/4.48 tff(30866,plain,
% 4.09/4.48 (~r(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[7112, 30861, 670, 490, 30715, 1, 902])).
% 4.09/4.48 tff(30867,plain,
% 4.09/4.48 (b(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[507, 30866])).
% 4.09/4.48 tff(30868,plain,
% 4.09/4.48 (~r(s(s(s(z))), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[7127, 30863, 670, 902, 30861, 77, 490, 30867])).
% 4.09/4.48 tff(30869,plain,
% 4.09/4.48 (b(s(s(s(z))), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[704, 30868, 698])).
% 4.09/4.48 tff(30870,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[4375, 30869, 30865, 134, 30861])).
% 4.09/4.48 tff(30871,plain,((elem!1 = s(elem!1)) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30872,plain,
% 4.09/4.48 (elem!1 = s(elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30871, 490, 698, 7265, 134, 1, 2323, 133, 286, 714, 322, 123, 30840])).
% 4.09/4.48 tff(30873,plain,
% 4.09/4.48 (s(elem!1) = elem!1),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1569, 30872])).
% 4.09/4.48 tff(30874,plain,
% 4.09/4.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[25941, 30873, 2323])).
% 4.09/4.48 tff(30875,plain,
% 4.09/4.48 (~r(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[24361, 30874, 322, 30713])).
% 4.09/4.48 tff(30876,plain,
% 4.09/4.48 (b(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[486, 30875, 1])).
% 4.09/4.48 tff(30877,plain,
% 4.09/4.48 (b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[890, 30876, 30872])).
% 4.09/4.48 tff(30878,plain,
% 4.09/4.48 (~b(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[27648, 30877, 30705, 2323, 134, 133, 698, 286])).
% 4.09/4.48 tff(30879,plain,
% 4.09/4.48 (r(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[396, 30878])).
% 4.09/4.48 tff(30880,plain,
% 4.09/4.48 (~b(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2974, 30872, 606])).
% 4.09/4.48 tff(30881,plain,
% 4.09/4.48 (r(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[583, 30880])).
% 4.09/4.48 tff(30882,plain,
% 4.09/4.48 (~r(s(z), s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1979, 333, 30713, 30881, 30879])).
% 4.09/4.48 tff(30883,plain,
% 4.09/4.48 (b(s(z), s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[172, 30882])).
% 4.09/4.48 tff(30884,plain,
% 4.09/4.48 (~r(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[11212, 30879, 7265, 30713])).
% 4.09/4.48 tff(30885,plain,
% 4.09/4.48 (b(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2794, 30884])).
% 4.09/4.48 tff(30886,plain,
% 4.09/4.48 (b(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[12198, 30872, 624])).
% 4.09/4.48 tff(30887,plain,
% 4.09/4.48 (~r(z, s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1990, 30885, 30713, 30886, 30881, 30878, 30876])).
% 4.09/4.48 tff(30888,plain,
% 4.09/4.48 (b(z, s(s(s(z))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[619, 30887])).
% 4.09/4.48 tff(30889,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2176, 144, 490, 30888, 30885, 30883])).
% 4.09/4.48 tff(30890,plain,((~b(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, elem!1) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30891,plain,
% 4.09/4.48 (~b(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30890, 698, 134, 133, 2323, 286, 1, 322, 606, 624, 714, 123])).
% 4.09/4.48 tff(30892,plain,
% 4.09/4.48 (r(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[372, 30891])).
% 4.09/4.48 tff(30893,plain,
% 4.09/4.48 (~r(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[727, 30892, 7265, 30713])).
% 4.09/4.48 tff(30894,plain,
% 4.09/4.48 (b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[720, 30893, 714])).
% 4.09/4.48 tff(30895,plain,
% 4.09/4.48 (~b(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[27648, 30894, 30705, 2323, 134, 133, 698, 286])).
% 4.09/4.48 tff(30896,plain,
% 4.09/4.48 (~r(s(s(s(z))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[25756, 30894, 2323, 7265, 698, 134, 30892, 30713])).
% 4.09/4.48 tff(30897,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[396, 30896, 30895])).
% 4.09/4.48 tff(30898,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, elem!1) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30899,plain,
% 4.09/4.48 (s(s(s(z))) = elem!1),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30898, 286, 134, 133, 2323, 713, 1, 322, 606, 30762, 123])).
% 4.09/4.48 tff(30900,plain,
% 4.09/4.48 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[12214, 30899])).
% 4.09/4.48 tff(30901,plain,
% 4.09/4.48 (~(s(s(elem!1)) = elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[7595, 30899, 863])).
% 4.09/4.48 tff(30902,plain,
% 4.09/4.48 (~(elem!1 = s(s(elem!1)))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[5603, 30901])).
% 4.09/4.48 tff(30903,plain,
% 4.09/4.48 (~(s(elem!1) = elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[5813, 30902])).
% 4.09/4.48 tff(30904,plain,
% 4.09/4.48 (~(elem!1 = s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1569, 30903])).
% 4.09/4.48 tff(30905,plain,
% 4.09/4.48 (~r(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[727, 354, 670, 30715])).
% 4.09/4.48 tff(30906,plain,
% 4.09/4.48 (b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[720, 30905, 714])).
% 4.09/4.48 tff(30907,plain,
% 4.09/4.48 (b(s(z), s(s(s(z))))),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[134, 125])).
% 4.09/4.48 tff(30908,plain,
% 4.09/4.48 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 4.09/4.48 inference(symmetry,[status(thm)],[7585])).
% 4.09/4.48 tff(30909,plain,
% 4.09/4.48 ((~r(elem!1, s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 4.09/4.48 inference(monotonicity,[status(thm)],[30908])).
% 4.09/4.48 tff(30910,plain,
% 4.09/4.48 (~r(s(s(s(z))), s(z))),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[30905, 30909])).
% 4.09/4.48 tff(30911,plain,
% 4.09/4.48 (b(s(s(s(z))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[2794, 30910])).
% 4.09/4.48 tff(30912,plain,
% 4.09/4.48 (~b(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[19646, 30911, 133, 27445, 1, 30715, 354, 30906, 134, 30907, 78])).
% 4.09/4.48 tff(30913,plain,
% 4.09/4.48 (r(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[448, 30912, 433])).
% 4.09/4.48 tff(30914,plain,
% 4.09/4.48 (~r(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[4411, 30913, 1, 670, 30715, 30906, 1722, 354])).
% 4.09/4.48 tff(30915,plain,
% 4.09/4.48 (b(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[507, 30914])).
% 4.09/4.48 tff(30916,plain,
% 4.09/4.48 (~r(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1670, 30915, 322, 30715, 22256, 354])).
% 4.09/4.48 tff(30917,plain,
% 4.09/4.48 (b(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[486, 30916, 1])).
% 4.09/4.48 tff(30918,plain,
% 4.09/4.48 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[4143, 144, 30915, 30917, 123, 286])).
% 4.09/4.48 tff(30919,plain,
% 4.09/4.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[472, 30918, 14872])).
% 4.09/4.48 tff(30920,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30746, 333, 30913, 2323, 322, 30919])).
% 4.09/4.48 tff(30921,plain,((~r(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30922,plain,
% 4.09/4.48 (~r(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30921, 286, 322, 123, 2323, 1, 7265, 30903, 133, 134, 30899, 713])).
% 4.09/4.48 tff(30923,plain,
% 4.09/4.48 (b(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[372, 30922])).
% 4.09/4.48 tff(30924,plain,
% 4.09/4.48 (~r(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30859, 30923, 1, 134, 30904, 2323, 286, 7265, 322, 123, 133, 30900])).
% 4.09/4.48 tff(30925,plain,
% 4.09/4.48 (b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[720, 30924, 713])).
% 4.09/4.48 tff(30926,plain,
% 4.09/4.48 (~r(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[7112, 30925, 7265, 30923, 30713, 1, 30904])).
% 4.09/4.48 tff(30927,plain,
% 4.09/4.48 (b(s(elem!1), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[507, 30926])).
% 4.09/4.48 tff(30928,plain,
% 4.09/4.48 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[10345, 144, 30927, 286, 30705])).
% 4.09/4.48 tff(30929,plain,
% 4.09/4.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[472, 30928, 30900])).
% 4.09/4.48 tff(30930,plain,
% 4.09/4.48 (~r(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[24361, 30929, 322, 30713])).
% 4.09/4.48 tff(30931,plain,
% 4.09/4.48 (b(s(elem!1), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[486, 30930, 1])).
% 4.09/4.48 tff(30932,plain,
% 4.09/4.48 (~b(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[8038, 144, 30923, 30931, 123, 30705])).
% 4.09/4.48 tff(30933,plain,
% 4.09/4.48 (~b(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[1820, 30931, 134, 30923, 30927])).
% 4.09/4.48 tff(30934,plain,
% 4.09/4.48 (r(s(elem!1), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[448, 30933, 30903])).
% 4.09/4.48 tff(30935,plain,
% 4.09/4.48 (((~![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, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, 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(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.48 inference(rewrite,[status(thm)],[])).
% 4.09/4.48 tff(30936,plain,
% 4.09/4.48 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.48 inference(rewrite,[status(thm)],[])).
% 4.09/4.48 tff(30937,plain,
% 4.09/4.48 (((~![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(s(s(z))))))))) | (~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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.48 inference(monotonicity,[status(thm)],[30936])).
% 4.09/4.48 tff(30938,plain,
% 4.09/4.48 (((~![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(s(s(z))))))))) | (~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(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.48 inference(transitivity,[status(thm)],[30937, 30935])).
% 4.09/4.48 tff(30939,plain,
% 4.09/4.48 ((~![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(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 4.09/4.48 inference(quant_inst,[status(thm)],[])).
% 4.09/4.48 tff(30940,plain,
% 4.09/4.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.48 inference(modus_ponens,[status(thm)],[30939, 30938])).
% 4.09/4.48 tff(30941,plain,
% 4.09/4.48 (~r(z, s(elem!1))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30940, 333, 30934, 7265, 2323])).
% 4.09/4.48 tff(30942,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[583, 30941, 30932])).
% 4.09/4.48 tff(30943,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30944,plain,
% 4.09/4.48 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30943, 30704, 123, 134, 1, 322, 2323, 606, 706])).
% 4.09/4.48 tff(30945,plain,
% 4.09/4.48 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[302, 30944])).
% 4.09/4.48 tff(30946,plain,
% 4.09/4.48 (~b(s(z), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30711, 144, 134, 123, 30704, 30705])).
% 4.09/4.48 tff(30947,plain,
% 4.09/4.48 (r(s(z), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[348, 30946])).
% 4.09/4.48 tff(30948,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[14799, 333, 7265, 30947, 322, 30945])).
% 4.09/4.48 tff(30949,plain,(b(z, elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30950,plain,
% 4.09/4.48 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30949, 30701, 50, 54, 606, 30700, 30656, 30699])).
% 4.09/4.48 tff(30951,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[319, 30950])).
% 4.09/4.48 tff(30952,plain,
% 4.09/4.48 (~(elem!1 = z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[76, 30655])).
% 4.09/4.48 tff(30953,plain,
% 4.09/4.48 (r(z, elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[658, 30655, 606])).
% 4.09/4.48 tff(30954,plain,
% 4.09/4.48 (~r(elem!1, z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[3282, 30700, 321, 30953])).
% 4.09/4.48 tff(30955,plain,
% 4.09/4.48 (~b(s(z), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[3332, 30954, 50, 54, 321, 30699, 30952])).
% 4.09/4.48 tff(30956,plain,
% 4.09/4.48 (r(s(z), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[348, 30955])).
% 4.09/4.48 tff(30957,plain,
% 4.09/4.48 (~(elem!1 = s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[712, 30701])).
% 4.09/4.48 tff(30958,plain,
% 4.09/4.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[23278, 30700])).
% 4.09/4.48 tff(30959,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[130, 30958, 54])).
% 4.09/4.48 tff(30960,plain,
% 4.09/4.48 (~b(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[3955, 30951, 30699, 30959])).
% 4.09/4.48 tff(30961,plain,
% 4.09/4.48 (r(elem!1, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[720, 30960, 30957])).
% 4.09/4.48 tff(30962,plain,
% 4.09/4.48 (~r(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[727, 30961, 30953, 30956])).
% 4.09/4.48 tff(30963,plain,
% 4.09/4.48 (b(z, s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[372, 30962])).
% 4.09/4.48 tff(30964,plain,
% 4.09/4.48 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[757, 30963, 50, 30951])).
% 4.09/4.48 tff(30965,plain,
% 4.09/4.48 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[279, 30964])).
% 4.09/4.48 tff(30966,plain,
% 4.09/4.48 ($false),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[3996, 333, 30953, 30700, 321, 30965])).
% 4.09/4.48 tff(30967,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.48 tff(30968,plain,
% 4.09/4.48 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30967, 606, 54, 4])).
% 4.09/4.48 tff(30969,plain,
% 4.09/4.48 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[27415, 30968, 54, 4])).
% 4.09/4.48 tff(30970,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[302, 30968])).
% 4.09/4.48 tff(30971,plain,
% 4.09/4.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[23278, 30969])).
% 4.09/4.48 tff(30972,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[130, 30971, 54])).
% 4.09/4.48 tff(30973,plain,
% 4.09/4.48 (~(s(z) = elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30660, 2323, 4])).
% 4.09/4.48 tff(30974,plain,
% 4.09/4.48 (b(s(z), elem!1)),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30698, 1, 4, 606])).
% 4.09/4.48 tff(30975,plain,
% 4.09/4.48 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.48 inference(unit_resolution,[status(thm)],[30943, 1, 50, 286, 133, 30974, 2323, 606, 30973])).
% 4.09/4.48 tff(30976,plain,
% 4.09/4.48 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[319, 30975])).
% 4.09/4.49 tff(30977,plain,
% 4.09/4.49 (~(elem!1 = s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[712, 30973])).
% 4.09/4.49 tff(30978,plain,
% 4.09/4.49 (~b(elem!1, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[3955, 30976, 30974, 133])).
% 4.09/4.49 tff(30979,plain,
% 4.09/4.49 (r(elem!1, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[720, 30978, 30977])).
% 4.09/4.49 tff(30980,plain,
% 4.09/4.49 (~b(elem!1, z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[3988, 30976, 286, 133, 30974])).
% 4.09/4.49 tff(30981,plain,
% 4.09/4.49 (r(elem!1, z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[653, 30980, 77])).
% 4.09/4.49 tff(30982,plain,
% 4.09/4.49 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[3282, 7265, 30657, 408])).
% 4.09/4.49 tff(30983,plain,
% 4.09/4.49 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[302, 30982])).
% 4.09/4.49 tff(30984,plain,
% 4.09/4.49 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[7741, 489, 30983, 50])).
% 4.09/4.49 tff(30985,plain,
% 4.09/4.49 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[279, 30984])).
% 4.09/4.49 tff(30986,plain,
% 4.09/4.49 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[2541, 30985, 30657, 7265])).
% 4.09/4.49 tff(30987,plain,
% 4.09/4.49 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[319, 30986])).
% 4.09/4.49 tff(30988,plain,
% 4.09/4.49 (~b(z, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[7093, 30987, 30983, 489])).
% 4.09/4.49 tff(30989,plain,
% 4.09/4.49 (r(z, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[372, 30988])).
% 4.09/4.49 tff(30990,plain,
% 4.09/4.49 (~r(s(z), elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[20228, 30989, 408, 7265])).
% 4.09/4.49 tff(30991,plain,
% 4.09/4.49 ($false),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[7011, 30990, 30989, 4, 1, 606, 30985])).
% 4.09/4.49 tff(30992,plain,((~b(s(z), z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | b(z, elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.49 tff(30993,plain,
% 4.09/4.49 (~b(s(z), z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[30992, 30981, 4, 606, 1])).
% 4.09/4.49 tff(30994,plain,
% 4.09/4.49 (r(s(z), z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[348, 30993])).
% 4.09/4.49 tff(30995,plain,
% 4.09/4.49 (~r(z, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[727, 30994, 2311, 30979])).
% 4.09/4.49 tff(30996,plain,
% 4.09/4.49 (b(z, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[372, 30995])).
% 4.09/4.49 tff(30997,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(30998,plain,
% 4.09/4.49 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(30999,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[30998])).
% 4.09/4.49 tff(31000,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.49 inference(transitivity,[status(thm)],[30999, 30997])).
% 4.09/4.49 tff(31001,plain,
% 4.09/4.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.09/4.49 inference(quant_inst,[status(thm)],[])).
% 4.09/4.49 tff(31002,plain,
% 4.09/4.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31001, 31000])).
% 4.09/4.49 tff(31003,plain,
% 4.09/4.49 ($false),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[31002, 144, 30974, 30996, 133, 30976, 286])).
% 4.09/4.49 tff(31004,plain,((s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(z, elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.09/4.49 tff(31005,plain,
% 4.09/4.49 (s(elem!1) = s(z)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[31004, 30972, 30970, 4, 606, 30969])).
% 4.09/4.49 tff(31006,plain,
% 4.09/4.49 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31005])).
% 4.09/4.49 tff(31007,plain,
% 4.09/4.49 ((s(elem!1) = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31005])).
% 4.09/4.49 tff(31008,plain,
% 4.09/4.49 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 4.09/4.49 inference(transitivity,[status(thm)],[31007, 157])).
% 4.09/4.49 tff(31009,plain,
% 4.09/4.49 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(s(s(z))))),
% 4.09/4.49 inference(symmetry,[status(thm)],[31008])).
% 4.09/4.49 tff(31010,plain,
% 4.09/4.49 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31009])).
% 4.09/4.49 tff(31011,plain,
% 4.09/4.49 (~(s(elem!1) = s(s(s(z))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[166, 31010])).
% 4.09/4.49 tff(31012,plain,
% 4.09/4.49 (z = elem!1),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[8683, 31005])).
% 4.09/4.49 tff(31013,plain,
% 4.09/4.49 (b(z, s(z)) <=> b(elem!1, s(z))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31012])).
% 4.09/4.49 tff(31014,plain,
% 4.09/4.49 (~(s(z) = elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[30660, 30969, 4])).
% 4.09/4.49 tff(31015,plain,
% 4.09/4.49 (b(z, s(elem!1)) <=> b(z, s(z))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[8677])).
% 4.09/4.49 tff(31016,plain,
% 4.09/4.49 (b(z, s(elem!1)) <=> b(elem!1, s(z))),
% 4.09/4.49 inference(transitivity,[status(thm)],[31015, 18024])).
% 4.09/4.49 tff(31017,plain,
% 4.09/4.49 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[18019])).
% 4.09/4.49 tff(31018,plain,
% 4.09/4.49 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.49 inference(symmetry,[status(thm)],[31017])).
% 4.09/4.49 tff(31019,plain,
% 4.09/4.49 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[2323, 31018])).
% 4.09/4.49 tff(31020,plain,
% 4.09/4.49 (b(s(elem!1), elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[448, 29033, 28897])).
% 4.09/4.49 tff(31021,plain,
% 4.09/4.49 (~b(s(elem!1), s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[29328, 31020, 133, 27211, 2254])).
% 4.09/4.49 tff(31022,plain,
% 4.09/4.49 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[8677])).
% 4.09/4.49 tff(31023,plain,
% 4.09/4.49 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 4.09/4.49 inference(symmetry,[status(thm)],[31022])).
% 4.09/4.49 tff(31024,plain,
% 4.09/4.49 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31023])).
% 4.09/4.49 tff(31025,plain,
% 4.09/4.49 (~b(s(s(s(z))), s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[6004, 144, 123, 2254, 304])).
% 4.09/4.49 tff(31026,plain,
% 4.09/4.49 (~b(s(s(s(z))), s(elem!1))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31025, 31024])).
% 4.09/4.49 tff(31027,plain,
% 4.09/4.49 ((s(elem!1) = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[8677])).
% 4.09/4.49 tff(31028,plain,
% 4.09/4.49 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 4.09/4.49 inference(transitivity,[status(thm)],[31027, 157])).
% 4.09/4.49 tff(31029,plain,
% 4.09/4.49 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(s(s(z))))),
% 4.09/4.49 inference(symmetry,[status(thm)],[31028])).
% 4.09/4.49 tff(31030,plain,
% 4.09/4.49 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31029])).
% 4.09/4.49 tff(31031,plain,
% 4.09/4.49 (~(s(elem!1) = s(s(s(z))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[166, 31030])).
% 4.09/4.49 tff(31032,plain,
% 4.09/4.49 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[304, 29828])).
% 4.09/4.49 tff(31033,plain,
% 4.09/4.49 (~b(z, s(elem!1))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[593, 31020, 133, 31032, 286])).
% 4.09/4.49 tff(31034,plain,
% 4.09/4.49 (r(z, s(elem!1))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[583, 31033])).
% 4.09/4.49 tff(31035,plain,
% 4.09/4.49 (~r(z, s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[4807, 31034, 31031, 31026, 31021])).
% 4.09/4.49 tff(31036,plain,
% 4.09/4.49 (b(z, s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[619, 31035])).
% 4.09/4.49 tff(31037,plain,
% 4.09/4.49 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[21435, 31036, 304, 286, 29043])).
% 4.09/4.49 tff(31038,plain,
% 4.09/4.49 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[249, 31037])).
% 4.09/4.49 tff(31039,plain,
% 4.09/4.49 (b(s(z), elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[406, 2310, 706])).
% 4.09/4.49 tff(31040,plain,
% 4.09/4.49 (~b(elem!1, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[3955, 31039, 304, 133])).
% 4.09/4.49 tff(31041,plain,
% 4.09/4.49 (r(elem!1, s(z))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[720, 31040, 713])).
% 4.09/4.49 tff(31042,plain,
% 4.09/4.49 (r(s(elem!1), s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[965, 31021, 31031])).
% 4.09/4.49 tff(31043,plain,
% 4.09/4.49 (r(s(z), s(s(s(z))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31042, 27206])).
% 4.09/4.49 tff(31044,plain,
% 4.09/4.49 (b(elem!1, s(s(s(z))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31036, 27350])).
% 4.09/4.49 tff(31045,plain,
% 4.09/4.49 (~b(s(s(elem!1)), s(elem!1))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[18895, 1426, 8677])).
% 4.09/4.49 tff(31046,plain,
% 4.09/4.49 (r(s(s(elem!1)), s(elem!1))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[1283, 31045, 22759])).
% 4.09/4.49 tff(31047,plain,
% 4.09/4.49 (r(s(s(z)), s(z))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31046, 22867])).
% 4.09/4.49 tff(31048,plain,
% 4.09/4.49 (((~![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)), s(z))) | (~r(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(31049,plain,
% 4.09/4.49 (((~r(s(z), s(s(s(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(31050,plain,
% 4.09/4.49 (((~![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(s(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31049])).
% 4.09/4.49 tff(31051,plain,
% 4.09/4.49 (((~![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(s(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 4.09/4.49 inference(transitivity,[status(thm)],[31050, 31048])).
% 4.09/4.49 tff(31052,plain,
% 4.09/4.49 ((~![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(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 4.09/4.49 inference(quant_inst,[status(thm)],[])).
% 4.09/4.49 tff(31053,plain,
% 4.09/4.49 ((~![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)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31052, 31051])).
% 4.09/4.49 tff(31054,plain,
% 4.09/4.49 (~r(s(s(z)), elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[31053, 333, 722, 353, 31047])).
% 4.09/4.49 tff(31055,plain,
% 4.09/4.49 (b(s(s(z)), elem!1)),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[7970, 31054, 26795])).
% 4.09/4.49 tff(31056,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(31057,plain,
% 4.09/4.49 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.49 inference(rewrite,[status(thm)],[])).
% 4.09/4.49 tff(31058,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.09/4.49 inference(monotonicity,[status(thm)],[31057])).
% 4.09/4.49 tff(31059,plain,
% 4.09/4.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.09/4.49 inference(transitivity,[status(thm)],[31058, 31056])).
% 4.09/4.49 tff(31060,plain,
% 4.09/4.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 4.09/4.49 inference(quant_inst,[status(thm)],[])).
% 4.09/4.49 tff(31061,plain,
% 4.09/4.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.09/4.49 inference(modus_ponens,[status(thm)],[31060, 31059])).
% 4.09/4.49 tff(31062,plain,
% 4.09/4.49 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[31061, 144, 2082, 1398, 2254])).
% 4.09/4.49 tff(31063,plain,
% 4.09/4.49 (~b(s(s(z)), s(s(s(z))))),
% 4.09/4.49 inference(unit_resolution,[status(thm)],[31062, 31055])).
% 4.09/4.49 tff(31064,plain,
% 4.09/4.49 (r(s(s(s(z))), s(z))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[2794, 31025])).
% 4.18/4.50 tff(31065,plain,
% 4.18/4.50 (((~r(s(z), 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(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31066,plain,
% 4.18/4.50 (((~![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(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(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[31065])).
% 4.18/4.50 tff(31067,plain,
% 4.18/4.50 (((~![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(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(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.50 inference(transitivity,[status(thm)],[31066, 29987])).
% 4.18/4.50 tff(31068,plain,
% 4.18/4.50 ((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31069,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31068, 31067])).
% 4.18/4.50 tff(31070,plain,
% 4.18/4.50 (~r(s(s(z)), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31069, 333, 31064, 353, 31047])).
% 4.18/4.50 tff(31071,plain,
% 4.18/4.50 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18132, 31070, 8677])).
% 4.18/4.50 tff(31072,plain,
% 4.18/4.50 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[4311, 31071, 22826])).
% 4.18/4.50 tff(31073,plain,
% 4.18/4.50 ($false),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18122, 31072, 31063, 8677])).
% 4.18/4.50 tff(31074,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.50 tff(31075,plain,
% 4.18/4.50 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31074, 31044, 8677, 2254, 31043, 31041, 123, 304])).
% 4.18/4.50 tff(31076,plain,
% 4.18/4.50 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[1451, 31075])).
% 4.18/4.50 tff(31077,plain,
% 4.18/4.50 (((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31078,plain,
% 4.18/4.50 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31079,plain,
% 4.18/4.50 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[31078])).
% 4.18/4.50 tff(31080,plain,
% 4.18/4.50 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(transitivity,[status(thm)],[31079, 31077])).
% 4.18/4.50 tff(31081,plain,
% 4.18/4.50 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31082,plain,
% 4.18/4.50 ((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31081, 31080])).
% 4.18/4.50 tff(31083,plain,
% 4.18/4.50 (~r(s(s(z)), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31082, 333, 31076, 2323, 31038])).
% 4.18/4.50 tff(31084,plain,
% 4.18/4.50 (b(s(s(z)), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[7970, 31083, 26795])).
% 4.18/4.50 tff(31085,plain,
% 4.18/4.50 (((~![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(s(s(z))), 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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31086,plain,
% 4.18/4.50 (((~r(s(z), s(s(s(z))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31087,plain,
% 4.18/4.50 (((~![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(z))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[31086])).
% 4.18/4.50 tff(31088,plain,
% 4.18/4.50 (((~![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(z))))) | (~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(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.18/4.50 inference(transitivity,[status(thm)],[31087, 31085])).
% 4.18/4.50 tff(31089,plain,
% 4.18/4.50 ((~![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(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31090,plain,
% 4.18/4.50 ((~![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(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31089, 31088])).
% 4.18/4.50 tff(31091,plain,
% 4.18/4.50 (~r(s(s(s(z))), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31090, 333, 31041, 31064, 31043])).
% 4.18/4.50 tff(31092,plain,
% 4.18/4.50 (b(s(s(s(z))), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[704, 31091, 22766])).
% 4.18/4.50 tff(31093,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31094,plain,
% 4.18/4.50 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31095,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[31094])).
% 4.18/4.50 tff(31096,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.18/4.50 inference(transitivity,[status(thm)],[31095, 31093])).
% 4.18/4.50 tff(31097,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31098,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31097, 31096])).
% 4.18/4.50 tff(31099,plain,
% 4.18/4.50 (~b(s(s(z)), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31098, 144, 31044, 31092, 31084])).
% 4.18/4.50 tff(31100,plain,
% 4.18/4.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18122, 31099, 8677])).
% 4.18/4.50 tff(31101,plain,
% 4.18/4.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[4311, 31100, 22826])).
% 4.18/4.50 tff(31102,plain,
% 4.18/4.50 (r(s(s(z)), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18132, 31101, 8677])).
% 4.18/4.50 tff(31103,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31104,plain,
% 4.18/4.50 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31105,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[31104])).
% 4.18/4.50 tff(31106,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(transitivity,[status(thm)],[31105, 31103])).
% 4.18/4.50 tff(31107,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31108,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31107, 31106])).
% 4.18/4.50 tff(31109,plain,
% 4.18/4.50 ($false),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31108, 333, 31064, 31076, 31038, 31102])).
% 4.18/4.50 tff(31110,plain,(r(s(z), elem!1) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.50 tff(31111,plain,
% 4.18/4.50 (r(s(z), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31110, 2254, 2323, 8677, 123, 304, 286, 133, 706])).
% 4.18/4.50 tff(31112,plain,
% 4.18/4.50 (r(s(z), z)),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31111, 22732])).
% 4.18/4.50 tff(31113,plain,
% 4.18/4.50 (~r(s(s(s(z))), z)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[13781, 31112, 123, 31019, 304])).
% 4.18/4.50 tff(31114,plain,
% 4.18/4.50 (b(s(s(s(z))), z)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[396, 31113])).
% 4.18/4.50 tff(31115,plain,
% 4.18/4.50 (b(s(s(s(z))), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[26887, 31114, 18019])).
% 4.18/4.50 tff(31116,plain,
% 4.18/4.50 (((~![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)))))),
% 4.18/4.50 inference(rewrite,[status(thm)],[])).
% 4.18/4.50 tff(31117,plain,
% 4.18/4.50 ((~![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)))))),
% 4.18/4.50 inference(quant_inst,[status(thm)],[])).
% 4.18/4.50 tff(31118,plain,
% 4.18/4.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31117, 31116])).
% 4.18/4.50 tff(31119,plain,
% 4.18/4.50 (~r(s(s(s(z))), s(s(z)))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31118, 333, 409, 31064, 31047])).
% 4.18/4.50 tff(31120,plain,
% 4.18/4.50 (~r(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31119, 25412])).
% 4.18/4.50 tff(31121,plain,
% 4.18/4.50 (~b(s(s(s(z))), s(s(z)))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[30073, 144, 1398, 133, 2254, 4367])).
% 4.18/4.50 tff(31122,plain,
% 4.18/4.50 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.50 inference(modus_ponens,[status(thm)],[31121, 22812])).
% 4.18/4.50 tff(31123,plain,
% 4.18/4.50 ($false),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[1301, 31122, 31120, 1184])).
% 4.18/4.50 tff(31124,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(elem!1))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.50 tff(31125,plain,
% 4.18/4.50 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31124, 2254, 8677, 133, 863, 31115, 31111, 123, 304])).
% 4.18/4.50 tff(31126,plain,
% 4.18/4.50 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[1451, 31125])).
% 4.18/4.50 tff(31127,plain,
% 4.18/4.50 (~r(s(s(z)), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31082, 333, 2671, 2323, 11862])).
% 4.18/4.50 tff(31128,plain,
% 4.18/4.50 (b(s(s(z)), elem!1)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[7970, 31127, 26795])).
% 4.18/4.50 tff(31129,plain,
% 4.18/4.50 (~b(s(s(z)), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31098, 144, 2082, 4367, 31128])).
% 4.18/4.50 tff(31130,plain,
% 4.18/4.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18122, 31129, 8677])).
% 4.18/4.50 tff(31131,plain,
% 4.18/4.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[4311, 31130, 22826])).
% 4.18/4.50 tff(31132,plain,
% 4.18/4.50 (r(s(s(z)), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18132, 31131, 8677])).
% 4.18/4.50 tff(31133,plain,
% 4.18/4.50 ($false),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31108, 333, 3193, 2671, 11862, 31132])).
% 4.18/4.50 tff(31134,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.50 tff(31135,plain,
% 4.18/4.50 (~b(elem!1, s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31134, 31064, 31126, 8677, 31115, 2323, 133])).
% 4.18/4.50 tff(31136,plain,
% 4.18/4.50 (r(elem!1, s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[1538, 31135, 22768])).
% 4.18/4.50 tff(31137,plain,
% 4.18/4.50 (~r(s(z), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[11876, 31136, 31064, 31111])).
% 4.18/4.50 tff(31138,plain,
% 4.18/4.50 (b(s(z), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[172, 31137])).
% 4.18/4.50 tff(31139,plain,
% 4.18/4.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[2262, 31138, 123, 2254])).
% 4.18/4.50 tff(31140,plain,
% 4.18/4.50 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[249, 31139])).
% 4.18/4.50 tff(31141,plain,
% 4.18/4.50 ($false),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[25500, 333, 31136, 31064, 2323, 31140])).
% 4.18/4.50 tff(31142,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.50 tff(31143,plain,
% 4.18/4.50 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[31142, 304, 123, 8677, 133, 2323, 286, 706])).
% 4.18/4.50 tff(31144,plain,
% 4.18/4.50 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[1137, 31143])).
% 4.18/4.50 tff(31145,plain,
% 4.18/4.50 (b(s(elem!1), z)),
% 4.18/4.50 inference(unit_resolution,[status(thm)],[18064, 29043, 18019])).
% 4.18/4.50 tff(31146,plain,
% 4.18/4.50 ((~r(elem!1, s(s(s(z))))) <=> (~r(z, s(s(s(z)))))),
% 4.18/4.50 inference(monotonicity,[status(thm)],[28572])).
% 4.18/4.50 tff(31147,plain,
% 4.18/4.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31148,plain,
% 4.18/4.51 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31149,plain,
% 4.18/4.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31148])).
% 4.18/4.51 tff(31150,plain,
% 4.18/4.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.51 inference(transitivity,[status(thm)],[31149, 31147])).
% 4.18/4.51 tff(31151,plain,
% 4.18/4.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))),
% 4.18/4.51 inference(quant_inst,[status(thm)],[])).
% 4.18/4.51 tff(31152,plain,
% 4.18/4.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31151, 31150])).
% 4.18/4.51 tff(31153,plain,
% 4.18/4.51 (~b(s(z), s(s(z)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[31152, 144, 134, 1398, 123, 133])).
% 4.18/4.51 tff(31154,plain,
% 4.18/4.51 (~b(s(z), s(s(elem!1)))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31153, 27204])).
% 4.18/4.51 tff(31155,plain,
% 4.18/4.51 (r(s(z), s(s(elem!1)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[5484, 31154])).
% 4.18/4.51 tff(31156,plain,
% 4.18/4.51 (r(s(z), s(s(z)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[22807, 31155, 8677])).
% 4.18/4.51 tff(31157,plain,
% 4.18/4.51 (((~![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)), s(z))) | (~r(s(z), s(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(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31158,plain,
% 4.18/4.51 (((~r(s(z), s(s(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(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31159,plain,
% 4.18/4.51 (((~![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(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(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31158])).
% 4.18/4.51 tff(31160,plain,
% 4.18/4.51 (((~![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(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(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 4.18/4.51 inference(transitivity,[status(thm)],[31159, 31157])).
% 4.18/4.51 tff(31161,plain,
% 4.18/4.51 ((~![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(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 4.18/4.51 inference(quant_inst,[status(thm)],[])).
% 4.18/4.51 tff(31162,plain,
% 4.18/4.51 ((~![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)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31161, 31160])).
% 4.18/4.51 tff(31163,plain,
% 4.18/4.51 (~r(elem!1, s(s(z)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[31162, 333, 722, 31047, 31156])).
% 4.18/4.51 tff(31164,plain,
% 4.18/4.51 (~r(elem!1, s(s(elem!1)))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31163, 22710])).
% 4.18/4.51 tff(31165,plain,
% 4.18/4.51 (b(elem!1, s(s(elem!1)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[2522, 31164, 22705])).
% 4.18/4.51 tff(31166,plain,
% 4.18/4.51 (b(elem!1, s(s(z)))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31165, 22760])).
% 4.18/4.51 tff(31167,plain,
% 4.18/4.51 (((~![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)), 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(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31168,plain,
% 4.18/4.51 (((~r(s(z), s(s(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31169,plain,
% 4.18/4.51 (((~![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(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31168])).
% 4.18/4.51 tff(31170,plain,
% 4.18/4.51 (((~![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(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(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 4.18/4.51 inference(transitivity,[status(thm)],[31169, 31167])).
% 4.18/4.51 tff(31171,plain,
% 4.18/4.51 ((~![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(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 4.18/4.51 inference(quant_inst,[status(thm)],[])).
% 4.18/4.51 tff(31172,plain,
% 4.18/4.51 ((~![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)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31171, 31170])).
% 4.18/4.51 tff(31173,plain,
% 4.18/4.51 (~r(s(s(z)), elem!1)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[31172, 333, 722, 31047, 31156])).
% 4.18/4.51 tff(31174,plain,
% 4.18/4.51 (b(s(s(z)), elem!1)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[7970, 31173, 26795])).
% 4.18/4.51 tff(31175,plain,
% 4.18/4.51 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[26868, 144, 133, 31174, 31166])).
% 4.18/4.51 tff(31176,plain,
% 4.18/4.51 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31175, 23138])).
% 4.18/4.51 tff(31177,plain,
% 4.18/4.51 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[2758, 31176, 23135])).
% 4.18/4.51 tff(31178,plain,
% 4.18/4.51 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31177, 26862])).
% 4.18/4.51 tff(31179,plain,
% 4.18/4.51 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31180,plain,
% 4.18/4.51 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31181,plain,
% 4.18/4.51 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31180])).
% 4.18/4.51 tff(31182,plain,
% 4.18/4.51 (((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(transitivity,[status(thm)],[31181, 31179])).
% 4.18/4.51 tff(31183,plain,
% 4.18/4.51 ((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.18/4.51 inference(quant_inst,[status(thm)],[])).
% 4.18/4.51 tff(31184,plain,
% 4.18/4.51 ((~![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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31183, 31182])).
% 4.18/4.51 tff(31185,plain,
% 4.18/4.51 (~r(elem!1, s(s(s(z))))),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[31184, 333, 2323, 6107, 31178])).
% 4.18/4.51 tff(31186,plain,
% 4.18/4.51 (~r(z, s(s(s(z))))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31185, 31146])).
% 4.18/4.51 tff(31187,plain,
% 4.18/4.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31188,plain,
% 4.18/4.51 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31189,plain,
% 4.18/4.51 (((~![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(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31188])).
% 4.18/4.51 tff(31190,plain,
% 4.18/4.51 (((~![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(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.51 inference(transitivity,[status(thm)],[31189, 31187])).
% 4.18/4.51 tff(31191,plain,
% 4.18/4.51 ((~![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(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 4.18/4.51 inference(quant_inst,[status(thm)],[])).
% 4.18/4.51 tff(31192,plain,
% 4.18/4.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31191, 31190])).
% 4.18/4.51 tff(31193,plain,
% 4.18/4.51 (~r(s(s(s(z))), elem!1)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[31192, 333, 2323, 6107, 31178])).
% 4.18/4.51 tff(31194,plain,
% 4.18/4.51 (~r(s(s(s(z))), z)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[22912, 31193, 18019])).
% 4.18/4.51 tff(31195,plain,
% 4.18/4.51 (b(s(s(s(z))), z)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[396, 31194])).
% 4.18/4.51 tff(31196,plain,
% 4.18/4.51 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 4.18/4.51 inference(monotonicity,[status(thm)],[18019])).
% 4.18/4.51 tff(31197,plain,
% 4.18/4.51 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.18/4.51 inference(symmetry,[status(thm)],[31196])).
% 4.18/4.51 tff(31198,plain,
% 4.18/4.51 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.18/4.51 inference(transitivity,[status(thm)],[23093, 31197])).
% 4.18/4.51 tff(31199,plain,
% 4.18/4.51 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 4.18/4.51 inference(monotonicity,[status(thm)],[31198])).
% 4.18/4.51 tff(31200,plain,
% 4.18/4.51 (~r(s(s(elem!1)), z)),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31173, 31199])).
% 4.18/4.51 tff(31201,plain,
% 4.18/4.51 (b(s(s(elem!1)), z)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[5509, 31200])).
% 4.18/4.51 tff(31202,plain,
% 4.18/4.51 (b(s(s(s(z))), elem!1)),
% 4.18/4.51 inference(unit_resolution,[status(thm)],[704, 31193, 22766])).
% 4.18/4.51 tff(31203,plain,
% 4.18/4.51 (b(s(s(elem!1)), elem!1)),
% 4.18/4.51 inference(modus_ponens,[status(thm)],[31174, 27325])).
% 4.18/4.51 tff(31204,plain,
% 4.18/4.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 4.18/4.51 inference(rewrite,[status(thm)],[])).
% 4.18/4.51 tff(31205,plain,
% 4.18/4.51 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31206,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 4.18/4.52 inference(monotonicity,[status(thm)],[31205])).
% 4.18/4.52 tff(31207,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 4.18/4.52 inference(transitivity,[status(thm)],[31206, 31204])).
% 4.18/4.52 tff(31208,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 4.18/4.52 inference(quant_inst,[status(thm)],[])).
% 4.18/4.52 tff(31209,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31208, 31207])).
% 4.18/4.52 tff(31210,plain,
% 4.18/4.52 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31209, 144, 285, 2812, 4367, 2726])).
% 4.18/4.52 tff(31211,plain,
% 4.18/4.52 (r(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[1301, 31210, 1184])).
% 4.18/4.52 tff(31212,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 4.18/4.52 tff(31213,plain,
% 4.18/4.52 (((~![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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(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(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31214,plain,
% 4.18/4.52 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31215,plain,
% 4.18/4.52 (((~![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(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 4.18/4.52 inference(monotonicity,[status(thm)],[31214])).
% 4.18/4.52 tff(31216,plain,
% 4.18/4.52 (((~![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(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 4.18/4.52 inference(transitivity,[status(thm)],[31215, 31213])).
% 4.18/4.52 tff(31217,plain,
% 4.18/4.52 ((~![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(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.18/4.52 inference(quant_inst,[status(thm)],[])).
% 4.18/4.52 tff(31218,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31217, 31216])).
% 4.18/4.52 tff(31219,plain,
% 4.18/4.52 ($false),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31218, 333, 2737, 31212, 1686, 4571])).
% 4.18/4.52 tff(31220,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.52 tff(31221,plain,
% 4.18/4.52 (~r(s(elem!1), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31220, 31211, 1686, 2737])).
% 4.18/4.52 tff(31222,plain,
% 4.18/4.52 (~b(s(elem!1), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[6380, 144, 451, 2812, 4972])).
% 4.18/4.52 tff(31223,plain,
% 4.18/4.52 ($false),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[2860, 44, 31222, 8456, 31221])).
% 4.18/4.52 tff(31224,plain,((~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.52 tff(31225,plain,
% 4.18/4.52 (~r(s(elem!1), s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31224, 31195, 451, 31046, 31165, 1184, 31203, 31202, 31201, 28207])).
% 4.18/4.52 tff(31226,plain,
% 4.18/4.52 (b(s(elem!1), s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[965, 31225, 31031])).
% 4.18/4.52 tff(31227,plain,
% 4.18/4.52 (~b(z, s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[1802, 31226, 491, 31195])).
% 4.18/4.52 tff(31228,plain,
% 4.18/4.52 (r(z, s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[619, 31227])).
% 4.18/4.52 tff(31229,plain,
% 4.18/4.52 ($false),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31228, 31186])).
% 4.18/4.52 tff(31230,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.52 tff(31231,plain,
% 4.18/4.52 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31230, 31145, 31020, 863, 2323, 31144, 8677, 133, 31041, 31039, 123, 304])).
% 4.18/4.52 tff(31232,plain,
% 4.18/4.52 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[1451, 31231])).
% 4.18/4.52 tff(31233,plain,
% 4.18/4.52 (~b(z, s(z))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[7093, 489, 304, 286])).
% 4.18/4.52 tff(31234,plain,
% 4.18/4.52 (r(z, s(z))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[372, 31233])).
% 4.18/4.52 tff(31235,plain,
% 4.18/4.52 (~b(z, s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[21435, 283, 304, 286, 489])).
% 4.18/4.52 tff(31236,plain,
% 4.18/4.52 (r(z, s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[619, 31235])).
% 4.18/4.52 tff(31237,plain,
% 4.18/4.52 (~r(s(z), s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[1519, 31236, 707, 31234])).
% 4.18/4.52 tff(31238,plain,
% 4.18/4.52 (b(s(z), s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[172, 31237])).
% 4.18/4.52 tff(31239,plain,
% 4.18/4.52 (~b(s(s(s(z))), s(z))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[846, 31238, 304, 283])).
% 4.18/4.52 tff(31240,plain,
% 4.18/4.52 (r(s(s(s(z))), s(z))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[2794, 31239])).
% 4.18/4.52 tff(31241,plain,
% 4.18/4.52 (~r(s(z), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[5732, 31240, 31236, 31234])).
% 4.18/4.52 tff(31242,plain,
% 4.18/4.52 (b(s(z), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[5484, 31241])).
% 4.18/4.52 tff(31243,plain,
% 4.18/4.52 (b(s(z), s(s(z)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[22799, 31242, 8677])).
% 4.18/4.52 tff(31244,plain,
% 4.18/4.52 (r(elem!1, s(s(s(elem!1))))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31236, 23015])).
% 4.18/4.52 tff(31245,plain,
% 4.18/4.52 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[23075, 31239, 8677])).
% 4.18/4.52 tff(31246,plain,
% 4.18/4.52 (r(s(s(s(elem!1))), s(elem!1))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[4697, 31245, 23041])).
% 4.18/4.52 tff(31247,plain,
% 4.18/4.52 (r(s(s(s(elem!1))), s(z))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[23064, 31246, 8677])).
% 4.18/4.52 tff(31248,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31249,plain,
% 4.18/4.52 (((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31250,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.18/4.52 inference(monotonicity,[status(thm)],[31249])).
% 4.18/4.52 tff(31251,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.18/4.52 inference(transitivity,[status(thm)],[31250, 31248])).
% 4.18/4.52 tff(31252,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.52 inference(quant_inst,[status(thm)],[])).
% 4.18/4.52 tff(31253,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31252, 31251])).
% 4.18/4.52 tff(31254,plain,
% 4.18/4.52 ($false),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31253, 144, 134, 123, 133, 22783, 22784])).
% 4.18/4.52 tff(31255,plain,((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.52 tff(31256,plain,
% 4.18/4.52 (~b(elem!1, s(s(z)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31255, 31243, 123, 133, 134])).
% 4.18/4.52 tff(31257,plain,
% 4.18/4.52 (~b(elem!1, s(s(elem!1)))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31256, 23021])).
% 4.18/4.52 tff(31258,plain,
% 4.18/4.52 (r(elem!1, s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[2522, 31257, 22705])).
% 4.18/4.52 tff(31259,plain,
% 4.18/4.52 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[23051, 31258, 31247, 31244])).
% 4.18/4.52 tff(31260,plain,
% 4.18/4.52 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[4311, 31259, 22826])).
% 4.18/4.52 tff(31261,plain,
% 4.18/4.52 (b(s(s(z)), s(s(s(z))))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[18122, 31260, 8677])).
% 4.18/4.52 tff(31262,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31263,plain,
% 4.18/4.52 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.52 inference(rewrite,[status(thm)],[])).
% 4.18/4.52 tff(31264,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 4.18/4.52 inference(monotonicity,[status(thm)],[31263])).
% 4.18/4.52 tff(31265,plain,
% 4.18/4.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.52 inference(transitivity,[status(thm)],[31264, 31262])).
% 4.18/4.52 tff(31266,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.52 inference(quant_inst,[status(thm)],[])).
% 4.18/4.52 tff(31267,plain,
% 4.18/4.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31266, 31265])).
% 4.18/4.52 tff(31268,plain,
% 4.18/4.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[31267, 144, 31261, 283, 304, 31243])).
% 4.18/4.52 tff(31269,plain,
% 4.18/4.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31268, 23138])).
% 4.18/4.52 tff(31270,plain,
% 4.18/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.52 inference(unit_resolution,[status(thm)],[2758, 31269, 23135])).
% 4.18/4.52 tff(31271,plain,
% 4.18/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31270, 26862])).
% 4.18/4.52 tff(31272,plain,
% 4.18/4.52 (r(z, s(s(z)))),
% 4.18/4.52 inference(modus_ponens,[status(thm)],[31258, 23018])).
% 4.18/4.53 tff(31273,plain,
% 4.18/4.53 (r(elem!1, s(s(z)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31272, 23017])).
% 4.18/4.53 tff(31274,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31275,plain,
% 4.18/4.53 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31276,plain,
% 4.18/4.53 (((~![X0: $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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.53 inference(monotonicity,[status(thm)],[31275])).
% 4.18/4.53 tff(31277,plain,
% 4.18/4.53 (((~![X0: $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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(transitivity,[status(thm)],[31276, 31274])).
% 4.18/4.53 tff(31278,plain,
% 4.18/4.53 ((~![X0: $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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(quant_inst,[status(thm)],[])).
% 4.18/4.53 tff(31279,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31278, 31277])).
% 4.18/4.53 tff(31280,plain,
% 4.18/4.53 ($false),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31279, 333, 2671, 2323, 31273, 31271])).
% 4.18/4.53 tff(31281,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.53 tff(31282,plain,
% 4.18/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31281, 707, 2323, 8677, 304, 123, 133, 134, 2671, 286, 489])).
% 4.18/4.53 tff(31283,plain,
% 4.18/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[249, 31282])).
% 4.18/4.53 tff(31284,plain,
% 4.18/4.53 (((~![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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, 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(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31285,plain,
% 4.18/4.53 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31286,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.53 inference(monotonicity,[status(thm)],[31285])).
% 4.18/4.53 tff(31287,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(transitivity,[status(thm)],[31286, 31284])).
% 4.18/4.53 tff(31288,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 4.18/4.53 inference(quant_inst,[status(thm)],[])).
% 4.18/4.53 tff(31289,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31288, 31287])).
% 4.18/4.53 tff(31290,plain,
% 4.18/4.53 ($false),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31289, 333, 707, 2323, 31283, 6107])).
% 4.18/4.53 tff(31291,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.53 tff(31292,plain,
% 4.18/4.53 (~r(s(s(s(z))), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31291, 31039, 31144, 8677, 304, 123, 133, 2323, 31232, 286, 29043])).
% 4.18/4.53 tff(31293,plain,
% 4.18/4.53 (b(s(s(s(z))), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[704, 31292, 22766])).
% 4.18/4.53 tff(31294,plain,
% 4.18/4.53 (~r(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[22912, 31292, 18019])).
% 4.18/4.53 tff(31295,plain,
% 4.18/4.53 (b(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[396, 31294])).
% 4.18/4.53 tff(31296,plain,
% 4.18/4.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[11642, 31295, 31019, 31144, 31232])).
% 4.18/4.53 tff(31297,plain,
% 4.18/4.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[249, 31296])).
% 4.18/4.53 tff(31298,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31299,plain,
% 4.18/4.53 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31300,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 4.18/4.53 inference(monotonicity,[status(thm)],[31299])).
% 4.18/4.53 tff(31301,plain,
% 4.18/4.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.53 inference(transitivity,[status(thm)],[31300, 31298])).
% 4.18/4.53 tff(31302,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(quant_inst,[status(thm)],[])).
% 4.18/4.53 tff(31303,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31302, 31301])).
% 4.18/4.53 tff(31304,plain,
% 4.18/4.53 (~b(s(z), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31303, 144, 31039, 123, 31297, 31293])).
% 4.18/4.53 tff(31305,plain,
% 4.18/4.53 (r(s(z), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[172, 31304])).
% 4.18/4.53 tff(31306,plain,
% 4.18/4.53 (~b(z, s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[21435, 31297, 304, 286, 29043])).
% 4.18/4.53 tff(31307,plain,
% 4.18/4.53 (r(z, s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[619, 31306])).
% 4.18/4.53 tff(31308,plain,
% 4.18/4.53 (r(elem!1, s(s(s(z))))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31307, 22983])).
% 4.18/4.53 tff(31309,plain,
% 4.18/4.53 ($false),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[28488, 333, 31308, 31041, 31305, 31144])).
% 4.18/4.53 tff(31310,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.53 tff(31311,plain,
% 4.18/4.53 (r(s(z), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31310, 304, 123, 286, 8677, 133, 2323, 706])).
% 4.18/4.53 tff(31312,plain,
% 4.18/4.53 (r(s(z), z)),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31311, 22732])).
% 4.18/4.53 tff(31313,plain,
% 4.18/4.53 (~r(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[13781, 31312, 123, 31019, 304])).
% 4.18/4.53 tff(31314,plain,
% 4.18/4.53 (b(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[396, 31313])).
% 4.18/4.53 tff(31315,plain,
% 4.18/4.53 (r(s(elem!1), elem!1)),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31311, 18035])).
% 4.18/4.53 tff(31316,plain,
% 4.18/4.53 (~r(s(s(z)), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[28548, 31047, 2323, 409])).
% 4.18/4.53 tff(31317,plain,
% 4.18/4.53 (b(s(s(z)), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[7970, 31316, 26795])).
% 4.18/4.53 tff(31318,plain,
% 4.18/4.53 (~b(s(z), s(s(z)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[27170, 144, 1398, 123, 9739])).
% 4.18/4.53 tff(31319,plain,
% 4.18/4.53 (~b(s(z), s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[22799, 31318, 8677])).
% 4.18/4.53 tff(31320,plain,
% 4.18/4.53 (r(s(z), s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[5484, 31319])).
% 4.18/4.53 tff(31321,plain,
% 4.18/4.53 (r(s(elem!1), s(s(elem!1)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31320, 27203])).
% 4.18/4.53 tff(31322,plain,
% 4.18/4.53 (~r(elem!1, s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[5242, 31321, 435, 2737])).
% 4.18/4.53 tff(31323,plain,
% 4.18/4.53 (b(elem!1, s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[2522, 31322, 22705])).
% 4.18/4.53 tff(31324,plain,
% 4.18/4.53 (b(elem!1, s(s(z)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31323, 22760])).
% 4.18/4.53 tff(31325,plain,
% 4.18/4.53 ($false),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[26868, 144, 133, 7928, 9739, 31324])).
% 4.18/4.53 tff(31326,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.53 tff(31327,plain,
% 4.18/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31326, 31317, 133, 8677, 28930, 31046, 1398, 123])).
% 4.18/4.53 tff(31328,plain,
% 4.18/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31327, 23138])).
% 4.18/4.53 tff(31329,plain,
% 4.18/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[2758, 31328, 23135])).
% 4.18/4.53 tff(31330,plain,
% 4.18/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31329, 26862])).
% 4.18/4.53 tff(31331,plain,
% 4.18/4.53 (~r(elem!1, s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[6233, 31329, 2323, 31046])).
% 4.18/4.53 tff(31332,plain,
% 4.18/4.53 (b(elem!1, s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[2522, 31331, 22705])).
% 4.18/4.53 tff(31333,plain,
% 4.18/4.53 (b(elem!1, s(s(z)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31332, 22760])).
% 4.18/4.53 tff(31334,plain,
% 4.18/4.53 (r(s(z), z)),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[409, 22732])).
% 4.18/4.53 tff(31335,plain,
% 4.18/4.53 (~r(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[13781, 31334, 123, 31019, 304])).
% 4.18/4.53 tff(31336,plain,
% 4.18/4.53 (b(s(s(s(z))), z)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[396, 31335])).
% 4.18/4.53 tff(31337,plain,
% 4.18/4.53 (b(s(s(s(z))), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[26887, 31336, 18019])).
% 4.18/4.53 tff(31338,plain,
% 4.18/4.53 (~b(s(s(s(z))), s(s(z)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[26978, 144, 31337, 31317, 31333])).
% 4.18/4.53 tff(31339,plain,
% 4.18/4.53 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31338, 22812])).
% 4.18/4.53 tff(31340,plain,
% 4.18/4.53 (r(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[1301, 31339, 1184])).
% 4.18/4.53 tff(31341,plain,
% 4.18/4.53 (r(s(s(s(z))), s(s(z)))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31340, 22809])).
% 4.18/4.53 tff(31342,plain,
% 4.18/4.53 (~r(elem!1, s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31184, 333, 2323, 6107, 31330])).
% 4.18/4.53 tff(31343,plain,
% 4.18/4.53 (b(elem!1, s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[1538, 31342, 22768])).
% 4.18/4.53 tff(31344,plain,
% 4.18/4.53 (~b(s(s(z)), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31098, 144, 31343, 31337, 31317])).
% 4.18/4.53 tff(31345,plain,
% 4.18/4.53 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[18122, 31344, 8677])).
% 4.18/4.53 tff(31346,plain,
% 4.18/4.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[4311, 31345, 22826])).
% 4.18/4.53 tff(31347,plain,
% 4.18/4.53 (r(s(s(z)), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[18132, 31346, 8677])).
% 4.18/4.53 tff(31348,plain,
% 4.18/4.53 (((~![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(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), 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(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31349,plain,
% 4.18/4.53 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(rewrite,[status(thm)],[])).
% 4.18/4.53 tff(31350,plain,
% 4.18/4.53 (((~![X0: $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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.53 inference(monotonicity,[status(thm)],[31349])).
% 4.18/4.53 tff(31351,plain,
% 4.18/4.53 (((~![X0: $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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(transitivity,[status(thm)],[31350, 31348])).
% 4.18/4.53 tff(31352,plain,
% 4.18/4.53 ((~![X0: $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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.53 inference(quant_inst,[status(thm)],[])).
% 4.18/4.53 tff(31353,plain,
% 4.18/4.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31352, 31351])).
% 4.18/4.53 tff(31354,plain,
% 4.18/4.53 ($false),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31353, 333, 6107, 31347, 31341, 31330])).
% 4.18/4.53 tff(31355,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.53 tff(31356,plain,
% 4.18/4.53 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[31355, 31144, 8677, 863, 2323, 133, 123, 31311, 304])).
% 4.18/4.53 tff(31357,plain,
% 4.18/4.53 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[1451, 31356])).
% 4.18/4.53 tff(31358,plain,
% 4.18/4.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[11642, 31357, 31019, 31144, 31314])).
% 4.18/4.53 tff(31359,plain,
% 4.18/4.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[249, 31358])).
% 4.18/4.53 tff(31360,plain,
% 4.18/4.53 (~r(z, s(elem!1))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[26913, 31359, 304, 31144, 8677, 31311, 31315, 286, 31314])).
% 4.18/4.53 tff(31361,plain,
% 4.18/4.53 (b(z, s(elem!1))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[583, 31360])).
% 4.18/4.53 tff(31362,plain,
% 4.18/4.53 (b(elem!1, s(z))),
% 4.18/4.53 inference(modus_ponens,[status(thm)],[31361, 31016])).
% 4.18/4.53 tff(31363,plain,
% 4.18/4.53 (b(s(s(s(z))), elem!1)),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[26887, 31314, 18019])).
% 4.18/4.53 tff(31364,plain,
% 4.18/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.53 inference(unit_resolution,[status(thm)],[11526, 144, 305, 133, 304, 4367])).
% 4.18/4.53 tff(31365,plain,
% 4.18/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[249, 31364])).
% 4.18/4.54 tff(31366,plain,
% 4.18/4.54 (~r(s(s(z)), elem!1)),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31082, 333, 2671, 2323, 31365])).
% 4.18/4.54 tff(31367,plain,
% 4.18/4.54 (b(s(s(z)), elem!1)),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[7970, 31366, 26795])).
% 4.18/4.54 tff(31368,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31369,plain,
% 4.18/4.54 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31370,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31369])).
% 4.18/4.54 tff(31371,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.18/4.54 inference(transitivity,[status(thm)],[31370, 31368])).
% 4.18/4.54 tff(31372,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.18/4.54 inference(quant_inst,[status(thm)],[])).
% 4.18/4.54 tff(31373,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31372, 31371])).
% 4.18/4.54 tff(31374,plain,
% 4.18/4.54 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31373, 144, 305, 133, 304, 31367])).
% 4.18/4.54 tff(31375,plain,
% 4.18/4.54 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31374, 23138])).
% 4.18/4.54 tff(31376,plain,
% 4.18/4.54 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[2758, 31375, 23135])).
% 4.18/4.54 tff(31377,plain,
% 4.18/4.54 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31376, 26862])).
% 4.18/4.54 tff(31378,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31379,plain,
% 4.18/4.54 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31380,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31379])).
% 4.18/4.54 tff(31381,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(transitivity,[status(thm)],[31380, 31378])).
% 4.18/4.54 tff(31382,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 4.18/4.54 inference(quant_inst,[status(thm)],[])).
% 4.18/4.54 tff(31383,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31382, 31381])).
% 4.18/4.54 tff(31384,plain,
% 4.18/4.54 (~r(elem!1, s(s(z)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31383, 333, 2671, 2323, 31365])).
% 4.18/4.54 tff(31385,plain,
% 4.18/4.54 (~r(elem!1, s(s(elem!1)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31384, 22710])).
% 4.18/4.54 tff(31386,plain,
% 4.18/4.54 (b(elem!1, s(s(elem!1)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[2522, 31385, 22705])).
% 4.18/4.54 tff(31387,plain,
% 4.18/4.54 (b(elem!1, s(s(z)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31386, 22760])).
% 4.18/4.54 tff(31388,plain,
% 4.18/4.54 (~b(s(s(s(z))), s(s(z)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[26978, 144, 4367, 31367, 31387])).
% 4.18/4.54 tff(31389,plain,
% 4.18/4.54 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31388, 22812])).
% 4.18/4.54 tff(31390,plain,
% 4.18/4.54 (r(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[1301, 31389, 1184])).
% 4.18/4.54 tff(31391,plain,
% 4.18/4.54 (r(s(s(s(z))), s(s(z)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31390, 22809])).
% 4.18/4.54 tff(31392,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), 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(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31393,plain,
% 4.18/4.54 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31394,plain,
% 4.18/4.54 (((~![X0: $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(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31393])).
% 4.18/4.54 tff(31395,plain,
% 4.18/4.54 (((~![X0: $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(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(transitivity,[status(thm)],[31394, 31392])).
% 4.18/4.54 tff(31396,plain,
% 4.18/4.54 ((~![X0: $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(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.54 inference(quant_inst,[status(thm)],[])).
% 4.18/4.54 tff(31397,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31396, 31395])).
% 4.18/4.54 tff(31398,plain,
% 4.18/4.54 ($false),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31397, 333, 2671, 31365, 31391, 31377])).
% 4.18/4.54 tff(31399,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.54 tff(31400,plain,
% 4.18/4.54 (~b(elem!1, s(z))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31399, 31357, 863, 31363, 8677, 133, 304, 2323])).
% 4.18/4.54 tff(31401,plain,
% 4.18/4.54 ($false),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31400, 31362])).
% 4.18/4.54 tff(31402,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.54 tff(31403,plain,
% 4.18/4.54 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31402, 31005, 30970, 30972, 30969, 50, 31014])).
% 4.18/4.54 tff(31404,plain,
% 4.18/4.54 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[319, 31403])).
% 4.18/4.54 tff(31405,plain,
% 4.18/4.54 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31012])).
% 4.18/4.54 tff(31406,plain,
% 4.18/4.54 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(symmetry,[status(thm)],[31405])).
% 4.18/4.54 tff(31407,plain,
% 4.18/4.54 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[30969, 31406])).
% 4.18/4.54 tff(31408,plain,
% 4.18/4.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[28782, 31039, 133, 322, 2323, 18019, 27205])).
% 4.18/4.54 tff(31409,plain,
% 4.18/4.54 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[29967, 31039, 8677, 133, 322, 2323])).
% 4.18/4.54 tff(31410,plain,
% 4.18/4.54 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[1451, 31409])).
% 4.18/4.54 tff(31411,plain,
% 4.18/4.54 (~b(s(elem!1), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[29328, 23185, 133, 27211, 451])).
% 4.18/4.54 tff(31412,plain,
% 4.18/4.54 (r(s(elem!1), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[965, 31411, 31031])).
% 4.18/4.54 tff(31413,plain,
% 4.18/4.54 (r(s(z), s(s(s(z))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31412, 27206])).
% 4.18/4.54 tff(31414,plain,
% 4.18/4.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[22780, 707, 353, 322])).
% 4.18/4.54 tff(31415,plain,
% 4.18/4.54 (~b(s(s(z)), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[7952, 31414, 1398, 7927])).
% 4.18/4.54 tff(31416,plain,
% 4.18/4.54 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[18122, 31415, 8677])).
% 4.18/4.54 tff(31417,plain,
% 4.18/4.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[4311, 31416, 22826])).
% 4.18/4.54 tff(31418,plain,
% 4.18/4.54 (r(s(s(z)), s(s(s(z))))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[18132, 31417, 8677])).
% 4.18/4.54 tff(31419,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), 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))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31420,plain,
% 4.18/4.54 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31421,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), 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(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31420])).
% 4.18/4.54 tff(31422,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), 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(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.54 inference(transitivity,[status(thm)],[31421, 31419])).
% 4.18/4.54 tff(31423,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 4.18/4.54 inference(quant_inst,[status(thm)],[])).
% 4.18/4.54 tff(31424,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31423, 31422])).
% 4.18/4.54 tff(31425,plain,
% 4.18/4.54 ($false),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31424, 333, 707, 353, 31418, 22831])).
% 4.18/4.54 tff(31426,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.54 tff(31427,plain,
% 4.18/4.54 (~r(s(s(s(z))), elem!1)),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31426, 31413, 22831, 8677, 1398, 7927, 322])).
% 4.18/4.54 tff(31428,plain,
% 4.18/4.54 (b(s(s(s(z))), elem!1)),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[704, 31427, 22766])).
% 4.18/4.54 tff(31429,plain,
% 4.18/4.54 (~b(s(s(s(z))), s(s(z)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[30073, 144, 1398, 133, 23185, 31428])).
% 4.18/4.54 tff(31430,plain,
% 4.18/4.54 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31429, 22812])).
% 4.18/4.54 tff(31431,plain,
% 4.18/4.54 (r(s(s(s(z))), s(s(elem!1)))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[1301, 31430, 1184])).
% 4.18/4.54 tff(31432,plain,
% 4.18/4.54 (r(s(s(s(z))), s(s(z)))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31431, 22809])).
% 4.18/4.54 tff(31433,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31434,plain,
% 4.18/4.54 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(rewrite,[status(thm)],[])).
% 4.18/4.54 tff(31435,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.54 inference(monotonicity,[status(thm)],[31434])).
% 4.18/4.54 tff(31436,plain,
% 4.18/4.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.54 inference(transitivity,[status(thm)],[31435, 31433])).
% 4.18/4.54 tff(31437,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.18/4.54 inference(quant_inst,[status(thm)],[])).
% 4.18/4.54 tff(31438,plain,
% 4.18/4.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.54 inference(modus_ponens,[status(thm)],[31437, 31436])).
% 4.18/4.54 tff(31439,plain,
% 4.18/4.54 (~b(s(s(s(z))), s(z))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[31438, 144, 123, 133, 23185, 31428])).
% 4.18/4.54 tff(31440,plain,
% 4.18/4.54 (r(s(s(s(z))), s(z))),
% 4.18/4.54 inference(unit_resolution,[status(thm)],[2794, 31439])).
% 4.18/4.54 tff(31441,plain,
% 4.18/4.54 (((~![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(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31442,plain,
% 4.18/4.55 ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.18/4.55 inference(quant_inst,[status(thm)],[])).
% 4.18/4.55 tff(31443,plain,
% 4.18/4.55 ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31442, 31441])).
% 4.18/4.55 tff(31444,plain,
% 4.18/4.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31443, 333, 31440, 31413, 322])).
% 4.18/4.55 tff(31445,plain,
% 4.18/4.55 (~b(s(s(z)), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[7952, 31444, 1398, 7927])).
% 4.18/4.55 tff(31446,plain,
% 4.18/4.55 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[18122, 31445, 8677])).
% 4.18/4.55 tff(31447,plain,
% 4.18/4.55 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[4311, 31446, 22826])).
% 4.18/4.55 tff(31448,plain,
% 4.18/4.55 (r(s(s(z)), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[18132, 31447, 8677])).
% 4.18/4.55 tff(31449,plain,
% 4.18/4.55 (((~![X0: $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(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), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31450,plain,
% 4.18/4.55 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31451,plain,
% 4.18/4.55 (((~![X0: $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(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31450])).
% 4.18/4.55 tff(31452,plain,
% 4.18/4.55 (((~![X0: $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(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.18/4.55 inference(transitivity,[status(thm)],[31451, 31449])).
% 4.18/4.55 tff(31453,plain,
% 4.18/4.55 ((~![X0: $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(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 4.18/4.55 inference(quant_inst,[status(thm)],[])).
% 4.18/4.55 tff(31454,plain,
% 4.18/4.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31453, 31452])).
% 4.18/4.55 tff(31455,plain,
% 4.18/4.55 ($false),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31454, 333, 31440, 31448, 31432, 22831])).
% 4.18/4.55 tff(31456,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.55 tff(31457,plain,
% 4.18/4.55 (~r(s(z), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31456, 31410, 8677, 31408, 863, 322, 123, 133, 31020])).
% 4.18/4.55 tff(31458,plain,
% 4.18/4.55 (~r(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22807, 31457, 8677])).
% 4.18/4.55 tff(31459,plain,
% 4.18/4.55 (b(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5484, 31458])).
% 4.18/4.55 tff(31460,plain,
% 4.18/4.55 (b(s(z), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22799, 31459, 8677])).
% 4.18/4.55 tff(31461,plain,
% 4.18/4.55 ($false),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31152, 144, 31039, 31410, 123, 133, 31460])).
% 4.18/4.55 tff(31462,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.55 tff(31463,plain,
% 4.18/4.55 (r(s(z), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31462, 30972, 50, 31005, 31404, 30969, 31014])).
% 4.18/4.55 tff(31464,plain,
% 4.18/4.55 (~r(z, s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[429, 31463, 31407, 31404])).
% 4.18/4.55 tff(31465,plain,
% 4.18/4.55 (b(z, s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[372, 31464])).
% 4.18/4.55 tff(31466,plain,
% 4.18/4.55 (b(elem!1, s(z))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31465, 31013])).
% 4.18/4.55 tff(31467,plain,
% 4.18/4.55 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[23169, 31404, 31005])).
% 4.18/4.55 tff(31468,plain,
% 4.18/4.55 (r(s(elem!1), z) <=> r(s(z), z)),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31005])).
% 4.18/4.55 tff(31469,plain,
% 4.18/4.55 (r(s(z), z) <=> r(s(elem!1), z)),
% 4.18/4.55 inference(symmetry,[status(thm)],[31468])).
% 4.18/4.55 tff(31470,plain,
% 4.18/4.55 (r(s(z), z) <=> r(s(z), elem!1)),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31012])).
% 4.18/4.55 tff(31471,plain,
% 4.18/4.55 (r(s(z), elem!1) <=> r(s(z), z)),
% 4.18/4.55 inference(symmetry,[status(thm)],[31470])).
% 4.18/4.55 tff(31472,plain,
% 4.18/4.55 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 4.18/4.55 inference(transitivity,[status(thm)],[31471, 31469])).
% 4.18/4.55 tff(31473,plain,
% 4.18/4.55 (r(s(elem!1), z)),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31463, 31472])).
% 4.18/4.55 tff(31474,plain,
% 4.18/4.55 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31005])).
% 4.18/4.55 tff(31475,plain,
% 4.18/4.55 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.18/4.55 inference(symmetry,[status(thm)],[31474])).
% 4.18/4.55 tff(31476,plain,
% 4.18/4.55 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 4.18/4.55 inference(transitivity,[status(thm)],[31013, 31475])).
% 4.18/4.55 tff(31477,plain,
% 4.18/4.55 (b(elem!1, s(elem!1))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31465, 31476])).
% 4.18/4.55 tff(31478,plain,
% 4.18/4.55 (~r(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[8191, 29948, 27205, 509])).
% 4.18/4.55 tff(31479,plain,
% 4.18/4.55 (b(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[1283, 31478, 22759])).
% 4.18/4.55 tff(31480,plain,
% 4.18/4.55 (~b(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5494, 31479, 305, 547, 29936])).
% 4.18/4.55 tff(31481,plain,
% 4.18/4.55 (r(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5484, 31480])).
% 4.18/4.55 tff(31482,plain,
% 4.18/4.55 (r(s(z), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22807, 31481, 8677])).
% 4.18/4.55 tff(31483,plain,
% 4.18/4.55 ($false),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[29965, 333, 2671, 322, 31482, 29949])).
% 4.18/4.55 tff(31484,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.55 tff(31485,plain,
% 4.18/4.55 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31484, 31404, 31005, 31466, 31477, 31473, 30972, 30969])).
% 4.18/4.55 tff(31486,plain,
% 4.18/4.55 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[1451, 31485])).
% 4.18/4.55 tff(31487,plain,
% 4.18/4.55 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31005])).
% 4.18/4.55 tff(31488,plain,
% 4.18/4.55 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 4.18/4.55 inference(symmetry,[status(thm)],[31487])).
% 4.18/4.55 tff(31489,plain,
% 4.18/4.55 (r(s(elem!1), elem!1)),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31463, 31488])).
% 4.18/4.55 tff(31490,plain,
% 4.18/4.55 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31012])).
% 4.18/4.55 tff(31491,plain,
% 4.18/4.55 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31490])).
% 4.18/4.55 tff(31492,plain,
% 4.18/4.55 (~(s(s(z)) = elem!1)),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[164, 31491])).
% 4.18/4.55 tff(31493,plain,
% 4.18/4.55 (((~![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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31494,plain,
% 4.18/4.55 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31495,plain,
% 4.18/4.55 (((~![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(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(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(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31494])).
% 4.18/4.55 tff(31496,plain,
% 4.18/4.55 (((~![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(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(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(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(transitivity,[status(thm)],[31495, 31493])).
% 4.18/4.55 tff(31497,plain,
% 4.18/4.55 ((~![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(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 4.18/4.55 inference(quant_inst,[status(thm)],[])).
% 4.18/4.55 tff(31498,plain,
% 4.18/4.55 ((~![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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31497, 31496])).
% 4.18/4.55 tff(31499,plain,
% 4.18/4.55 (~r(s(z), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31498, 333, 409, 2323, 7155])).
% 4.18/4.55 tff(31500,plain,
% 4.18/4.55 (~r(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22807, 31499, 8677])).
% 4.18/4.55 tff(31501,plain,
% 4.18/4.55 (b(s(z), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5484, 31500])).
% 4.18/4.55 tff(31502,plain,
% 4.18/4.55 (b(s(z), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22799, 31501, 8677])).
% 4.18/4.55 tff(31503,plain,
% 4.18/4.55 (r(s(s(elem!1)), elem!1)),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[7155, 23093])).
% 4.18/4.55 tff(31504,plain,
% 4.18/4.55 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(symmetry,[status(thm)],[22866])).
% 4.18/4.55 tff(31505,plain,
% 4.18/4.55 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(transitivity,[status(thm)],[22864, 31504])).
% 4.18/4.55 tff(31506,plain,
% 4.18/4.55 ((~r(s(s(z)), s(z))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31505])).
% 4.18/4.55 tff(31507,plain,
% 4.18/4.55 (~r(s(s(z)), s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[28548, 7155, 2323, 409])).
% 4.18/4.55 tff(31508,plain,
% 4.18/4.55 (~r(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31507, 31506])).
% 4.18/4.55 tff(31509,plain,
% 4.18/4.55 (b(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[1283, 31508, 22759])).
% 4.18/4.55 tff(31510,plain,
% 4.18/4.55 (~b(elem!1, s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5494, 31509, 305, 547, 31501])).
% 4.18/4.55 tff(31511,plain,
% 4.18/4.55 (r(elem!1, s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[2522, 31510, 22705])).
% 4.18/4.55 tff(31512,plain,
% 4.18/4.55 (r(z, s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[23130, 31511, 18019])).
% 4.18/4.55 tff(31513,plain,
% 4.18/4.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[10021, 31512, 31503, 31019])).
% 4.18/4.55 tff(31514,plain,
% 4.18/4.55 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[2758, 31513, 23135])).
% 4.18/4.55 tff(31515,plain,
% 4.18/4.55 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31514, 23136])).
% 4.18/4.55 tff(31516,plain,
% 4.18/4.55 ($false),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[27170, 144, 1398, 123, 31515, 31502])).
% 4.18/4.55 tff(31517,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.55 tff(31518,plain,
% 4.18/4.55 (~r(s(s(z)), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31517, 31486, 50, 31005, 31466, 31477, 31463, 30969])).
% 4.18/4.55 tff(31519,plain,
% 4.18/4.55 (b(s(s(z)), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[7970, 31518, 31492])).
% 4.18/4.55 tff(31520,plain,
% 4.18/4.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31521,plain,
% 4.18/4.55 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(rewrite,[status(thm)],[])).
% 4.18/4.55 tff(31522,plain,
% 4.18/4.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31521])).
% 4.18/4.55 tff(31523,plain,
% 4.18/4.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.55 inference(transitivity,[status(thm)],[31522, 31520])).
% 4.18/4.55 tff(31524,plain,
% 4.18/4.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 4.18/4.55 inference(quant_inst,[status(thm)],[])).
% 4.18/4.55 tff(31525,plain,
% 4.18/4.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31524, 31523])).
% 4.18/4.55 tff(31526,plain,
% 4.18/4.55 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31525, 144, 305, 1398, 123])).
% 4.18/4.55 tff(31527,plain,
% 4.18/4.55 (~b(s(s(z)), s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31526, 7928])).
% 4.18/4.55 tff(31528,plain,
% 4.18/4.55 (~b(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[18895, 31527, 8677])).
% 4.18/4.55 tff(31529,plain,
% 4.18/4.55 (r(s(s(elem!1)), s(elem!1))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[1283, 31528, 22759])).
% 4.18/4.55 tff(31530,plain,
% 4.18/4.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[5258, 31529, 524, 1686])).
% 4.18/4.55 tff(31531,plain,
% 4.18/4.55 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[2758, 31530, 23135])).
% 4.18/4.55 tff(31532,plain,
% 4.18/4.55 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31531, 23136])).
% 4.18/4.55 tff(31533,plain,
% 4.18/4.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31326, 31529, 133, 8677, 435, 7928, 1398, 123])).
% 4.18/4.55 tff(31534,plain,
% 4.18/4.55 ($false),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31533, 31532])).
% 4.18/4.55 tff(31535,plain,((~b(s(s(z)), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.55 tff(31536,plain,
% 4.18/4.55 (~r(s(elem!1), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31535, 31519, 30972, 31489, 31486, 50, 31467, 31005, 31466])).
% 4.18/4.55 tff(31537,plain,
% 4.18/4.55 (b(s(elem!1), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[965, 31536, 31011])).
% 4.18/4.55 tff(31538,plain,
% 4.18/4.55 (b(s(z), s(s(s(z))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31537, 31006])).
% 4.18/4.55 tff(31539,plain,
% 4.18/4.55 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 4.18/4.55 inference(transitivity,[status(thm)],[18024, 28637])).
% 4.18/4.55 tff(31540,plain,
% 4.18/4.55 (~r(z, s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[429, 409, 31019, 322])).
% 4.18/4.55 tff(31541,plain,
% 4.18/4.55 (b(z, s(z))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[372, 31540])).
% 4.18/4.55 tff(31542,plain,
% 4.18/4.55 (b(elem!1, s(elem!1))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31541, 31539])).
% 4.18/4.55 tff(31543,plain,
% 4.18/4.55 (b(elem!1, s(z))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31541, 18024])).
% 4.18/4.55 tff(31544,plain,
% 4.18/4.55 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31484, 322, 8677, 31543, 31542, 28297, 133, 2323])).
% 4.18/4.55 tff(31545,plain,
% 4.18/4.55 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[1451, 31544])).
% 4.18/4.55 tff(31546,plain,
% 4.18/4.55 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[8677])).
% 4.18/4.55 tff(31547,plain,
% 4.18/4.55 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 4.18/4.55 inference(symmetry,[status(thm)],[31546])).
% 4.18/4.55 tff(31548,plain,
% 4.18/4.55 ((~b(s(z), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 4.18/4.55 inference(monotonicity,[status(thm)],[31547])).
% 4.18/4.55 tff(31549,plain,
% 4.18/4.55 (~b(s(z), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[2262, 17795, 123, 23185])).
% 4.18/4.55 tff(31550,plain,
% 4.18/4.55 (~b(s(elem!1), s(s(s(z))))),
% 4.18/4.55 inference(modus_ponens,[status(thm)],[31549, 31548])).
% 4.18/4.55 tff(31551,plain,
% 4.18/4.55 (r(s(elem!1), s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[965, 31550, 31031])).
% 4.18/4.55 tff(31552,plain,
% 4.18/4.55 (~b(s(s(z)), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[31535, 31551, 133, 28930, 1398, 123, 524, 8677, 305])).
% 4.18/4.55 tff(31553,plain,
% 4.18/4.55 (r(s(s(z)), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[7970, 31552, 26795])).
% 4.18/4.55 tff(31554,plain,
% 4.18/4.55 (~r(s(s(s(z))), elem!1)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[30355, 31553, 2323, 23035])).
% 4.18/4.55 tff(31555,plain,
% 4.18/4.55 (~r(s(s(s(z))), z)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[22912, 31554, 18019])).
% 4.18/4.55 tff(31556,plain,
% 4.18/4.55 (b(s(s(s(z))), z)),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[396, 31555])).
% 4.18/4.55 tff(31557,plain,
% 4.18/4.55 (~b(z, s(s(s(z))))),
% 4.18/4.55 inference(unit_resolution,[status(thm)],[294, 31556, 286, 17795])).
% 4.18/4.55 tff(31558,plain,
% 4.18/4.56 (r(z, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[619, 31557])).
% 4.18/4.56 tff(31559,plain,
% 4.18/4.56 (r(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31558, 22983])).
% 4.18/4.56 tff(31560,plain,
% 4.18/4.56 (r(s(z), s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[172, 31549])).
% 4.18/4.56 tff(31561,plain,
% 4.18/4.56 (b(s(s(s(z))), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[704, 31554, 22766])).
% 4.18/4.56 tff(31562,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31563,plain,
% 4.18/4.56 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31564,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31563])).
% 4.18/4.56 tff(31565,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(transitivity,[status(thm)],[31564, 31562])).
% 4.18/4.56 tff(31566,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 4.18/4.56 inference(quant_inst,[status(thm)],[])).
% 4.18/4.56 tff(31567,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31566, 31565])).
% 4.18/4.56 tff(31568,plain,
% 4.18/4.56 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31567, 144, 305, 123, 23185])).
% 4.18/4.56 tff(31569,plain,
% 4.18/4.56 (~b(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31568, 31561])).
% 4.18/4.56 tff(31570,plain,
% 4.18/4.56 (r(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[2794, 31569])).
% 4.18/4.56 tff(31571,plain,
% 4.18/4.56 (~r(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[11876, 31570, 409, 31560])).
% 4.18/4.56 tff(31572,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31571, 31559])).
% 4.18/4.56 tff(31573,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~(s(elem!1) = s(z))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31574,plain,
% 4.18/4.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31573, 7927, 286, 31543, 123, 2323, 133, 31545, 27205, 8677, 409])).
% 4.18/4.56 tff(31575,plain,
% 4.18/4.56 (~r(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[20837, 31574, 322, 31334])).
% 4.18/4.56 tff(31576,plain,
% 4.18/4.56 (b(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[2794, 31575])).
% 4.18/4.56 tff(31577,plain,
% 4.18/4.56 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31567, 144, 31543, 123, 23185])).
% 4.18/4.56 tff(31578,plain,
% 4.18/4.56 (~b(s(s(s(z))), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31577, 31576])).
% 4.18/4.56 tff(31579,plain,
% 4.18/4.56 (~b(s(s(s(z))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[26887, 31578, 18019])).
% 4.18/4.56 tff(31580,plain,
% 4.18/4.56 (r(s(s(s(z))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[396, 31579])).
% 4.18/4.56 tff(31581,plain,
% 4.18/4.56 (~r(z, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[15762, 31580, 31019, 31574])).
% 4.18/4.56 tff(31582,plain,
% 4.18/4.56 (b(z, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[619, 31581])).
% 4.18/4.56 tff(31583,plain,
% 4.18/4.56 (b(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31582, 27350])).
% 4.18/4.56 tff(31584,plain,
% 4.18/4.56 (r(s(s(s(z))), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[704, 31578, 22766])).
% 4.18/4.56 tff(31585,plain,
% 4.18/4.56 (~r(s(z), s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[22780, 31584, 31574, 322])).
% 4.18/4.56 tff(31586,plain,
% 4.18/4.56 (b(s(z), s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[172, 31585])).
% 4.18/4.56 tff(31587,plain,
% 4.18/4.56 (~b(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[22776, 31586, 31543, 31576])).
% 4.18/4.56 tff(31588,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31587, 31583])).
% 4.18/4.56 tff(31589,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31590,plain,
% 4.18/4.56 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31589, 31404, 50, 30970, 30969, 30972, 31005, 31463])).
% 4.18/4.56 tff(31591,plain,
% 4.18/4.56 (~r(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[27257, 31590, 31404, 31463])).
% 4.18/4.56 tff(31592,plain,
% 4.18/4.56 (b(s(s(s(z))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[2794, 31591])).
% 4.18/4.56 tff(31593,plain,
% 4.18/4.56 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31012])).
% 4.18/4.56 tff(31594,plain,
% 4.18/4.56 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 4.18/4.56 inference(transitivity,[status(thm)],[31593, 2])).
% 4.18/4.56 tff(31595,plain,
% 4.18/4.56 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31594])).
% 4.18/4.56 tff(31596,plain,
% 4.18/4.56 (~(elem!1 = s(s(s(z))))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[392, 31595])).
% 4.18/4.56 tff(31597,plain,
% 4.18/4.56 (~r(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[27620, 333, 30969, 31590, 31404])).
% 4.18/4.56 tff(31598,plain,
% 4.18/4.56 (b(elem!1, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1538, 31597, 31596])).
% 4.18/4.56 tff(31599,plain,
% 4.18/4.56 (~b(s(z), s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[22776, 31598, 31466, 31592])).
% 4.18/4.56 tff(31600,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31599, 31538])).
% 4.18/4.56 tff(31601,plain,(b(z, elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31602,plain,
% 4.18/4.56 (b(z, elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31601, 30654, 54])).
% 4.18/4.56 tff(31603,plain,
% 4.18/4.56 (b(z, elem!1) <=> b(z, z)),
% 4.18/4.56 inference(monotonicity,[status(thm)],[72])).
% 4.18/4.56 tff(31604,plain,
% 4.18/4.56 (b(z, z) <=> b(z, elem!1)),
% 4.18/4.56 inference(symmetry,[status(thm)],[31603])).
% 4.18/4.56 tff(31605,plain,
% 4.18/4.56 ((~b(z, z)) <=> (~b(z, elem!1))),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31604])).
% 4.18/4.56 tff(31606,plain,
% 4.18/4.56 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 4.18/4.56 inference(quant_inst,[status(thm)],[])).
% 4.18/4.56 tff(31607,plain,
% 4.18/4.56 (~b(z, z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31606, 5880])).
% 4.18/4.56 tff(31608,plain,
% 4.18/4.56 (~b(z, elem!1)),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31607, 31605])).
% 4.18/4.56 tff(31609,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[251, 31608])).
% 4.18/4.56 tff(31610,plain,((~(elem!1 = z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31611,plain,
% 4.18/4.56 (~(elem!1 = z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31610, 31602])).
% 4.18/4.56 tff(31612,plain,
% 4.18/4.56 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[27415, 3, 54, 30654])).
% 4.18/4.56 tff(31613,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[22687, 22670, 31612, 54])).
% 4.18/4.56 tff(31614,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31615,plain,
% 4.18/4.56 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31614, 54])).
% 4.18/4.56 tff(31616,plain,
% 4.18/4.56 (~(s(z) = elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[30660, 31615, 30654])).
% 4.18/4.56 tff(31617,plain,
% 4.18/4.56 (~(z = elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[18287, 31611])).
% 4.18/4.56 tff(31618,plain,
% 4.18/4.56 (~(s(elem!1) = s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[8683, 31617])).
% 4.18/4.56 tff(31619,plain,
% 4.18/4.56 (b(z, elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[30696, 2169, 713, 4, 350, 1])).
% 4.18/4.56 tff(31620,plain,
% 4.18/4.56 (~b(z, s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[803, 259, 133, 123, 251])).
% 4.18/4.56 tff(31621,plain,
% 4.18/4.56 (r(z, s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[372, 31620])).
% 4.18/4.56 tff(31622,plain,
% 4.18/4.56 (~r(elem!1, z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1376, 323, 409, 31621])).
% 4.18/4.56 tff(31623,plain,
% 4.18/4.56 (b(elem!1, z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1380, 31622, 77])).
% 4.18/4.56 tff(31624,plain,
% 4.18/4.56 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[880, 31623, 133, 251])).
% 4.18/4.56 tff(31625,plain,
% 4.18/4.56 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[302, 31624])).
% 4.18/4.56 tff(31626,plain,
% 4.18/4.56 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[14521, 31625, 409, 31621])).
% 4.18/4.56 tff(31627,plain,
% 4.18/4.56 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[319, 31626])).
% 4.18/4.56 tff(31628,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31629,plain,
% 4.18/4.56 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31630,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31629])).
% 4.18/4.56 tff(31631,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.56 inference(transitivity,[status(thm)],[31630, 31628])).
% 4.18/4.56 tff(31632,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))),
% 4.18/4.56 inference(quant_inst,[status(thm)],[])).
% 4.18/4.56 tff(31633,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31632, 31631])).
% 4.18/4.56 tff(31634,plain,
% 4.18/4.56 (~b(z, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31633, 144, 251, 133, 2254, 259])).
% 4.18/4.56 tff(31635,plain,
% 4.18/4.56 (r(z, s(s(s(z))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[619, 31634])).
% 4.18/4.56 tff(31636,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[8665, 333, 409, 31621, 31635, 31064])).
% 4.18/4.56 tff(31637,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31638,plain,
% 4.18/4.56 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31637, 31627, 123, 409, 251, 133, 259])).
% 4.18/4.56 tff(31639,plain,
% 4.18/4.56 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1137, 31638])).
% 4.18/4.56 tff(31640,plain,
% 4.18/4.56 (((~![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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(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))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31641,plain,
% 4.18/4.56 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.56 inference(rewrite,[status(thm)],[])).
% 4.18/4.56 tff(31642,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31641])).
% 4.18/4.56 tff(31643,plain,
% 4.18/4.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.56 inference(transitivity,[status(thm)],[31642, 31640])).
% 4.18/4.56 tff(31644,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 4.18/4.56 inference(quant_inst,[status(thm)],[])).
% 4.18/4.56 tff(31645,plain,
% 4.18/4.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.18/4.56 inference(modus_ponens,[status(thm)],[31644, 31643])).
% 4.18/4.56 tff(31646,plain,
% 4.18/4.56 (~r(s(s(s(z))), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31645, 333, 2323, 6107, 321])).
% 4.18/4.56 tff(31647,plain,
% 4.18/4.56 (b(s(s(s(z))), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[704, 31646, 698])).
% 4.18/4.56 tff(31648,plain,
% 4.18/4.56 (~b(s(s(s(z))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[10565, 31647, 624, 251])).
% 4.18/4.56 tff(31649,plain,
% 4.18/4.56 (r(s(s(s(z))), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[396, 31648])).
% 4.18/4.56 tff(31650,plain,
% 4.18/4.56 ($false),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[12296, 333, 354, 31649, 6107, 321])).
% 4.18/4.56 tff(31651,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.56 tff(31652,plain,
% 4.18/4.56 (s(s(s(z))) = elem!1),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[31651, 31639, 31625, 31623, 251, 31621, 2323])).
% 4.18/4.56 tff(31653,plain,
% 4.18/4.56 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.18/4.56 inference(monotonicity,[status(thm)],[31652])).
% 4.18/4.56 tff(31654,plain,
% 4.18/4.56 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 4.18/4.56 inference(symmetry,[status(thm)],[31653])).
% 4.18/4.56 tff(31655,plain,
% 4.18/4.56 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 4.18/4.56 inference(transitivity,[status(thm)],[31654, 12981])).
% 4.18/4.56 tff(31656,plain,
% 4.18/4.56 (~(s(s(elem!1)) = elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[7595, 31652, 863])).
% 4.18/4.56 tff(31657,plain,
% 4.18/4.56 (~(elem!1 = s(s(elem!1)))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[5603, 31656])).
% 4.18/4.56 tff(31658,plain,
% 4.18/4.56 (~(s(elem!1) = elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[5813, 31657])).
% 4.18/4.56 tff(31659,plain,
% 4.18/4.56 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[12214, 31652])).
% 4.18/4.56 tff(31660,plain,
% 4.18/4.56 (~(elem!1 = s(elem!1))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1569, 31658])).
% 4.18/4.56 tff(31661,plain,
% 4.18/4.56 (~r(s(elem!1), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[1392, 31660, 409, 31621, 77, 251, 323])).
% 4.18/4.56 tff(31662,plain,
% 4.18/4.56 (b(s(elem!1), s(z))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[486, 31661, 1])).
% 4.18/4.56 tff(31663,plain,
% 4.18/4.56 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[869, 144, 31662, 123, 31627])).
% 4.18/4.56 tff(31664,plain,
% 4.18/4.56 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[472, 31663, 31659])).
% 4.18/4.56 tff(31665,plain,
% 4.18/4.56 (~r(s(elem!1), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[14540, 31664, 31621, 31625])).
% 4.18/4.56 tff(31666,plain,
% 4.18/4.56 (b(s(elem!1), z)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[507, 31665])).
% 4.18/4.56 tff(31667,plain,
% 4.18/4.56 (~b(s(elem!1), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[916, 31666, 31623, 251])).
% 4.18/4.56 tff(31668,plain,
% 4.18/4.56 (r(s(elem!1), elem!1)),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[448, 31667, 31658])).
% 4.18/4.56 tff(31669,plain,
% 4.18/4.56 (~r(elem!1, s(elem!1))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[4103, 31664, 2323, 31625])).
% 4.18/4.56 tff(31670,plain,
% 4.18/4.56 (b(elem!1, s(elem!1))),
% 4.18/4.56 inference(unit_resolution,[status(thm)],[560, 31669, 31660])).
% 4.18/4.56 tff(31671,plain,
% 4.18/4.56 (((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31672,plain,
% 4.18/4.57 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31673,plain,
% 4.18/4.57 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.18/4.57 inference(monotonicity,[status(thm)],[31672])).
% 4.18/4.57 tff(31674,plain,
% 4.18/4.57 (((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.57 inference(transitivity,[status(thm)],[31673, 31671])).
% 4.18/4.57 tff(31675,plain,
% 4.18/4.57 ((~![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(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.18/4.57 inference(quant_inst,[status(thm)],[])).
% 4.18/4.57 tff(31676,plain,
% 4.18/4.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.18/4.57 inference(modus_ponens,[status(thm)],[31675, 31674])).
% 4.18/4.57 tff(31677,plain,
% 4.18/4.57 (~r(elem!1, s(s(s(z))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31676, 333, 2323, 31639, 31625])).
% 4.18/4.57 tff(31678,plain,
% 4.18/4.57 (b(z, s(s(s(z))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[257, 31652, 251])).
% 4.18/4.57 tff(31679,plain,
% 4.18/4.57 (~b(z, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[949, 31670, 31623, 31666])).
% 4.18/4.57 tff(31680,plain,
% 4.18/4.57 (r(z, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[583, 31679])).
% 4.18/4.57 tff(31681,plain,
% 4.18/4.57 (~r(s(s(s(z))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[10450, 31680, 31625, 31639])).
% 4.18/4.57 tff(31682,plain,
% 4.18/4.57 (b(s(s(s(z))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[396, 31681])).
% 4.18/4.57 tff(31683,plain,
% 4.18/4.57 (~b(elem!1, s(s(s(z))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[8728, 144, 31623, 31682, 31678])).
% 4.18/4.57 tff(31684,plain,
% 4.18/4.57 (elem!1 = s(s(s(z)))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1538, 31683, 31677])).
% 4.18/4.57 tff(31685,plain,
% 4.18/4.57 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[3246, 31684, 706])).
% 4.18/4.57 tff(31686,plain,
% 4.18/4.57 (s(s(s(elem!1))) = elem!1),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[18357, 31685, 251, 31621, 1229, 31623, 323, 31670, 31662, 31668, 713])).
% 4.18/4.57 tff(31687,plain,
% 4.18/4.57 (s(s(s(z))) = s(s(s(elem!1)))),
% 4.18/4.57 inference(modus_ponens,[status(thm)],[31686, 31655])).
% 4.18/4.57 tff(31688,plain,
% 4.18/4.57 ($false),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[9480, 31687])).
% 4.18/4.57 tff(31689,plain,((~r(s(z), z)) | (~b(z, elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.57 tff(31690,plain,
% 4.18/4.57 (~r(s(z), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31689, 259, 706, 2323, 123, 1, 2169, 133, 251])).
% 4.18/4.57 tff(31691,plain,
% 4.18/4.57 (b(s(z), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[348, 31690])).
% 4.18/4.57 tff(31692,plain,
% 4.18/4.57 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[7741, 31691, 259, 123])).
% 4.18/4.57 tff(31693,plain,
% 4.18/4.57 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[302, 31692])).
% 4.18/4.57 tff(31694,plain,
% 4.18/4.57 (~r(elem!1, z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[24027, 31693, 2323, 31621])).
% 4.18/4.57 tff(31695,plain,
% 4.18/4.57 (b(elem!1, z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1380, 31694, 77])).
% 4.18/4.57 tff(31696,plain,
% 4.18/4.57 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[14521, 31693, 2169, 31621])).
% 4.18/4.57 tff(31697,plain,
% 4.18/4.57 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[319, 31696])).
% 4.18/4.57 tff(31698,plain,
% 4.18/4.57 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31637, 31697, 123, 2169, 251, 133, 259])).
% 4.18/4.57 tff(31699,plain,
% 4.18/4.57 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1137, 31698])).
% 4.18/4.57 tff(31700,plain,
% 4.18/4.57 (s(s(s(z))) = elem!1),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31651, 31699, 31693, 31695, 251, 31621, 2323])).
% 4.18/4.57 tff(31701,plain,
% 4.18/4.57 (~(s(s(elem!1)) = elem!1)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[7595, 31700, 863])).
% 4.18/4.57 tff(31702,plain,
% 4.18/4.57 (~(elem!1 = s(s(elem!1)))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[5603, 31701])).
% 4.18/4.57 tff(31703,plain,
% 4.18/4.57 (~(s(elem!1) = elem!1)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[5813, 31702])).
% 4.18/4.57 tff(31704,plain,
% 4.18/4.57 (~(elem!1 = s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1569, 31703])).
% 4.18/4.57 tff(31705,plain,
% 4.18/4.57 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[12214, 31700])).
% 4.18/4.57 tff(31706,plain,
% 4.18/4.57 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[7741, 489, 259, 123])).
% 4.18/4.57 tff(31707,plain,
% 4.18/4.57 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[302, 31706])).
% 4.18/4.57 tff(31708,plain,
% 4.18/4.57 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[14521, 31707, 2169, 354])).
% 4.18/4.57 tff(31709,plain,
% 4.18/4.57 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[319, 31708])).
% 4.18/4.57 tff(31710,plain,
% 4.18/4.57 (((~![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(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31711,plain,
% 4.18/4.57 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31712,plain,
% 4.18/4.57 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.57 inference(monotonicity,[status(thm)],[31711])).
% 4.18/4.57 tff(31713,plain,
% 4.18/4.57 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(transitivity,[status(thm)],[31712, 31710])).
% 4.18/4.57 tff(31714,plain,
% 4.18/4.57 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 4.18/4.57 inference(quant_inst,[status(thm)],[])).
% 4.18/4.57 tff(31715,plain,
% 4.18/4.57 ((~![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(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.57 inference(modus_ponens,[status(thm)],[31714, 31713])).
% 4.18/4.57 tff(31716,plain,
% 4.18/4.57 (~r(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31715, 333, 435, 409, 2323])).
% 4.18/4.57 tff(31717,plain,
% 4.18/4.57 (b(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[486, 31716, 1])).
% 4.18/4.57 tff(31718,plain,
% 4.18/4.57 (((~![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(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31719,plain,
% 4.18/4.57 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31720,plain,
% 4.18/4.57 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~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(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.57 inference(monotonicity,[status(thm)],[31719])).
% 4.18/4.57 tff(31721,plain,
% 4.18/4.57 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~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(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(transitivity,[status(thm)],[31720, 31718])).
% 4.18/4.57 tff(31722,plain,
% 4.18/4.57 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 4.18/4.57 inference(quant_inst,[status(thm)],[])).
% 4.18/4.57 tff(31723,plain,
% 4.18/4.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.57 inference(modus_ponens,[status(thm)],[31722, 31721])).
% 4.18/4.57 tff(31724,plain,
% 4.18/4.57 (~r(s(z), s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31723, 333, 435, 409, 2323])).
% 4.18/4.57 tff(31725,plain,
% 4.18/4.57 (b(s(z), s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1244, 31724, 1229])).
% 4.18/4.57 tff(31726,plain,
% 4.18/4.57 (~b(elem!1, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[4409, 31725, 305, 31717])).
% 4.18/4.57 tff(31727,plain,
% 4.18/4.57 (r(elem!1, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[560, 31726, 902])).
% 4.18/4.57 tff(31728,plain,
% 4.18/4.57 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[4103, 31727, 2323, 321])).
% 4.18/4.57 tff(31729,plain,
% 4.18/4.57 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[472, 31728, 432])).
% 4.18/4.57 tff(31730,plain,
% 4.18/4.57 ($false),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[869, 144, 31717, 123, 304, 31729])).
% 4.18/4.57 tff(31731,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.57 tff(31732,plain,
% 4.18/4.57 (~b(elem!1, s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31731, 435, 31709, 432, 2323, 31707, 902, 123, 1, 2169])).
% 4.18/4.57 tff(31733,plain,
% 4.18/4.57 (~r(s(z), s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[7675, 31732, 706, 350, 435])).
% 4.18/4.57 tff(31734,plain,
% 4.18/4.57 (b(s(z), s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1244, 31733, 1229])).
% 4.18/4.57 tff(31735,plain,
% 4.18/4.57 (~r(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31715, 333, 435, 2169, 2323])).
% 4.18/4.57 tff(31736,plain,
% 4.18/4.57 (b(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[486, 31735, 1])).
% 4.18/4.57 tff(31737,plain,
% 4.18/4.57 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[869, 144, 31736, 123, 31709])).
% 4.18/4.57 tff(31738,plain,
% 4.18/4.57 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[472, 31737, 432])).
% 4.18/4.57 tff(31739,plain,
% 4.18/4.57 (~r(s(elem!1), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[14540, 31738, 354, 31707])).
% 4.18/4.57 tff(31740,plain,
% 4.18/4.57 (b(s(elem!1), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[507, 31739])).
% 4.18/4.57 tff(31741,plain,
% 4.18/4.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31742,plain,
% 4.18/4.57 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(rewrite,[status(thm)],[])).
% 4.18/4.57 tff(31743,plain,
% 4.18/4.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.57 inference(monotonicity,[status(thm)],[31742])).
% 4.18/4.57 tff(31744,plain,
% 4.18/4.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.57 inference(transitivity,[status(thm)],[31743, 31741])).
% 4.18/4.57 tff(31745,plain,
% 4.18/4.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 4.18/4.57 inference(quant_inst,[status(thm)],[])).
% 4.18/4.57 tff(31746,plain,
% 4.18/4.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.57 inference(modus_ponens,[status(thm)],[31745, 31744])).
% 4.18/4.57 tff(31747,plain,
% 4.18/4.57 ($false),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31746, 144, 31740, 489, 31734, 123, 259])).
% 4.18/4.57 tff(31748,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | b(s(z), elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.57 tff(31749,plain,
% 4.18/4.57 (~r(s(elem!1), elem!1)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31748, 31691, 123, 259, 31621, 31705, 1, 2323, 706, 350, 31704])).
% 4.18/4.57 tff(31750,plain,
% 4.18/4.57 (b(s(elem!1), elem!1)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[448, 31749, 31703])).
% 4.18/4.57 tff(31751,plain,
% 4.18/4.57 (~b(s(elem!1), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[916, 31750, 31695, 251])).
% 4.18/4.57 tff(31752,plain,
% 4.18/4.57 (r(s(elem!1), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[507, 31751])).
% 4.18/4.57 tff(31753,plain,
% 4.18/4.57 (~r(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1589, 31752, 2169, 31621])).
% 4.18/4.57 tff(31754,plain,
% 4.18/4.57 (b(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[486, 31753, 1])).
% 4.18/4.57 tff(31755,plain,
% 4.18/4.57 (r(s(elem!1), z)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[507, 14927])).
% 4.18/4.57 tff(31756,plain,
% 4.18/4.57 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[14540, 31755, 354, 321])).
% 4.18/4.57 tff(31757,plain,
% 4.18/4.57 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[472, 31756, 432])).
% 4.18/4.57 tff(31758,plain,
% 4.18/4.57 (b(s(elem!1), s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[1653, 31755, 1, 354, 706, 1575, 902])).
% 4.18/4.57 tff(31759,plain,
% 4.18/4.57 ($false),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[3930, 144, 451, 31758, 123, 133, 31757])).
% 4.18/4.57 tff(31760,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (s(z) = elem!1) | r(z, elem!1) | (elem!1 = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.57 tff(31761,plain,
% 4.18/4.57 (r(z, elem!1)),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31760, 31750, 133, 31705, 31621, 31693, 1, 706, 123, 31704, 31695, 251])).
% 4.18/4.57 tff(31762,plain,
% 4.18/4.57 (b(elem!1, s(z))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[13826, 31761, 706, 31621, 350])).
% 4.18/4.57 tff(31763,plain,
% 4.18/4.57 (~r(elem!1, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[10119, 31761, 2169, 31621])).
% 4.18/4.57 tff(31764,plain,
% 4.18/4.57 (b(elem!1, s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[560, 31763, 31704])).
% 4.18/4.57 tff(31765,plain,
% 4.18/4.57 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[20734, 31705])).
% 4.18/4.57 tff(31766,plain,
% 4.18/4.57 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[7745, 31761, 123, 133, 31765, 31695, 31750, 31752, 31691])).
% 4.18/4.57 tff(31767,plain,
% 4.18/4.57 (b(s(z), s(elem!1))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[3415, 31764, 123, 31621, 1, 31697, 31766, 31695])).
% 4.18/4.57 tff(31768,plain,
% 4.18/4.57 ($false),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[4409, 31767, 31764, 31762, 31754])).
% 4.18/4.57 tff(31769,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | b(s(z), elem!1) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.57 tff(31770,plain,
% 4.18/4.57 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31769, 9095, 1, 50, 706, 350, 31619, 30657])).
% 4.18/4.57 tff(31771,plain,
% 4.18/4.57 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[279, 31770])).
% 4.18/4.57 tff(31772,plain,
% 4.18/4.57 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.57 inference(unit_resolution,[status(thm)],[31769, 133, 1, 123, 706, 350, 251, 2323])).
% 4.18/4.57 tff(31773,plain,
% 4.18/4.58 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[279, 31772])).
% 4.18/4.58 tff(31774,plain,
% 4.18/4.58 (~b(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[880, 286, 133, 251])).
% 4.18/4.58 tff(31775,plain,
% 4.18/4.58 (r(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[653, 31774, 1368])).
% 4.18/4.58 tff(31776,plain,
% 4.18/4.58 (~r(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[417, 31775, 409, 51])).
% 4.18/4.58 tff(31777,plain,
% 4.18/4.58 (b(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[348, 31776])).
% 4.18/4.58 tff(31778,plain,
% 4.18/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2331, 31775, 2323, 51])).
% 4.18/4.58 tff(31779,plain,
% 4.18/4.58 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[319, 31778])).
% 4.18/4.58 tff(31780,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7093, 31779, 31777, 490, 286])).
% 4.18/4.58 tff(31781,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31782,plain,
% 4.18/4.58 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31781, 490, 2323, 31773, 2169, 77, 133, 251])).
% 4.18/4.58 tff(31783,plain,
% 4.18/4.58 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[302, 31782])).
% 4.18/4.58 tff(31784,plain,
% 4.18/4.58 (~r(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[27689, 333, 2323, 31783, 31773])).
% 4.18/4.58 tff(31785,plain,
% 4.18/4.58 (b(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1380, 31784, 77])).
% 4.18/4.58 tff(31786,plain,
% 4.18/4.58 (~r(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[341, 322, 51, 321])).
% 4.18/4.58 tff(31787,plain,
% 4.18/4.58 (b(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[348, 31786])).
% 4.18/4.58 tff(31788,plain,
% 4.18/4.58 (~b(elem!1, s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[387, 144, 624, 490, 31787])).
% 4.18/4.58 tff(31789,plain,
% 4.18/4.58 (r(elem!1, s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[720, 31788, 714])).
% 4.18/4.58 tff(31790,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[18811, 333, 409, 31789, 2323, 322])).
% 4.18/4.58 tff(31791,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31792,plain,
% 4.18/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31791, 31785, 2323, 713, 2169, 490, 31773, 31783])).
% 4.18/4.58 tff(31793,plain,
% 4.18/4.58 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[319, 31792])).
% 4.18/4.58 tff(31794,plain,
% 4.18/4.58 (~r(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[13781, 323, 123, 31773, 31793])).
% 4.18/4.58 tff(31795,plain,
% 4.18/4.58 (b(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[396, 31794])).
% 4.18/4.58 tff(31796,plain,
% 4.18/4.58 (~b(s(s(s(z))), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[10565, 31795, 31785, 251])).
% 4.18/4.58 tff(31797,plain,
% 4.18/4.58 (~r(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[27689, 333, 2323, 321, 51])).
% 4.18/4.58 tff(31798,plain,
% 4.18/4.58 (b(elem!1, z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1380, 31797, 77])).
% 4.18/4.58 tff(31799,plain,
% 4.18/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31791, 31798, 2323, 713, 2169, 490, 51, 321])).
% 4.18/4.58 tff(31800,plain,
% 4.18/4.58 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[319, 31799])).
% 4.18/4.58 tff(31801,plain,
% 4.18/4.58 (~r(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[13781, 323, 123, 51, 31800])).
% 4.18/4.58 tff(31802,plain,
% 4.18/4.58 (b(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[396, 31801])).
% 4.18/4.58 tff(31803,plain,
% 4.18/4.58 (~b(s(s(s(z))), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[10565, 31802, 31798, 251])).
% 4.18/4.58 tff(31804,plain,
% 4.18/4.58 (~r(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[9910, 707, 722, 409])).
% 4.18/4.58 tff(31805,plain,
% 4.18/4.58 (b(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2794, 31804])).
% 4.18/4.58 tff(31806,plain,
% 4.18/4.58 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1124, 144, 31805, 123, 304])).
% 4.18/4.58 tff(31807,plain,
% 4.18/4.58 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1137, 31806])).
% 4.18/4.58 tff(31808,plain,
% 4.18/4.58 (((~![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))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.58 inference(rewrite,[status(thm)],[])).
% 4.18/4.58 tff(31809,plain,
% 4.18/4.58 (((~r(elem!1, s(s(s(s(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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.58 inference(rewrite,[status(thm)],[])).
% 4.18/4.58 tff(31810,plain,
% 4.18/4.58 (((~![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(s(s(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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.18/4.58 inference(monotonicity,[status(thm)],[31809])).
% 4.18/4.58 tff(31811,plain,
% 4.18/4.58 (((~![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(s(s(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(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.58 inference(transitivity,[status(thm)],[31810, 31808])).
% 4.18/4.58 tff(31812,plain,
% 4.18/4.58 ((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 4.18/4.58 inference(quant_inst,[status(thm)],[])).
% 4.18/4.58 tff(31813,plain,
% 4.18/4.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.18/4.58 inference(modus_ponens,[status(thm)],[31812, 31811])).
% 4.18/4.58 tff(31814,plain,
% 4.18/4.58 (~r(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31813, 333, 409, 707, 2323])).
% 4.18/4.58 tff(31815,plain,
% 4.18/4.58 (b(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[172, 31814])).
% 4.18/4.58 tff(31816,plain,
% 4.18/4.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[846, 31815, 304, 31805])).
% 4.18/4.58 tff(31817,plain,
% 4.18/4.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[249, 31816])).
% 4.18/4.58 tff(31818,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31289, 333, 707, 2323, 31817, 31807])).
% 4.18/4.58 tff(31819,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31820,plain,
% 4.18/4.58 (~r(s(s(s(z))), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31819, 721, 123, 31800, 2169, 2323])).
% 4.18/4.58 tff(31821,plain,
% 4.18/4.58 (s(s(s(z))) = elem!1),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[704, 31820, 31803])).
% 4.18/4.58 tff(31822,plain,
% 4.18/4.58 (~(s(s(elem!1)) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7595, 31821, 863])).
% 4.18/4.58 tff(31823,plain,
% 4.18/4.58 (~(elem!1 = s(s(elem!1)))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5603, 31822])).
% 4.18/4.58 tff(31824,plain,
% 4.18/4.58 (~(s(elem!1) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5813, 31823])).
% 4.18/4.58 tff(31825,plain,
% 4.18/4.58 (~(elem!1 = s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1569, 31824])).
% 4.18/4.58 tff(31826,plain,
% 4.18/4.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[12214, 31821])).
% 4.18/4.58 tff(31827,plain,
% 4.18/4.58 (~r(s(elem!1), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1911, 31824, 323, 31798, 251, 721])).
% 4.18/4.58 tff(31828,plain,
% 4.18/4.58 (b(s(elem!1), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[486, 31827, 1])).
% 4.18/4.58 tff(31829,plain,
% 4.18/4.58 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[869, 144, 31828, 123, 31800])).
% 4.18/4.58 tff(31830,plain,
% 4.18/4.58 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[472, 31829, 31826])).
% 4.18/4.58 tff(31831,plain,
% 4.18/4.58 (~r(elem!1, s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[4103, 31830, 2323, 321])).
% 4.18/4.58 tff(31832,plain,
% 4.18/4.58 (b(elem!1, s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[560, 31831, 31825])).
% 4.18/4.58 tff(31833,plain,
% 4.18/4.58 (~r(z, s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[940, 31830, 51, 321])).
% 4.18/4.58 tff(31834,plain,
% 4.18/4.58 (b(z, s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[583, 31833])).
% 4.18/4.58 tff(31835,plain,
% 4.18/4.58 (~b(s(elem!1), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1642, 31834, 251, 31832])).
% 4.18/4.58 tff(31836,plain,
% 4.18/4.58 (r(s(elem!1), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[448, 31835, 31824])).
% 4.18/4.58 tff(31837,plain,
% 4.18/4.58 (~b(s(z), s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1853, 31834, 490, 31828])).
% 4.18/4.58 tff(31838,plain,
% 4.18/4.58 (r(s(z), s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1244, 31837, 1229])).
% 4.18/4.58 tff(31839,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7675, 31838, 31836, 706, 350, 708])).
% 4.18/4.58 tff(31840,plain,(b(elem!1, s(z)) | (s(z) = elem!1) | b(s(z), elem!1) | (~b(z, s(z))) | (~b(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31841,plain,
% 4.18/4.58 (b(elem!1, s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31840, 323, 350, 490, 251, 31773, 31783, 2323, 123, 1, 706])).
% 4.18/4.58 tff(31842,plain,
% 4.18/4.58 (~r(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[26742, 333, 409, 12399, 2323])).
% 4.18/4.58 tff(31843,plain,
% 4.18/4.58 (b(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2794, 31842])).
% 4.18/4.58 tff(31844,plain,
% 4.18/4.58 (~r(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31813, 333, 409, 12399, 2323])).
% 4.18/4.58 tff(31845,plain,
% 4.18/4.58 (b(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[172, 31844])).
% 4.18/4.58 tff(31846,plain,
% 4.18/4.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[846, 31845, 304, 31843])).
% 4.18/4.58 tff(31847,plain,
% 4.18/4.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[249, 31846])).
% 4.18/4.58 tff(31848,plain,
% 4.18/4.58 (r(elem!1, s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1538, 11215, 12398])).
% 4.18/4.58 tff(31849,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[29203, 333, 31848, 12399, 2323, 31847])).
% 4.18/4.58 tff(31850,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31851,plain,
% 4.18/4.58 (s(s(s(z))) = elem!1),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31850, 31841, 31785, 490, 2323, 31795, 31793, 2169, 31796])).
% 4.18/4.58 tff(31852,plain,
% 4.18/4.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[12214, 31851])).
% 4.18/4.58 tff(31853,plain,
% 4.18/4.58 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[20734, 31852])).
% 4.18/4.58 tff(31854,plain,
% 4.18/4.58 (~(s(s(elem!1)) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7595, 31851, 863])).
% 4.18/4.58 tff(31855,plain,
% 4.18/4.58 (~(elem!1 = s(s(elem!1)))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5603, 31854])).
% 4.18/4.58 tff(31856,plain,
% 4.18/4.58 (~(s(elem!1) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5813, 31855])).
% 4.18/4.58 tff(31857,plain,
% 4.18/4.58 (~(elem!1 = s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1569, 31856])).
% 4.18/4.58 tff(31858,plain,
% 4.18/4.58 (~r(s(elem!1), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31731, 31857, 31793, 31841, 2323, 31783, 31852, 123, 1, 2169])).
% 4.18/4.58 tff(31859,plain,
% 4.18/4.58 (b(s(elem!1), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[448, 31858, 31856])).
% 4.18/4.58 tff(31860,plain,
% 4.18/4.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.18/4.58 inference(rewrite,[status(thm)],[])).
% 4.18/4.58 tff(31861,plain,
% 4.18/4.58 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.18/4.58 inference(rewrite,[status(thm)],[])).
% 4.18/4.58 tff(31862,plain,
% 4.18/4.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 4.18/4.58 inference(monotonicity,[status(thm)],[31861])).
% 4.18/4.58 tff(31863,plain,
% 4.18/4.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.18/4.58 inference(transitivity,[status(thm)],[31862, 31860])).
% 4.18/4.58 tff(31864,plain,
% 4.18/4.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.18/4.58 inference(quant_inst,[status(thm)],[])).
% 4.18/4.58 tff(31865,plain,
% 4.18/4.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.18/4.58 inference(modus_ponens,[status(thm)],[31864, 31863])).
% 4.18/4.58 tff(31866,plain,
% 4.18/4.58 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31865, 144, 31859, 31841, 133, 31793])).
% 4.18/4.58 tff(31867,plain,
% 4.18/4.58 (~b(s(elem!1), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[916, 31859, 31785, 251])).
% 4.18/4.58 tff(31868,plain,
% 4.18/4.58 (r(s(elem!1), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[507, 31867])).
% 4.18/4.58 tff(31869,plain,
% 4.18/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7702, 333, 31868, 31783, 31773])).
% 4.18/4.58 tff(31870,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[542, 31869, 31866, 31853])).
% 4.18/4.58 tff(31871,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | b(s(z), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31872,plain,
% 4.18/4.58 (~r(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31871, 490, 251, 2323, 123, 1, 133, 350, 706])).
% 4.18/4.58 tff(31873,plain,
% 4.18/4.58 (b(s(z), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[348, 31872])).
% 4.18/4.58 tff(31874,plain,
% 4.18/4.58 (~b(elem!1, s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[387, 144, 31785, 490, 31873])).
% 4.18/4.58 tff(31875,plain,
% 4.18/4.58 (r(elem!1, s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[720, 31874, 713])).
% 4.18/4.58 tff(31876,plain,
% 4.18/4.58 (~r(s(s(s(z))), elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31819, 31875, 123, 31793, 2169, 2323])).
% 4.18/4.58 tff(31877,plain,
% 4.18/4.58 (~b(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[10565, 19936, 624, 251])).
% 4.18/4.58 tff(31878,plain,
% 4.18/4.58 (r(s(s(s(z))), z)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[396, 31877])).
% 4.18/4.58 tff(31879,plain,
% 4.18/4.58 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[11754, 31878, 51, 321])).
% 4.18/4.58 tff(31880,plain,
% 4.18/4.58 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1137, 31879])).
% 4.18/4.58 tff(31881,plain,
% 4.18/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2199, 333, 31878, 321, 51])).
% 4.18/4.58 tff(31882,plain,
% 4.18/4.58 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[249, 31881])).
% 4.18/4.58 tff(31883,plain,
% 4.18/4.58 (~b(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2262, 31882, 123, 31880])).
% 4.18/4.58 tff(31884,plain,
% 4.18/4.58 (~b(elem!1, s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[11966, 31878, 133, 51, 251, 19936])).
% 4.18/4.58 tff(31885,plain,
% 4.18/4.58 (r(elem!1, s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[1538, 31884, 12398])).
% 4.18/4.58 tff(31886,plain,
% 4.18/4.58 (~b(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[6004, 144, 123, 31880, 304])).
% 4.18/4.58 tff(31887,plain,
% 4.18/4.58 (r(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2794, 31886])).
% 4.18/4.58 tff(31888,plain,
% 4.18/4.58 (~r(s(z), s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[11876, 31887, 409, 31885])).
% 4.18/4.58 tff(31889,plain,
% 4.18/4.58 ($false),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[172, 31888, 31883])).
% 4.18/4.58 tff(31890,plain,((s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.58 tff(31891,plain,
% 4.18/4.58 (s(s(s(z))) = elem!1),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[31890, 31793, 123, 2169, 31783, 31773, 133, 251, 31785, 31876])).
% 4.18/4.58 tff(31892,plain,
% 4.18/4.58 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 4.18/4.58 inference(monotonicity,[status(thm)],[31891])).
% 4.18/4.58 tff(31893,plain,
% 4.18/4.58 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 4.18/4.58 inference(symmetry,[status(thm)],[31892])).
% 4.18/4.58 tff(31894,plain,
% 4.18/4.58 (b(s(s(s(z))), z)),
% 4.18/4.58 inference(modus_ponens,[status(thm)],[31785, 31893])).
% 4.18/4.58 tff(31895,plain,
% 4.18/4.58 (b(z, s(s(s(z))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[257, 31891, 251])).
% 4.18/4.58 tff(31896,plain,
% 4.18/4.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[12214, 31891])).
% 4.18/4.58 tff(31897,plain,
% 4.18/4.58 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[20734, 31896])).
% 4.18/4.58 tff(31898,plain,
% 4.18/4.58 (~(s(s(elem!1)) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[7595, 31891, 863])).
% 4.18/4.58 tff(31899,plain,
% 4.18/4.58 (~(elem!1 = s(s(elem!1)))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5603, 31898])).
% 4.18/4.58 tff(31900,plain,
% 4.18/4.58 (~(s(elem!1) = elem!1)),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[5813, 31899])).
% 4.18/4.58 tff(31901,plain,
% 4.18/4.58 (~b(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2273, 285, 490, 489])).
% 4.18/4.58 tff(31902,plain,
% 4.18/4.58 (r(s(s(s(z))), s(z))),
% 4.18/4.58 inference(unit_resolution,[status(thm)],[2794, 31901])).
% 4.18/4.58 tff(31903,plain,
% 4.18/4.58 (~r(elem!1, s(s(s(z))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[11876, 31902, 409, 17023])).
% 4.18/4.59 tff(31904,plain,
% 4.18/4.59 (~b(elem!1, s(s(s(z))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[8728, 144, 624, 285, 284])).
% 4.18/4.59 tff(31905,plain,
% 4.18/4.59 (elem!1 = s(s(s(z)))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[1538, 31904, 31903])).
% 4.18/4.59 tff(31906,plain,
% 4.18/4.59 (s(elem!1) = s(s(s(s(z))))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31905])).
% 4.18/4.59 tff(31907,plain,
% 4.18/4.59 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31906])).
% 4.18/4.59 tff(31908,plain,
% 4.18/4.59 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31906])).
% 4.18/4.59 tff(31909,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 4.18/4.59 inference(symmetry,[status(thm)],[31908])).
% 4.18/4.59 tff(31910,plain,
% 4.18/4.59 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31909])).
% 4.18/4.59 tff(31911,plain,
% 4.18/4.59 (s(s(s(s(z)))) = s(elem!1)),
% 4.18/4.59 inference(symmetry,[status(thm)],[31906])).
% 4.18/4.59 tff(31912,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31911, 31905])).
% 4.18/4.59 tff(31913,plain,
% 4.18/4.59 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.18/4.59 inference(symmetry,[status(thm)],[31912])).
% 4.18/4.59 tff(31914,plain,
% 4.18/4.59 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31905])).
% 4.18/4.59 tff(31915,plain,
% 4.18/4.59 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 4.18/4.59 inference(transitivity,[status(thm)],[31914, 31913])).
% 4.18/4.59 tff(31916,plain,
% 4.18/4.59 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31911])).
% 4.18/4.59 tff(31917,plain,
% 4.18/4.59 ((s(elem!1) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 4.18/4.59 inference(symmetry,[status(thm)],[31916])).
% 4.18/4.59 tff(31918,plain,
% 4.18/4.59 ((~(s(elem!1) = s(z))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31917])).
% 4.18/4.59 tff(31919,plain,
% 4.18/4.59 (~(s(s(s(s(z)))) = s(z))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[1, 31918])).
% 4.18/4.59 tff(31920,plain,
% 4.18/4.59 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[3239])).
% 4.18/4.59 tff(31921,plain,
% 4.18/4.59 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 4.18/4.59 inference(symmetry,[status(thm)],[31920])).
% 4.18/4.59 tff(31922,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), z)),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31755, 19808])).
% 4.18/4.59 tff(31923,plain,
% 4.18/4.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[12729, 333, 321, 51, 31922])).
% 4.18/4.59 tff(31924,plain,
% 4.18/4.59 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31923, 20425])).
% 4.18/4.59 tff(31925,plain,
% 4.18/4.59 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[542, 31924, 537])).
% 4.18/4.59 tff(31926,plain,
% 4.18/4.59 (~b(elem!1, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[555, 31925, 133, 451])).
% 4.18/4.59 tff(31927,plain,
% 4.18/4.59 (r(elem!1, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[560, 31926, 902])).
% 4.18/4.59 tff(31928,plain,
% 4.18/4.59 (r(elem!1, s(s(s(s(z)))))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31927, 19693])).
% 4.18/4.59 tff(31929,plain,
% 4.18/4.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31928, 31921])).
% 4.18/4.59 tff(31930,plain,
% 4.18/4.59 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[12669, 333, 321, 51, 31922])).
% 4.18/4.59 tff(31931,plain,
% 4.18/4.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[9761, 31930])).
% 4.18/4.59 tff(31932,plain,
% 4.18/4.59 (~b(s(s(s(s(z)))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[26574, 31931, 304, 123])).
% 4.18/4.59 tff(31933,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[24600, 31932, 24596])).
% 4.18/4.59 tff(31934,plain,
% 4.18/4.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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)))))))) <=> ((~![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(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.18/4.59 inference(rewrite,[status(thm)],[])).
% 4.18/4.59 tff(31935,plain,
% 4.18/4.59 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), 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)))))))),
% 4.18/4.59 inference(rewrite,[status(thm)],[])).
% 4.18/4.59 tff(31936,plain,
% 4.18/4.59 (((~![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(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(s(s(z))), 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))))))))),
% 4.18/4.59 inference(monotonicity,[status(thm)],[31935])).
% 4.18/4.59 tff(31937,plain,
% 4.18/4.59 (((~![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(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(s(s(z))), 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)))))))),
% 4.18/4.59 inference(transitivity,[status(thm)],[31936, 31934])).
% 4.18/4.59 tff(31938,plain,
% 4.18/4.59 ((~![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(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)))))))),
% 4.18/4.59 inference(quant_inst,[status(thm)],[])).
% 4.18/4.59 tff(31939,plain,
% 4.18/4.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31938, 31937])).
% 4.18/4.59 tff(31940,plain,
% 4.18/4.59 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31939, 333, 3193, 31933, 353])).
% 4.18/4.59 tff(31941,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31940, 31929])).
% 4.18/4.59 tff(31942,plain,((~b(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(s(s(s(z)))) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(31943,plain,
% 4.18/4.59 (~b(s(elem!1), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31942, 31905, 31902, 17023, 1722, 133, 537, 31919, 304, 123, 321, 51, 624, 251])).
% 4.18/4.59 tff(31944,plain,
% 4.18/4.59 (r(s(elem!1), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[448, 31943, 433])).
% 4.18/4.59 tff(31945,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), elem!1)),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31944, 31915])).
% 4.18/4.59 tff(31946,plain,
% 4.18/4.59 (~r(s(s(s(s(z)))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[26847, 31945, 722, 409])).
% 4.18/4.59 tff(31947,plain,
% 4.18/4.59 (~r(s(elem!1), s(z))),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31946, 31910])).
% 4.18/4.59 tff(31948,plain,
% 4.18/4.59 (b(s(elem!1), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[486, 31947, 1])).
% 4.18/4.59 tff(31949,plain,
% 4.18/4.59 (~b(s(elem!1), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[499, 31948, 490, 489])).
% 4.18/4.59 tff(31950,plain,
% 4.18/4.59 (r(s(elem!1), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[507, 31949])).
% 4.18/4.59 tff(31951,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), z)),
% 4.18/4.59 inference(modus_ponens,[status(thm)],[31950, 31907])).
% 4.18/4.59 tff(31952,plain,
% 4.18/4.59 (b(s(s(s(s(z)))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[24600, 31946, 31919])).
% 4.18/4.59 tff(31953,plain,
% 4.18/4.59 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[26574, 31952, 304, 123])).
% 4.18/4.59 tff(31954,plain,
% 4.18/4.59 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[9761, 31953])).
% 4.18/4.59 tff(31955,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[12669, 333, 321, 51, 31954, 31951])).
% 4.18/4.59 tff(31956,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(elem!1) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(31957,plain,
% 4.18/4.59 (~b(s(s(s(z))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31956, 31783, 31773, 490, 31873, 1, 31793, 123, 31875, 2169, 31900, 133, 31897, 31785, 251, 31895])).
% 4.18/4.59 tff(31958,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31957, 31894])).
% 4.18/4.59 tff(31959,plain,((~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(31960,plain,
% 4.18/4.59 (~b(z, s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31959, 9095, 50, 1, 31619, 30657, 350, 706])).
% 4.18/4.59 tff(31961,plain,
% 4.18/4.59 (r(z, s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[372, 31960])).
% 4.18/4.59 tff(31962,plain,
% 4.18/4.59 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[24027, 408, 2323, 354])).
% 4.18/4.59 tff(31963,plain,
% 4.18/4.59 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[302, 31962])).
% 4.18/4.59 tff(31964,plain,
% 4.18/4.59 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[429, 354, 409, 51])).
% 4.18/4.59 tff(31965,plain,
% 4.18/4.59 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[319, 31964])).
% 4.18/4.59 tff(31966,plain,
% 4.18/4.59 (~r(s(z), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[417, 408, 409, 51])).
% 4.18/4.59 tff(31967,plain,
% 4.18/4.59 (b(s(z), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[348, 31966])).
% 4.18/4.59 tff(31968,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[7634, 144, 251, 31967, 133, 31965, 31963])).
% 4.18/4.59 tff(31969,plain,((~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(31970,plain,
% 4.18/4.59 (~r(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31969, 31619, 9095, 30657, 31961, 2169, 31771])).
% 4.18/4.59 tff(31971,plain,
% 4.18/4.59 (b(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[1380, 31970, 77])).
% 4.18/4.59 tff(31972,plain,
% 4.18/4.59 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[880, 31971, 9095, 31619])).
% 4.18/4.59 tff(31973,plain,
% 4.18/4.59 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[302, 31972])).
% 4.18/4.59 tff(31974,plain,
% 4.18/4.59 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[429, 31961, 2169, 31771])).
% 4.18/4.59 tff(31975,plain,
% 4.18/4.59 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[319, 31974])).
% 4.18/4.59 tff(31976,plain,
% 4.18/4.59 (~r(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31969, 251, 133, 2323, 354, 409, 51])).
% 4.18/4.59 tff(31977,plain,
% 4.18/4.59 (b(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[1380, 31976, 77])).
% 4.18/4.59 tff(31978,plain,
% 4.18/4.59 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[880, 31977, 133, 251])).
% 4.18/4.59 tff(31979,plain,
% 4.18/4.59 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[302, 31978])).
% 4.18/4.59 tff(31980,plain,
% 4.18/4.59 (~r(z, elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[3996, 333, 2323, 31979, 51])).
% 4.18/4.59 tff(31981,plain,
% 4.18/4.59 (~b(s(elem!1), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31760, 14077, 133, 354, 31980, 31979, 1, 706, 123, 14872, 31977, 251])).
% 4.18/4.59 tff(31982,plain,
% 4.18/4.59 (r(s(elem!1), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[448, 31981, 14076])).
% 4.18/4.59 tff(31983,plain,
% 4.18/4.59 (~r(s(elem!1), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31715, 333, 31982, 409, 2323])).
% 4.18/4.59 tff(31984,plain,
% 4.18/4.59 (b(s(elem!1), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[486, 31983, 1])).
% 4.18/4.59 tff(31985,plain,
% 4.18/4.59 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[869, 144, 31984, 123, 31965])).
% 4.18/4.59 tff(31986,plain,
% 4.18/4.59 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[472, 31985, 14872])).
% 4.18/4.59 tff(31987,plain,
% 4.18/4.59 (~r(elem!1, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[4103, 31986, 2323, 31979])).
% 4.18/4.59 tff(31988,plain,
% 4.18/4.59 (b(elem!1, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[560, 31987, 14077])).
% 4.18/4.59 tff(31989,plain,
% 4.18/4.59 (~r(z, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[940, 31986, 51, 31979])).
% 4.18/4.59 tff(31990,plain,
% 4.18/4.59 (b(z, s(elem!1))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[583, 31989])).
% 4.18/4.59 tff(31991,plain,
% 4.18/4.59 (~r(s(elem!1), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[14540, 31986, 354, 31979])).
% 4.18/4.59 tff(31992,plain,
% 4.18/4.59 (b(s(elem!1), z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[507, 31991])).
% 4.18/4.59 tff(31993,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[949, 31992, 31990, 31977, 31988])).
% 4.18/4.59 tff(31994,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(31995,plain,
% 4.18/4.59 (~(s(s(s(z))) = elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31994, 31961, 31771, 30657, 50, 1, 2169, 9095, 706, 31619])).
% 4.18/4.59 tff(31996,plain,
% 4.18/4.59 (r(s(s(s(z))), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31890, 31995, 50, 2169, 31975, 31771, 9095, 31619, 31971, 31973])).
% 4.18/4.59 tff(31997,plain,
% 4.18/4.59 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[31651, 31995, 31961, 31971, 31619, 31973, 30657])).
% 4.18/4.59 tff(31998,plain,
% 4.18/4.59 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[1137, 31997])).
% 4.18/4.59 tff(31999,plain,
% 4.18/4.59 (~b(s(s(s(z))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[6004, 144, 50, 31998, 31975])).
% 4.18/4.59 tff(32000,plain,
% 4.18/4.59 (r(s(s(s(z))), s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[2794, 31999])).
% 4.18/4.59 tff(32001,plain,
% 4.18/4.59 ($false),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[26742, 333, 2169, 32000, 31996, 30657])).
% 4.18/4.59 tff(32002,plain,(b(s(z), elem!1) | (s(elem!1) = s(z)) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.59 tff(32003,plain,
% 4.18/4.59 (b(s(z), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[32002, 31618, 54, 30654, 31616])).
% 4.18/4.59 tff(32004,plain,
% 4.18/4.59 (~(elem!1 = s(z))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[712, 31616])).
% 4.18/4.59 tff(32005,plain,
% 4.18/4.59 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[49, 30654])).
% 4.18/4.59 tff(32006,plain,
% 4.18/4.59 (b(s(z), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[32002, 8684, 54, 30654, 31616])).
% 4.18/4.59 tff(32007,plain,
% 4.18/4.59 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[130, 23983, 54])).
% 4.18/4.59 tff(32008,plain,
% 4.18/4.59 (~b(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[880, 286, 251, 133])).
% 4.18/4.59 tff(32009,plain,
% 4.18/4.59 (r(elem!1, z)),
% 4.18/4.59 inference(unit_resolution,[status(thm)],[653, 32008, 1368])).
% 4.18/4.59 tff(32010,plain,
% 4.18/4.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.59 inference(rewrite,[status(thm)],[])).
% 4.18/4.59 tff(32011,plain,
% 4.18/4.59 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.60 inference(rewrite,[status(thm)],[])).
% 4.18/4.60 tff(32012,plain,
% 4.18/4.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.18/4.60 inference(monotonicity,[status(thm)],[32011])).
% 4.18/4.60 tff(32013,plain,
% 4.18/4.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.18/4.60 inference(transitivity,[status(thm)],[32012, 32010])).
% 4.18/4.60 tff(32014,plain,
% 4.18/4.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.60 inference(quant_inst,[status(thm)],[])).
% 4.18/4.60 tff(32015,plain,
% 4.18/4.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.18/4.60 inference(modus_ponens,[status(thm)],[32014, 32013])).
% 4.18/4.60 tff(32016,plain,
% 4.18/4.60 (~b(s(z), z)),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[32015, 144, 251, 134, 123, 286])).
% 4.18/4.60 tff(32017,plain,
% 4.18/4.60 (r(s(z), z)),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[348, 32016])).
% 4.18/4.60 tff(32018,plain,
% 4.18/4.60 (~r(z, s(z))),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[747, 32017, 32009, 722])).
% 4.18/4.60 tff(32019,plain,
% 4.18/4.60 (b(z, s(z))),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[372, 32018])).
% 4.18/4.60 tff(32020,plain,
% 4.18/4.60 ($false),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[31002, 144, 134, 32019, 133, 304, 286])).
% 4.18/4.60 tff(32021,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.18/4.60 tff(32022,plain,
% 4.18/4.60 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[32021, 304, 32007, 134, 722, 251, 123, 77])).
% 4.18/4.60 tff(32023,plain,
% 4.18/4.60 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.18/4.60 inference(unit_resolution,[status(thm)],[302, 32022])).
% 4.18/4.60 tff(32024,plain,
% 4.18/4.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.60 inference(rewrite,[status(thm)],[])).
% 4.18/4.60 tff(32025,plain,
% 4.18/4.60 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.18/4.60 inference(rewrite,[status(thm)],[])).
% 4.18/4.60 tff(32026,plain,
% 4.18/4.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32025])).
% 4.27/4.60 tff(32027,plain,
% 4.27/4.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.60 inference(transitivity,[status(thm)],[32026, 32024])).
% 4.27/4.60 tff(32028,plain,
% 4.27/4.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 4.27/4.60 inference(quant_inst,[status(thm)],[])).
% 4.27/4.60 tff(32029,plain,
% 4.27/4.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[32028, 32027])).
% 4.27/4.60 tff(32030,plain,
% 4.27/4.60 (~b(s(z), s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[32029, 144, 134, 123, 32007, 23185])).
% 4.27/4.60 tff(32031,plain,
% 4.27/4.60 (r(s(z), s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[172, 32030])).
% 4.27/4.60 tff(32032,plain,
% 4.27/4.60 (~b(s(s(s(z))), s(z))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[6004, 144, 123, 23185, 304])).
% 4.27/4.60 tff(32033,plain,
% 4.27/4.60 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[803, 32019, 251, 123, 133])).
% 4.27/4.60 tff(32034,plain,
% 4.27/4.60 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[279, 32033])).
% 4.27/4.60 tff(32035,plain,
% 4.27/4.60 (~r(s(s(s(z))), z)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[13781, 32034, 123, 304, 32017])).
% 4.27/4.60 tff(32036,plain,
% 4.27/4.60 (b(s(s(s(z))), z)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[396, 32035])).
% 4.27/4.60 tff(32037,plain,
% 4.27/4.60 (~b(z, s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[294, 32036, 283, 286])).
% 4.27/4.60 tff(32038,plain,
% 4.27/4.60 (~(s(s(s(z))) = elem!1)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[380, 32036, 32008])).
% 4.27/4.60 tff(32039,plain,
% 4.27/4.60 (~r(z, s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[20631, 32038, 251, 134, 714, 32009, 32017])).
% 4.27/4.60 tff(32040,plain,
% 4.27/4.60 ($false),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[619, 32039, 32037])).
% 4.27/4.60 tff(32041,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.60 tff(32042,plain,
% 4.27/4.60 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[32041, 283, 134, 713, 251, 123, 304, 133, 722, 77])).
% 4.27/4.60 tff(32043,plain,
% 4.27/4.60 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[302, 32042])).
% 4.27/4.60 tff(32044,plain,
% 4.27/4.60 (s(s(z)) = elem!1),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[27825, 32043, 2671, 251, 133, 23943])).
% 4.27/4.60 tff(32045,plain,
% 4.27/4.60 (s(elem!1) = s(s(s(z)))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[11670, 32044])).
% 4.27/4.60 tff(32046,plain,
% 4.27/4.60 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32045])).
% 4.27/4.60 tff(32047,plain,
% 4.27/4.60 (s(elem!1) = s(s(s(z)))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[11670, 11666])).
% 4.27/4.60 tff(32048,plain,
% 4.27/4.60 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(z))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32047])).
% 4.27/4.60 tff(32049,plain,
% 4.27/4.60 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.27/4.60 inference(symmetry,[status(thm)],[32048])).
% 4.27/4.60 tff(32050,plain,
% 4.27/4.60 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32049])).
% 4.27/4.60 tff(32051,plain,
% 4.27/4.60 (~(s(s(s(z))) = elem!1)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[14611, 11666, 706])).
% 4.27/4.60 tff(32052,plain,
% 4.27/4.60 (~(elem!1 = s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[10997, 32051])).
% 4.27/4.60 tff(32053,plain,
% 4.27/4.60 (~(elem!1 = s(elem!1))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[32052, 32050])).
% 4.27/4.60 tff(32054,plain,
% 4.27/4.60 (~b(s(elem!1), s(z))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[8633, 32047, 2789])).
% 4.27/4.60 tff(32055,plain,
% 4.27/4.60 (r(s(elem!1), s(z))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[486, 32054, 1])).
% 4.27/4.60 tff(32056,plain,
% 4.27/4.60 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32047])).
% 4.27/4.60 tff(32057,plain,
% 4.27/4.60 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 4.27/4.60 inference(symmetry,[status(thm)],[32056])).
% 4.27/4.60 tff(32058,plain,
% 4.27/4.60 (r(s(z), s(elem!1))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[353, 32057])).
% 4.27/4.60 tff(32059,plain,
% 4.27/4.60 (~r(elem!1, s(elem!1))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[7799, 32058, 722, 32055])).
% 4.27/4.60 tff(32060,plain,
% 4.27/4.60 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32047])).
% 4.27/4.60 tff(32061,plain,
% 4.27/4.60 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 4.27/4.60 inference(symmetry,[status(thm)],[32060])).
% 4.27/4.60 tff(32062,plain,
% 4.27/4.60 (b(s(s(s(z))), elem!1)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[17954, 32047, 1727, 1])).
% 4.27/4.60 tff(32063,plain,
% 4.27/4.60 (b(s(elem!1), elem!1)),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[32062, 32061])).
% 4.27/4.60 tff(32064,plain,
% 4.27/4.60 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32047])).
% 4.27/4.60 tff(32065,plain,
% 4.27/4.60 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.60 inference(symmetry,[status(thm)],[32064])).
% 4.27/4.60 tff(32066,plain,
% 4.27/4.60 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[283, 32065])).
% 4.27/4.60 tff(32067,plain,
% 4.27/4.60 (~b(elem!1, s(elem!1))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[555, 32066, 133, 32063])).
% 4.27/4.60 tff(32068,plain,
% 4.27/4.60 ($false),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[560, 32067, 32059, 32053])).
% 4.27/4.60 tff(32069,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | b(s(s(s(z))), s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.60 tff(32070,plain,
% 4.27/4.60 (r(s(elem!1), elem!1)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[32069, 32044, 722, 283, 353, 1, 133, 2789, 706])).
% 4.27/4.60 tff(32071,plain,
% 4.27/4.60 (r(s(s(s(z))), elem!1)),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[32070, 32046])).
% 4.27/4.60 tff(32072,plain,
% 4.27/4.60 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32045])).
% 4.27/4.60 tff(32073,plain,
% 4.27/4.60 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 4.27/4.60 inference(symmetry,[status(thm)],[32072])).
% 4.27/4.60 tff(32074,plain,
% 4.27/4.60 (r(s(z), s(elem!1))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[353, 32073])).
% 4.27/4.60 tff(32075,plain,
% 4.27/4.60 ($false),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[8957, 32074, 32071, 7586, 722])).
% 4.27/4.60 tff(32076,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | b(s(s(s(z))), s(z)) | (s(z) = elem!1) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.60 tff(32077,plain,
% 4.27/4.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[32076, 32032, 32031, 1, 32007, 722, 706, 2671, 251, 134, 123, 304])).
% 4.27/4.60 tff(32078,plain,
% 4.27/4.60 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[249, 32077])).
% 4.27/4.60 tff(32079,plain,
% 4.27/4.60 (~(s(s(s(z))) = elem!1)),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[227, 32078, 54])).
% 4.27/4.60 tff(32080,plain,
% 4.27/4.60 (r(s(s(s(z))), s(z))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[2794, 32032])).
% 4.27/4.60 tff(32081,plain,
% 4.27/4.60 (s(s(z)) = elem!1),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[27825, 32023, 2671, 251, 32007, 23943])).
% 4.27/4.60 tff(32082,plain,
% 4.27/4.60 (s(elem!1) = s(s(s(z)))),
% 4.27/4.60 inference(unit_resolution,[status(thm)],[11670, 32081])).
% 4.27/4.60 tff(32083,plain,
% 4.27/4.60 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 4.27/4.60 inference(monotonicity,[status(thm)],[32082])).
% 4.27/4.60 tff(32084,plain,
% 4.27/4.60 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 4.27/4.60 inference(symmetry,[status(thm)],[32083])).
% 4.27/4.60 tff(32085,plain,
% 4.27/4.60 (r(s(z), s(elem!1))),
% 4.27/4.60 inference(modus_ponens,[status(thm)],[32031, 32084])).
% 4.27/4.61 tff(32086,plain,
% 4.27/4.61 (~r(s(s(s(z))), elem!1)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[8957, 32085, 32080, 722])).
% 4.27/4.61 tff(32087,plain,
% 4.27/4.61 (b(s(s(s(z))), elem!1)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[704, 32086, 32079])).
% 4.27/4.61 tff(32088,plain,
% 4.27/4.61 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32082])).
% 4.27/4.61 tff(32089,plain,
% 4.27/4.61 ((s(s(z)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32081])).
% 4.27/4.61 tff(32090,plain,
% 4.27/4.61 ((~(s(s(z)) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32089])).
% 4.27/4.61 tff(32091,plain,
% 4.27/4.61 (~(elem!1 = s(elem!1))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[856, 32090])).
% 4.27/4.61 tff(32092,plain,
% 4.27/4.61 (~b(s(elem!1), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[8633, 32082, 32032])).
% 4.27/4.61 tff(32093,plain,
% 4.27/4.61 (r(s(elem!1), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[486, 32092, 1])).
% 4.27/4.61 tff(32094,plain,
% 4.27/4.61 (~r(elem!1, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[7799, 32085, 722, 32093])).
% 4.27/4.61 tff(32095,plain,
% 4.27/4.61 (b(elem!1, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[560, 32094, 32091])).
% 4.27/4.61 tff(32096,plain,
% 4.27/4.61 (b(elem!1, s(s(s(z))))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32095, 32088])).
% 4.27/4.61 tff(32097,plain,
% 4.27/4.61 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[11866, 32096, 251, 32007, 32080, 32087])).
% 4.27/4.61 tff(32098,plain,
% 4.27/4.61 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[279, 32097])).
% 4.27/4.61 tff(32099,plain,
% 4.27/4.61 (~b(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[757, 32098, 123, 304])).
% 4.27/4.61 tff(32100,plain,
% 4.27/4.61 (r(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[372, 32099])).
% 4.27/4.61 tff(32101,plain,
% 4.27/4.61 (~r(elem!1, z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[24027, 32100, 32023, 23943])).
% 4.27/4.61 tff(32102,plain,
% 4.27/4.61 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32082])).
% 4.27/4.61 tff(32103,plain,
% 4.27/4.61 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(symmetry,[status(thm)],[32102])).
% 4.27/4.61 tff(32104,plain,
% 4.27/4.61 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32103])).
% 4.27/4.61 tff(32105,plain,
% 4.27/4.61 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[7927, 32104])).
% 4.27/4.61 tff(32106,plain,
% 4.27/4.61 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32082])).
% 4.27/4.61 tff(32107,plain,
% 4.27/4.61 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 4.27/4.61 inference(symmetry,[status(thm)],[32106])).
% 4.27/4.61 tff(32108,plain,
% 4.27/4.61 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), s(elem!1)))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32107])).
% 4.27/4.61 tff(32109,plain,
% 4.27/4.61 (~b(s(z), s(elem!1))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32030, 32108])).
% 4.27/4.61 tff(32110,plain,
% 4.27/4.61 (~b(elem!1, z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[3415, 32100, 123, 1, 32109, 304, 32105, 32095])).
% 4.27/4.61 tff(32111,plain,
% 4.27/4.61 ($false),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[1380, 32110, 32101, 77])).
% 4.27/4.61 tff(32112,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.61 tff(32113,plain,
% 4.27/4.61 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32112, 722, 1, 251, 123, 7927, 2671, 134, 54, 706])).
% 4.27/4.61 tff(32114,plain,
% 4.27/4.61 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[319, 32113])).
% 4.27/4.61 tff(32115,plain,
% 4.27/4.61 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[2331, 32009, 2323, 322])).
% 4.27/4.61 tff(32116,plain,
% 4.27/4.61 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[279, 32115])).
% 4.27/4.61 tff(32117,plain,
% 4.27/4.61 (~b(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[803, 32116, 251, 123, 133])).
% 4.27/4.61 tff(32118,plain,
% 4.27/4.61 (r(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[372, 32117])).
% 4.27/4.61 tff(32119,plain,
% 4.27/4.61 (~b(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[7741, 32116, 123, 286])).
% 4.27/4.61 tff(32120,plain,
% 4.27/4.61 (r(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[348, 32119])).
% 4.27/4.61 tff(32121,plain,
% 4.27/4.61 ($false),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[747, 32120, 32118, 32009, 722])).
% 4.27/4.61 tff(32122,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.61 tff(32123,plain,
% 4.27/4.61 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32122, 722, 123, 251, 32007, 23943, 32114, 77])).
% 4.27/4.61 tff(32124,plain,
% 4.27/4.61 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[302, 32123])).
% 4.27/4.61 tff(32125,plain,
% 4.27/4.61 (~r(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[362, 32124, 32114, 32031])).
% 4.27/4.61 tff(32126,plain,
% 4.27/4.61 (b(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[372, 32125])).
% 4.27/4.61 tff(32127,plain,
% 4.27/4.61 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[803, 32126, 251, 123, 32007])).
% 4.27/4.61 tff(32128,plain,
% 4.27/4.61 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[279, 32127])).
% 4.27/4.61 tff(32129,plain,
% 4.27/4.61 (~r(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[341, 32128, 32114, 32124])).
% 4.27/4.61 tff(32130,plain,
% 4.27/4.61 (~r(elem!1, z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[2331, 32128, 23943, 32114])).
% 4.27/4.61 tff(32131,plain,
% 4.27/4.61 (~b(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[3332, 32130, 123, 54, 32124, 134, 77])).
% 4.27/4.61 tff(32132,plain,
% 4.27/4.61 ($false),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[348, 32131, 32129])).
% 4.27/4.61 tff(32133,plain,((~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.61 tff(32134,plain,
% 4.27/4.61 (~r(elem!1, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32133, 7927, 54, 134, 251, 1, 123, 2671, 706])).
% 4.27/4.61 tff(32135,plain,
% 4.27/4.61 (b(elem!1, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[720, 32134, 713])).
% 4.27/4.61 tff(32136,plain,
% 4.27/4.61 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[3955, 32135, 134, 32007])).
% 4.27/4.61 tff(32137,plain,
% 4.27/4.61 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[319, 32136])).
% 4.27/4.61 tff(32138,plain,
% 4.27/4.61 (~b(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[7079, 32135, 251, 134])).
% 4.27/4.61 tff(32139,plain,
% 4.27/4.61 (r(z, s(z))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[372, 32138])).
% 4.27/4.61 tff(32140,plain,
% 4.27/4.61 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[362, 32139, 32137, 32031])).
% 4.27/4.61 tff(32141,plain,
% 4.27/4.61 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[302, 32140])).
% 4.27/4.61 tff(32142,plain,
% 4.27/4.61 (~b(elem!1, z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[880, 32141, 251, 32007])).
% 4.27/4.61 tff(32143,plain,
% 4.27/4.61 (r(elem!1, z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[653, 32142, 77])).
% 4.27/4.61 tff(32144,plain,
% 4.27/4.61 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[2331, 32143, 23943, 32137])).
% 4.27/4.61 tff(32145,plain,
% 4.27/4.61 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[279, 32144])).
% 4.27/4.61 tff(32146,plain,
% 4.27/4.61 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[31633, 144, 251, 32007, 23185])).
% 4.27/4.61 tff(32147,plain,
% 4.27/4.61 (~b(z, s(s(s(z))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32146, 32145])).
% 4.27/4.61 tff(32148,plain,
% 4.27/4.61 (r(z, s(s(s(z))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[619, 32147])).
% 4.27/4.61 tff(32149,plain,
% 4.27/4.61 (~(s(s(s(z))) = elem!1)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[257, 32147, 251])).
% 4.27/4.61 tff(32150,plain,
% 4.27/4.61 (~b(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[7741, 32145, 123, 32141])).
% 4.27/4.61 tff(32151,plain,
% 4.27/4.61 (r(s(z), z)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[348, 32150])).
% 4.27/4.61 tff(32152,plain,
% 4.27/4.61 ($false),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[20631, 32151, 32149, 251, 134, 713, 32143, 32148])).
% 4.27/4.61 tff(32153,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.61 tff(32154,plain,
% 4.27/4.61 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32153, 2671, 134, 123, 54, 1, 251, 706])).
% 4.27/4.61 tff(32155,plain,
% 4.27/4.61 (s(s(z)) = elem!1),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[27825, 321, 2671, 251, 133, 23943])).
% 4.27/4.61 tff(32156,plain,
% 4.27/4.61 (s(elem!1) = s(s(s(z)))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[11670, 32155])).
% 4.27/4.61 tff(32157,plain,
% 4.27/4.61 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32156])).
% 4.27/4.61 tff(32158,plain,
% 4.27/4.61 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(symmetry,[status(thm)],[32157])).
% 4.27/4.61 tff(32159,plain,
% 4.27/4.61 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[6107, 32158])).
% 4.27/4.61 tff(32160,plain,
% 4.27/4.61 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(z))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32156])).
% 4.27/4.61 tff(32161,plain,
% 4.27/4.61 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.27/4.61 inference(symmetry,[status(thm)],[32160])).
% 4.27/4.61 tff(32162,plain,
% 4.27/4.61 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32161])).
% 4.27/4.61 tff(32163,plain,
% 4.27/4.61 (~(s(s(s(z))) = elem!1)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[14611, 32155, 706])).
% 4.27/4.61 tff(32164,plain,
% 4.27/4.61 (~(elem!1 = s(s(s(z))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[10997, 32163])).
% 4.27/4.61 tff(32165,plain,
% 4.27/4.61 (~(elem!1 = s(elem!1))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32164, 32162])).
% 4.27/4.61 tff(32166,plain,
% 4.27/4.61 (~r(elem!1, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[4103, 32159, 321, 23943])).
% 4.27/4.61 tff(32167,plain,
% 4.27/4.61 (b(elem!1, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[560, 32166, 32165])).
% 4.27/4.61 tff(32168,plain,
% 4.27/4.61 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.27/4.61 inference(transitivity,[status(thm)],[32161, 199])).
% 4.27/4.61 tff(32169,plain,
% 4.27/4.61 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32168])).
% 4.27/4.61 tff(32170,plain,
% 4.27/4.61 (~(s(elem!1) = elem!1)),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32164, 32169])).
% 4.27/4.61 tff(32171,plain,
% 4.27/4.61 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32156])).
% 4.27/4.61 tff(32172,plain,
% 4.27/4.61 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 4.27/4.61 inference(symmetry,[status(thm)],[32171])).
% 4.27/4.61 tff(32173,plain,
% 4.27/4.61 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32156])).
% 4.27/4.61 tff(32174,plain,
% 4.27/4.61 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 4.27/4.61 inference(symmetry,[status(thm)],[32173])).
% 4.27/4.61 tff(32175,plain,
% 4.27/4.61 (s(s(z)) = elem!1),
% 4.27/4.61 inference(transitivity,[status(thm)],[87, 32174, 850])).
% 4.27/4.61 tff(32176,plain,
% 4.27/4.61 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32175])).
% 4.27/4.61 tff(32177,plain,
% 4.27/4.61 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), elem!1)),
% 4.27/4.61 inference(transitivity,[status(thm)],[32176, 32172])).
% 4.27/4.61 tff(32178,plain,
% 4.27/4.61 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(elem!1), elem!1))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32177])).
% 4.27/4.61 tff(32179,plain,
% 4.27/4.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.61 inference(rewrite,[status(thm)],[])).
% 4.27/4.61 tff(32180,plain,
% 4.27/4.61 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.61 inference(rewrite,[status(thm)],[])).
% 4.27/4.61 tff(32181,plain,
% 4.27/4.61 (((~![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(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.27/4.61 inference(monotonicity,[status(thm)],[32180])).
% 4.27/4.61 tff(32182,plain,
% 4.27/4.61 (((~![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(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.61 inference(transitivity,[status(thm)],[32181, 32179])).
% 4.27/4.61 tff(32183,plain,
% 4.27/4.61 ((~![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(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.27/4.61 inference(quant_inst,[status(thm)],[])).
% 4.27/4.61 tff(32184,plain,
% 4.27/4.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32183, 32182])).
% 4.27/4.61 tff(32185,plain,
% 4.27/4.61 (~r(s(s(s(z))), s(s(z)))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[32184, 333, 2671, 6107, 321])).
% 4.27/4.61 tff(32186,plain,
% 4.27/4.61 (~r(s(elem!1), elem!1)),
% 4.27/4.61 inference(modus_ponens,[status(thm)],[32185, 32178])).
% 4.27/4.61 tff(32187,plain,
% 4.27/4.61 (b(s(elem!1), elem!1)),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[448, 32186, 32170])).
% 4.27/4.61 tff(32188,plain,
% 4.27/4.61 (~b(z, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[1642, 32187, 251, 32167])).
% 4.27/4.61 tff(32189,plain,
% 4.27/4.61 (r(z, s(elem!1))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[583, 32188])).
% 4.27/4.61 tff(32190,plain,
% 4.27/4.61 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[940, 32189, 32159, 321])).
% 4.27/4.61 tff(32191,plain,
% 4.27/4.61 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.61 inference(unit_resolution,[status(thm)],[279, 32190])).
% 4.27/4.61 tff(32192,plain,
% 4.27/4.61 (~b(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[803, 32191, 251, 123, 133])).
% 4.27/4.62 tff(32193,plain,
% 4.27/4.62 (r(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[372, 32192])).
% 4.27/4.62 tff(32194,plain,
% 4.27/4.62 (b(s(s(s(z))), elem!1)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[17954, 32186, 32156, 1])).
% 4.27/4.62 tff(32195,plain,
% 4.27/4.62 (~r(s(s(s(z))), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[10450, 32189, 6107, 321])).
% 4.27/4.62 tff(32196,plain,
% 4.27/4.62 (b(s(s(s(z))), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[396, 32195])).
% 4.27/4.62 tff(32197,plain,
% 4.27/4.62 (~b(elem!1, z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[10565, 32196, 251, 32194])).
% 4.27/4.62 tff(32198,plain,
% 4.27/4.62 (r(elem!1, z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[653, 32197, 77])).
% 4.27/4.62 tff(32199,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[24027, 32198, 32193, 321, 23943])).
% 4.27/4.62 tff(32200,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.62 tff(32201,plain,
% 4.27/4.62 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32200, 32154, 123, 32007, 251, 1, 2671, 706])).
% 4.27/4.62 tff(32202,plain,
% 4.27/4.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[302, 32201])).
% 4.27/4.62 tff(32203,plain,
% 4.27/4.62 (((~![X0: $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(s(z))))))), s(z))) | (~r(s(s(z)), 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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(rewrite,[status(thm)],[])).
% 4.27/4.62 tff(32204,plain,
% 4.27/4.62 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(rewrite,[status(thm)],[])).
% 4.27/4.62 tff(32205,plain,
% 4.27/4.62 (((~![X0: $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(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), 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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.62 inference(monotonicity,[status(thm)],[32204])).
% 4.27/4.62 tff(32206,plain,
% 4.27/4.62 (((~![X0: $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(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), 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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(transitivity,[status(thm)],[32205, 32203])).
% 4.27/4.62 tff(32207,plain,
% 4.27/4.62 ((~![X0: $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(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(quant_inst,[status(thm)],[])).
% 4.27/4.62 tff(32208,plain,
% 4.27/4.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.62 inference(modus_ponens,[status(thm)],[32207, 32206])).
% 4.27/4.62 tff(32209,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32208, 333, 323, 2671, 322, 9770])).
% 4.27/4.62 tff(32210,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.62 tff(32211,plain,
% 4.27/4.62 (~r(s(s(z)), s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32210, 322, 2671, 32017])).
% 4.27/4.62 tff(32212,plain,
% 4.27/4.62 (b(s(s(z)), s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[1429, 44, 32211, 1416])).
% 4.27/4.62 tff(32213,plain,
% 4.27/4.62 (~r(elem!1, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32122, 322, 123, 251, 133, 2323, 286, 1368])).
% 4.27/4.62 tff(32214,plain,
% 4.27/4.62 (b(elem!1, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[720, 32213, 713])).
% 4.27/4.62 tff(32215,plain,
% 4.27/4.62 (~b(s(s(z)), elem!1)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[23000, 144, 134, 32214, 32212])).
% 4.27/4.62 tff(32216,plain,
% 4.27/4.62 (s(s(z)) = elem!1),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[7970, 32215, 29944])).
% 4.27/4.62 tff(32217,plain,
% 4.27/4.62 (~(s(s(s(z))) = elem!1)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[14611, 32216, 706])).
% 4.27/4.62 tff(32218,plain,
% 4.27/4.62 (~r(z, s(s(s(z))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[20631, 32217, 251, 134, 713, 32009, 32017])).
% 4.27/4.62 tff(32219,plain,
% 4.27/4.62 (~r(s(s(s(z))), elem!1)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[27590, 333, 2323, 6107, 322])).
% 4.27/4.62 tff(32220,plain,
% 4.27/4.62 (~b(z, s(s(s(z))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[21799, 32217, 251, 28775, 32219])).
% 4.27/4.62 tff(32221,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[619, 32220, 32218])).
% 4.27/4.62 tff(32222,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(z) = elem!1) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.62 tff(32223,plain,
% 4.27/4.62 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32222, 2671, 134, 706, 251, 23943, 32154, 123, 32007, 32202, 77])).
% 4.27/4.62 tff(32224,plain,
% 4.27/4.62 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[319, 32223])).
% 4.27/4.62 tff(32225,plain,
% 4.27/4.62 (~b(elem!1, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[3955, 32224, 134, 32007])).
% 4.27/4.62 tff(32226,plain,
% 4.27/4.62 (~r(elem!1, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32021, 32224, 32007, 134, 32202, 251, 123, 77])).
% 4.27/4.62 tff(32227,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[720, 32226, 32225, 713])).
% 4.27/4.62 tff(32228,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (s(elem!1) = s(z)) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.62 tff(32229,plain,
% 4.27/4.62 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32228, 8684, 54, 32005, 31602, 31616, 32006])).
% 4.27/4.62 tff(32230,plain,
% 4.27/4.62 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 4.27/4.62 inference(commutativity,[status(thm)],[])).
% 4.27/4.62 tff(32231,plain,
% 4.27/4.62 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 4.27/4.62 inference(symmetry,[status(thm)],[32230])).
% 4.27/4.62 tff(32232,plain,
% 4.27/4.62 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 4.27/4.62 inference(monotonicity,[status(thm)],[32231])).
% 4.27/4.62 tff(32233,plain,
% 4.27/4.62 (~(s(z) = s(s(z)))),
% 4.27/4.62 inference(modus_ponens,[status(thm)],[1416, 32232])).
% 4.27/4.62 tff(32234,plain,
% 4.27/4.62 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[130, 24230, 54])).
% 4.27/4.62 tff(32235,plain,
% 4.27/4.62 (~b(s(z), s(s(z)))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[31152, 144, 134, 1398, 123, 32234])).
% 4.27/4.62 tff(32236,plain,
% 4.27/4.62 (((~![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))))),
% 4.27/4.62 inference(rewrite,[status(thm)],[])).
% 4.27/4.62 tff(32237,plain,
% 4.27/4.62 ((~![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))))),
% 4.27/4.62 inference(quant_inst,[status(thm)],[])).
% 4.27/4.62 tff(32238,plain,
% 4.27/4.62 ((~![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)))),
% 4.27/4.62 inference(modus_ponens,[status(thm)],[32237, 32236])).
% 4.27/4.62 tff(32239,plain,
% 4.27/4.62 ((s(z) = s(s(z))) | r(s(z), s(s(z)))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32238, 44, 32235])).
% 4.27/4.62 tff(32240,plain,
% 4.27/4.62 (r(s(z), s(s(z)))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32239, 32233])).
% 4.27/4.62 tff(32241,plain,
% 4.27/4.62 (~r(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[24027, 408, 321, 2323])).
% 4.27/4.62 tff(32242,plain,
% 4.27/4.62 (b(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[372, 32241])).
% 4.27/4.62 tff(32243,plain,
% 4.27/4.62 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[803, 32242, 251, 123, 133])).
% 4.27/4.62 tff(32244,plain,
% 4.27/4.62 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[279, 32243])).
% 4.27/4.62 tff(32245,plain,
% 4.27/4.62 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(rewrite,[status(thm)],[])).
% 4.27/4.62 tff(32246,plain,
% 4.27/4.62 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.62 inference(monotonicity,[status(thm)],[32245])).
% 4.27/4.62 tff(32247,plain,
% 4.27/4.62 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(transitivity,[status(thm)],[32246, 27684])).
% 4.27/4.62 tff(32248,plain,
% 4.27/4.62 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.62 inference(quant_inst,[status(thm)],[])).
% 4.27/4.62 tff(32249,plain,
% 4.27/4.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.62 inference(modus_ponens,[status(thm)],[32248, 32247])).
% 4.27/4.62 tff(32250,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32249, 333, 408, 2323, 321, 32244])).
% 4.27/4.62 tff(32251,plain,((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.62 tff(32252,plain,
% 4.27/4.62 (~r(elem!1, z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[32251, 321, 2323, 251, 123, 32234])).
% 4.27/4.62 tff(32253,plain,
% 4.27/4.62 (~b(s(z), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[3332, 32252, 123, 54, 321, 134, 1368])).
% 4.27/4.62 tff(32254,plain,
% 4.27/4.62 (r(s(z), z)),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[348, 32253])).
% 4.27/4.62 tff(32255,plain,
% 4.27/4.62 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[341, 32254, 321, 322])).
% 4.27/4.62 tff(32256,plain,
% 4.27/4.62 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[279, 32255])).
% 4.27/4.62 tff(32257,plain,
% 4.27/4.62 (~b(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[803, 32256, 251, 123, 32234])).
% 4.27/4.62 tff(32258,plain,
% 4.27/4.62 (r(z, s(z))),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[372, 32257])).
% 4.27/4.62 tff(32259,plain,
% 4.27/4.62 ($false),
% 4.27/4.62 inference(unit_resolution,[status(thm)],[14867, 333, 32258, 32254, 322, 321])).
% 4.27/4.62 tff(32260,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32261,plain,
% 4.27/4.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32260, 322, 251, 123, 54, 134, 1368, 2323])).
% 4.27/4.63 tff(32262,plain,
% 4.27/4.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[302, 32261])).
% 4.27/4.63 tff(32263,plain,
% 4.27/4.63 (~b(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[880, 32262, 251, 32234])).
% 4.27/4.63 tff(32264,plain,
% 4.27/4.63 (r(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[653, 32263, 1368])).
% 4.27/4.63 tff(32265,plain,
% 4.27/4.63 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[2331, 32264, 2323, 322])).
% 4.27/4.63 tff(32266,plain,
% 4.27/4.63 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[279, 32265])).
% 4.27/4.63 tff(32267,plain,
% 4.27/4.63 (~b(s(s(z)), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[19968, 144, 1398, 32262, 32266])).
% 4.27/4.63 tff(32268,plain,
% 4.27/4.63 (r(s(s(z)), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1462, 44, 164, 32267])).
% 4.27/4.63 tff(32269,plain,
% 4.27/4.63 (~b(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[7741, 32266, 123, 32262])).
% 4.27/4.63 tff(32270,plain,
% 4.27/4.63 (r(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[348, 32269])).
% 4.27/4.63 tff(32271,plain,
% 4.27/4.63 (~r(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32122, 32262, 123, 251, 32234, 2323, 322, 1368])).
% 4.27/4.63 tff(32272,plain,
% 4.27/4.63 (b(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[720, 32271, 714])).
% 4.27/4.63 tff(32273,plain,
% 4.27/4.63 (~b(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[7079, 32272, 251, 134])).
% 4.27/4.63 tff(32274,plain,
% 4.27/4.63 (r(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[372, 32273])).
% 4.27/4.63 tff(32275,plain,
% 4.27/4.63 (((~![X0: $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)))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32276,plain,
% 4.27/4.63 (((~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)))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32277,plain,
% 4.27/4.63 (((~![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))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32276])).
% 4.27/4.63 tff(32278,plain,
% 4.27/4.63 (((~![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)))),
% 4.27/4.63 inference(transitivity,[status(thm)],[32277, 32275])).
% 4.27/4.63 tff(32279,plain,
% 4.27/4.63 ((~![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)))))),
% 4.27/4.63 inference(quant_inst,[status(thm)],[])).
% 4.27/4.63 tff(32280,plain,
% 4.27/4.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[32279, 32278])).
% 4.27/4.63 tff(32281,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32280, 333, 32274, 32270, 32268, 32240])).
% 4.27/4.63 tff(32282,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(z)) | (elem!1 = z) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32283,plain,
% 4.27/4.63 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32282, 32006, 54, 31602, 32005, 31615, 32004, 730, 322])).
% 4.27/4.63 tff(32284,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1451, 32283, 32229])).
% 4.27/4.63 tff(32285,plain,((z = elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32286,plain,
% 4.27/4.63 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32285, 31617, 54])).
% 4.27/4.63 tff(32287,plain,
% 4.27/4.63 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[319, 32286])).
% 4.27/4.63 tff(32288,plain,
% 4.27/4.63 (~b(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[3955, 304, 134, 133])).
% 4.27/4.63 tff(32289,plain,
% 4.27/4.63 (~r(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32021, 304, 133, 134, 286, 251, 123, 1368])).
% 4.27/4.63 tff(32290,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[720, 32289, 32288, 714])).
% 4.27/4.63 tff(32291,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32292,plain,
% 4.27/4.63 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32291, 32287, 27421, 32005, 31602, 32004, 32003, 31611])).
% 4.27/4.63 tff(32293,plain,
% 4.27/4.63 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[302, 32292])).
% 4.27/4.63 tff(32294,plain,
% 4.27/4.63 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32228, 31618, 54, 32005, 31602, 31616, 32003])).
% 4.27/4.63 tff(32295,plain,
% 4.27/4.63 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1451, 32294])).
% 4.27/4.63 tff(32296,plain,
% 4.27/4.63 (b(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1380, 32252, 1368])).
% 4.27/4.63 tff(32297,plain,
% 4.27/4.63 (r(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[720, 32288, 714])).
% 4.27/4.63 tff(32298,plain,
% 4.27/4.63 (~r(s(s(s(z))), elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[8824, 32080, 323, 32297])).
% 4.27/4.63 tff(32299,plain,
% 4.27/4.63 (~b(s(s(z)), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1425, 304, 123, 1398])).
% 4.27/4.63 tff(32300,plain,
% 4.27/4.63 (r(s(s(z)), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1429, 44, 32299, 1416])).
% 4.27/4.63 tff(32301,plain,
% 4.27/4.63 (~r(s(s(z)), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[9276, 333, 323, 32080, 32300])).
% 4.27/4.63 tff(32302,plain,
% 4.27/4.63 (b(s(s(z)), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1473, 44, 32301, 217])).
% 4.27/4.63 tff(32303,plain,
% 4.27/4.63 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[7952, 32302, 1398, 7927])).
% 4.27/4.63 tff(32304,plain,
% 4.27/4.63 (~(s(s(s(z))) = elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[227, 32303, 54])).
% 4.27/4.63 tff(32305,plain,
% 4.27/4.63 (b(s(s(s(z))), elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[704, 32304, 32298])).
% 4.27/4.63 tff(32306,plain,
% 4.27/4.63 (~b(s(s(s(z))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[10565, 32305, 251, 624])).
% 4.27/4.63 tff(32307,plain,
% 4.27/4.63 (r(s(s(s(z))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[396, 32306])).
% 4.27/4.63 tff(32308,plain,
% 4.27/4.63 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[13781, 32307, 123, 323, 304])).
% 4.27/4.63 tff(32309,plain,
% 4.27/4.63 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[279, 32308])).
% 4.27/4.63 tff(32310,plain,
% 4.27/4.63 (~b(s(z), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32029, 144, 134, 123, 133, 23185])).
% 4.27/4.63 tff(32311,plain,
% 4.27/4.63 (r(s(z), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[172, 32310])).
% 4.27/4.63 tff(32312,plain,
% 4.27/4.63 (~r(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[7314, 32307, 32311, 323])).
% 4.27/4.63 tff(32313,plain,
% 4.27/4.63 (b(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[372, 32312])).
% 4.27/4.63 tff(32314,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[803, 32313, 32309, 251, 123, 133])).
% 4.27/4.63 tff(32315,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32316,plain,
% 4.27/4.63 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32315, 32254, 123, 32234, 251, 32296, 54, 1398, 7927, 714, 134])).
% 4.27/4.63 tff(32317,plain,
% 4.27/4.63 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[319, 32316])).
% 4.27/4.63 tff(32318,plain,
% 4.27/4.63 (~r(z, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[642, 32317, 321, 32254])).
% 4.27/4.63 tff(32319,plain,
% 4.27/4.63 (b(z, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[619, 32318])).
% 4.27/4.63 tff(32320,plain,
% 4.27/4.63 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[341, 32317, 32254, 321])).
% 4.27/4.63 tff(32321,plain,
% 4.27/4.63 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[279, 32320])).
% 4.27/4.63 tff(32322,plain,
% 4.27/4.63 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[31633, 144, 251, 32234, 23185])).
% 4.27/4.63 tff(32323,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32322, 32321, 32319])).
% 4.27/4.63 tff(32324,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32325,plain,
% 4.27/4.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32324, 7927, 123, 54, 1398, 251, 714, 134, 1368, 2323])).
% 4.27/4.63 tff(32326,plain,
% 4.27/4.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[302, 32325])).
% 4.27/4.63 tff(32327,plain,
% 4.27/4.63 (~b(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32015, 144, 251, 134, 123, 32326])).
% 4.27/4.63 tff(32328,plain,
% 4.27/4.63 (r(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[348, 32327])).
% 4.27/4.63 tff(32329,plain,
% 4.27/4.63 (~b(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[880, 32326, 251, 32234])).
% 4.27/4.63 tff(32330,plain,
% 4.27/4.63 (r(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[653, 32329, 1368])).
% 4.27/4.63 tff(32331,plain,
% 4.27/4.63 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32291, 32326, 32234, 134, 714, 251, 123, 1368])).
% 4.27/4.63 tff(32332,plain,
% 4.27/4.63 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[319, 32331])).
% 4.27/4.63 tff(32333,plain,
% 4.27/4.63 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[2331, 32332, 2323, 32330])).
% 4.27/4.63 tff(32334,plain,
% 4.27/4.63 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[279, 32333])).
% 4.27/4.63 tff(32335,plain,
% 4.27/4.63 (~b(z, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32322, 32334])).
% 4.27/4.63 tff(32336,plain,
% 4.27/4.63 (r(z, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[619, 32335])).
% 4.27/4.63 tff(32337,plain,
% 4.27/4.63 (~(s(s(s(z))) = elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[257, 32335, 251])).
% 4.27/4.63 tff(32338,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[20631, 32337, 32336, 251, 134, 714, 32330, 32328])).
% 4.27/4.63 tff(32339,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32340,plain,
% 4.27/4.63 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32339, 32295, 54, 32005, 31615, 31602, 32004, 31611, 32003])).
% 4.27/4.63 tff(32341,plain,
% 4.27/4.63 (~r(elem!1, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[31676, 333, 31615, 32340, 32293])).
% 4.27/4.63 tff(32342,plain,
% 4.27/4.63 (~r(s(s(s(z))), elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[31645, 333, 31615, 32340, 32293])).
% 4.27/4.63 tff(32343,plain,
% 4.27/4.63 (~(s(s(z)) = s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[855, 31616])).
% 4.27/4.63 tff(32344,plain,
% 4.27/4.63 (~(s(s(s(z))) = s(s(elem!1)))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[862, 32343])).
% 4.27/4.63 tff(32345,plain,
% 4.27/4.63 (~b(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[3955, 32287, 27421, 32003])).
% 4.27/4.63 tff(32346,plain,
% 4.27/4.63 (r(elem!1, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[720, 32345, 32004])).
% 4.27/4.63 tff(32347,plain,
% 4.27/4.63 (~r(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32251, 32293, 27421, 32005, 31615, 31602])).
% 4.27/4.63 tff(32348,plain,
% 4.27/4.63 (~b(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[3332, 32293, 54, 32005, 32003, 32347, 31611])).
% 4.27/4.63 tff(32349,plain,
% 4.27/4.63 (r(s(z), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[348, 32348])).
% 4.27/4.63 tff(32350,plain,
% 4.27/4.63 (~(elem!1 = z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[31610, 251])).
% 4.27/4.63 tff(32351,plain,
% 4.27/4.63 (~r(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32251, 321, 133, 123, 2323, 251])).
% 4.27/4.63 tff(32352,plain,
% 4.27/4.63 (b(elem!1, z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[653, 32351, 32350])).
% 4.27/4.63 tff(32353,plain,
% 4.27/4.63 (~r(elem!1, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[31676, 333, 2323, 6107, 321])).
% 4.27/4.63 tff(32354,plain,
% 4.27/4.63 (~b(elem!1, s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[30099, 283, 133, 304, 134])).
% 4.27/4.63 tff(32355,plain,
% 4.27/4.63 (elem!1 = s(s(s(z)))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1538, 32354, 32353])).
% 4.27/4.63 tff(32356,plain,
% 4.27/4.63 (s(s(s(z))) = elem!1),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[10997, 32355])).
% 4.27/4.63 tff(32357,plain,
% 4.27/4.63 (~(s(s(elem!1)) = elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[7595, 32356, 1184])).
% 4.27/4.63 tff(32358,plain,
% 4.27/4.63 (~(elem!1 = s(s(elem!1)))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[5603, 32357])).
% 4.27/4.63 tff(32359,plain,
% 4.27/4.63 (~(s(elem!1) = elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[5813, 32358])).
% 4.27/4.63 tff(32360,plain,
% 4.27/4.63 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32355])).
% 4.27/4.63 tff(32361,plain,
% 4.27/4.63 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 4.27/4.63 inference(symmetry,[status(thm)],[32360])).
% 4.27/4.63 tff(32362,plain,
% 4.27/4.63 (s(elem!1) = s(s(s(s(z))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32355])).
% 4.27/4.63 tff(32363,plain,
% 4.27/4.63 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32362])).
% 4.27/4.63 tff(32364,plain,
% 4.27/4.63 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 4.27/4.63 inference(symmetry,[status(thm)],[32363])).
% 4.27/4.63 tff(32365,plain,
% 4.27/4.63 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 4.27/4.63 inference(transitivity,[status(thm)],[32364, 32361])).
% 4.27/4.63 tff(32366,plain,
% 4.27/4.63 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(elem!1), elem!1))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32365])).
% 4.27/4.63 tff(32367,plain,
% 4.27/4.63 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32362])).
% 4.27/4.63 tff(32368,plain,
% 4.27/4.63 (~(z = elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[18287, 32350])).
% 4.27/4.63 tff(32369,plain,
% 4.27/4.63 (~(s(elem!1) = s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[8683, 32368])).
% 4.27/4.63 tff(32370,plain,
% 4.27/4.63 (~r(s(elem!1), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1911, 32359, 722, 32352, 251, 323])).
% 4.27/4.63 tff(32371,plain,
% 4.27/4.63 (b(s(elem!1), s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[486, 32370, 32369])).
% 4.27/4.63 tff(32372,plain,
% 4.27/4.63 (b(s(s(s(s(z)))), s(z))),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[32371, 32367])).
% 4.27/4.63 tff(32373,plain,
% 4.27/4.63 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[9573, 144, 32372, 123, 304])).
% 4.27/4.63 tff(32374,plain,
% 4.27/4.63 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[9761, 32373])).
% 4.27/4.63 tff(32375,plain,
% 4.27/4.63 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32376,plain,
% 4.27/4.63 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32377,plain,
% 4.27/4.63 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32376])).
% 4.27/4.63 tff(32378,plain,
% 4.27/4.63 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.63 inference(transitivity,[status(thm)],[32377, 32375])).
% 4.27/4.63 tff(32379,plain,
% 4.27/4.63 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.27/4.63 inference(quant_inst,[status(thm)],[])).
% 4.27/4.63 tff(32380,plain,
% 4.27/4.63 ((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[32379, 32378])).
% 4.27/4.63 tff(32381,plain,
% 4.27/4.63 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32380, 333, 6107, 321, 32374])).
% 4.27/4.63 tff(32382,plain,
% 4.27/4.63 (~r(s(elem!1), elem!1)),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[32381, 32366])).
% 4.27/4.63 tff(32383,plain,
% 4.27/4.63 (b(s(elem!1), elem!1)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[448, 32382, 32359])).
% 4.27/4.63 tff(32384,plain,
% 4.27/4.63 (~b(s(elem!1), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[916, 32383, 251, 32352])).
% 4.27/4.63 tff(32385,plain,
% 4.27/4.63 (r(s(elem!1), z)),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[507, 32384])).
% 4.27/4.63 tff(32386,plain,
% 4.27/4.63 (~(s(z) = s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1228, 32369])).
% 4.27/4.63 tff(32387,plain,
% 4.27/4.63 (~(elem!1 = s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1569, 32359])).
% 4.27/4.63 tff(32388,plain,
% 4.27/4.63 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[12214, 32356])).
% 4.27/4.63 tff(32389,plain,
% 4.27/4.63 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32362])).
% 4.27/4.63 tff(32390,plain,
% 4.27/4.63 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(symmetry,[status(thm)],[32389])).
% 4.27/4.63 tff(32391,plain,
% 4.27/4.63 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32390])).
% 4.27/4.63 tff(32392,plain,
% 4.27/4.63 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[32373, 32391])).
% 4.27/4.63 tff(32393,plain,
% 4.27/4.63 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[472, 32392, 32388])).
% 4.27/4.63 tff(32394,plain,
% 4.27/4.63 (~r(elem!1, s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[4103, 32393, 321, 2323])).
% 4.27/4.63 tff(32395,plain,
% 4.27/4.63 (~b(s(z), s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1732, 32382, 32394, 134, 32387])).
% 4.27/4.63 tff(32396,plain,
% 4.27/4.63 (r(s(z), s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1244, 32395, 32386])).
% 4.27/4.63 tff(32397,plain,
% 4.27/4.63 (~r(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[1235, 32396, 323, 32385])).
% 4.27/4.63 tff(32398,plain,
% 4.27/4.63 (b(z, s(z))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[372, 32397])).
% 4.27/4.63 tff(32399,plain,
% 4.27/4.63 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[20734, 32388])).
% 4.27/4.63 tff(32400,plain,
% 4.27/4.63 (s(s(s(s(z)))) = s(elem!1)),
% 4.27/4.63 inference(symmetry,[status(thm)],[32362])).
% 4.27/4.63 tff(32401,plain,
% 4.27/4.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32400])).
% 4.27/4.63 tff(32402,plain,
% 4.27/4.63 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.27/4.63 inference(monotonicity,[status(thm)],[32401])).
% 4.27/4.63 tff(32403,plain,
% 4.27/4.63 (b(s(z), s(s(s(z))))),
% 4.27/4.63 inference(modus_ponens,[status(thm)],[134, 27516])).
% 4.27/4.63 tff(32404,plain,
% 4.27/4.63 ($false),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[156, 32403])).
% 4.27/4.63 tff(32405,plain,((~b(s(z), elem!1)) | b(s(z), s(s(s(z)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.63 tff(32406,plain,
% 4.27/4.63 (b(s(z), s(s(s(z))))),
% 4.27/4.63 inference(unit_resolution,[status(thm)],[32405, 32355, 134])).
% 4.27/4.63 tff(32407,plain,
% 4.27/4.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32408,plain,
% 4.27/4.63 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.27/4.63 inference(rewrite,[status(thm)],[])).
% 4.27/4.63 tff(32409,plain,
% 4.27/4.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32408])).
% 4.27/4.64 tff(32410,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.27/4.64 inference(transitivity,[status(thm)],[32409, 32407])).
% 4.27/4.64 tff(32411,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.27/4.64 inference(quant_inst,[status(thm)],[])).
% 4.27/4.64 tff(32412,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32411, 32410])).
% 4.27/4.64 tff(32413,plain,
% 4.27/4.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[32412, 144, 32372, 32406, 283, 304])).
% 4.27/4.64 tff(32414,plain,
% 4.27/4.64 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32413, 32402])).
% 4.27/4.64 tff(32415,plain,
% 4.27/4.64 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[542, 32414, 32399])).
% 4.27/4.64 tff(32416,plain,
% 4.27/4.64 (b(elem!1, s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[560, 32394, 32387])).
% 4.27/4.64 tff(32417,plain,
% 4.27/4.64 (~b(z, s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[1642, 32383, 251, 32416])).
% 4.27/4.64 tff(32418,plain,
% 4.27/4.64 (r(z, s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[583, 32417])).
% 4.27/4.64 tff(32419,plain,
% 4.27/4.64 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[3607, 32418, 32393, 32415])).
% 4.27/4.64 tff(32420,plain,
% 4.27/4.64 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[279, 32419])).
% 4.27/4.64 tff(32421,plain,
% 4.27/4.64 ($false),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[757, 32420, 32398, 123, 304])).
% 4.27/4.64 tff(32422,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.64 tff(32423,plain,
% 4.27/4.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[32422, 32005, 32287, 32349, 31602, 32003, 32340, 32293, 31615, 32346, 32344, 27421])).
% 4.27/4.64 tff(32424,plain,
% 4.27/4.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[249, 32423])).
% 4.27/4.64 tff(32425,plain,
% 4.27/4.64 (~(s(s(s(z))) = elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[227, 32424, 54])).
% 4.27/4.64 tff(32426,plain,
% 4.27/4.64 (~b(z, s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[21799, 32425, 32342, 31602, 32341])).
% 4.27/4.64 tff(32427,plain,
% 4.27/4.64 (r(z, s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[619, 32426])).
% 4.27/4.64 tff(32428,plain,
% 4.27/4.64 (b(elem!1, z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[653, 32347, 31611])).
% 4.27/4.64 tff(32429,plain,
% 4.27/4.64 (b(s(s(s(z))), elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[704, 32425, 32342])).
% 4.27/4.64 tff(32430,plain,
% 4.27/4.64 (~b(s(s(s(z))), z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[10565, 32429, 31602, 32428])).
% 4.27/4.64 tff(32431,plain,
% 4.27/4.64 (r(s(s(s(z))), z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[396, 32430])).
% 4.27/4.64 tff(32432,plain,
% 4.27/4.64 (~r(z, s(z))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[31651, 32425, 32293, 32428, 31602, 32340, 31615])).
% 4.27/4.64 tff(32433,plain,
% 4.27/4.64 (b(z, s(z))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[372, 32432])).
% 4.27/4.64 tff(32434,plain,
% 4.27/4.64 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[757, 32433, 32005, 32287])).
% 4.27/4.64 tff(32435,plain,
% 4.27/4.64 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[279, 32434])).
% 4.27/4.64 tff(32436,plain,
% 4.27/4.64 ($false),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[15762, 32435, 32431, 32424, 32427])).
% 4.27/4.64 tff(32437,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.64 tff(32438,plain,
% 4.27/4.64 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[12011, 32437])).
% 4.27/4.64 tff(32439,plain,
% 4.27/4.64 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[121, 3, 32438])).
% 4.27/4.64 tff(32440,plain,
% 4.27/4.64 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32437, 22683])).
% 4.27/4.64 tff(32441,plain,
% 4.27/4.64 (elem!1 = z),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[18287, 66])).
% 4.27/4.64 tff(32442,plain,
% 4.27/4.64 (b(s(z), elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[22716, 489, 32441])).
% 4.27/4.64 tff(32443,plain,
% 4.27/4.64 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[25349, 66])).
% 4.27/4.64 tff(32444,plain,
% 4.27/4.64 (b(s(elem!1), z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[18064, 489, 66])).
% 4.27/4.64 tff(32445,plain,
% 4.27/4.64 (b(s(elem!1), elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[25335, 32444, 66])).
% 4.27/4.64 tff(32446,plain,
% 4.27/4.64 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.27/4.64 inference(monotonicity,[status(thm)],[66])).
% 4.27/4.64 tff(32447,plain,
% 4.27/4.64 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 4.27/4.64 inference(transitivity,[status(thm)],[32446, 203])).
% 4.27/4.64 tff(32448,plain,
% 4.27/4.64 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.27/4.64 inference(transitivity,[status(thm)],[32447, 24285])).
% 4.27/4.64 tff(32449,plain,
% 4.27/4.64 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32448])).
% 4.27/4.64 tff(32450,plain,
% 4.27/4.64 (~(s(s(s(s(z)))) = elem!1)),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[242, 32449])).
% 4.27/4.64 tff(32451,plain,
% 4.27/4.64 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32447])).
% 4.27/4.64 tff(32452,plain,
% 4.27/4.64 (~(elem!1 = s(s(s(s(z)))))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[242, 32451])).
% 4.27/4.64 tff(32453,plain,
% 4.27/4.64 (~b(elem!1, s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[27148, 56, 123, 305, 132])).
% 4.27/4.64 tff(32454,plain,
% 4.27/4.64 (r(elem!1, s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[1538, 32453, 1524])).
% 4.27/4.64 tff(32455,plain,
% 4.27/4.64 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[23181, 333, 32454, 20613, 2484])).
% 4.27/4.64 tff(32456,plain,
% 4.27/4.64 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[1137, 32455])).
% 4.27/4.64 tff(32457,plain,
% 4.27/4.64 (~b(s(s(s(z))), z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[2273, 56, 490, 489])).
% 4.27/4.64 tff(32458,plain,
% 4.27/4.64 (r(s(s(s(z))), z)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[396, 32457])).
% 4.27/4.64 tff(32459,plain,
% 4.27/4.64 ($false),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[21803, 333, 1525, 1699, 2484, 224])).
% 4.27/4.64 tff(32460,plain,((~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.64 tff(32461,plain,
% 4.27/4.64 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[32460, 32454, 2484, 32458])).
% 4.27/4.64 tff(32462,plain,
% 4.27/4.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[249, 32461])).
% 4.27/4.64 tff(32463,plain,
% 4.27/4.64 (~b(s(z), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[2262, 32456, 123, 32462])).
% 4.27/4.64 tff(32464,plain,
% 4.27/4.64 (r(s(z), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[172, 32463])).
% 4.27/4.64 tff(32465,plain,
% 4.27/4.64 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[28682, 20613, 25190, 28638, 451, 24296, 8677, 32464, 32454])).
% 4.27/4.64 tff(32466,plain,
% 4.27/4.64 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[27512, 32465])).
% 4.27/4.64 tff(32467,plain,
% 4.27/4.64 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[28686, 32466, 32456, 32462])).
% 4.27/4.64 tff(32468,plain,
% 4.27/4.64 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[9761, 32467])).
% 4.27/4.64 tff(32469,plain,
% 4.27/4.64 (~r(s(s(s(s(z)))), s(z))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[28690, 32464, 322, 32468])).
% 4.27/4.64 tff(32470,plain,
% 4.27/4.64 (b(s(s(s(s(z)))), s(z))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[24600, 32469, 24294])).
% 4.27/4.64 tff(32471,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32472,plain,
% 4.27/4.64 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32473,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32472])).
% 4.27/4.64 tff(32474,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.64 inference(transitivity,[status(thm)],[32473, 32471])).
% 4.27/4.64 tff(32475,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 4.27/4.64 inference(quant_inst,[status(thm)],[])).
% 4.27/4.64 tff(32476,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32475, 32474])).
% 4.27/4.64 tff(32477,plain,
% 4.27/4.64 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[32476, 144, 56, 32470, 123, 32456])).
% 4.27/4.64 tff(32478,plain,
% 4.27/4.64 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 32477])).
% 4.27/4.64 tff(32479,plain,
% 4.27/4.64 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32469, 25520])).
% 4.27/4.64 tff(32480,plain,
% 4.27/4.64 (b(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[24448, 32479, 25190])).
% 4.27/4.64 tff(32481,plain,
% 4.27/4.64 (~b(s(s(s(s(z)))), elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[24997, 32480, 28638, 451])).
% 4.27/4.64 tff(32482,plain,
% 4.27/4.64 (r(s(s(s(s(z)))), elem!1)),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[24301, 32481, 24296])).
% 4.27/4.64 tff(32483,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 4.27/4.64 tff(32484,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32485,plain,
% 4.27/4.64 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32486,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32485])).
% 4.27/4.64 tff(32487,plain,
% 4.27/4.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.27/4.64 inference(transitivity,[status(thm)],[32486, 32484])).
% 4.27/4.64 tff(32488,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.27/4.64 inference(quant_inst,[status(thm)],[])).
% 4.27/4.64 tff(32489,plain,
% 4.27/4.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 4.27/4.64 inference(modus_ponens,[status(thm)],[32488, 32487])).
% 4.27/4.64 tff(32490,plain,
% 4.27/4.64 (~b(elem!1, s(s(s(s(z)))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[32489, 144, 305, 32470, 123, 132])).
% 4.27/4.64 tff(32491,plain,
% 4.27/4.64 (r(elem!1, s(s(s(s(z)))))),
% 4.27/4.64 inference(unit_resolution,[status(thm)],[6873, 32490, 32483])).
% 4.27/4.64 tff(32492,plain,
% 4.27/4.64 (((~![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))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32493,plain,
% 4.27/4.64 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.27/4.64 inference(rewrite,[status(thm)],[])).
% 4.27/4.64 tff(32494,plain,
% 4.27/4.64 (((~![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)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, 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(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 4.27/4.64 inference(monotonicity,[status(thm)],[32493])).
% 4.27/4.64 tff(32495,plain,
% 4.27/4.64 (((~![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)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, 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(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.27/4.65 inference(transitivity,[status(thm)],[32494, 32492])).
% 4.27/4.65 tff(32496,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32497,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32496, 32495])).
% 4.27/4.65 tff(32498,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32497, 333, 20613, 32491, 32482, 32478])).
% 4.27/4.65 tff(32499,plain,((~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32500,plain,
% 4.27/4.65 (~b(s(s(s(z))), s(z))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32499, 132, 123, 305, 32452, 32450, 32445, 32443, 18054, 322, 2484, 25347, 22891, 28818, 489, 32442])).
% 4.27/4.65 tff(32501,plain,
% 4.27/4.65 (r(s(s(s(z))), s(z))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[2794, 32500])).
% 4.27/4.65 tff(32502,plain,
% 4.27/4.65 (r(s(s(s(z))), elem!1)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[22912, 1699, 66])).
% 4.27/4.65 tff(32503,plain,
% 4.27/4.65 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.27/4.65 inference(monotonicity,[status(thm)],[66])).
% 4.27/4.65 tff(32504,plain,
% 4.27/4.65 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.27/4.65 inference(transitivity,[status(thm)],[32503, 1218])).
% 4.27/4.65 tff(32505,plain,
% 4.27/4.65 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.27/4.65 inference(monotonicity,[status(thm)],[32504])).
% 4.27/4.65 tff(32506,plain,
% 4.27/4.65 (~(elem!1 = s(s(elem!1)))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[1094, 32505])).
% 4.27/4.65 tff(32507,plain,
% 4.27/4.65 (((~![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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32508,plain,
% 4.27/4.65 ((~![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(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32509,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32508, 32507])).
% 4.27/4.65 tff(32510,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32509, 333, 3193, 224, 322, 22831])).
% 4.27/4.65 tff(32511,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32512,plain,
% 4.27/4.65 (~r(s(z), s(s(z)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32511, 224, 3193, 322])).
% 4.27/4.65 tff(32513,plain,
% 4.27/4.65 (~r(s(z), s(s(elem!1)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[22807, 32512, 8677])).
% 4.27/4.65 tff(32514,plain,
% 4.27/4.65 (b(s(z), s(s(elem!1)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[5484, 32513])).
% 4.27/4.65 tff(32515,plain,
% 4.27/4.65 (b(s(z), s(s(z)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[22799, 32514, 8677])).
% 4.27/4.65 tff(32516,plain,
% 4.27/4.65 (((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32517,plain,
% 4.27/4.65 ((~![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(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32518,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32517, 32516])).
% 4.27/4.65 tff(32519,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32518, 333, 707, 2484, 224, 22740])).
% 4.27/4.65 tff(32520,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32521,plain,
% 4.27/4.65 (~r(elem!1, s(s(z)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32520, 224, 2484, 707])).
% 4.27/4.65 tff(32522,plain,
% 4.27/4.65 (~r(elem!1, s(s(elem!1)))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32521, 28273])).
% 4.27/4.65 tff(32523,plain,
% 4.27/4.65 (b(elem!1, s(s(elem!1)))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[2522, 32522, 1221])).
% 4.27/4.65 tff(32524,plain,
% 4.27/4.65 (b(elem!1, s(s(z)))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32523, 22760])).
% 4.27/4.65 tff(32525,plain,
% 4.27/4.65 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[22792, 32515, 305, 132, 32524])).
% 4.27/4.65 tff(32526,plain,
% 4.27/4.65 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[1451, 32525])).
% 4.27/4.65 tff(32527,plain,
% 4.27/4.65 (~r(s(s(z)), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[7412, 32526, 1699, 224])).
% 4.27/4.65 tff(32528,plain,
% 4.27/4.65 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[18132, 32527, 8677])).
% 4.27/4.65 tff(32529,plain,
% 4.27/4.65 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[4311, 32528, 22826])).
% 4.27/4.65 tff(32530,plain,
% 4.27/4.65 (b(s(s(z)), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[18122, 32529, 8677])).
% 4.27/4.65 tff(32531,plain,
% 4.27/4.65 (~r(elem!1, s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[22410, 224, 2484, 3193])).
% 4.27/4.65 tff(32532,plain,
% 4.27/4.65 (b(elem!1, s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[1538, 32531, 1524])).
% 4.27/4.65 tff(32533,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32534,plain,
% 4.27/4.65 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32535,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 4.27/4.65 inference(monotonicity,[status(thm)],[32534])).
% 4.27/4.65 tff(32536,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 4.27/4.65 inference(transitivity,[status(thm)],[32535, 32533])).
% 4.27/4.65 tff(32537,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32538,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32537, 32536])).
% 4.27/4.65 tff(32539,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32538, 144, 32532, 305, 32530, 32524, 32515])).
% 4.27/4.65 tff(32540,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32541,plain,
% 4.27/4.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32540, 1699, 18054, 305, 132, 3193, 322, 32506, 2484, 32502, 25347])).
% 4.27/4.65 tff(32542,plain,
% 4.27/4.65 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[249, 32541])).
% 4.27/4.65 tff(32543,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32544,plain,
% 4.27/4.65 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32545,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.65 inference(monotonicity,[status(thm)],[32544])).
% 4.27/4.65 tff(32546,plain,
% 4.27/4.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(transitivity,[status(thm)],[32545, 32543])).
% 4.27/4.65 tff(32547,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32548,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32547, 32546])).
% 4.27/4.65 tff(32549,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32548, 144, 134, 838, 123, 132, 283])).
% 4.27/4.65 tff(32550,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32551,plain,
% 4.27/4.65 (~b(s(z), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32550, 32542, 134, 123, 132])).
% 4.27/4.65 tff(32552,plain,
% 4.27/4.65 (r(s(z), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[172, 32551])).
% 4.27/4.65 tff(32553,plain,
% 4.27/4.65 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[10422, 32552, 322, 3193])).
% 4.27/4.65 tff(32554,plain,
% 4.27/4.65 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[1137, 32553])).
% 4.27/4.65 tff(32555,plain,
% 4.27/4.65 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.27/4.65 inference(monotonicity,[status(thm)],[18054])).
% 4.27/4.65 tff(32556,plain,
% 4.27/4.65 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.27/4.65 inference(symmetry,[status(thm)],[32555])).
% 4.27/4.65 tff(32557,plain,
% 4.27/4.65 (b(elem!1, s(elem!1))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[305, 32556])).
% 4.27/4.65 tff(32558,plain,
% 4.27/4.65 (~b(elem!1, s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[18960, 32554, 132, 32542])).
% 4.27/4.65 tff(32559,plain,
% 4.27/4.65 (r(elem!1, s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[1538, 32558, 25347])).
% 4.27/4.65 tff(32560,plain,
% 4.27/4.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[28682, 32559, 32443, 32557, 451, 32450, 18054, 32502, 32552])).
% 4.27/4.65 tff(32561,plain,
% 4.27/4.65 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[27512, 32560])).
% 4.27/4.65 tff(32562,plain,
% 4.27/4.65 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[28686, 32561, 32554, 32542])).
% 4.27/4.65 tff(32563,plain,
% 4.27/4.65 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[9761, 32562])).
% 4.27/4.65 tff(32564,plain,
% 4.27/4.65 (~r(s(s(s(s(z)))), s(z))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[28690, 32563, 322, 32552])).
% 4.27/4.65 tff(32565,plain,
% 4.27/4.65 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[28694, 32564, 18054])).
% 4.27/4.65 tff(32566,plain,
% 4.27/4.65 (b(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[24448, 32565, 32443])).
% 4.27/4.65 tff(32567,plain,
% 4.27/4.65 (~b(s(s(s(s(z)))), elem!1)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[24997, 32566, 32557, 451])).
% 4.27/4.65 tff(32568,plain,
% 4.27/4.65 (r(s(s(s(s(z)))), elem!1)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[24301, 32567, 32450])).
% 4.27/4.65 tff(32569,plain,
% 4.27/4.65 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32570,plain,
% 4.27/4.65 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(rewrite,[status(thm)],[])).
% 4.27/4.65 tff(32571,plain,
% 4.27/4.65 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.65 inference(monotonicity,[status(thm)],[32570])).
% 4.27/4.65 tff(32572,plain,
% 4.27/4.65 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(transitivity,[status(thm)],[32571, 32569])).
% 4.27/4.65 tff(32573,plain,
% 4.27/4.65 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.65 inference(quant_inst,[status(thm)],[])).
% 4.27/4.65 tff(32574,plain,
% 4.27/4.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.65 inference(modus_ponens,[status(thm)],[32573, 32572])).
% 4.27/4.65 tff(32575,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32574, 333, 32559, 32568, 2484, 32563])).
% 4.27/4.65 tff(32576,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32577,plain,
% 4.27/4.65 (~r(s(s(s(z))), z)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32576, 132, 32445, 322, 2484, 32501, 32442, 123, 305, 66])).
% 4.27/4.65 tff(32578,plain,
% 4.27/4.65 (b(s(s(s(z))), z)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[396, 32577])).
% 4.27/4.65 tff(32579,plain,
% 4.27/4.65 (b(s(s(s(z))), elem!1)),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[26887, 32578, 66])).
% 4.27/4.65 tff(32580,plain,
% 4.27/4.65 ($false),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[14009, 144, 134, 838, 123, 132, 4367])).
% 4.27/4.65 tff(32581,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.65 tff(32582,plain,
% 4.27/4.65 (~b(s(z), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[32581, 32579, 132, 123, 32442])).
% 4.27/4.65 tff(32583,plain,
% 4.27/4.65 (r(s(z), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[172, 32582])).
% 4.27/4.65 tff(32584,plain,
% 4.27/4.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.65 inference(unit_resolution,[status(thm)],[31443, 333, 32501, 32583, 322])).
% 4.27/4.66 tff(32585,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[249, 32584])).
% 4.27/4.66 tff(32586,plain,
% 4.27/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[14015, 32579, 123, 305, 32442, 132])).
% 4.27/4.66 tff(32587,plain,
% 4.27/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1137, 32586])).
% 4.27/4.66 tff(32588,plain,
% 4.27/4.66 (~b(elem!1, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[18960, 32585, 132, 32587])).
% 4.27/4.66 tff(32589,plain,
% 4.27/4.66 (r(elem!1, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1538, 32588, 25347])).
% 4.27/4.66 tff(32590,plain,
% 4.27/4.66 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32574, 333, 1525, 9507, 2484])).
% 4.27/4.66 tff(32591,plain,
% 4.27/4.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[9761, 32590])).
% 4.27/4.66 tff(32592,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[28686, 32591, 2254, 283])).
% 4.27/4.66 tff(32593,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[27512, 32592])).
% 4.27/4.66 tff(32594,plain,
% 4.27/4.66 (((~![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))), s(z))) | (~r(s(s(s(s(z)))), s(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(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32595,plain,
% 4.27/4.66 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, 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(s(z)))), elem!1)))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32596,plain,
% 4.27/4.66 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[32595])).
% 4.27/4.66 tff(32597,plain,
% 4.27/4.66 (((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.27/4.66 inference(transitivity,[status(thm)],[32596, 32594])).
% 4.27/4.66 tff(32598,plain,
% 4.27/4.66 ((~![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(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.27/4.66 inference(quant_inst,[status(thm)],[])).
% 4.27/4.66 tff(32599,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32598, 32597])).
% 4.27/4.66 tff(32600,plain,
% 4.27/4.66 ($false),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32599, 333, 1525, 3193, 9507, 32593])).
% 4.27/4.66 tff(32601,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.66 tff(32602,plain,
% 4.27/4.66 (~r(s(s(s(s(z)))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32601, 32589, 32501, 32587, 32585, 2484])).
% 4.27/4.66 tff(32603,plain,
% 4.27/4.66 (b(s(s(s(s(z)))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24301, 32602, 32450])).
% 4.27/4.66 tff(32604,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24997, 32603, 32557, 32445])).
% 4.27/4.66 tff(32605,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(elem!1))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24448, 32604, 32443])).
% 4.27/4.66 tff(32606,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[28694, 32605, 18054])).
% 4.27/4.66 tff(32607,plain,
% 4.27/4.66 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[28690, 32606, 322, 32583])).
% 4.27/4.66 tff(32608,plain,
% 4.27/4.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[9761, 32607])).
% 4.27/4.66 tff(32609,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[28686, 32608, 32587, 32585])).
% 4.27/4.66 tff(32610,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[27512, 32609])).
% 4.27/4.66 tff(32611,plain,
% 4.27/4.66 ($false),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[23683, 333, 32501, 32606, 32583, 32610])).
% 4.27/4.66 tff(32612,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~(z = elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.66 tff(32613,plain,
% 4.27/4.66 (~b(s(z), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32612, 622, 32437, 123, 132, 66, 305])).
% 4.27/4.66 tff(32614,plain,
% 4.27/4.66 (r(s(z), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[348, 32613])).
% 4.27/4.66 tff(32615,plain,
% 4.27/4.66 (~r(z, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[642, 32614, 32440, 622])).
% 4.27/4.66 tff(32616,plain,
% 4.27/4.66 (b(z, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[619, 32615])).
% 4.27/4.66 tff(32617,plain,
% 4.27/4.66 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[66])).
% 4.27/4.66 tff(32618,plain,
% 4.27/4.66 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(symmetry,[status(thm)],[32617])).
% 4.27/4.66 tff(32619,plain,
% 4.27/4.66 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[132, 32618])).
% 4.27/4.66 tff(32620,plain,
% 4.27/4.66 (r(s(z), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[25327, 32614, 66])).
% 4.27/4.66 tff(32621,plain,
% 4.27/4.66 (~r(z, s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[14521, 32620, 32440, 622])).
% 4.27/4.66 tff(32622,plain,
% 4.27/4.66 (b(z, s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[372, 32621])).
% 4.27/4.66 tff(32623,plain,
% 4.27/4.66 (~b(s(s(s(z))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[779, 32622, 123, 32440, 622, 32614])).
% 4.27/4.66 tff(32624,plain,
% 4.27/4.66 (r(s(s(s(z))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[2794, 32623])).
% 4.27/4.66 tff(32625,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[20837, 32624, 622, 32614])).
% 4.27/4.66 tff(32626,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[249, 32625])).
% 4.27/4.66 tff(32627,plain,
% 4.27/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[27257, 32624, 622, 32620])).
% 4.27/4.66 tff(32628,plain,
% 4.27/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1137, 32627])).
% 4.27/4.66 tff(32629,plain,
% 4.27/4.66 ($false),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[16228, 32628, 32626, 32619, 32616])).
% 4.27/4.66 tff(32630,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.66 tff(32631,plain,
% 4.27/4.66 (~b(elem!1, s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32630, 22670, 50, 32439])).
% 4.27/4.66 tff(32632,plain,
% 4.27/4.66 (r(elem!1, s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[720, 32631, 713])).
% 4.27/4.66 tff(32633,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[27420, 2545])).
% 4.27/4.66 tff(32634,plain,
% 4.27/4.66 (~(s(z) = elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[30660, 23943, 4])).
% 4.27/4.66 tff(32635,plain,
% 4.27/4.66 (~r(elem!1, z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[12025, 51, 321, 2484])).
% 4.27/4.66 tff(32636,plain,
% 4.27/4.66 (b(elem!1, z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1380, 32635, 77])).
% 4.27/4.66 tff(32637,plain,
% 4.27/4.66 (~r(z, elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[25313, 23943, 321, 2484])).
% 4.27/4.66 tff(32638,plain,
% 4.27/4.66 (b(z, elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[658, 32637, 71])).
% 4.27/4.66 tff(32639,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[12830, 32636, 2484, 6065, 32638, 706])).
% 4.27/4.66 tff(32640,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[319, 32639])).
% 4.27/4.66 tff(32641,plain,
% 4.27/4.66 (~r(s(s(s(z))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[31819, 2169, 123, 23943, 6065, 32640])).
% 4.27/4.66 tff(32642,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.27/4.66 inference(monotonicity,[status(thm)],[6165])).
% 4.27/4.66 tff(32643,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(symmetry,[status(thm)],[32642])).
% 4.27/4.66 tff(32644,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[2484, 32643])).
% 4.27/4.66 tff(32645,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.27/4.66 inference(monotonicity,[status(thm)],[6165])).
% 4.27/4.66 tff(32646,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(symmetry,[status(thm)],[32645])).
% 4.27/4.66 tff(32647,plain,
% 4.27/4.66 (~(s(s(s(s(z)))) = elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24637, 3326, 14202])).
% 4.27/4.66 tff(32648,plain,
% 4.27/4.66 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[24627])).
% 4.27/4.66 tff(32649,plain,
% 4.27/4.66 (b(s(s(s(z))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[704, 20929, 699])).
% 4.27/4.66 tff(32650,plain,
% 4.27/4.66 (~b(s(s(s(z))), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[10565, 32649, 624, 251])).
% 4.27/4.66 tff(32651,plain,
% 4.27/4.66 (r(s(s(s(z))), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[396, 32650])).
% 4.27/4.66 tff(32652,plain,
% 4.27/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[11754, 32651, 51, 321])).
% 4.27/4.66 tff(32653,plain,
% 4.27/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1137, 32652])).
% 4.27/4.66 tff(32654,plain,
% 4.27/4.66 (~b(s(s(s(z))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[6004, 144, 123, 32653, 304])).
% 4.27/4.66 tff(32655,plain,
% 4.27/4.66 (r(s(s(s(z))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[2794, 32654])).
% 4.27/4.66 tff(32656,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[2199, 333, 32651, 321, 51])).
% 4.27/4.66 tff(32657,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[249, 32656])).
% 4.27/4.66 tff(32658,plain,
% 4.27/4.66 (~b(s(z), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[2262, 32657, 123, 32653])).
% 4.27/4.66 tff(32659,plain,
% 4.27/4.66 (r(s(z), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[172, 32658])).
% 4.27/4.66 tff(32660,plain,
% 4.27/4.66 (~r(elem!1, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[11876, 32659, 409, 32655])).
% 4.27/4.66 tff(32661,plain,
% 4.27/4.66 (b(elem!1, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1538, 32660, 20930])).
% 4.27/4.66 tff(32662,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32661, 20661])).
% 4.27/4.66 tff(32663,plain,
% 4.27/4.66 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[14198])).
% 4.27/4.66 tff(32664,plain,
% 4.27/4.66 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32649, 32663])).
% 4.27/4.66 tff(32665,plain,
% 4.27/4.66 (~b(z, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[21799, 32660, 251, 699, 20929])).
% 4.27/4.66 tff(32666,plain,
% 4.27/4.66 (r(z, s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[619, 32665])).
% 4.27/4.66 tff(32667,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 4.27/4.66 tff(32668,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 4.27/4.66 tff(32669,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[26200, 144, 26206, 32668, 32667])).
% 4.27/4.66 tff(32670,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[9821, 44, 219, 32669])).
% 4.27/4.66 tff(32671,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 4.27/4.66 tff(32672,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32673,plain,
% 4.27/4.66 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32674,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[32673])).
% 4.27/4.66 tff(32675,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.27/4.66 inference(transitivity,[status(thm)],[32674, 32672])).
% 4.27/4.66 tff(32676,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.27/4.66 inference(quant_inst,[status(thm)],[])).
% 4.27/4.66 tff(32677,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32676, 32675])).
% 4.27/4.66 tff(32678,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32677, 144, 20668, 32671, 32667])).
% 4.27/4.66 tff(32679,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[4243, 44, 242, 32678])).
% 4.27/4.66 tff(32680,plain,
% 4.27/4.66 (((~![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))))))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32681,plain,
% 4.27/4.66 ((~![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))))))),
% 4.27/4.66 inference(quant_inst,[status(thm)],[])).
% 4.27/4.66 tff(32682,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32681, 32680])).
% 4.27/4.66 tff(32683,plain,
% 4.27/4.66 ($false),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32682, 333, 1699, 623, 32679, 32670])).
% 4.27/4.66 tff(32684,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(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(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.66 tff(32685,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32684, 32651, 32666, 32664, 32662, 20667, 30828])).
% 4.27/4.66 tff(32686,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), elem!1)),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32685, 32648])).
% 4.27/4.66 tff(32687,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24301, 32686, 32647])).
% 4.27/4.66 tff(32688,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32687, 32646])).
% 4.27/4.66 tff(32689,plain,
% 4.27/4.66 (~r(s(s(s(s(z)))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[26847, 32687, 722, 409])).
% 4.27/4.66 tff(32690,plain,
% 4.27/4.66 (b(s(s(s(s(z)))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[24600, 32689, 24294])).
% 4.27/4.66 tff(32691,plain,
% 4.27/4.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[26574, 32690, 123, 304])).
% 4.27/4.66 tff(32692,plain,
% 4.27/4.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[9761, 32691])).
% 4.27/4.66 tff(32693,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32694,plain,
% 4.27/4.66 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.66 inference(rewrite,[status(thm)],[])).
% 4.27/4.66 tff(32695,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), 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(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[32694])).
% 4.27/4.66 tff(32696,plain,
% 4.27/4.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), 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(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.66 inference(transitivity,[status(thm)],[32695, 32693])).
% 4.27/4.66 tff(32697,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.66 inference(quant_inst,[status(thm)],[])).
% 4.27/4.66 tff(32698,plain,
% 4.27/4.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[32697, 32696])).
% 4.27/4.66 tff(32699,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32698, 333, 32692, 6220, 32688])).
% 4.27/4.66 tff(32700,plain,
% 4.27/4.66 ($false),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32699, 32644])).
% 4.27/4.66 tff(32701,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.66 tff(32702,plain,
% 4.27/4.66 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[32701, 2169, 123, 32640, 6065, 2484, 32636, 32638, 32641, 321, 51])).
% 4.27/4.66 tff(32703,plain,
% 4.27/4.66 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[20734, 32702])).
% 4.27/4.66 tff(32704,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[12830, 32636, 2484, 722, 32638, 706])).
% 4.27/4.66 tff(32705,plain,
% 4.27/4.66 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[319, 32704])).
% 4.27/4.66 tff(32706,plain,
% 4.27/4.66 (~r(s(s(s(z))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[31819, 409, 123, 23943, 722, 32705])).
% 4.27/4.66 tff(32707,plain,
% 4.27/4.66 (~b(s(s(s(z))), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[10565, 285, 32636, 32638])).
% 4.27/4.66 tff(32708,plain,
% 4.27/4.66 (s(s(s(z))) = elem!1),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[704, 32707, 32706])).
% 4.27/4.66 tff(32709,plain,
% 4.27/4.66 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(monotonicity,[status(thm)],[32708])).
% 4.27/4.66 tff(32710,plain,
% 4.27/4.66 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(symmetry,[status(thm)],[32709])).
% 4.27/4.66 tff(32711,plain,
% 4.27/4.66 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[23943, 32710])).
% 4.27/4.66 tff(32712,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.27/4.66 inference(monotonicity,[status(thm)],[32708])).
% 4.27/4.66 tff(32713,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(symmetry,[status(thm)],[32712])).
% 4.27/4.66 tff(32714,plain,
% 4.27/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.66 inference(modus_ponens,[status(thm)],[2484, 32713])).
% 4.27/4.66 tff(32715,plain,
% 4.27/4.66 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[11642, 32714, 51, 32711, 285])).
% 4.27/4.66 tff(32716,plain,
% 4.27/4.66 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1451, 32715])).
% 4.27/4.66 tff(32717,plain,
% 4.27/4.66 (~b(s(s(z)), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1425, 32716, 123, 32705])).
% 4.27/4.66 tff(32718,plain,
% 4.27/4.66 (r(s(s(z)), s(z))),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1429, 44, 32717, 1416])).
% 4.27/4.66 tff(32719,plain,
% 4.27/4.66 (~(s(s(z)) = elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[14611, 32708, 706])).
% 4.27/4.66 tff(32720,plain,
% 4.27/4.66 (~r(s(s(z)), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[28548, 32718, 23943, 409])).
% 4.27/4.66 tff(32721,plain,
% 4.27/4.66 (b(s(s(z)), elem!1)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[7970, 32720, 32719])).
% 4.27/4.66 tff(32722,plain,
% 4.27/4.66 (~b(s(s(z)), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[7365, 144, 32638, 32636, 32721])).
% 4.27/4.66 tff(32723,plain,
% 4.27/4.66 (r(s(s(z)), z)),
% 4.27/4.66 inference(unit_resolution,[status(thm)],[1462, 44, 164, 32722])).
% 4.27/4.66 tff(32724,plain,
% 4.27/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[9706, 333, 321, 51, 32723])).
% 4.27/4.67 tff(32725,plain,
% 4.27/4.67 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[9653, 44, 32724])).
% 4.27/4.67 tff(32726,plain,
% 4.27/4.67 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32725, 9614])).
% 4.27/4.67 tff(32727,plain,
% 4.27/4.67 (~b(s(z), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[27170, 144, 32716, 123, 32726])).
% 4.27/4.67 tff(32728,plain,
% 4.27/4.67 ((s(z) = s(s(z))) | r(s(z), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32238, 44, 32727])).
% 4.27/4.67 tff(32729,plain,
% 4.27/4.67 (r(s(z), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32728, 32233])).
% 4.27/4.67 tff(32730,assumption,(z = s(s(z))), introduced(assumption)).
% 4.27/4.67 tff(32731,plain,
% 4.27/4.67 (s(s(z)) = z),
% 4.27/4.67 inference(symmetry,[status(thm)],[32730])).
% 4.27/4.67 tff(32732,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[164, 32731])).
% 4.27/4.67 tff(32733,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32734,plain,
% 4.27/4.67 (~(elem!1 = s(s(z)))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[32719, 17962])).
% 4.27/4.67 tff(32735,plain,
% 4.27/4.67 (~r(elem!1, s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[26788, 333, 409, 722, 32718])).
% 4.27/4.67 tff(32736,plain,
% 4.27/4.67 ((elem!1 = s(s(z))) | b(elem!1, s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[18919, 44, 32735])).
% 4.27/4.67 tff(32737,plain,
% 4.27/4.67 (b(elem!1, s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32736, 32734])).
% 4.27/4.67 tff(32738,plain,
% 4.27/4.67 (~b(z, s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[27809, 144, 32638, 32721, 32737])).
% 4.27/4.67 tff(32739,plain,
% 4.27/4.67 (r(z, s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[27813, 44, 32738, 32733])).
% 4.27/4.67 tff(32740,plain,
% 4.27/4.67 (((~![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)), 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)), z)))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32741,plain,
% 4.27/4.67 (((~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(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32742,plain,
% 4.27/4.67 (((~![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(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 4.27/4.67 inference(monotonicity,[status(thm)],[32741])).
% 4.27/4.67 tff(32743,plain,
% 4.27/4.67 (((~![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(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 4.27/4.67 inference(transitivity,[status(thm)],[32742, 32740])).
% 4.27/4.67 tff(32744,plain,
% 4.27/4.67 ((~![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))))),
% 4.27/4.67 inference(quant_inst,[status(thm)],[])).
% 4.27/4.67 tff(32745,plain,
% 4.27/4.67 ((~![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)), z))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[32744, 32743])).
% 4.27/4.67 tff(32746,plain,
% 4.27/4.67 (~r(z, s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32745, 333, 32723, 32739, 32729])).
% 4.27/4.67 tff(32747,plain,
% 4.27/4.67 (b(z, s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[372, 32746])).
% 4.27/4.67 tff(32748,plain,
% 4.27/4.67 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32701, 409, 123, 32705, 722, 2484, 32636, 32638, 32706, 321, 51])).
% 4.27/4.67 tff(32749,plain,
% 4.27/4.67 (((~![X0: $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)), 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)), z)))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32750,plain,
% 4.27/4.67 (((~r(s(s(z)), 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)), z)))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32751,plain,
% 4.27/4.67 (((~![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(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)), z))))),
% 4.27/4.67 inference(monotonicity,[status(thm)],[32750])).
% 4.27/4.67 tff(32752,plain,
% 4.27/4.67 (((~![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(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)), z)))),
% 4.27/4.67 inference(transitivity,[status(thm)],[32751, 32749])).
% 4.27/4.67 tff(32753,plain,
% 4.27/4.67 ((~![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(z), s(s(z)))) | (~r(s(z), z)))),
% 4.27/4.67 inference(quant_inst,[status(thm)],[])).
% 4.27/4.67 tff(32754,plain,
% 4.27/4.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[32753, 32752])).
% 4.27/4.67 tff(32755,plain,
% 4.27/4.67 (~r(s(z), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32754, 333, 32723, 32739, 32729])).
% 4.27/4.67 tff(32756,plain,
% 4.27/4.67 (b(s(z), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[348, 32755])).
% 4.27/4.67 tff(32757,plain,
% 4.27/4.67 (~b(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[499, 488, 489, 490])).
% 4.27/4.67 tff(32758,plain,
% 4.27/4.67 (r(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[507, 32757])).
% 4.27/4.67 tff(32759,plain,
% 4.27/4.67 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[13493, 32758, 2484, 51])).
% 4.27/4.67 tff(32760,plain,
% 4.27/4.67 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[472, 32759, 432])).
% 4.27/4.67 tff(32761,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[869, 144, 488, 123, 304, 32760])).
% 4.27/4.67 tff(32762,plain,((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32763,plain,
% 4.27/4.67 (~b(s(elem!1), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32762, 32756, 123, 2484, 51, 32705, 32748, 32747])).
% 4.27/4.67 tff(32764,plain,
% 4.27/4.67 (r(s(elem!1), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[486, 32763, 1])).
% 4.27/4.67 tff(32765,plain,
% 4.27/4.67 (((~![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(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32766,plain,
% 4.27/4.67 (((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32767,plain,
% 4.27/4.67 (((~![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(elem!1), s(z))) | (~r(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), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))))),
% 4.27/4.67 inference(monotonicity,[status(thm)],[32766])).
% 4.27/4.67 tff(32768,plain,
% 4.27/4.67 (((~![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(elem!1), s(z))) | (~r(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), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(transitivity,[status(thm)],[32767, 32765])).
% 4.27/4.67 tff(32769,plain,
% 4.27/4.67 ((~![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(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(quant_inst,[status(thm)],[])).
% 4.27/4.67 tff(32770,plain,
% 4.27/4.67 ((~![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(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[32769, 32768])).
% 4.27/4.67 tff(32771,plain,
% 4.27/4.67 (~r(s(elem!1), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32770, 333, 409, 32764, 32718])).
% 4.27/4.67 tff(32772,plain,
% 4.27/4.67 (b(s(elem!1), s(s(z)))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[7466, 44, 7435, 32771])).
% 4.27/4.67 tff(32773,plain,
% 4.27/4.67 (~r(s(elem!1), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[11068, 333, 409, 32764, 722])).
% 4.27/4.67 tff(32774,plain,
% 4.27/4.67 (b(s(elem!1), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[448, 32773, 433])).
% 4.27/4.67 tff(32775,plain,
% 4.27/4.67 (~b(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[916, 32774, 32638, 32636])).
% 4.27/4.67 tff(32776,plain,
% 4.27/4.67 (r(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[507, 32775])).
% 4.27/4.67 tff(32777,plain,
% 4.27/4.67 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[13493, 32776, 2484, 51])).
% 4.27/4.67 tff(32778,plain,
% 4.27/4.67 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[472, 32777, 32748])).
% 4.27/4.67 tff(32779,plain,
% 4.27/4.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32780,plain,
% 4.27/4.67 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(rewrite,[status(thm)],[])).
% 4.27/4.67 tff(32781,plain,
% 4.27/4.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z))))))),
% 4.27/4.67 inference(monotonicity,[status(thm)],[32780])).
% 4.27/4.67 tff(32782,plain,
% 4.27/4.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))))),
% 4.27/4.67 inference(transitivity,[status(thm)],[32781, 32779])).
% 4.27/4.67 tff(32783,plain,
% 4.27/4.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.67 inference(quant_inst,[status(thm)],[])).
% 4.27/4.67 tff(32784,plain,
% 4.27/4.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z))))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[32783, 32782])).
% 4.27/4.67 tff(32785,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32784, 144, 32774, 32721, 32778, 32726, 32772])).
% 4.27/4.67 tff(32786,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32787,plain,
% 4.27/4.67 (~b(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32786, 2169, 51, 433, 2484, 6065, 1, 123, 321, 706])).
% 4.27/4.67 tff(32788,plain,
% 4.27/4.67 (r(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[396, 32787])).
% 4.27/4.67 tff(32789,plain,
% 4.27/4.67 (~r(s(z), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[13781, 32788, 123, 51, 32640])).
% 4.27/4.67 tff(32790,plain,
% 4.27/4.67 (b(s(z), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[348, 32789])).
% 4.27/4.67 tff(32791,plain,
% 4.27/4.67 (~(s(s(s(z))) = elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[24196, 32787, 32636])).
% 4.27/4.67 tff(32792,plain,
% 4.27/4.67 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[31651, 698, 354, 624, 251, 321, 2323])).
% 4.27/4.67 tff(32793,plain,
% 4.27/4.67 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[1137, 32792])).
% 4.27/4.67 tff(32794,plain,
% 4.27/4.67 (~b(s(s(s(z))), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[6004, 144, 123, 32793, 304])).
% 4.27/4.67 tff(32795,plain,
% 4.27/4.67 (r(s(s(s(z))), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[2794, 32794])).
% 4.27/4.67 tff(32796,plain,
% 4.27/4.67 (~r(z, s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[8665, 333, 409, 354, 32795])).
% 4.27/4.67 tff(32797,plain,
% 4.27/4.67 (b(z, s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[619, 32796])).
% 4.27/4.67 tff(32798,plain,
% 4.27/4.67 (~r(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[8673, 333, 409, 354, 32795])).
% 4.27/4.67 tff(32799,plain,
% 4.27/4.67 (b(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[396, 32798])).
% 4.27/4.67 tff(32800,plain,
% 4.27/4.67 (~b(s(z), s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[2156, 32799, 489, 32797])).
% 4.27/4.67 tff(32801,plain,
% 4.27/4.67 (r(s(z), s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[172, 32800])).
% 4.27/4.67 tff(32802,plain,
% 4.27/4.67 (~r(elem!1, s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[11876, 32801, 409, 32795])).
% 4.27/4.67 tff(32803,plain,
% 4.27/4.67 (b(elem!1, s(s(s(z))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[1538, 32802, 12398])).
% 4.27/4.67 tff(32804,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[9164, 144, 624, 32803, 32799, 32797])).
% 4.27/4.67 tff(32805,plain,((s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32806,plain,
% 4.27/4.67 (~r(s(z), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32805, 9363, 489, 698, 624, 123, 304, 251, 321, 2323])).
% 4.27/4.67 tff(32807,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[406, 32806, 9367, 350])).
% 4.27/4.67 tff(32808,plain,(b(z, s(z)) | b(s(z), elem!1) | (~b(s(z), z)) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32809,plain,
% 4.27/4.67 (b(z, s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32808, 32790, 123, 32636, 350, 32791, 32640, 32638, 321, 23943])).
% 4.27/4.67 tff(32810,plain,
% 4.27/4.67 (~b(s(elem!1), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32762, 32809, 123, 2484, 51, 32640, 32702, 32790])).
% 4.27/4.67 tff(32811,plain,
% 4.27/4.67 (r(s(elem!1), s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[486, 32810, 1])).
% 4.27/4.67 tff(32812,plain,
% 4.27/4.67 (~r(s(elem!1), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[11068, 333, 2169, 32811, 6065])).
% 4.27/4.67 tff(32813,plain,
% 4.27/4.67 (b(s(elem!1), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[448, 32812, 433])).
% 4.27/4.67 tff(32814,plain,
% 4.27/4.67 (~b(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[916, 32813, 32638, 32636])).
% 4.27/4.67 tff(32815,plain,
% 4.27/4.67 (r(s(elem!1), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[507, 32814])).
% 4.27/4.67 tff(32816,plain,
% 4.27/4.67 (~r(elem!1, z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[12025, 51, 2484, 321])).
% 4.27/4.67 tff(32817,plain,
% 4.27/4.67 (b(elem!1, z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[1380, 32816, 77])).
% 4.27/4.67 tff(32818,plain,
% 4.27/4.67 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(modus_ponens,[status(thm)],[2925, 6021])).
% 4.27/4.67 tff(32819,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[123, 32818])).
% 4.27/4.67 tff(32820,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32821,plain,
% 4.27/4.67 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32820, 57, 123])).
% 4.27/4.67 tff(32822,plain,
% 4.27/4.67 ($false),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[12684, 32821, 57, 321, 51, 251, 624, 2484, 509])).
% 4.27/4.67 tff(32823,plain,((~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.67 tff(32824,plain,
% 4.27/4.67 (~(s(z) = elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[32823, 509, 51, 251, 32817, 2484, 321, 123])).
% 4.27/4.67 tff(32825,plain,
% 4.27/4.67 (r(s(z), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[406, 32824, 350])).
% 4.27/4.67 tff(32826,plain,
% 4.27/4.67 (~(elem!1 = s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[712, 32824])).
% 4.27/4.67 tff(32827,plain,
% 4.27/4.67 (r(elem!1, s(z))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[720, 32826, 708])).
% 4.27/4.67 tff(32828,plain,
% 4.27/4.67 (~r(s(s(s(z))), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[12189, 32827, 123, 2484, 32825])).
% 4.27/4.67 tff(32829,plain,
% 4.27/4.67 (b(s(s(s(z))), elem!1)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[704, 32828, 698])).
% 4.27/4.67 tff(32830,plain,
% 4.27/4.67 (~b(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[10565, 32829, 251, 32817])).
% 4.27/4.67 tff(32831,plain,
% 4.27/4.67 (r(s(s(s(z))), z)),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[396, 32830])).
% 4.27/4.67 tff(32832,plain,
% 4.27/4.67 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[542, 12618, 537])).
% 4.27/4.67 tff(32833,plain,
% 4.27/4.67 (~b(s(z), s(elem!1))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[3388, 144, 123, 32832, 450])).
% 4.27/4.67 tff(32834,plain,
% 4.27/4.67 (r(s(z), s(elem!1))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[1244, 32833, 1229])).
% 4.27/4.67 tff(32835,plain,
% 4.27/4.67 (~r(elem!1, s(elem!1))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[7651, 32825, 32834, 434])).
% 4.27/4.67 tff(32836,plain,
% 4.27/4.67 (b(elem!1, s(elem!1))),
% 4.27/4.67 inference(unit_resolution,[status(thm)],[560, 32835, 1722])).
% 4.27/4.68 tff(32837,plain,
% 4.27/4.68 (~r(s(elem!1), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7675, 32824, 350, 32834, 708])).
% 4.27/4.68 tff(32838,plain,
% 4.27/4.68 (b(s(elem!1), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[448, 32837, 433])).
% 4.27/4.68 tff(32839,plain,
% 4.27/4.68 (~b(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1642, 32838, 251, 32836])).
% 4.27/4.68 tff(32840,plain,
% 4.27/4.68 (r(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[583, 32839])).
% 4.27/4.68 tff(32841,plain,
% 4.27/4.68 (~r(s(s(s(z))), s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[10842, 333, 509, 32840, 32831])).
% 4.27/4.68 tff(32842,plain,
% 4.27/4.68 (~b(s(s(s(z))), s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[4819, 32836, 32829, 32838])).
% 4.27/4.68 tff(32843,plain,
% 4.27/4.68 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[19995])).
% 4.27/4.68 tff(32844,plain,
% 4.27/4.68 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(symmetry,[status(thm)],[32843])).
% 4.27/4.68 tff(32845,plain,
% 4.27/4.68 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32844])).
% 4.27/4.68 tff(32846,plain,
% 4.27/4.68 (s(s(z)) = elem!1),
% 4.27/4.68 inference(transitivity,[status(thm)],[87, 1003, 850])).
% 4.27/4.68 tff(32847,plain,
% 4.27/4.68 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32846])).
% 4.27/4.68 tff(32848,plain,
% 4.27/4.68 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 4.27/4.68 inference(transitivity,[status(thm)],[32847, 52])).
% 4.27/4.68 tff(32849,plain,
% 4.27/4.68 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 4.27/4.68 inference(transitivity,[status(thm)],[32848, 53])).
% 4.27/4.68 tff(32850,plain,
% 4.27/4.68 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32849])).
% 4.27/4.68 tff(32851,plain,
% 4.27/4.68 (~(elem!1 = s(z))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[1416, 32850])).
% 4.27/4.68 tff(32852,plain,
% 4.27/4.68 (r(elem!1, s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[720, 32851, 708])).
% 4.27/4.68 tff(32853,plain,
% 4.27/4.68 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32848])).
% 4.27/4.68 tff(32854,plain,
% 4.27/4.68 (~(s(z) = elem!1)),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[1416, 32853])).
% 4.27/4.68 tff(32855,plain,
% 4.27/4.68 (~r(s(elem!1), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7675, 32854, 350, 1230, 708])).
% 4.27/4.68 tff(32856,plain,
% 4.27/4.68 (b(s(elem!1), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[448, 32855, 433])).
% 4.27/4.68 tff(32857,plain,
% 4.27/4.68 (~(s(s(elem!1)) = s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1196, 1722])).
% 4.27/4.68 tff(32858,plain,
% 4.27/4.68 (r(s(z), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[406, 32854, 350])).
% 4.27/4.68 tff(32859,plain,
% 4.27/4.68 (~r(elem!1, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7651, 32858, 1230, 434])).
% 4.27/4.68 tff(32860,plain,
% 4.27/4.68 (b(elem!1, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[560, 32859, 1722])).
% 4.27/4.68 tff(32861,plain,
% 4.27/4.68 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 4.27/4.68 inference(rewrite,[status(thm)],[])).
% 4.27/4.68 tff(32862,plain,
% 4.27/4.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32861])).
% 4.27/4.68 tff(32863,plain,
% 4.27/4.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 4.27/4.68 inference(transitivity,[status(thm)],[32862, 13365])).
% 4.27/4.68 tff(32864,plain,
% 4.27/4.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 4.27/4.68 inference(quant_inst,[status(thm)],[])).
% 4.27/4.68 tff(32865,plain,
% 4.27/4.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[32864, 32863])).
% 4.27/4.68 tff(32866,plain,
% 4.27/4.68 (~b(s(s(elem!1)), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32865, 144, 251, 624, 4972])).
% 4.27/4.68 tff(32867,plain,
% 4.27/4.68 (r(s(s(elem!1)), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[5509, 32866])).
% 4.27/4.68 tff(32868,plain,
% 4.27/4.68 (((~![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(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), 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(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 4.27/4.68 inference(rewrite,[status(thm)],[])).
% 4.27/4.68 tff(32869,plain,
% 4.27/4.68 (((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 4.27/4.68 inference(rewrite,[status(thm)],[])).
% 4.27/4.68 tff(32870,plain,
% 4.27/4.68 (((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(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(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32869])).
% 4.27/4.68 tff(32871,plain,
% 4.27/4.68 (((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(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(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 4.27/4.68 inference(transitivity,[status(thm)],[32870, 32868])).
% 4.27/4.68 tff(32872,plain,
% 4.27/4.68 ((~![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(z))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 4.27/4.68 inference(quant_inst,[status(thm)],[])).
% 4.27/4.68 tff(32873,plain,
% 4.27/4.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[32872, 32871])).
% 4.27/4.68 tff(32874,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32873, 333, 4991, 434, 7520, 32867])).
% 4.27/4.68 tff(32875,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32876,plain,
% 4.27/4.68 (~b(s(s(elem!1)), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32875, 32860, 32857, 251, 624, 434, 32856])).
% 4.27/4.68 tff(32877,plain,
% 4.27/4.68 (r(s(s(elem!1)), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1260, 44, 11096, 32876])).
% 4.27/4.68 tff(32878,plain,
% 4.27/4.68 (((~![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)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.68 inference(rewrite,[status(thm)],[])).
% 4.27/4.68 tff(32879,plain,
% 4.27/4.68 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.68 inference(rewrite,[status(thm)],[])).
% 4.27/4.68 tff(32880,plain,
% 4.27/4.68 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32879])).
% 4.27/4.68 tff(32881,plain,
% 4.27/4.68 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.68 inference(transitivity,[status(thm)],[32880, 32878])).
% 4.27/4.68 tff(32882,plain,
% 4.27/4.68 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.68 inference(quant_inst,[status(thm)],[])).
% 4.27/4.68 tff(32883,plain,
% 4.27/4.68 ((~![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)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[32882, 32881])).
% 4.27/4.68 tff(32884,plain,
% 4.27/4.68 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32883, 333, 32877, 32852, 2484])).
% 4.27/4.68 tff(32885,plain,
% 4.27/4.68 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[32884, 32845])).
% 4.27/4.68 tff(32886,plain,
% 4.27/4.68 ((s(s(s(s(z)))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[19995])).
% 4.27/4.68 tff(32887,plain,
% 4.27/4.68 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 4.27/4.68 inference(symmetry,[status(thm)],[32886])).
% 4.27/4.68 tff(32888,plain,
% 4.27/4.68 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 4.27/4.68 inference(monotonicity,[status(thm)],[32887])).
% 4.27/4.68 tff(32889,plain,
% 4.27/4.68 (~(s(s(s(s(z)))) = s(z))),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[107, 32888])).
% 4.27/4.68 tff(32890,plain,
% 4.27/4.68 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.27/4.68 inference(monotonicity,[status(thm)],[19995])).
% 4.27/4.68 tff(32891,plain,
% 4.27/4.68 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 4.27/4.68 inference(symmetry,[status(thm)],[32890])).
% 4.27/4.68 tff(32892,plain,
% 4.27/4.68 (r(s(s(s(s(z)))), elem!1)),
% 4.27/4.68 inference(modus_ponens,[status(thm)],[32877, 32891])).
% 4.27/4.68 tff(32893,plain,
% 4.27/4.68 (~r(s(s(s(s(z)))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[26847, 32892, 32852, 32858])).
% 4.27/4.68 tff(32894,plain,
% 4.27/4.68 (b(s(s(s(s(z)))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[24600, 32893, 32889])).
% 4.27/4.68 tff(32895,plain,
% 4.27/4.68 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[26574, 32894, 304, 123])).
% 4.27/4.68 tff(32896,plain,
% 4.27/4.68 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[9761, 32895])).
% 4.27/4.68 tff(32897,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32896, 32885])).
% 4.27/4.68 tff(32898,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), s(z))) | (s(elem!1) = elem!1) | (~r(s(z), s(elem!1))) | b(elem!1, s(z)) | b(s(z), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32899,plain,
% 4.27/4.68 (~(s(s(s(z))) = s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32898, 32834, 123, 2484, 251, 32817, 434, 433, 304, 708, 350, 1])).
% 4.27/4.68 tff(32900,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1951, 44, 32899, 32842, 32841])).
% 4.27/4.68 tff(32901,plain,((~r(s(elem!1), z)) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = elem!1) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | b(s(z), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32902,plain,
% 4.27/4.68 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32901, 32815, 123, 2484, 433, 32638, 32791, 708, 350, 51, 321, 32640, 1, 32811, 32703])).
% 4.27/4.68 tff(32903,plain,
% 4.27/4.68 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[13493, 32815, 2484, 51])).
% 4.27/4.68 tff(32904,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[472, 32903, 32902, 32702])).
% 4.27/4.68 tff(32905,plain,(b(s(z), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | b(elem!1, s(z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32906,plain,
% 4.27/4.68 (b(s(z), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32905, 907, 51, 123, 2484, 708, 321, 1, 706])).
% 4.27/4.68 tff(32907,plain,
% 4.27/4.68 (~b(s(z), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1602, 32906, 32638, 32636])).
% 4.27/4.68 tff(32908,plain,
% 4.27/4.68 (r(s(z), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[348, 32907])).
% 4.27/4.68 tff(32909,plain,
% 4.27/4.68 (~r(s(elem!1), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1911, 32908, 6065, 32638, 32636, 907])).
% 4.27/4.68 tff(32910,plain,
% 4.27/4.68 (b(s(elem!1), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[486, 32909, 1])).
% 4.27/4.68 tff(32911,plain,
% 4.27/4.68 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[869, 144, 32910, 123, 32640])).
% 4.27/4.68 tff(32912,plain,
% 4.27/4.68 (~r(s(s(s(z))), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[13781, 32908, 123, 51, 32640])).
% 4.27/4.68 tff(32913,plain,
% 4.27/4.68 (b(s(s(s(z))), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[396, 32912])).
% 4.27/4.68 tff(32914,plain,
% 4.27/4.68 (~b(s(s(s(z))), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[10565, 32913, 32636, 32638])).
% 4.27/4.68 tff(32915,plain,
% 4.27/4.68 (~r(s(s(s(z))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[8824, 707, 722, 323])).
% 4.27/4.68 tff(32916,plain,
% 4.27/4.68 (b(s(s(s(z))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[2794, 32915])).
% 4.27/4.68 tff(32917,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[6004, 144, 32916, 123, 25846, 304])).
% 4.27/4.68 tff(32918,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32919,plain,
% 4.27/4.68 (~r(s(s(s(z))), elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32918, 32908, 32640, 6065, 123, 23943, 2484])).
% 4.27/4.68 tff(32920,plain,
% 4.27/4.68 (s(s(s(z))) = elem!1),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[704, 32919, 32914])).
% 4.27/4.68 tff(32921,plain,
% 4.27/4.68 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[12214, 32920])).
% 4.27/4.68 tff(32922,plain,
% 4.27/4.68 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[472, 32921, 32911])).
% 4.27/4.68 tff(32923,plain,
% 4.27/4.68 (~r(s(elem!1), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[13493, 32922, 2484, 51])).
% 4.27/4.68 tff(32924,plain,
% 4.27/4.68 (b(s(elem!1), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[507, 32923])).
% 4.27/4.68 tff(32925,plain,
% 4.27/4.68 (~r(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[940, 32922, 321, 51])).
% 4.27/4.68 tff(32926,plain,
% 4.27/4.68 (b(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[583, 32925])).
% 4.27/4.68 tff(32927,plain,
% 4.27/4.68 (~r(elem!1, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[4103, 32922, 321, 23943])).
% 4.27/4.68 tff(32928,plain,
% 4.27/4.68 (b(elem!1, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[560, 32927, 902])).
% 4.27/4.68 tff(32929,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[949, 32928, 32926, 32636, 32924])).
% 4.27/4.68 tff(32930,plain,((elem!1 = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | b(elem!1, s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32931,plain,
% 4.27/4.68 (elem!1 = s(elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32930, 51, 2484, 321, 123, 1, 708, 706])).
% 4.27/4.68 tff(32932,plain,
% 4.27/4.68 (s(elem!1) = elem!1),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1569, 32931])).
% 4.27/4.68 tff(32933,plain,
% 4.27/4.68 (elem!1 = s(s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[5813, 32932])).
% 4.27/4.68 tff(32934,plain,
% 4.27/4.68 (s(s(elem!1)) = elem!1),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[5603, 32933])).
% 4.27/4.68 tff(32935,plain,
% 4.27/4.68 (~(s(s(s(z))) = elem!1)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7595, 32934, 863])).
% 4.27/4.68 tff(32936,plain,
% 4.27/4.68 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[25941, 32932, 23943])).
% 4.27/4.68 tff(32937,plain,
% 4.27/4.68 (~r(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[940, 32936, 321, 51])).
% 4.27/4.68 tff(32938,plain,
% 4.27/4.68 (b(z, s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[583, 32937])).
% 4.27/4.68 tff(32939,plain,
% 4.27/4.68 (b(s(elem!1), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[12198, 32931, 32636])).
% 4.27/4.68 tff(32940,plain,
% 4.27/4.68 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7918, 32938, 856, 51, 321, 32936, 32939])).
% 4.27/4.68 tff(32941,plain,
% 4.27/4.68 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1451, 32940])).
% 4.27/4.68 tff(32942,plain,
% 4.27/4.68 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[11754, 1699, 51, 321])).
% 4.27/4.68 tff(32943,plain,
% 4.27/4.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[2199, 333, 1699, 321, 51])).
% 4.27/4.68 tff(32944,plain,
% 4.27/4.68 (~b(s(s(z)), s(s(s(z))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[7952, 32943, 1398, 32942])).
% 4.27/4.68 tff(32945,plain,
% 4.27/4.68 (r(s(s(z)), s(s(s(z))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1473, 44, 32944, 217])).
% 4.27/4.68 tff(32946,plain,
% 4.27/4.68 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1137, 32942])).
% 4.27/4.68 tff(32947,plain,
% 4.27/4.68 (~b(s(s(s(z))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[6004, 144, 123, 32946, 304])).
% 4.27/4.68 tff(32948,plain,
% 4.27/4.68 (r(s(s(s(z))), s(z))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[2794, 32947])).
% 4.27/4.68 tff(32949,plain,
% 4.27/4.68 (~r(s(z), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[13781, 1699, 123, 51, 304])).
% 4.27/4.68 tff(32950,plain,
% 4.27/4.68 (b(s(z), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[348, 32949])).
% 4.27/4.68 tff(32951,plain,
% 4.27/4.68 (~b(s(z), s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[2383, 32950, 491, 585])).
% 4.27/4.68 tff(32952,plain,
% 4.27/4.68 (r(s(z), s(elem!1))),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[1244, 32951, 1237])).
% 4.27/4.68 tff(32953,plain,
% 4.27/4.68 ($false),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[11512, 333, 32952, 32948, 32945, 1430])).
% 4.27/4.68 tff(32954,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.68 tff(32955,plain,
% 4.27/4.68 (~r(s(s(s(z))), z)),
% 4.27/4.68 inference(unit_resolution,[status(thm)],[32954, 32941, 123, 32640, 321, 51, 1229, 32939, 32938])).
% 4.27/4.68 tff(32956,plain,
% 4.27/4.68 (b(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[396, 32955])).
% 4.27/4.69 tff(32957,plain,
% 4.27/4.69 (~b(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[10565, 32956, 32636, 32638])).
% 4.27/4.69 tff(32958,plain,
% 4.27/4.69 (r(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[704, 32957, 32935])).
% 4.27/4.69 tff(32959,plain,
% 4.27/4.69 (~r(s(z), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12189, 32958, 123, 2484, 6065])).
% 4.27/4.69 tff(32960,plain,
% 4.27/4.69 (b(s(z), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[406, 32959, 706])).
% 4.27/4.69 tff(32961,plain,
% 4.27/4.69 (~r(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32918, 32958, 32640, 6065, 123, 23943, 2484])).
% 4.27/4.69 tff(32962,plain,
% 4.27/4.69 (b(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[348, 32961])).
% 4.27/4.69 tff(32963,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1602, 32962, 32960, 32638, 32636])).
% 4.27/4.69 tff(32964,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(32965,plain,
% 4.27/4.69 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32964, 32634, 50, 2484, 12153, 1, 708])).
% 4.27/4.69 tff(32966,plain,
% 4.27/4.69 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[279, 32965])).
% 4.27/4.69 tff(32967,plain,
% 4.27/4.69 (~(elem!1 = s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[712, 32634])).
% 4.27/4.69 tff(32968,plain,
% 4.27/4.69 (r(elem!1, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[720, 32967, 708])).
% 4.27/4.69 tff(32969,plain,
% 4.27/4.69 (~r(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[14348, 408, 321, 2484])).
% 4.27/4.69 tff(32970,plain,
% 4.27/4.69 (b(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[372, 32969])).
% 4.27/4.69 tff(32971,plain,
% 4.27/4.69 (b(s(z), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[14373, 32970, 123, 2484, 706, 32638, 259])).
% 4.27/4.69 tff(32972,plain,
% 4.27/4.69 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[757, 32970, 123, 259])).
% 4.27/4.69 tff(32973,plain,
% 4.27/4.69 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[319, 32972])).
% 4.27/4.69 tff(32974,plain,
% 4.27/4.69 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(32975,plain,
% 4.27/4.69 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(32976,plain,
% 4.27/4.69 (((~![X0: $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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.27/4.69 inference(monotonicity,[status(thm)],[32975])).
% 4.27/4.69 tff(32977,plain,
% 4.27/4.69 (((~![X0: $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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.27/4.69 inference(transitivity,[status(thm)],[32976, 32974])).
% 4.27/4.69 tff(32978,plain,
% 4.27/4.69 ((~![X0: $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(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.27/4.69 inference(quant_inst,[status(thm)],[])).
% 4.27/4.69 tff(32979,plain,
% 4.27/4.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.27/4.69 inference(modus_ponens,[status(thm)],[32978, 32977])).
% 4.27/4.69 tff(32980,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32979, 333, 722, 353, 2484, 322])).
% 4.27/4.69 tff(32981,plain,((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(32982,plain,
% 4.27/4.69 (~r(s(z), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32981, 32973, 2484, 722])).
% 4.27/4.69 tff(32983,plain,
% 4.27/4.69 (b(s(z), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[172, 32982])).
% 4.27/4.69 tff(32984,plain,
% 4.27/4.69 (~r(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[820, 32973, 123, 32638, 13793, 713, 259, 32970])).
% 4.27/4.69 tff(32985,plain,
% 4.27/4.69 (b(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[348, 32984])).
% 4.27/4.69 tff(32986,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[2144, 144, 251, 134, 489, 285, 838])).
% 4.27/4.69 tff(32987,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(32988,plain,
% 4.27/4.69 (~b(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32987, 32971, 32638, 32985, 32983])).
% 4.27/4.69 tff(32989,plain,
% 4.27/4.69 (r(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[396, 32988])).
% 4.27/4.69 tff(32990,plain,
% 4.27/4.69 (((~![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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(32991,plain,
% 4.27/4.69 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(32992,plain,
% 4.27/4.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.27/4.69 inference(monotonicity,[status(thm)],[32991])).
% 4.27/4.69 tff(32993,plain,
% 4.27/4.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.27/4.69 inference(transitivity,[status(thm)],[32992, 32990])).
% 4.27/4.69 tff(32994,plain,
% 4.27/4.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.27/4.69 inference(quant_inst,[status(thm)],[])).
% 4.27/4.69 tff(32995,plain,
% 4.27/4.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.27/4.69 inference(modus_ponens,[status(thm)],[32994, 32993])).
% 4.27/4.69 tff(32996,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32995, 333, 408, 623, 2484, 321])).
% 4.27/4.69 tff(32997,plain,((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(32998,plain,
% 4.27/4.69 (~r(z, s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32997, 408, 2484, 321])).
% 4.27/4.69 tff(32999,plain,
% 4.27/4.69 (b(z, s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[619, 32998])).
% 4.27/4.69 tff(33000,plain,
% 4.27/4.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(33001,plain,
% 4.27/4.69 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.69 inference(rewrite,[status(thm)],[])).
% 4.27/4.69 tff(33002,plain,
% 4.27/4.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.27/4.69 inference(monotonicity,[status(thm)],[33001])).
% 4.27/4.69 tff(33003,plain,
% 4.27/4.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.27/4.69 inference(transitivity,[status(thm)],[33002, 33000])).
% 4.27/4.69 tff(33004,plain,
% 4.27/4.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 4.27/4.69 inference(quant_inst,[status(thm)],[])).
% 4.27/4.69 tff(33005,plain,
% 4.27/4.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.27/4.69 inference(modus_ponens,[status(thm)],[33004, 33003])).
% 4.27/4.69 tff(33006,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33005, 144, 489, 284, 838, 123, 2254])).
% 4.27/4.69 tff(33007,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33008,plain,
% 4.27/4.69 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33007, 32985, 32999, 32983, 123])).
% 4.27/4.69 tff(33009,plain,
% 4.27/4.69 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1137, 33008])).
% 4.27/4.69 tff(33010,plain,
% 4.27/4.69 (~r(z, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[10450, 33009, 321, 32989])).
% 4.27/4.69 tff(33011,plain,
% 4.27/4.69 (b(z, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[583, 33010])).
% 4.27/4.69 tff(33012,plain,
% 4.27/4.69 (~b(elem!1, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[22334, 33011, 32638, 32970, 32971])).
% 4.27/4.69 tff(33013,plain,
% 4.27/4.69 (~r(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[23315, 33009, 23943, 2484])).
% 4.27/4.69 tff(33014,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[10812, 19936, 12398, 251, 134, 489, 1699, 490, 284, 722])).
% 4.27/4.69 tff(33015,plain,((s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33016,plain,
% 4.27/4.69 (s(s(s(z))) = elem!1),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33015, 33013, 32971, 32985, 32989, 32970, 32999, 722, 32638])).
% 4.27/4.69 tff(33017,plain,
% 4.27/4.69 (~(s(s(elem!1)) = elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[7595, 33016, 863])).
% 4.27/4.69 tff(33018,plain,
% 4.27/4.69 (~(elem!1 = s(s(elem!1)))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[5603, 33017])).
% 4.27/4.69 tff(33019,plain,
% 4.27/4.69 (~(s(elem!1) = elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[5813, 33018])).
% 4.27/4.69 tff(33020,plain,
% 4.27/4.69 (~(elem!1 = s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1569, 33019])).
% 4.27/4.69 tff(33021,plain,
% 4.27/4.69 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12214, 33016])).
% 4.27/4.69 tff(33022,plain,
% 4.27/4.69 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[20734, 33021])).
% 4.27/4.69 tff(33023,plain,
% 4.27/4.69 (r(s(elem!1), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[448, 3616, 433])).
% 4.27/4.69 tff(33024,plain,
% 4.27/4.69 (~r(z, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[9017, 33023, 408, 509])).
% 4.27/4.69 tff(33025,plain,
% 4.27/4.69 (b(z, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[583, 33024])).
% 4.27/4.69 tff(33026,plain,
% 4.27/4.69 (~b(elem!1, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[22334, 33025, 251, 490, 134])).
% 4.27/4.69 tff(33027,plain,
% 4.27/4.69 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[20897, 33026, 2484, 1722, 3616])).
% 4.27/4.69 tff(33028,plain,
% 4.27/4.69 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[8386, 33027, 259, 537, 33025])).
% 4.27/4.69 tff(33029,plain,
% 4.27/4.69 (r(elem!1, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[560, 33026, 1722])).
% 4.27/4.69 tff(33030,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12793, 333, 33029, 33023, 2484, 33028])).
% 4.27/4.69 tff(33031,plain,(b(s(elem!1), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33032,plain,
% 4.27/4.69 (b(s(elem!1), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33031, 33022, 259, 2484, 32638, 32970, 32971, 408, 509, 33019])).
% 4.27/4.69 tff(33033,plain,
% 4.27/4.69 (~r(elem!1, s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[8975, 33032, 32638, 32970, 1, 32971, 32985, 722, 408, 509])).
% 4.27/4.69 tff(33034,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[560, 33033, 33020, 33012])).
% 4.27/4.69 tff(33035,plain,((~r(elem!1, z)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33036,plain,
% 4.27/4.69 (~r(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33035, 12191, 722, 1, 259, 2484, 321, 123, 706])).
% 4.27/4.69 tff(33037,plain,
% 4.27/4.69 (b(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1380, 33036, 77])).
% 4.27/4.69 tff(33038,plain,
% 4.27/4.69 (~(elem!1 = s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12198, 33037, 502])).
% 4.27/4.69 tff(33039,plain,
% 4.27/4.69 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12830, 33037, 2484, 722, 32638, 706])).
% 4.27/4.69 tff(33040,plain,
% 4.27/4.69 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[319, 33039])).
% 4.27/4.69 tff(33041,plain,
% 4.27/4.69 (~b(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[757, 33040, 123, 259])).
% 4.27/4.69 tff(33042,plain,
% 4.27/4.69 (r(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[372, 33041])).
% 4.27/4.69 tff(33043,plain,
% 4.27/4.69 (b(s(elem!1), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1653, 33042, 706, 1, 32637, 33038, 12191])).
% 4.27/4.69 tff(33044,plain,
% 4.27/4.69 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[14540, 33042, 321, 12191])).
% 4.27/4.69 tff(33045,plain,
% 4.27/4.69 (~r(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12308, 33044, 123, 33040, 321, 33042, 33043])).
% 4.27/4.69 tff(33046,plain,
% 4.27/4.69 (b(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[396, 33045])).
% 4.27/4.69 tff(33047,plain,
% 4.27/4.69 (~b(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[10565, 33046, 33037, 32638])).
% 4.27/4.69 tff(33048,plain,
% 4.27/4.69 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[869, 144, 33043, 123, 33040])).
% 4.27/4.69 tff(33049,plain,
% 4.27/4.69 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[472, 33048, 33044])).
% 4.27/4.69 tff(33050,plain,
% 4.27/4.69 (~(s(s(s(z))) = elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12214, 33049])).
% 4.27/4.69 tff(33051,plain,
% 4.27/4.69 (r(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[704, 33050, 33047])).
% 4.27/4.69 tff(33052,plain,
% 4.27/4.69 (~r(s(z), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12189, 33051, 123, 2484, 722])).
% 4.27/4.69 tff(33053,plain,
% 4.27/4.69 (b(s(z), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[406, 33052, 706])).
% 4.27/4.69 tff(33054,plain,
% 4.27/4.69 (~r(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32918, 33051, 33040, 722, 123, 23943, 2484])).
% 4.27/4.69 tff(33055,plain,
% 4.27/4.69 (b(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[348, 33054])).
% 4.27/4.69 tff(33056,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1602, 33055, 33053, 32638, 33037])).
% 4.27/4.69 tff(33057,plain,(b(s(elem!1), z) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33058,plain,
% 4.27/4.69 (b(s(elem!1), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33057, 32634, 32968, 50, 2484, 12153, 1, 32966])).
% 4.27/4.69 tff(33059,plain,
% 4.27/4.69 (~r(z, elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[25313, 23943, 12153, 2484])).
% 4.27/4.69 tff(33060,plain,
% 4.27/4.69 (b(z, elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[658, 33059, 71])).
% 4.27/4.69 tff(33061,plain,
% 4.27/4.69 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12517, 33058, 296])).
% 4.27/4.69 tff(33062,plain,
% 4.27/4.69 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[32964, 706, 123, 2484, 321, 1, 708])).
% 4.27/4.69 tff(33063,plain,
% 4.27/4.69 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[279, 33062])).
% 4.27/4.69 tff(33064,plain,
% 4.27/4.69 (b(s(elem!1), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33057, 706, 6065, 123, 2484, 321, 1, 33063])).
% 4.27/4.69 tff(33065,plain,
% 4.27/4.69 (~b(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[14373, 350, 123, 2484, 706, 32638, 33063])).
% 4.27/4.69 tff(33066,plain,
% 4.27/4.69 (r(z, s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[372, 33065])).
% 4.27/4.69 tff(33067,plain,
% 4.27/4.69 (~r(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[24027, 33066, 321, 23943])).
% 4.27/4.69 tff(33068,plain,
% 4.27/4.69 (b(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1380, 33067, 77])).
% 4.27/4.69 tff(33069,plain,
% 4.27/4.69 (~b(s(elem!1), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[916, 33068, 32638, 33064])).
% 4.27/4.69 tff(33070,plain,
% 4.27/4.69 (~r(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12189, 2169, 123, 2484, 6065])).
% 4.27/4.69 tff(33071,plain,
% 4.27/4.69 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12172, 2169, 2484, 6065])).
% 4.27/4.69 tff(33072,plain,
% 4.27/4.69 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[319, 33071])).
% 4.27/4.69 tff(33073,plain,
% 4.27/4.69 (~r(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[24027, 354, 321, 23943])).
% 4.27/4.69 tff(33074,plain,
% 4.27/4.69 (b(elem!1, z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1380, 33073, 77])).
% 4.27/4.69 tff(33075,plain,
% 4.27/4.69 (~r(s(elem!1), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[1911, 433, 722, 251, 624, 323])).
% 4.27/4.69 tff(33076,plain,
% 4.27/4.69 (b(s(elem!1), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[486, 33075, 1])).
% 4.27/4.69 tff(33077,plain,
% 4.27/4.69 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[869, 144, 33076, 123, 304])).
% 4.27/4.69 tff(33078,plain,
% 4.27/4.69 (r(s(elem!1), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[448, 433, 3616])).
% 4.27/4.69 tff(33079,plain,
% 4.27/4.69 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12270, 333, 33078, 722, 2484])).
% 4.27/4.69 tff(33080,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[472, 33079, 33077, 432])).
% 4.27/4.69 tff(33081,plain,((s(elem!1) = elem!1) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33082,plain,
% 4.27/4.69 (s(elem!1) = elem!1),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33081, 323, 722, 2484, 123, 304, 1, 32638, 33074, 432, 3616])).
% 4.27/4.69 tff(33083,plain,
% 4.27/4.69 (elem!1 = s(elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[906, 33082])).
% 4.27/4.69 tff(33084,plain,
% 4.27/4.69 (s(s(s(elem!1))) = elem!1),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[2482, 33083])).
% 4.27/4.69 tff(33085,plain,
% 4.27/4.69 (s(elem!1) = s(s(s(elem!1)))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[2584, 33084, 33083])).
% 4.27/4.69 tff(33086,plain,
% 4.27/4.69 (~r(s(s(s(z))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12437, 33085, 722, 32638, 33074, 323, 1184, 354])).
% 4.27/4.69 tff(33087,plain,
% 4.27/4.69 (b(s(s(s(z))), s(z))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[2794, 33086])).
% 4.27/4.69 tff(33088,plain,
% 4.27/4.69 (elem!1 = s(s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[5813, 33082])).
% 4.27/4.69 tff(33089,plain,
% 4.27/4.69 (s(s(elem!1)) = elem!1),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[5603, 33088])).
% 4.27/4.69 tff(33090,plain,
% 4.27/4.69 (~(s(s(s(z))) = elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[7595, 33089, 1184])).
% 4.27/4.69 tff(33091,plain,
% 4.27/4.69 (b(s(s(s(z))), elem!1)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[704, 33090, 699])).
% 4.27/4.69 tff(33092,plain,
% 4.27/4.69 (~b(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[10565, 33091, 33074, 32638])).
% 4.27/4.69 tff(33093,plain,
% 4.27/4.69 (r(s(s(s(z))), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[396, 33092])).
% 4.27/4.69 tff(33094,plain,
% 4.27/4.69 (~r(s(z), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[7314, 33093, 354, 323])).
% 4.27/4.69 tff(33095,plain,
% 4.27/4.69 (b(s(z), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[172, 33094])).
% 4.27/4.69 tff(33096,plain,
% 4.27/4.69 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[846, 33095, 304, 33087])).
% 4.27/4.69 tff(33097,plain,
% 4.27/4.69 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[249, 33096])).
% 4.27/4.69 tff(33098,plain,
% 4.27/4.69 ($false),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[12304, 333, 354, 33093, 33097, 321])).
% 4.27/4.69 tff(33099,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(z))), elem!1) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.27/4.69 tff(33100,plain,
% 4.27/4.69 (~r(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33099, 33066, 321, 33072, 33070, 6065, 863, 2484, 123, 1, 432, 33069])).
% 4.27/4.69 tff(33101,plain,
% 4.27/4.69 (b(s(z), z)),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[348, 33100])).
% 4.27/4.69 tff(33102,plain,
% 4.27/4.69 ((~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[31746, 144, 33064, 123, 33063])).
% 4.27/4.69 tff(33103,plain,
% 4.27/4.69 (~b(s(z), s(elem!1))),
% 4.27/4.69 inference(unit_resolution,[status(thm)],[33102, 33101])).
% 4.27/4.69 tff(33104,plain,
% 4.27/4.69 (r(s(z), s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1244, 33103, 1229])).
% 4.37/4.70 tff(33105,plain,
% 4.37/4.70 (~r(s(elem!1), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[7675, 33104, 706, 350, 708])).
% 4.37/4.70 tff(33106,plain,
% 4.37/4.70 (s(s(s(z))) = elem!1),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32805, 33101, 2169, 33066, 33068, 123, 33072, 32638, 321, 23943])).
% 4.37/4.70 tff(33107,plain,
% 4.37/4.70 (~(s(s(elem!1)) = elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[7595, 33106, 863])).
% 4.37/4.70 tff(33108,plain,
% 4.37/4.70 (~(elem!1 = s(s(elem!1)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[5603, 33107])).
% 4.37/4.70 tff(33109,plain,
% 4.37/4.70 (~(s(elem!1) = elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[5813, 33108])).
% 4.37/4.70 tff(33110,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[448, 33109, 33105, 33069])).
% 4.37/4.70 tff(33111,plain,(b(s(z), elem!1) | (s(z) = elem!1) | b(elem!1, s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33112,plain,
% 4.37/4.70 (b(s(z), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33111, 32634, 708, 50, 12153, 2484, 1, 33061])).
% 4.37/4.70 tff(33113,plain,
% 4.37/4.70 (~b(elem!1, z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1602, 489, 32638, 134])).
% 4.37/4.70 tff(33114,plain,
% 4.37/4.70 (r(elem!1, z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[653, 33113, 77])).
% 4.37/4.70 tff(33115,plain,
% 4.37/4.70 (~r(z, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[14348, 33114, 321, 2484])).
% 4.37/4.70 tff(33116,plain,
% 4.37/4.70 (b(z, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[372, 33115])).
% 4.37/4.70 tff(33117,plain,
% 4.37/4.70 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[757, 33116, 123, 259])).
% 4.37/4.70 tff(33118,plain,
% 4.37/4.70 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[319, 33117])).
% 4.37/4.70 tff(33119,plain,
% 4.37/4.70 (~r(s(z), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32981, 33118, 2484, 722])).
% 4.37/4.70 tff(33120,plain,
% 4.37/4.70 (b(s(z), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[172, 33119])).
% 4.37/4.70 tff(33121,plain,
% 4.37/4.70 (~b(s(s(s(z))), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32987, 33120, 32638, 134, 489])).
% 4.37/4.70 tff(33122,plain,
% 4.37/4.70 (r(s(s(s(z))), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[396, 33121])).
% 4.37/4.70 tff(33123,plain,
% 4.37/4.70 (~r(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32997, 33114, 2484, 321])).
% 4.37/4.70 tff(33124,plain,
% 4.37/4.70 (b(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[619, 33123])).
% 4.37/4.70 tff(33125,plain,
% 4.37/4.70 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33007, 33120, 489, 33124, 123])).
% 4.37/4.70 tff(33126,plain,
% 4.37/4.70 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1137, 33125])).
% 4.37/4.70 tff(33127,plain,
% 4.37/4.70 ((~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[31746, 144, 491, 123, 259])).
% 4.37/4.70 tff(33128,plain,
% 4.37/4.70 (~b(s(z), s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33127, 489])).
% 4.37/4.70 tff(33129,plain,
% 4.37/4.70 (~(s(elem!1) = elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[3262, 33128, 134])).
% 4.37/4.70 tff(33130,plain,
% 4.37/4.70 (~(elem!1 = s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1569, 33129])).
% 4.37/4.70 tff(33131,plain,
% 4.37/4.70 (r(s(z), s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1244, 33128, 1229])).
% 4.37/4.70 tff(33132,plain,
% 4.37/4.70 (~b(s(elem!1), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[499, 33116, 491, 489])).
% 4.37/4.70 tff(33133,plain,
% 4.37/4.70 (r(s(elem!1), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[486, 33132, 1])).
% 4.37/4.70 tff(33134,plain,
% 4.37/4.70 (~r(elem!1, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[7799, 33133, 722, 33131])).
% 4.37/4.70 tff(33135,plain,
% 4.37/4.70 (b(elem!1, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[560, 33134, 33130])).
% 4.37/4.70 tff(33136,plain,
% 4.37/4.70 (~b(z, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[22334, 33135, 32638, 33116, 134])).
% 4.37/4.70 tff(33137,plain,
% 4.37/4.70 (r(z, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[583, 33136])).
% 4.37/4.70 tff(33138,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[10450, 33137, 33126, 321, 33122])).
% 4.37/4.70 tff(33139,plain,((~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33140,plain,
% 4.37/4.70 (~b(s(z), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33139, 33112, 12153, 50, 32968, 2484, 1, 33058, 32966])).
% 4.37/4.70 tff(33141,plain,
% 4.37/4.70 (r(s(z), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[348, 33140])).
% 4.37/4.70 tff(33142,plain,
% 4.37/4.70 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[820, 490, 123, 251, 114, 714, 259, 323])).
% 4.37/4.70 tff(33143,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[319, 33142, 13803])).
% 4.37/4.70 tff(33144,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (elem!1 = s(z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33145,plain,
% 4.37/4.70 (~b(z, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33144, 33060, 50, 13793, 32967, 32966, 33141])).
% 4.37/4.70 tff(33146,plain,
% 4.37/4.70 (r(z, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[372, 33145])).
% 4.37/4.70 tff(33147,plain,
% 4.37/4.70 (~r(elem!1, z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[24027, 33146, 12153, 23943])).
% 4.37/4.70 tff(33148,plain,
% 4.37/4.70 (b(elem!1, z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1380, 33147, 77])).
% 4.37/4.70 tff(33149,plain,
% 4.37/4.70 (~b(s(elem!1), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[916, 33148, 33060, 33058])).
% 4.37/4.70 tff(33150,plain,
% 4.37/4.70 (~(s(s(z)) = s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[855, 32634])).
% 4.37/4.70 tff(33151,plain,
% 4.37/4.70 (~(s(s(s(z))) = s(s(elem!1)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[862, 33150])).
% 4.37/4.70 tff(33152,plain,
% 4.37/4.70 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[12830, 33148, 2484, 32968, 33060, 32634])).
% 4.37/4.70 tff(33153,plain,
% 4.37/4.70 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[319, 33152])).
% 4.37/4.70 tff(33154,plain,
% 4.37/4.70 (~r(s(s(s(z))), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32918, 33153, 33141, 32968, 50, 23943, 2484])).
% 4.37/4.70 tff(33155,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33099, 33154, 33153, 12153, 33141, 33146, 32968, 33151, 2484, 50, 1, 33061, 33149])).
% 4.37/4.70 tff(33156,plain,((s(elem!1) = s(z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z)) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33157,plain,
% 4.37/4.70 (s(elem!1) = s(z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33156, 296, 708, 2484, 4])).
% 4.37/4.70 tff(33158,plain,
% 4.37/4.70 (z = elem!1),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[8683, 33157])).
% 4.37/4.70 tff(33159,plain,
% 4.37/4.70 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33158])).
% 4.37/4.70 tff(33160,plain,
% 4.37/4.70 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33159, 2])).
% 4.37/4.70 tff(33161,plain,
% 4.37/4.70 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 4.37/4.70 inference(transitivity,[status(thm)],[33160, 4795])).
% 4.37/4.70 tff(33162,plain,
% 4.37/4.70 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33161])).
% 4.37/4.70 tff(33163,plain,
% 4.37/4.70 (~(s(s(s(z))) = elem!1)),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[392, 33162])).
% 4.37/4.70 tff(33164,plain,
% 4.37/4.70 ((s(z) = z) <=> (s(z) = elem!1)),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33158])).
% 4.37/4.70 tff(33165,plain,
% 4.37/4.70 ((s(z) = z) <=> (elem!1 = s(z))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33164, 53])).
% 4.37/4.70 tff(33166,plain,
% 4.37/4.70 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33165])).
% 4.37/4.70 tff(33167,plain,
% 4.37/4.70 (~(elem!1 = s(z))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[344, 33166])).
% 4.37/4.70 tff(33168,plain,
% 4.37/4.70 (r(elem!1, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[718, 44, 708, 33167])).
% 4.37/4.70 tff(33169,plain,
% 4.37/4.70 (b(z, s(elem!1)) <=> b(z, s(z))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33157])).
% 4.37/4.70 tff(33170,plain,
% 4.37/4.70 (b(z, s(z)) <=> b(z, s(elem!1))),
% 4.37/4.70 inference(symmetry,[status(thm)],[33169])).
% 4.37/4.70 tff(33171,plain,
% 4.37/4.70 (b(z, s(z)) <=> b(elem!1, s(z))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33158])).
% 4.37/4.70 tff(33172,plain,
% 4.37/4.70 (b(elem!1, s(z)) <=> b(z, s(z))),
% 4.37/4.70 inference(symmetry,[status(thm)],[33171])).
% 4.37/4.70 tff(33173,plain,
% 4.37/4.70 (b(elem!1, s(z)) <=> b(z, s(elem!1))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33172, 33170])).
% 4.37/4.70 tff(33174,plain,
% 4.37/4.70 ((~b(elem!1, s(z))) <=> (~b(z, s(elem!1)))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33173])).
% 4.37/4.70 tff(33175,plain,
% 4.37/4.70 (~b(z, s(elem!1))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[708, 33174])).
% 4.37/4.70 tff(33176,plain,
% 4.37/4.70 (r(z, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[583, 33175])).
% 4.37/4.70 tff(33177,plain,
% 4.37/4.70 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33172])).
% 4.37/4.70 tff(33178,plain,
% 4.37/4.70 (~b(z, s(z))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[708, 33177])).
% 4.37/4.70 tff(33179,plain,
% 4.37/4.70 (r(z, s(z))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[372, 33178])).
% 4.37/4.70 tff(33180,plain,
% 4.37/4.70 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33157])).
% 4.37/4.70 tff(33181,plain,
% 4.37/4.70 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 4.37/4.70 inference(transitivity,[status(thm)],[33180, 52])).
% 4.37/4.70 tff(33182,plain,
% 4.37/4.70 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 4.37/4.70 inference(symmetry,[status(thm)],[33181])).
% 4.37/4.70 tff(33183,plain,
% 4.37/4.70 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33164, 33182])).
% 4.37/4.70 tff(33184,plain,
% 4.37/4.70 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33183])).
% 4.37/4.70 tff(33185,plain,
% 4.37/4.70 (~(elem!1 = s(elem!1))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[344, 33184])).
% 4.37/4.70 tff(33186,plain,
% 4.37/4.70 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33157])).
% 4.37/4.70 tff(33187,plain,
% 4.37/4.70 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.37/4.70 inference(symmetry,[status(thm)],[33186])).
% 4.37/4.70 tff(33188,plain,
% 4.37/4.70 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33187])).
% 4.37/4.70 tff(33189,plain,
% 4.37/4.70 (~b(elem!1, s(elem!1))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[708, 33188])).
% 4.37/4.70 tff(33190,plain,
% 4.37/4.70 (r(elem!1, s(elem!1))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[560, 33189, 33185])).
% 4.37/4.70 tff(33191,plain,
% 4.37/4.70 (((~![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(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.70 inference(rewrite,[status(thm)],[])).
% 4.37/4.70 tff(33192,plain,
% 4.37/4.70 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.70 inference(rewrite,[status(thm)],[])).
% 4.37/4.70 tff(33193,plain,
% 4.37/4.70 (((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33192])).
% 4.37/4.70 tff(33194,plain,
% 4.37/4.70 (((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33193, 33191])).
% 4.37/4.70 tff(33195,plain,
% 4.37/4.70 ((~![X0: $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(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.70 inference(quant_inst,[status(thm)],[])).
% 4.37/4.70 tff(33196,plain,
% 4.37/4.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33195, 33194])).
% 4.37/4.70 tff(33197,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33196, 333, 722, 2484, 322, 22831])).
% 4.37/4.70 tff(33198,plain,((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33199,plain,
% 4.37/4.70 (~r(s(z), s(s(z)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33198, 322, 2484, 722])).
% 4.37/4.70 tff(33200,plain,
% 4.37/4.70 (~r(s(z), s(s(elem!1)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[22807, 33199, 8677])).
% 4.37/4.70 tff(33201,plain,
% 4.37/4.70 (b(s(z), s(s(elem!1)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[5484, 33200])).
% 4.37/4.70 tff(33202,plain,
% 4.37/4.70 (b(s(z), s(s(z)))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[22799, 33201, 8677])).
% 4.37/4.70 tff(33203,plain,
% 4.37/4.70 (b(s(z), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[22716, 489, 22711])).
% 4.37/4.70 tff(33204,plain,
% 4.37/4.70 (~r(s(z), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[362, 322, 321, 354])).
% 4.37/4.70 tff(33205,plain,
% 4.37/4.70 (b(s(z), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[172, 33204])).
% 4.37/4.70 tff(33206,plain,
% 4.37/4.70 (~b(s(s(s(z))), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[26887, 55, 66])).
% 4.37/4.70 tff(33207,plain,
% 4.37/4.70 (r(s(s(s(z))), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[396, 33206])).
% 4.37/4.70 tff(33208,plain,
% 4.37/4.70 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[10450, 33207, 321, 562])).
% 4.37/4.70 tff(33209,plain,
% 4.37/4.70 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1137, 33208])).
% 4.37/4.70 tff(33210,plain,
% 4.37/4.70 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[2262, 33209, 123, 838])).
% 4.37/4.70 tff(33211,plain,
% 4.37/4.70 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[249, 33210])).
% 4.37/4.70 tff(33212,plain,
% 4.37/4.70 (r(s(s(s(z))), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[704, 55, 22891])).
% 4.37/4.70 tff(33213,plain,
% 4.37/4.70 (~b(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33007, 33209, 489, 838, 123])).
% 4.37/4.70 tff(33214,plain,
% 4.37/4.70 (r(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[619, 33213])).
% 4.37/4.70 tff(33215,plain,
% 4.37/4.70 (r(elem!1, s(s(s(z))))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33214, 22906])).
% 4.37/4.70 tff(33216,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[14901, 333, 33215, 33212, 2484, 33211])).
% 4.37/4.70 tff(33217,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33218,plain,
% 4.37/4.70 (b(s(s(s(z))), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33217, 33205, 18019, 123, 2484, 489, 321, 562])).
% 4.37/4.70 tff(33219,plain,
% 4.37/4.70 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[32581, 33218, 33205, 123, 33203])).
% 4.37/4.70 tff(33220,plain,
% 4.37/4.70 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[121, 33219, 12014])).
% 4.37/4.70 tff(33221,plain,
% 4.37/4.70 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 4.37/4.70 inference(monotonicity,[status(thm)],[18019])).
% 4.37/4.70 tff(33222,plain,
% 4.37/4.70 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 4.37/4.70 inference(symmetry,[status(thm)],[33221])).
% 4.37/4.70 tff(33223,plain,
% 4.37/4.70 (b(s(s(s(z))), z)),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33218, 33222])).
% 4.37/4.70 tff(33224,plain,
% 4.37/4.70 (~b(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[2156, 33223, 489, 33205])).
% 4.37/4.70 tff(33225,plain,
% 4.37/4.70 (r(z, s(s(s(z))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[619, 33224])).
% 4.37/4.70 tff(33226,plain,
% 4.37/4.70 (r(elem!1, s(s(s(z))))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33225, 22983])).
% 4.37/4.70 tff(33227,plain,
% 4.37/4.70 ($false),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[25642, 333, 1525, 2484, 2323, 6107])).
% 4.37/4.70 tff(33228,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.70 tff(33229,plain,
% 4.37/4.70 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[33228, 33226, 2484, 33220])).
% 4.37/4.70 tff(33230,plain,
% 4.37/4.70 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[1137, 33229])).
% 4.37/4.70 tff(33231,plain,
% 4.37/4.70 (b(s(elem!1), z)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[18064, 489, 18019])).
% 4.37/4.70 tff(33232,plain,
% 4.37/4.70 (b(s(elem!1), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[25335, 33231, 18019])).
% 4.37/4.70 tff(33233,plain,
% 4.37/4.70 (b(s(elem!1), s(s(elem!1)))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33201, 28265])).
% 4.37/4.70 tff(33234,plain,
% 4.37/4.70 (~r(s(s(z)), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[12787, 2671, 2484, 563])).
% 4.37/4.70 tff(33235,plain,
% 4.37/4.70 (b(s(s(z)), elem!1)),
% 4.37/4.70 inference(unit_resolution,[status(thm)],[7970, 33234, 22830])).
% 4.37/4.70 tff(33236,plain,
% 4.37/4.70 (b(s(s(elem!1)), elem!1)),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33235, 27325])).
% 4.37/4.70 tff(33237,plain,
% 4.37/4.70 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.70 inference(rewrite,[status(thm)],[])).
% 4.37/4.70 tff(33238,plain,
% 4.37/4.70 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.70 inference(rewrite,[status(thm)],[])).
% 4.37/4.70 tff(33239,plain,
% 4.37/4.70 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.70 inference(monotonicity,[status(thm)],[33238])).
% 4.37/4.70 tff(33240,plain,
% 4.37/4.70 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.70 inference(transitivity,[status(thm)],[33239, 33237])).
% 4.37/4.70 tff(33241,plain,
% 4.37/4.70 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 4.37/4.70 inference(quant_inst,[status(thm)],[])).
% 4.37/4.70 tff(33242,plain,
% 4.37/4.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.70 inference(modus_ponens,[status(thm)],[33241, 33240])).
% 4.37/4.71 tff(33243,plain,
% 4.37/4.71 (~r(elem!1, s(s(z)))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33242, 333, 2671, 2484, 2323])).
% 4.37/4.71 tff(33244,plain,
% 4.37/4.71 (~r(elem!1, s(s(elem!1)))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33243, 28273])).
% 4.37/4.71 tff(33245,plain,
% 4.37/4.71 (b(elem!1, s(s(elem!1)))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[2522, 33244, 22705])).
% 4.37/4.71 tff(33246,plain,
% 4.37/4.71 (~b(s(s(elem!1)), elem!1)),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[24923, 33245, 451, 3627])).
% 4.37/4.71 tff(33247,plain,
% 4.37/4.71 ($false),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33246, 33236])).
% 4.37/4.71 tff(33248,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.71 tff(33249,plain,
% 4.37/4.71 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33248, 33233, 33232, 8677, 2484, 33220, 563])).
% 4.37/4.71 tff(33250,plain,
% 4.37/4.71 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[1451, 33249])).
% 4.37/4.71 tff(33251,plain,
% 4.37/4.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[2262, 33230, 123, 33205])).
% 4.37/4.71 tff(33252,plain,
% 4.37/4.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[249, 33251])).
% 4.37/4.71 tff(33253,plain,
% 4.37/4.71 (~r(s(s(s(z))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[22410, 33252, 2484, 33226])).
% 4.37/4.71 tff(33254,plain,
% 4.37/4.71 (b(s(s(s(z))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[2794, 33253])).
% 4.37/4.71 tff(33255,plain,
% 4.37/4.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33256,plain,
% 4.37/4.71 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33257,plain,
% 4.37/4.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.71 inference(monotonicity,[status(thm)],[33256])).
% 4.37/4.71 tff(33258,plain,
% 4.37/4.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(transitivity,[status(thm)],[33257, 33255])).
% 4.37/4.71 tff(33259,plain,
% 4.37/4.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 4.37/4.71 inference(quant_inst,[status(thm)],[])).
% 4.37/4.71 tff(33260,plain,
% 4.37/4.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33259, 33258])).
% 4.37/4.71 tff(33261,plain,
% 4.37/4.71 (~b(s(s(s(z))), s(s(z)))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33260, 144, 33254, 33250, 33230, 33202])).
% 4.37/4.71 tff(33262,plain,
% 4.37/4.71 (~b(s(s(s(z))), s(s(elem!1)))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33261, 22812])).
% 4.37/4.71 tff(33263,plain,
% 4.37/4.71 (r(s(s(s(z))), s(s(elem!1)))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[1301, 33262, 26805])).
% 4.37/4.71 tff(33264,plain,
% 4.37/4.71 (r(s(s(s(z))), s(s(z)))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33263, 22809])).
% 4.37/4.71 tff(33265,plain,
% 4.37/4.71 (((~![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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33266,plain,
% 4.37/4.71 (((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33267,plain,
% 4.37/4.71 (((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.37/4.71 inference(monotonicity,[status(thm)],[33266])).
% 4.37/4.71 tff(33268,plain,
% 4.37/4.71 (((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), 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))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.71 inference(transitivity,[status(thm)],[33267, 33265])).
% 4.37/4.71 tff(33269,plain,
% 4.37/4.71 ((~![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(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.71 inference(quant_inst,[status(thm)],[])).
% 4.37/4.71 tff(33270,plain,
% 4.37/4.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33269, 33268])).
% 4.37/4.71 tff(33271,plain,
% 4.37/4.71 ($false),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33270, 333, 33226, 2484, 33252, 33264])).
% 4.37/4.71 tff(33272,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.71 tff(33273,plain,
% 4.37/4.71 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33272, 489, 8677, 563, 123, 2484, 321, 562, 722, 354])).
% 4.37/4.71 tff(33274,plain,
% 4.37/4.71 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[319, 33273])).
% 4.37/4.71 tff(33275,plain,
% 4.37/4.71 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[10450, 1699, 321, 562])).
% 4.37/4.71 tff(33276,plain,
% 4.37/4.71 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[1137, 33275])).
% 4.37/4.71 tff(33277,plain,
% 4.37/4.71 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[12177, 333, 722, 32502, 2484])).
% 4.37/4.71 tff(33278,plain,
% 4.37/4.71 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[249, 33277])).
% 4.37/4.71 tff(33279,plain,
% 4.37/4.71 (~b(s(z), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[2262, 33278, 123, 33276])).
% 4.37/4.71 tff(33280,plain,
% 4.37/4.71 (~b(s(s(s(z))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[6004, 144, 123, 33276, 304])).
% 4.37/4.71 tff(33281,plain,
% 4.37/4.71 (r(s(s(s(z))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[2794, 33280])).
% 4.37/4.71 tff(33282,plain,
% 4.37/4.71 (~r(s(z), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[26130, 33281, 354, 1699])).
% 4.37/4.71 tff(33283,plain,
% 4.37/4.71 ($false),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[172, 33282, 33279])).
% 4.37/4.71 tff(33284,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.71 tff(33285,plain,
% 4.37/4.71 (~r(s(s(s(z))), z)),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33284, 33274, 123, 354, 722, 2484, 321, 562, 18019])).
% 4.37/4.71 tff(33286,plain,
% 4.37/4.71 (b(s(s(s(z))), z)),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[396, 33285])).
% 4.37/4.71 tff(33287,plain,
% 4.37/4.71 (b(s(s(s(z))), elem!1)),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[26887, 33286, 18019])).
% 4.37/4.71 tff(33288,plain,
% 4.37/4.71 (~b(s(z), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[32581, 132, 4367, 123, 134])).
% 4.37/4.71 tff(33289,plain,
% 4.37/4.71 (r(s(z), s(s(s(z))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[172, 33288])).
% 4.37/4.71 tff(33290,plain,
% 4.37/4.71 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33291,plain,
% 4.37/4.71 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33292,plain,
% 4.37/4.71 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.71 inference(monotonicity,[status(thm)],[33291])).
% 4.37/4.71 tff(33293,plain,
% 4.37/4.71 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(transitivity,[status(thm)],[33292, 33290])).
% 4.37/4.71 tff(33294,plain,
% 4.37/4.71 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.71 inference(quant_inst,[status(thm)],[])).
% 4.37/4.71 tff(33295,plain,
% 4.37/4.71 ((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33294, 33293])).
% 4.37/4.71 tff(33296,plain,
% 4.37/4.71 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33295, 333, 722, 9507, 2484])).
% 4.37/4.71 tff(33297,plain,
% 4.37/4.71 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[9761, 33296])).
% 4.37/4.71 tff(33298,plain,
% 4.37/4.71 (~b(s(s(s(s(z)))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[26574, 33297, 123, 304])).
% 4.37/4.71 tff(33299,plain,
% 4.37/4.71 (r(s(s(s(s(z)))), s(z))),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[24600, 33298, 24294])).
% 4.37/4.71 tff(33300,plain,
% 4.37/4.71 (((~![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(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(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33301,plain,
% 4.37/4.71 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.37/4.71 inference(rewrite,[status(thm)],[])).
% 4.37/4.71 tff(33302,plain,
% 4.37/4.71 (((~![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(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), 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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 4.37/4.71 inference(monotonicity,[status(thm)],[33301])).
% 4.37/4.71 tff(33303,plain,
% 4.37/4.71 (((~![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(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), 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(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.37/4.71 inference(transitivity,[status(thm)],[33302, 33300])).
% 4.37/4.71 tff(33304,plain,
% 4.37/4.71 ((~![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(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.37/4.71 inference(quant_inst,[status(thm)],[])).
% 4.37/4.71 tff(33305,plain,
% 4.37/4.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 4.37/4.71 inference(modus_ponens,[status(thm)],[33304, 33303])).
% 4.37/4.71 tff(33306,plain,
% 4.37/4.71 ($false),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33305, 333, 722, 9507, 33299, 353])).
% 4.37/4.71 tff(33307,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.71 tff(33308,plain,
% 4.37/4.71 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.71 inference(unit_resolution,[status(thm)],[33307, 33289, 722, 123, 304, 2484])).
% 4.37/4.71 tff(33309,plain,
% 4.37/4.71 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[24301, 33308, 26567])).
% 4.37/4.72 tff(33310,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33311,plain,
% 4.37/4.72 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33312,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.72 inference(monotonicity,[status(thm)],[33311])).
% 4.37/4.72 tff(33313,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(transitivity,[status(thm)],[33312, 33310])).
% 4.37/4.72 tff(33314,plain,
% 4.37/4.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(quant_inst,[status(thm)],[])).
% 4.37/4.72 tff(33315,plain,
% 4.37/4.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33314, 33313])).
% 4.37/4.72 tff(33316,plain,
% 4.37/4.72 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33315, 144, 134, 304, 4367])).
% 4.37/4.72 tff(33317,plain,
% 4.37/4.72 (~b(s(s(s(z))), s(z))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33316, 2254])).
% 4.37/4.72 tff(33318,plain,
% 4.37/4.72 (r(s(s(s(z))), s(z))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[2794, 33317])).
% 4.37/4.72 tff(33319,plain,
% 4.37/4.72 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[27075, 144, 2082, 3529, 4367])).
% 4.37/4.72 tff(33320,plain,
% 4.37/4.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33319])).
% 4.37/4.72 tff(33321,plain,
% 4.37/4.72 (((~![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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33322,plain,
% 4.37/4.72 (((~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(s(s(z))), 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)))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33323,plain,
% 4.37/4.72 (((~![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(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(s(s(z))), 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))))))))),
% 4.37/4.72 inference(monotonicity,[status(thm)],[33322])).
% 4.37/4.72 tff(33324,plain,
% 4.37/4.72 (((~![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(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(s(s(z))), 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)))))))),
% 4.37/4.72 inference(transitivity,[status(thm)],[33323, 33321])).
% 4.37/4.72 tff(33325,plain,
% 4.37/4.72 ((~![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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 4.37/4.72 inference(quant_inst,[status(thm)],[])).
% 4.37/4.72 tff(33326,plain,
% 4.37/4.72 ((~![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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33325, 33324])).
% 4.37/4.72 tff(33327,plain,
% 4.37/4.72 (~r(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33326, 333, 3193, 33289, 33320])).
% 4.37/4.72 tff(33328,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33329,plain,
% 4.37/4.72 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33330,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.72 inference(monotonicity,[status(thm)],[33329])).
% 4.37/4.72 tff(33331,plain,
% 4.37/4.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(transitivity,[status(thm)],[33330, 33328])).
% 4.37/4.72 tff(33332,plain,
% 4.37/4.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 4.37/4.72 inference(quant_inst,[status(thm)],[])).
% 4.37/4.72 tff(33333,plain,
% 4.37/4.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33332, 33331])).
% 4.37/4.72 tff(33334,plain,
% 4.37/4.72 (~b(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33333, 144, 134, 3529, 123, 132])).
% 4.37/4.72 tff(33335,plain,
% 4.37/4.72 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[19906, 44, 33334])).
% 4.37/4.72 tff(33336,plain,
% 4.37/4.72 ($false),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33335, 33327, 25692])).
% 4.37/4.72 tff(33337,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~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(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.72 tff(33338,plain,
% 4.37/4.72 (~b(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33337, 33318, 3529, 4367, 134, 123, 132])).
% 4.37/4.72 tff(33339,plain,
% 4.37/4.72 (r(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1538, 33338, 22768])).
% 4.37/4.72 tff(33340,plain,
% 4.37/4.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[22410, 33339, 2484, 33318])).
% 4.37/4.72 tff(33341,plain,
% 4.37/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[249, 33340])).
% 4.37/4.72 tff(33342,plain,
% 4.37/4.72 (~b(z, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[16228, 33341, 22725, 2254])).
% 4.37/4.72 tff(33343,plain,
% 4.37/4.72 (r(z, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[619, 33342])).
% 4.37/4.72 tff(33344,plain,
% 4.37/4.72 (~r(s(s(s(z))), s(elem!1))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[3011, 33343, 354, 33289])).
% 4.37/4.72 tff(33345,plain,
% 4.37/4.72 (~r(s(s(s(z))), s(z))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33344, 22951])).
% 4.37/4.72 tff(33346,plain,
% 4.37/4.72 ($false),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33318, 33345])).
% 4.37/4.72 tff(33347,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.72 tff(33348,plain,
% 4.37/4.72 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33347, 33309, 354, 2484, 8677, 4367, 134, 123, 132, 304])).
% 4.37/4.72 tff(33349,plain,
% 4.37/4.72 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1137, 33348])).
% 4.37/4.72 tff(33350,plain,
% 4.37/4.72 (~r(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[28490, 33289, 722, 33349])).
% 4.37/4.72 tff(33351,plain,
% 4.37/4.72 (b(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1538, 33350, 22768])).
% 4.37/4.72 tff(33352,plain,
% 4.37/4.72 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[27075, 144, 33351, 33309, 4367])).
% 4.37/4.72 tff(33353,plain,
% 4.37/4.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33352])).
% 4.37/4.72 tff(33354,plain,
% 4.37/4.72 (~b(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33333, 144, 134, 33309, 123, 132])).
% 4.37/4.72 tff(33355,plain,
% 4.37/4.72 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[19906, 44, 33354])).
% 4.37/4.72 tff(33356,plain,
% 4.37/4.72 (r(s(z), s(s(s(s(z)))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33355, 25692])).
% 4.37/4.72 tff(33357,plain,
% 4.37/4.72 (((~![X0: $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(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(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(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33358,plain,
% 4.37/4.72 (((~r(s(s(s(z))), s(s(s(s(s(s(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(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(rewrite,[status(thm)],[])).
% 4.37/4.72 tff(33359,plain,
% 4.37/4.72 (((~![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(s(s(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(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.72 inference(monotonicity,[status(thm)],[33358])).
% 4.37/4.72 tff(33360,plain,
% 4.37/4.72 (((~![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(s(s(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(s(s(s(s(s(s(z))))))))))),
% 4.37/4.72 inference(transitivity,[status(thm)],[33359, 33357])).
% 4.37/4.72 tff(33361,plain,
% 4.37/4.72 ((~![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(s(s(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)))))))),
% 4.37/4.72 inference(quant_inst,[status(thm)],[])).
% 4.37/4.72 tff(33362,plain,
% 4.37/4.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33361, 33360])).
% 4.37/4.72 tff(33363,plain,
% 4.37/4.72 ($false),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33362, 333, 33356, 33289, 33349, 33353])).
% 4.37/4.72 tff(33364,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.72 tff(33365,plain,
% 4.37/4.72 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33364, 33287, 722, 354, 2484, 8677, 33203, 123, 33274])).
% 4.37/4.72 tff(33366,plain,
% 4.37/4.72 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[121, 33365, 12014])).
% 4.37/4.72 tff(33367,plain,
% 4.37/4.72 (~b(z, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[2156, 838, 489, 285])).
% 4.37/4.72 tff(33368,plain,
% 4.37/4.72 (r(z, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[619, 33367])).
% 4.37/4.72 tff(33369,plain,
% 4.37/4.72 (r(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(modus_ponens,[status(thm)],[33368, 22906])).
% 4.37/4.72 tff(33370,plain,
% 4.37/4.72 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33228, 33369, 2484, 2323])).
% 4.37/4.72 tff(33371,plain,
% 4.37/4.72 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1137, 33370])).
% 4.37/4.72 tff(33372,plain,
% 4.37/4.72 (b(s(s(s(z))), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[26887, 285, 66])).
% 4.37/4.72 tff(33373,plain,
% 4.37/4.72 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33315, 144, 32442, 304, 33372])).
% 4.37/4.72 tff(33374,plain,
% 4.37/4.72 (~b(s(s(s(z))), s(z))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33373, 33371])).
% 4.37/4.72 tff(33375,plain,
% 4.37/4.72 (r(s(s(s(z))), s(z))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[2794, 33374])).
% 4.37/4.72 tff(33376,plain,
% 4.37/4.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[2262, 33371, 123, 838])).
% 4.37/4.72 tff(33377,plain,
% 4.37/4.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[249, 33376])).
% 4.37/4.72 tff(33378,plain,
% 4.37/4.72 ($false),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[22410, 33377, 33375, 2484, 33369])).
% 4.37/4.72 tff(33379,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.72 tff(33380,plain,
% 4.37/4.72 (~b(s(z), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33379, 33274, 123, 2484, 33366, 18019, 489, 33286])).
% 4.37/4.72 tff(33381,plain,
% 4.37/4.72 (r(s(z), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[172, 33380])).
% 4.37/4.72 tff(33382,plain,
% 4.37/4.72 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33307, 33381, 722, 123, 33274, 2484])).
% 4.37/4.72 tff(33383,plain,
% 4.37/4.72 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[24301, 33382, 26567])).
% 4.37/4.72 tff(33384,plain,
% 4.37/4.72 (~r(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[10898, 333, 722, 33318, 353])).
% 4.37/4.72 tff(33385,plain,
% 4.37/4.72 (b(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1538, 33384, 22768])).
% 4.37/4.72 tff(33386,plain,
% 4.37/4.72 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[31074, 33385, 123, 8677, 722, 304, 2254, 353])).
% 4.37/4.72 tff(33387,plain,
% 4.37/4.72 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1451, 33386])).
% 4.37/4.72 tff(33388,plain,
% 4.37/4.72 (~b(s(elem!1), s(s(elem!1)))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33248, 33387, 451, 8677, 2484, 2323, 563])).
% 4.37/4.72 tff(33389,plain,
% 4.37/4.72 (~b(s(z), s(s(elem!1)))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[28269, 33388, 8677])).
% 4.37/4.72 tff(33390,plain,
% 4.37/4.72 (r(s(z), s(s(elem!1)))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[5484, 33389])).
% 4.37/4.72 tff(33391,plain,
% 4.37/4.72 (r(s(z), s(s(z)))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[22807, 33390, 8677])).
% 4.37/4.72 tff(33392,plain,
% 4.37/4.72 (~r(s(s(z)), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[12787, 33387, 2484, 563])).
% 4.37/4.72 tff(33393,plain,
% 4.37/4.72 (b(s(s(z)), elem!1)),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[7970, 33392, 22830])).
% 4.37/4.72 tff(33394,plain,
% 4.37/4.72 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[31098, 144, 33385, 4367, 33393])).
% 4.37/4.72 tff(33395,plain,
% 4.37/4.72 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[18122, 33394, 8677])).
% 4.37/4.72 tff(33396,plain,
% 4.37/4.72 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[4311, 33395, 22826])).
% 4.37/4.72 tff(33397,plain,
% 4.37/4.72 (r(s(s(z)), s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[18132, 33396, 8677])).
% 4.37/4.72 tff(33398,plain,
% 4.37/4.72 ($false),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[23647, 333, 33318, 353, 33397, 33391])).
% 4.37/4.72 tff(33399,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.72 tff(33400,plain,
% 4.37/4.72 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33399, 33381, 8677, 33287, 33232, 2484, 33366, 563, 123, 722, 33274, 33203])).
% 4.37/4.72 tff(33401,plain,
% 4.37/4.72 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[1137, 33400])).
% 4.37/4.72 tff(33402,plain,
% 4.37/4.72 (~r(elem!1, s(s(s(z))))),
% 4.37/4.72 inference(unit_resolution,[status(thm)],[33228, 33401, 2484, 33366])).
% 4.37/4.73 tff(33403,plain,
% 4.37/4.73 (b(elem!1, s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[1538, 33402, 22768])).
% 4.37/4.73 tff(33404,plain,
% 4.37/4.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[27075, 144, 33403, 33383, 33287])).
% 4.37/4.73 tff(33405,plain,
% 4.37/4.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33404])).
% 4.37/4.73 tff(33406,plain,
% 4.37/4.73 (((~![X0: $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(s(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(s(s(z))))))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33407,plain,
% 4.37/4.73 (((~r(s(s(s(z))), s(s(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(s(s(z))))))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33408,plain,
% 4.37/4.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(s(s(z)))))))))))),
% 4.37/4.73 inference(monotonicity,[status(thm)],[33407])).
% 4.37/4.73 tff(33409,plain,
% 4.37/4.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(s(s(z))))))))))),
% 4.37/4.73 inference(transitivity,[status(thm)],[33408, 33406])).
% 4.37/4.73 tff(33410,plain,
% 4.37/4.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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))))),
% 4.37/4.73 inference(quant_inst,[status(thm)],[])).
% 4.37/4.73 tff(33411,plain,
% 4.37/4.73 ((~![X0: $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(s(s(z)))))))))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33410, 33409])).
% 4.37/4.73 tff(33412,plain,
% 4.37/4.73 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33411, 333, 33381, 33401, 33405])).
% 4.37/4.73 tff(33413,plain,
% 4.37/4.73 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[24600, 33412, 24294])).
% 4.37/4.73 tff(33414,plain,
% 4.37/4.73 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[26574, 33413, 123, 33274])).
% 4.37/4.73 tff(33415,plain,
% 4.37/4.73 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9761, 33414])).
% 4.37/4.73 tff(33416,plain,
% 4.37/4.73 (((~![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(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), 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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33417,plain,
% 4.37/4.73 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33418,plain,
% 4.37/4.73 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.73 inference(monotonicity,[status(thm)],[33417])).
% 4.37/4.73 tff(33419,plain,
% 4.37/4.73 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.73 inference(transitivity,[status(thm)],[33418, 33416])).
% 4.37/4.73 tff(33420,plain,
% 4.37/4.73 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.73 inference(quant_inst,[status(thm)],[])).
% 4.37/4.73 tff(33421,plain,
% 4.37/4.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33420, 33419])).
% 4.37/4.73 tff(33422,plain,
% 4.37/4.73 ($false),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33421, 333, 2484, 33401, 33415, 33405])).
% 4.37/4.73 tff(33423,plain,((~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.73 tff(33424,plain,
% 4.37/4.73 (~b(s(z), z)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33423, 33157, 50, 2484, 33190, 33168, 33179, 12153, 33176])).
% 4.37/4.73 tff(33425,plain,
% 4.37/4.73 (r(s(z), z)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[348, 33424])).
% 4.37/4.73 tff(33426,plain,
% 4.37/4.73 (r(s(z), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[25327, 33425, 33158])).
% 4.37/4.73 tff(33427,plain,
% 4.37/4.73 (~r(s(s(s(z))), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[12189, 33426, 50, 2484, 33168])).
% 4.37/4.73 tff(33428,plain,
% 4.37/4.73 (b(s(s(s(z))), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[704, 33427, 33163])).
% 4.37/4.73 tff(33429,plain,
% 4.37/4.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.37/4.73 inference(monotonicity,[status(thm)],[33158])).
% 4.37/4.73 tff(33430,plain,
% 4.37/4.73 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 4.37/4.73 inference(transitivity,[status(thm)],[33429, 203])).
% 4.37/4.73 tff(33431,plain,
% 4.37/4.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.37/4.73 inference(transitivity,[status(thm)],[33430, 24285])).
% 4.37/4.73 tff(33432,plain,
% 4.37/4.73 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.37/4.73 inference(monotonicity,[status(thm)],[33431])).
% 4.37/4.73 tff(33433,plain,
% 4.37/4.73 (~(s(s(s(s(z)))) = elem!1)),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[242, 33432])).
% 4.37/4.73 tff(33434,plain,
% 4.37/4.73 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[8274, 33425, 12153, 33176])).
% 4.37/4.73 tff(33435,plain,
% 4.37/4.73 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[319, 33434])).
% 4.37/4.73 tff(33436,plain,
% 4.37/4.73 (~r(s(s(s(z))), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[12189, 409, 123, 2484, 722])).
% 4.37/4.73 tff(33437,plain,
% 4.37/4.73 (~r(s(s(s(z))), z)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[22912, 33436, 18019])).
% 4.37/4.73 tff(33438,plain,
% 4.37/4.73 (b(s(s(s(z))), z)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[396, 33437])).
% 4.37/4.73 tff(33439,plain,
% 4.37/4.73 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 4.37/4.73 inference(transitivity,[status(thm)],[23014, 26895])).
% 4.37/4.73 tff(33440,plain,
% 4.37/4.73 (r(z, s(s(s(elem!1))))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[1525, 33439])).
% 4.37/4.73 tff(33441,plain,
% 4.37/4.73 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[13102, 33440, 435, 562])).
% 4.37/4.73 tff(33442,plain,
% 4.37/4.73 (b(s(s(s(elem!1))), s(elem!1))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[4697, 33441, 23041])).
% 4.37/4.73 tff(33443,plain,
% 4.37/4.73 (b(s(s(s(z))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[23075, 33442, 8677])).
% 4.37/4.73 tff(33444,plain,
% 4.37/4.73 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[846, 33443, 304, 838])).
% 4.37/4.73 tff(33445,plain,
% 4.37/4.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[249, 33444])).
% 4.37/4.73 tff(33446,plain,
% 4.37/4.73 ($false),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[22940, 333, 1525, 2484, 33445, 6107])).
% 4.37/4.73 tff(33447,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.73 tff(33448,plain,
% 4.37/4.73 (~r(elem!1, s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33447, 6107, 2484, 304, 838, 8677, 28930, 562])).
% 4.37/4.73 tff(33449,plain,
% 4.37/4.73 (b(elem!1, s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[1538, 33448, 22768])).
% 4.37/4.73 tff(33450,plain,
% 4.37/4.73 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[27363, 56, 8677, 28930, 562, 285, 10356, 284])).
% 4.37/4.73 tff(33451,plain,
% 4.37/4.73 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[18122, 33450, 8677])).
% 4.37/4.73 tff(33452,plain,
% 4.37/4.73 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[4311, 33451, 22826])).
% 4.37/4.73 tff(33453,plain,
% 4.37/4.73 (r(s(s(z)), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[18132, 33452, 8677])).
% 4.37/4.73 tff(33454,plain,
% 4.37/4.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[27389, 333, 23100, 6107, 33453])).
% 4.37/4.73 tff(33455,plain,
% 4.37/4.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33454, 25414])).
% 4.37/4.73 tff(33456,plain,
% 4.37/4.73 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[2758, 33455, 23135])).
% 4.37/4.73 tff(33457,plain,
% 4.37/4.73 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33456, 23136])).
% 4.37/4.73 tff(33458,plain,
% 4.37/4.73 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[28939, 333, 23100, 6107, 33453])).
% 4.37/4.73 tff(33459,plain,
% 4.37/4.73 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[1451, 33458])).
% 4.37/4.73 tff(33460,plain,
% 4.37/4.73 (~b(elem!1, s(s(z)))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[23240, 144, 33459, 132, 33457])).
% 4.37/4.73 tff(33461,plain,
% 4.37/4.73 (~b(elem!1, s(s(elem!1)))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33460, 23021])).
% 4.37/4.73 tff(33462,plain,
% 4.37/4.73 (~b(s(s(z)), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[1425, 33459, 123, 304])).
% 4.37/4.73 tff(33463,plain,
% 4.37/4.73 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[18895, 33462, 8677])).
% 4.37/4.73 tff(33464,plain,
% 4.37/4.73 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[1283, 33463, 22759])).
% 4.37/4.73 tff(33465,plain,
% 4.37/4.73 (r(s(s(z)), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[22871, 33464, 8677])).
% 4.37/4.73 tff(33466,plain,
% 4.37/4.73 (~r(elem!1, s(s(z)))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[26788, 333, 409, 722, 33465])).
% 4.37/4.73 tff(33467,plain,
% 4.37/4.73 (~r(elem!1, s(s(elem!1)))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33466, 28273])).
% 4.37/4.73 tff(33468,plain,
% 4.37/4.73 (b(elem!1, s(s(elem!1)))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[2522, 33467, 22705])).
% 4.37/4.73 tff(33469,plain,
% 4.37/4.73 ($false),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33468, 33461])).
% 4.37/4.73 tff(33470,plain,((~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.73 tff(33471,plain,
% 4.37/4.73 (~b(s(s(s(z))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33470, 27352, 132, 409, 722, 123, 304, 6107, 562, 33438, 10356, 8677, 838])).
% 4.37/4.73 tff(33472,plain,
% 4.37/4.73 (r(s(s(s(z))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[2794, 33471])).
% 4.37/4.73 tff(33473,plain,
% 4.37/4.73 (b(s(s(s(z))), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[704, 33436, 22766])).
% 4.37/4.73 tff(33474,plain,
% 4.37/4.73 (((~![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(s(s(z)))), 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(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33475,plain,
% 4.37/4.73 ((~![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(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.73 inference(quant_inst,[status(thm)],[])).
% 4.37/4.73 tff(33476,plain,
% 4.37/4.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33475, 33474])).
% 4.37/4.73 tff(33477,plain,
% 4.37/4.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33476, 333, 409, 3193, 25527])).
% 4.37/4.73 tff(33478,plain,
% 4.37/4.73 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[24301, 28379, 24296])).
% 4.37/4.73 tff(33479,plain,
% 4.37/4.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[27075, 144, 2082, 33478, 4367])).
% 4.37/4.73 tff(33480,plain,
% 4.37/4.73 ($false),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33479, 33477])).
% 4.37/4.73 tff(33481,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.73 tff(33482,plain,
% 4.37/4.73 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33481, 2082, 33473, 409, 33472, 26567, 722])).
% 4.37/4.73 tff(33483,plain,
% 4.37/4.73 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[24600, 33482, 24294])).
% 4.37/4.73 tff(33484,plain,
% 4.37/4.73 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[26574, 33483, 123, 304])).
% 4.37/4.73 tff(33485,plain,
% 4.37/4.73 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9761, 33484])).
% 4.37/4.73 tff(33486,plain,
% 4.37/4.73 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[32412, 144, 26572, 838, 283, 304])).
% 4.37/4.73 tff(33487,plain,
% 4.37/4.73 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[12733, 44, 33486])).
% 4.37/4.73 tff(33488,plain,
% 4.37/4.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33487, 12723])).
% 4.37/4.73 tff(33489,plain,
% 4.37/4.73 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[26574, 26572, 123, 304])).
% 4.37/4.73 tff(33490,plain,
% 4.37/4.73 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9761, 33489])).
% 4.37/4.73 tff(33491,plain,
% 4.37/4.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33492,plain,
% 4.37/4.73 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33493,plain,
% 4.37/4.73 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 4.37/4.73 inference(monotonicity,[status(thm)],[33492])).
% 4.37/4.73 tff(33494,plain,
% 4.37/4.73 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.37/4.73 inference(transitivity,[status(thm)],[33493, 33491])).
% 4.37/4.73 tff(33495,plain,
% 4.37/4.73 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.37/4.73 inference(quant_inst,[status(thm)],[])).
% 4.37/4.73 tff(33496,plain,
% 4.37/4.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.37/4.73 inference(modus_ponens,[status(thm)],[33495, 33494])).
% 4.37/4.73 tff(33497,plain,
% 4.37/4.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33496, 333, 2484, 6107, 33490])).
% 4.37/4.73 tff(33498,plain,
% 4.37/4.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 33497])).
% 4.37/4.73 tff(33499,plain,
% 4.37/4.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[33421, 333, 2484, 6107, 33490])).
% 4.37/4.73 tff(33500,plain,
% 4.37/4.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.73 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33499])).
% 4.37/4.73 tff(33501,plain,
% 4.37/4.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.73 inference(rewrite,[status(thm)],[])).
% 4.37/4.73 tff(33502,plain,
% 4.37/4.73 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33503,plain,
% 4.37/4.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 4.37/4.74 inference(monotonicity,[status(thm)],[33502])).
% 4.37/4.74 tff(33504,plain,
% 4.37/4.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.74 inference(transitivity,[status(thm)],[33503, 33501])).
% 4.37/4.74 tff(33505,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(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))))))),
% 4.37/4.74 inference(quant_inst,[status(thm)],[])).
% 4.37/4.74 tff(33506,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33505, 33504])).
% 4.37/4.74 tff(33507,plain,
% 4.37/4.74 (~b(elem!1, s(s(s(s(z)))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33506, 144, 2082, 33500, 33498])).
% 4.37/4.74 tff(33508,plain,
% 4.37/4.74 (r(elem!1, s(s(s(s(z)))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[6873, 33507, 32483])).
% 4.37/4.74 tff(33509,plain,
% 4.37/4.74 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(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(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33510,plain,
% 4.37/4.74 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33511,plain,
% 4.37/4.74 (((~![X0: $i, X3: $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(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.37/4.74 inference(monotonicity,[status(thm)],[33510])).
% 4.37/4.74 tff(33512,plain,
% 4.37/4.74 (((~![X0: $i, X3: $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(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, 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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.74 inference(transitivity,[status(thm)],[33511, 33509])).
% 4.37/4.74 tff(33513,plain,
% 4.37/4.74 ((~![X0: $i, X3: $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(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.37/4.74 inference(quant_inst,[status(thm)],[])).
% 4.37/4.74 tff(33514,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33513, 33512])).
% 4.37/4.74 tff(33515,plain,
% 4.37/4.74 ($false),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33514, 333, 33508, 2484, 33490, 33488])).
% 4.37/4.74 tff(33516,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.74 tff(33517,plain,
% 4.37/4.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33516, 33483, 28316, 2082, 6107, 838, 2484, 304, 123])).
% 4.37/4.74 tff(33518,plain,
% 4.37/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[249, 33517])).
% 4.37/4.74 tff(33519,plain,
% 4.37/4.74 (~b(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[26958, 33518, 8677, 6107, 33483, 33485, 123, 304])).
% 4.37/4.74 tff(33520,plain,
% 4.37/4.74 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18895, 33519, 8677])).
% 4.37/4.74 tff(33521,plain,
% 4.37/4.74 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[1283, 33520, 22759])).
% 4.37/4.74 tff(33522,plain,
% 4.37/4.74 (~r(s(s(elem!1)), z)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5505, 33521, 28930, 562])).
% 4.37/4.74 tff(33523,plain,
% 4.37/4.74 (b(s(s(elem!1)), z)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5509, 33522])).
% 4.37/4.74 tff(33524,plain,
% 4.37/4.74 (~b(s(s(elem!1)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5708, 33523, 27352, 33438])).
% 4.37/4.74 tff(33525,plain,
% 4.37/4.74 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33524, 27354])).
% 4.37/4.74 tff(33526,plain,
% 4.37/4.74 (r(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[22871, 33521, 8677])).
% 4.37/4.74 tff(33527,plain,
% 4.37/4.74 (((~![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(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(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33528,plain,
% 4.37/4.74 (((~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(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33529,plain,
% 4.37/4.74 (((~![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(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.37/4.74 inference(monotonicity,[status(thm)],[33528])).
% 4.37/4.74 tff(33530,plain,
% 4.37/4.74 (((~![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(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.37/4.74 inference(transitivity,[status(thm)],[33529, 33527])).
% 4.37/4.74 tff(33531,plain,
% 4.37/4.74 ((~![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))))))),
% 4.37/4.74 inference(quant_inst,[status(thm)],[])).
% 4.37/4.74 tff(33532,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33531, 33530])).
% 4.37/4.74 tff(33533,plain,
% 4.37/4.74 (~r(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33532, 333, 409, 33472, 33526])).
% 4.37/4.74 tff(33534,plain,
% 4.37/4.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18132, 33533, 8677])).
% 4.37/4.74 tff(33535,plain,
% 4.37/4.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[4311, 33534, 22826])).
% 4.37/4.74 tff(33536,plain,
% 4.37/4.74 (b(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18122, 33535, 8677])).
% 4.37/4.74 tff(33537,plain,
% 4.37/4.74 ($false),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33536, 33525])).
% 4.37/4.74 tff(33538,plain,((~b(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(z), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.74 tff(33539,plain,
% 4.37/4.74 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33538, 33449, 409, 562, 6107, 123, 304, 838, 2484, 722, 8677, 10356])).
% 4.37/4.74 tff(33540,plain,
% 4.37/4.74 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[121, 33539, 12014])).
% 4.37/4.74 tff(33541,plain,
% 4.37/4.74 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33540, 31018])).
% 4.37/4.74 tff(33542,plain,
% 4.37/4.74 (b(z, s(s(s(z))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33449, 27351])).
% 4.37/4.74 tff(33543,plain,
% 4.37/4.74 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33481, 3193, 33473, 409, 33449, 26567, 722])).
% 4.37/4.74 tff(33544,plain,
% 4.37/4.74 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[24600, 33543, 24294])).
% 4.37/4.74 tff(33545,plain,
% 4.37/4.74 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[26574, 33544, 123, 304])).
% 4.37/4.74 tff(33546,plain,
% 4.37/4.74 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[9761, 33545])).
% 4.37/4.74 tff(33547,plain,
% 4.37/4.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33516, 33544, 28316, 33449, 6107, 838, 2484, 304, 123])).
% 4.37/4.74 tff(33548,plain,
% 4.37/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[249, 33547])).
% 4.37/4.74 tff(33549,plain,
% 4.37/4.74 (~b(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[26958, 33548, 8677, 6107, 33544, 33546, 123, 304])).
% 4.37/4.74 tff(33550,plain,
% 4.37/4.74 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18895, 33549, 8677])).
% 4.37/4.74 tff(33551,plain,
% 4.37/4.74 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[1283, 33550, 22759])).
% 4.37/4.74 tff(33552,plain,
% 4.37/4.74 (~r(s(s(elem!1)), z)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5505, 33551, 28930, 562])).
% 4.37/4.74 tff(33553,plain,
% 4.37/4.74 (b(s(s(elem!1)), z)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5509, 33552])).
% 4.37/4.74 tff(33554,plain,
% 4.37/4.74 (~b(s(s(elem!1)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[5708, 33553, 33542, 33438])).
% 4.37/4.74 tff(33555,plain,
% 4.37/4.74 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33554, 27354])).
% 4.37/4.74 tff(33556,plain,
% 4.37/4.74 (r(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[22871, 33551, 8677])).
% 4.37/4.74 tff(33557,plain,
% 4.37/4.74 (~r(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33532, 333, 409, 3193, 33556])).
% 4.37/4.74 tff(33558,plain,
% 4.37/4.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18132, 33557, 8677])).
% 4.37/4.74 tff(33559,plain,
% 4.37/4.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[4311, 33558, 22826])).
% 4.37/4.74 tff(33560,plain,
% 4.37/4.74 (b(s(s(z)), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18122, 33559, 8677])).
% 4.37/4.74 tff(33561,plain,
% 4.37/4.74 ($false),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33560, 33555])).
% 4.37/4.74 tff(33562,plain,((~r(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.74 tff(33563,plain,
% 4.37/4.74 (~r(s(s(s(z))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33562, 6107, 409, 562, 8677, 123, 304, 838, 2484, 722])).
% 4.37/4.74 tff(33564,plain,
% 4.37/4.74 (b(s(s(s(z))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[2794, 33563])).
% 4.37/4.74 tff(33565,plain,
% 4.37/4.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[846, 33564, 304, 838])).
% 4.37/4.74 tff(33566,plain,
% 4.37/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[249, 33565])).
% 4.37/4.74 tff(33567,plain,
% 4.37/4.74 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[11642, 33566, 33541, 6107, 33438])).
% 4.37/4.74 tff(33568,plain,
% 4.37/4.74 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[1451, 33567])).
% 4.37/4.74 tff(33569,plain,
% 4.37/4.74 (~b(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[1425, 33568, 123, 304])).
% 4.37/4.74 tff(33570,plain,
% 4.37/4.74 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[18895, 33569, 8677])).
% 4.37/4.74 tff(33571,plain,
% 4.37/4.74 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[1283, 33570, 22759])).
% 4.37/4.74 tff(33572,plain,
% 4.37/4.74 (r(s(s(z)), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[22871, 33571, 8677])).
% 4.37/4.74 tff(33573,plain,
% 4.37/4.74 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[24597, 25520])).
% 4.37/4.74 tff(33574,plain,
% 4.37/4.74 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[25199, 33573, 26568, 27211, 31032, 2484, 2323])).
% 4.37/4.74 tff(33575,plain,
% 4.37/4.74 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[24301, 33574, 26567])).
% 4.37/4.74 tff(33576,plain,
% 4.37/4.74 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[24600, 24597, 24294])).
% 4.37/4.74 tff(33577,plain,
% 4.37/4.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33578,plain,
% 4.37/4.74 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33579,plain,
% 4.37/4.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 4.37/4.74 inference(monotonicity,[status(thm)],[33578])).
% 4.37/4.74 tff(33580,plain,
% 4.37/4.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.74 inference(transitivity,[status(thm)],[33579, 33577])).
% 4.37/4.74 tff(33581,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.37/4.74 inference(quant_inst,[status(thm)],[])).
% 4.37/4.74 tff(33582,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33581, 33580])).
% 4.37/4.74 tff(33583,plain,
% 4.37/4.74 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33582, 144, 2082, 56, 33576, 33575])).
% 4.37/4.74 tff(33584,plain,
% 4.37/4.74 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33583])).
% 4.37/4.74 tff(33585,plain,
% 4.37/4.74 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[26574, 33576, 123, 304])).
% 4.37/4.74 tff(33586,plain,
% 4.37/4.74 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[9761, 33585])).
% 4.37/4.74 tff(33587,plain,
% 4.37/4.74 ($false),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[21343, 333, 224, 6107, 33586, 33584])).
% 4.37/4.74 tff(33588,plain,(r(s(s(s(s(z)))), s(z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.74 tff(33589,plain,
% 4.37/4.74 (r(s(s(s(s(z)))), s(z))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33588, 33566, 6107, 33449, 33564, 2484, 33540, 8677, 123, 304])).
% 4.37/4.74 tff(33590,plain,
% 4.37/4.74 (((~![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(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), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.74 inference(rewrite,[status(thm)],[])).
% 4.37/4.74 tff(33591,plain,
% 4.37/4.74 ((~![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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.74 inference(quant_inst,[status(thm)],[])).
% 4.37/4.74 tff(33592,plain,
% 4.37/4.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 4.37/4.74 inference(modus_ponens,[status(thm)],[33591, 33590])).
% 4.37/4.74 tff(33593,plain,
% 4.37/4.74 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[33592, 333, 409, 33589, 33572])).
% 4.37/4.74 tff(33594,plain,
% 4.37/4.74 (b(s(s(s(s(z)))), s(s(z)))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 33593])).
% 4.37/4.74 tff(33595,plain,
% 4.37/4.74 (~r(elem!1, s(s(z)))),
% 4.37/4.74 inference(unit_resolution,[status(thm)],[26788, 333, 409, 722, 33572])).
% 4.37/4.74 tff(33596,plain,
% 4.37/4.75 (~r(elem!1, s(s(elem!1)))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33595, 28273])).
% 4.37/4.75 tff(33597,plain,
% 4.37/4.75 (b(elem!1, s(s(elem!1)))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2522, 33596, 22705])).
% 4.37/4.75 tff(33598,plain,
% 4.37/4.75 (b(elem!1, s(s(z)))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33597, 22760])).
% 4.37/4.75 tff(33599,plain,
% 4.37/4.75 (~r(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[28548, 33572, 33540, 409])).
% 4.37/4.75 tff(33600,plain,
% 4.37/4.75 (b(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[7970, 33599, 22830])).
% 4.37/4.75 tff(33601,plain,
% 4.37/4.75 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[26847, 33589, 722, 409])).
% 4.37/4.75 tff(33602,plain,
% 4.37/4.75 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[24301, 33601, 26567])).
% 4.37/4.75 tff(33603,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[26859, 144, 33602, 33600, 33598, 33594])).
% 4.37/4.75 tff(33604,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33605,plain,
% 4.37/4.75 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33604, 28440, 722, 2484, 8677, 123, 304, 409, 562, 28586])).
% 4.37/4.75 tff(33606,plain,
% 4.37/4.75 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1137, 33605])).
% 4.37/4.75 tff(33607,plain,
% 4.37/4.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2262, 33606, 123, 28440])).
% 4.37/4.75 tff(33608,plain,
% 4.37/4.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[249, 33607])).
% 4.37/4.75 tff(33609,plain,
% 4.37/4.75 (~b(s(s(s(z))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[6004, 144, 123, 33606, 304])).
% 4.37/4.75 tff(33610,plain,
% 4.37/4.75 (r(s(s(s(z))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2794, 33609])).
% 4.37/4.75 tff(33611,plain,
% 4.37/4.75 (~r(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[22410, 33610, 2484, 33608])).
% 4.37/4.75 tff(33612,plain,
% 4.37/4.75 (b(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1538, 33611, 22768])).
% 4.37/4.75 tff(33613,plain,
% 4.37/4.75 (b(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1538, 23252, 22768])).
% 4.37/4.75 tff(33614,plain,
% 4.37/4.75 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.37/4.75 inference(rewrite,[status(thm)],[])).
% 4.37/4.75 tff(33615,plain,
% 4.37/4.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 4.37/4.75 inference(monotonicity,[status(thm)],[33614])).
% 4.37/4.75 tff(33616,plain,
% 4.37/4.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.37/4.75 inference(transitivity,[status(thm)],[33615, 31093])).
% 4.37/4.75 tff(33617,plain,
% 4.37/4.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 4.37/4.75 inference(quant_inst,[status(thm)],[])).
% 4.37/4.75 tff(33618,plain,
% 4.37/4.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33617, 33616])).
% 4.37/4.75 tff(33619,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33618, 144, 2082, 7943, 4367, 7928])).
% 4.37/4.75 tff(33620,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33621,plain,
% 4.37/4.75 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33620, 33235, 4367, 33613])).
% 4.37/4.75 tff(33622,plain,
% 4.37/4.75 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18122, 33621, 8677])).
% 4.37/4.75 tff(33623,plain,
% 4.37/4.75 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[4311, 33622, 22826])).
% 4.37/4.75 tff(33624,plain,
% 4.37/4.75 (r(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18132, 33623, 8677])).
% 4.37/4.75 tff(33625,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[31108, 333, 3193, 2671, 224, 33624])).
% 4.37/4.75 tff(33626,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33627,plain,
% 4.37/4.75 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33626, 33610, 33608, 8677, 33473, 2484, 563])).
% 4.37/4.75 tff(33628,plain,
% 4.37/4.75 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1451, 33627])).
% 4.37/4.75 tff(33629,plain,
% 4.37/4.75 (~b(s(s(z)), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1425, 33628, 123, 304])).
% 4.37/4.75 tff(33630,plain,
% 4.37/4.75 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18895, 33629, 8677])).
% 4.37/4.75 tff(33631,plain,
% 4.37/4.75 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1283, 33630, 22759])).
% 4.37/4.75 tff(33632,plain,
% 4.37/4.75 (r(s(s(z)), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[22871, 33631, 8677])).
% 4.37/4.75 tff(33633,plain,
% 4.37/4.75 (~r(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[7974, 333, 409, 722, 33632])).
% 4.37/4.75 tff(33634,plain,
% 4.37/4.75 (b(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[7970, 33633, 22830])).
% 4.37/4.75 tff(33635,plain,
% 4.37/4.75 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33620, 33634, 33473, 33612])).
% 4.37/4.75 tff(33636,plain,
% 4.37/4.75 (~r(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33532, 333, 409, 33610, 33632])).
% 4.37/4.75 tff(33637,plain,
% 4.37/4.75 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18132, 33636, 8677])).
% 4.37/4.75 tff(33638,plain,
% 4.37/4.75 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[4311, 33637, 22826])).
% 4.37/4.75 tff(33639,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18122, 33638, 33635, 8677])).
% 4.37/4.75 tff(33640,plain,(r(s(z), s(s(s(z)))) | (~(s(elem!1) = s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33641,plain,
% 4.37/4.75 (r(s(z), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33640, 33157, 33426, 33168, 50, 33435, 2484, 33190, 33176])).
% 4.37/4.75 tff(33642,plain,
% 4.37/4.75 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33307, 33641, 33168, 50, 33435, 2484])).
% 4.37/4.75 tff(33643,plain,
% 4.37/4.75 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[24301, 33642, 33433])).
% 4.37/4.75 tff(33644,plain,
% 4.37/4.75 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 4.37/4.75 inference(monotonicity,[status(thm)],[33160])).
% 4.37/4.75 tff(33645,plain,
% 4.37/4.75 (~(elem!1 = s(s(s(z))))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[392, 33644])).
% 4.37/4.75 tff(33646,plain,
% 4.37/4.75 (~r(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[11876, 31064, 409, 353])).
% 4.37/4.75 tff(33647,plain,
% 4.37/4.75 (b(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1538, 33646, 22768])).
% 4.37/4.75 tff(33648,plain,
% 4.37/4.75 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[31074, 33647, 123, 8677, 722, 304, 353, 2254])).
% 4.37/4.75 tff(33649,plain,
% 4.37/4.75 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1451, 33648])).
% 4.37/4.75 tff(33650,plain,
% 4.37/4.75 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33626, 33649, 31064, 8677, 33473, 2484, 563])).
% 4.37/4.75 tff(33651,plain,
% 4.37/4.75 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[249, 33650])).
% 4.37/4.75 tff(33652,plain,
% 4.37/4.75 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18960, 33651, 2254, 33647])).
% 4.37/4.75 tff(33653,plain,
% 4.37/4.75 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[121, 33652, 12014])).
% 4.37/4.75 tff(33654,plain,
% 4.37/4.75 (~r(elem!1, s(s(z)))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33242, 333, 33649, 2484, 33653])).
% 4.37/4.75 tff(33655,plain,
% 4.37/4.75 (~r(elem!1, s(s(elem!1)))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33654, 28273])).
% 4.37/4.75 tff(33656,plain,
% 4.37/4.75 (b(elem!1, s(s(elem!1)))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2522, 33655, 22705])).
% 4.37/4.75 tff(33657,plain,
% 4.37/4.75 (b(elem!1, s(s(z)))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33656, 22760])).
% 4.37/4.75 tff(33658,plain,
% 4.37/4.75 (~r(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[12787, 33649, 2484, 563])).
% 4.37/4.75 tff(33659,plain,
% 4.37/4.75 (b(s(s(z)), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[7970, 33658, 22830])).
% 4.37/4.75 tff(33660,plain,
% 4.37/4.75 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33307, 353, 722, 123, 304, 2484])).
% 4.37/4.75 tff(33661,plain,
% 4.37/4.75 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[24301, 33660, 26567])).
% 4.37/4.75 tff(33662,plain,
% 4.37/4.75 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[26859, 144, 33661, 33659, 33657])).
% 4.37/4.75 tff(33663,plain,
% 4.37/4.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[27075, 144, 33647, 33661, 33473])).
% 4.37/4.75 tff(33664,plain,
% 4.37/4.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33663])).
% 4.37/4.75 tff(33665,plain,
% 4.37/4.75 (~b(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33620, 33659, 33473, 33647])).
% 4.37/4.75 tff(33666,plain,
% 4.37/4.75 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18122, 33665, 8677])).
% 4.37/4.75 tff(33667,plain,
% 4.37/4.75 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[4311, 33666, 22826])).
% 4.37/4.75 tff(33668,plain,
% 4.37/4.75 (r(s(s(z)), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18132, 33667, 8677])).
% 4.37/4.75 tff(33669,plain,
% 4.37/4.75 (((~![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(s(z)), 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(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.75 inference(rewrite,[status(thm)],[])).
% 4.37/4.75 tff(33670,plain,
% 4.37/4.75 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.75 inference(rewrite,[status(thm)],[])).
% 4.37/4.75 tff(33671,plain,
% 4.37/4.75 (((~![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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 4.37/4.75 inference(monotonicity,[status(thm)],[33670])).
% 4.37/4.75 tff(33672,plain,
% 4.37/4.75 (((~![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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.75 inference(transitivity,[status(thm)],[33671, 33669])).
% 4.37/4.75 tff(33673,plain,
% 4.37/4.75 ((~![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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.37/4.75 inference(quant_inst,[status(thm)],[])).
% 4.37/4.75 tff(33674,plain,
% 4.37/4.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[33673, 33672])).
% 4.37/4.75 tff(33675,plain,
% 4.37/4.75 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33674, 333, 31064, 33668, 33664])).
% 4.37/4.75 tff(33676,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 33675, 33662])).
% 4.37/4.75 tff(33677,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33678,plain,
% 4.37/4.75 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33677, 33157, 2484, 33190, 50, 33168, 33435, 33641, 33426])).
% 4.37/4.75 tff(33679,plain,
% 4.37/4.75 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1137, 33678])).
% 4.37/4.75 tff(33680,plain,
% 4.37/4.75 (~r(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[27266, 33679, 33426, 33641])).
% 4.37/4.75 tff(33681,plain,
% 4.37/4.75 (b(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1538, 33680, 33645])).
% 4.37/4.75 tff(33682,plain,
% 4.37/4.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[27075, 144, 33681, 33643, 33428])).
% 4.37/4.75 tff(33683,plain,
% 4.37/4.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[9821, 44, 219, 33682])).
% 4.37/4.75 tff(33684,plain,
% 4.37/4.75 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33411, 333, 33641, 33679, 33683])).
% 4.37/4.75 tff(33685,plain,
% 4.37/4.75 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[24600, 33684, 24294])).
% 4.37/4.75 tff(33686,plain,
% 4.37/4.75 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[26574, 33685, 50, 33435])).
% 4.37/4.75 tff(33687,plain,
% 4.37/4.75 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[9761, 33686])).
% 4.37/4.75 tff(33688,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33421, 333, 2484, 33679, 33687, 33683])).
% 4.37/4.75 tff(33689,plain,(b(s(s(s(s(s(s(s(z))))))), z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z)) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33690,plain,
% 4.37/4.75 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33689, 708, 32633, 26540])).
% 4.37/4.75 tff(33691,plain,
% 4.37/4.75 (~(elem!1 = z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[14770, 33690, 2545])).
% 4.37/4.75 tff(33692,plain,
% 4.37/4.75 (~(z = elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[18287, 33691])).
% 4.37/4.75 tff(33693,plain,
% 4.37/4.75 (~(s(elem!1) = s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[8683, 33692])).
% 4.37/4.75 tff(33694,plain,
% 4.37/4.75 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[22668, 33693])).
% 4.37/4.75 tff(33695,plain,
% 4.37/4.75 (~(s(z) = elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[30660, 33694, 26540])).
% 4.37/4.75 tff(33696,plain,
% 4.37/4.75 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[49, 26540])).
% 4.37/4.75 tff(33697,plain,
% 4.37/4.75 (~(elem!1 = s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[712, 33695])).
% 4.37/4.75 tff(33698,plain,
% 4.37/4.75 (r(elem!1, s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[720, 33697, 708])).
% 4.37/4.75 tff(33699,plain,
% 4.37/4.75 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[22668, 25636])).
% 4.37/4.75 tff(33700,plain,
% 4.37/4.75 (~r(z, elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2541, 51, 33699, 322])).
% 4.37/4.75 tff(33701,plain,
% 4.37/4.75 (b(z, elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[658, 33700, 25631])).
% 4.37/4.75 tff(33702,plain,
% 4.37/4.75 (~r(elem!1, z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[2331, 51, 33699, 322])).
% 4.37/4.75 tff(33703,plain,
% 4.37/4.75 (b(elem!1, z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1380, 33702, 1368])).
% 4.37/4.75 tff(33704,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[12830, 33703, 33701, 2484, 722, 322, 706])).
% 4.37/4.75 tff(33705,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33706,plain,
% 4.37/4.75 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33705, 322, 722, 2484, 706, 1368])).
% 4.37/4.75 tff(33707,plain,
% 4.37/4.75 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[279, 33706])).
% 4.37/4.75 tff(33708,plain,
% 4.37/4.75 (~b(s(z), z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[7741, 33707, 123, 286])).
% 4.37/4.75 tff(33709,plain,
% 4.37/4.75 (r(s(z), z)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[348, 33708])).
% 4.37/4.75 tff(33710,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[818, 333, 33709, 722, 2484, 322])).
% 4.37/4.75 tff(33711,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33712,plain,
% 4.37/4.75 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33711, 33698, 32633, 33696, 33690, 33695, 33691])).
% 4.37/4.75 tff(33713,plain,
% 4.37/4.75 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[319, 33712])).
% 4.37/4.75 tff(33714,plain,
% 4.37/4.75 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[22668, 8684])).
% 4.37/4.75 tff(33715,plain,
% 4.37/4.75 (~(s(z) = elem!1)),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[30660, 33714, 4])).
% 4.37/4.75 tff(33716,plain,
% 4.37/4.75 (~(elem!1 = s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[712, 33715])).
% 4.37/4.75 tff(33717,plain,
% 4.37/4.75 (r(elem!1, s(z))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[720, 33716, 708])).
% 4.37/4.75 tff(33718,plain,
% 4.37/4.75 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 4.37/4.75 inference(monotonicity,[status(thm)],[3238])).
% 4.37/4.75 tff(33719,plain,
% 4.37/4.75 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 4.37/4.75 inference(symmetry,[status(thm)],[33718])).
% 4.37/4.75 tff(33720,plain,
% 4.37/4.75 ((~r(s(s(s(z))), s(z))) <=> (~r(elem!1, s(z)))),
% 4.37/4.75 inference(monotonicity,[status(thm)],[33719])).
% 4.37/4.75 tff(33721,plain,
% 4.37/4.75 (~r(elem!1, s(z))),
% 4.37/4.75 inference(modus_ponens,[status(thm)],[2788, 33720])).
% 4.37/4.75 tff(33722,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[722, 33721])).
% 4.37/4.75 tff(33723,plain,((~(elem!1 = s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.75 tff(33724,plain,
% 4.37/4.75 (~(elem!1 = s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33723, 2788, 722])).
% 4.37/4.75 tff(33725,plain,
% 4.37/4.75 (r(elem!1, s(s(s(z))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1538, 33724, 12397])).
% 4.37/4.75 tff(33726,plain,
% 4.37/4.75 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[33228, 33725, 2484, 2323])).
% 4.37/4.75 tff(33727,plain,
% 4.37/4.75 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[1137, 33726])).
% 4.37/4.75 tff(33728,plain,
% 4.37/4.75 ($false),
% 4.37/4.75 inference(unit_resolution,[status(thm)],[6004, 144, 22678, 123, 33727, 304])).
% 4.37/4.75 tff(33729,plain,(r(s(s(s(z))), s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(z)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.76 tff(33730,plain,
% 4.37/4.76 (r(s(s(s(z))), s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33729, 12397, 304, 2484, 33714, 50, 33717])).
% 4.37/4.76 tff(33731,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[19609])).
% 4.37/4.76 tff(33732,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.37/4.76 inference(symmetry,[status(thm)],[33731])).
% 4.37/4.76 tff(33733,plain,
% 4.37/4.76 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[7608, 22465, 33715])).
% 4.37/4.76 tff(33734,plain,
% 4.37/4.76 (~b(s(z), elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[32405, 156, 3238])).
% 4.37/4.76 tff(33735,plain,
% 4.37/4.76 (b(z, elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[30698, 33734, 4, 8684])).
% 4.37/4.76 tff(33736,plain,
% 4.37/4.76 (b(z, s(s(s(z))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[257, 33735, 22465])).
% 4.37/4.76 tff(33737,plain,
% 4.37/4.76 (~(s(s(z)) = elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[14611, 22465, 33715])).
% 4.37/4.76 tff(33738,plain,
% 4.37/4.76 (~(s(elem!1) = s(s(s(z))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1508, 33737])).
% 4.37/4.76 tff(33739,plain,
% 4.37/4.76 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[19607])).
% 4.37/4.76 tff(33740,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 4.37/4.76 inference(symmetry,[status(thm)],[33739])).
% 4.37/4.76 tff(33741,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[3238])).
% 4.37/4.76 tff(33742,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 4.37/4.76 inference(transitivity,[status(thm)],[33741, 33740])).
% 4.37/4.76 tff(33743,plain,
% 4.37/4.76 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(elem!1), s(s(s(z)))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33742])).
% 4.37/4.76 tff(33744,plain,
% 4.37/4.76 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33307, 27663, 33717, 50, 304, 2484])).
% 4.37/4.76 tff(33745,plain,
% 4.37/4.76 (~r(s(elem!1), s(s(s(z))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33744, 33743])).
% 4.37/4.76 tff(33746,plain,
% 4.37/4.76 (b(s(elem!1), s(s(s(z))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[965, 33745, 33738])).
% 4.37/4.76 tff(33747,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33689, 708, 2484, 4])).
% 4.37/4.76 tff(33748,plain,
% 4.37/4.76 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[7741, 489, 123, 286])).
% 4.37/4.76 tff(33749,plain,
% 4.37/4.76 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[279, 33748])).
% 4.37/4.76 tff(33750,plain,
% 4.37/4.76 (r(z, s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[372, 27697])).
% 4.37/4.76 tff(33751,plain,
% 4.37/4.76 (~r(s(s(s(z))), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[26130, 33750, 3193, 353])).
% 4.37/4.76 tff(33752,plain,
% 4.37/4.76 (b(s(s(s(z))), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[396, 33751])).
% 4.37/4.76 tff(33753,plain,
% 4.37/4.76 (~b(s(elem!1), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1802, 33752, 1794, 284])).
% 4.37/4.76 tff(33754,plain,
% 4.37/4.76 (r(s(elem!1), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[507, 33753])).
% 4.37/4.76 tff(33755,plain,
% 4.37/4.76 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13493, 33754, 2484, 33749])).
% 4.37/4.76 tff(33756,plain,
% 4.37/4.76 (b(elem!1, z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[380, 33752, 78])).
% 4.37/4.76 tff(33757,plain,
% 4.37/4.76 (~r(z, elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13826, 33750, 706, 350, 708])).
% 4.37/4.76 tff(33758,plain,
% 4.37/4.76 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13646, 33754, 123, 286, 2484, 1, 14077, 33757, 706, 33756, 708])).
% 4.37/4.76 tff(33759,plain,
% 4.37/4.76 ($false),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[472, 33758, 33755, 14872])).
% 4.37/4.76 tff(33760,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (s(z) = elem!1) | b(elem!1, s(z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~(s(s(s(z))) = elem!1)) | b(s(z), elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.76 tff(33761,plain,
% 4.37/4.76 (~b(s(z), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33760, 33746, 33747, 2484, 8684, 33715, 708, 50, 33736, 22465, 33734, 3193, 27663, 304])).
% 4.37/4.76 tff(33762,plain,
% 4.37/4.76 (r(s(z), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[348, 33761])).
% 4.37/4.76 tff(33763,plain,
% 4.37/4.76 (~r(z, s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[26130, 1699, 3193, 353])).
% 4.37/4.76 tff(33764,plain,
% 4.37/4.76 (b(z, s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[372, 33763])).
% 4.37/4.76 tff(33765,plain,
% 4.37/4.76 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13781, 1699, 123, 323, 304])).
% 4.37/4.76 tff(33766,plain,
% 4.37/4.76 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[279, 33765])).
% 4.37/4.76 tff(33767,plain,
% 4.37/4.76 ($false),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[757, 33766, 33764, 123, 304])).
% 4.37/4.76 tff(33768,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.76 tff(33769,plain,
% 4.37/4.76 (~r(s(s(s(z))), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33768, 33762, 304, 50, 3193, 27663])).
% 4.37/4.76 tff(33770,plain,
% 4.37/4.76 (b(s(s(s(z))), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[396, 33769])).
% 4.37/4.76 tff(33771,plain,
% 4.37/4.76 (~b(s(elem!1), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1802, 33770, 33746, 33736])).
% 4.37/4.76 tff(33772,plain,
% 4.37/4.76 (r(s(elem!1), z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[507, 33771])).
% 4.37/4.76 tff(33773,plain,
% 4.37/4.76 (~(s(s(z)) = s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[855, 33715])).
% 4.37/4.76 tff(33774,plain,
% 4.37/4.76 (~(s(s(s(z))) = s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[862, 33773])).
% 4.37/4.76 tff(33775,plain,
% 4.37/4.76 (~(s(s(elem!1)) = elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[7595, 22465, 33774])).
% 4.37/4.76 tff(33776,plain,
% 4.37/4.76 (~(elem!1 = s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[5603, 33775])).
% 4.37/4.76 tff(33777,plain,
% 4.37/4.76 (~(s(elem!1) = elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[5813, 33776])).
% 4.37/4.76 tff(33778,plain,
% 4.37/4.76 (~(elem!1 = s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1569, 33777])).
% 4.37/4.76 tff(33779,plain,
% 4.37/4.76 (~(s(s(elem!1)) = s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1196, 33778])).
% 4.37/4.76 tff(33780,plain,
% 4.37/4.76 (r(s(z), elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[406, 33734, 33715])).
% 4.37/4.76 tff(33781,plain,
% 4.37/4.76 (b(elem!1, z)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[380, 33770, 22465])).
% 4.37/4.76 tff(33782,plain,
% 4.37/4.76 (~r(s(elem!1), s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1911, 33781, 33717, 33777, 33735, 33762])).
% 4.37/4.76 tff(33783,plain,
% 4.37/4.76 (b(s(elem!1), s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[486, 33782, 8684])).
% 4.37/4.76 tff(33784,plain,
% 4.37/4.76 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 4.37/4.76 inference(symmetry,[status(thm)],[19668])).
% 4.37/4.76 tff(33785,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 4.37/4.76 inference(transitivity,[status(thm)],[33741, 33740, 33784])).
% 4.37/4.76 tff(33786,plain,
% 4.37/4.76 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33785])).
% 4.37/4.76 tff(33787,plain,
% 4.37/4.76 (~r(s(elem!1), elem!1)),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33744, 33786])).
% 4.37/4.76 tff(33788,plain,
% 4.37/4.76 (b(s(elem!1), elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[448, 33787, 33777])).
% 4.37/4.76 tff(33789,plain,
% 4.37/4.76 (~(s(z) = s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1228, 8684])).
% 4.37/4.76 tff(33790,plain,
% 4.37/4.76 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33783, 19636])).
% 4.37/4.76 tff(33791,plain,
% 4.37/4.76 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[9573, 144, 33790, 50, 304])).
% 4.37/4.76 tff(33792,plain,
% 4.37/4.76 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33791, 26370])).
% 4.37/4.76 tff(33793,plain,
% 4.37/4.76 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[472, 33792, 22466])).
% 4.37/4.76 tff(33794,plain,
% 4.37/4.76 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13493, 33793, 2484, 33772])).
% 4.37/4.76 tff(33795,plain,
% 4.37/4.76 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[279, 33794])).
% 4.37/4.76 tff(33796,plain,
% 4.37/4.76 (~b(z, s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[757, 33795, 50, 304])).
% 4.37/4.76 tff(33797,plain,
% 4.37/4.76 (r(z, s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[372, 33796])).
% 4.37/4.76 tff(33798,plain,
% 4.37/4.76 (~r(s(z), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1235, 33797, 33762, 33772])).
% 4.37/4.76 tff(33799,plain,
% 4.37/4.76 (b(s(z), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1244, 33798, 33789])).
% 4.37/4.76 tff(33800,plain,
% 4.37/4.76 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 4.37/4.76 inference(symmetry,[status(thm)],[19692])).
% 4.37/4.76 tff(33801,plain,
% 4.37/4.76 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 4.37/4.76 inference(transitivity,[status(thm)],[31920, 19690, 33800])).
% 4.37/4.76 tff(33802,plain,
% 4.37/4.76 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(elem!1, s(elem!1)))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33801])).
% 4.37/4.76 tff(33803,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[9761, 33791])).
% 4.37/4.76 tff(33804,plain,
% 4.37/4.76 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[3238])).
% 4.37/4.76 tff(33805,plain,
% 4.37/4.76 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33714, 33804])).
% 4.37/4.76 tff(33806,plain,
% 4.37/4.76 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[9806, 333, 22490, 33805, 33803])).
% 4.37/4.76 tff(33807,plain,
% 4.37/4.76 (~r(elem!1, s(elem!1))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33806, 33802])).
% 4.37/4.76 tff(33808,plain,
% 4.37/4.76 (b(elem!1, s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[560, 33807, 33778])).
% 4.37/4.76 tff(33809,plain,
% 4.37/4.76 (~b(s(s(elem!1)), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1278, 33808, 33717, 33799, 33788, 33775, 33783, 33780])).
% 4.37/4.76 tff(33810,plain,
% 4.37/4.76 (r(s(s(elem!1)), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1283, 33809, 33779])).
% 4.37/4.76 tff(33811,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[19631])).
% 4.37/4.76 tff(33812,plain,
% 4.37/4.76 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33811])).
% 4.37/4.76 tff(33813,plain,
% 4.37/4.76 (r(s(s(s(s(z)))), z)),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33772, 19808])).
% 4.37/4.76 tff(33814,plain,
% 4.37/4.76 (((~![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(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)))),
% 4.37/4.76 inference(rewrite,[status(thm)],[])).
% 4.37/4.76 tff(33815,plain,
% 4.37/4.76 (((~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)))),
% 4.37/4.76 inference(rewrite,[status(thm)],[])).
% 4.37/4.76 tff(33816,plain,
% 4.37/4.76 (((~![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(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))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33815])).
% 4.37/4.76 tff(33817,plain,
% 4.37/4.76 (((~![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(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)))),
% 4.37/4.76 inference(transitivity,[status(thm)],[33816, 33814])).
% 4.37/4.76 tff(33818,plain,
% 4.37/4.76 ((~![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(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 4.37/4.76 inference(quant_inst,[status(thm)],[])).
% 4.37/4.76 tff(33819,plain,
% 4.37/4.76 ((~![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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33818, 33817])).
% 4.37/4.76 tff(33820,plain,
% 4.37/4.76 (~r(s(z), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33819, 333, 33797, 33762, 33813])).
% 4.37/4.76 tff(33821,plain,
% 4.37/4.76 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[19906, 44, 33820])).
% 4.37/4.76 tff(33822,plain,
% 4.37/4.76 (b(s(z), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33821, 25692])).
% 4.37/4.76 tff(33823,plain,
% 4.37/4.76 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[25729, 144, 33822, 33790, 304])).
% 4.37/4.76 tff(33824,plain,
% 4.37/4.76 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33823, 33812])).
% 4.37/4.76 tff(33825,plain,
% 4.37/4.76 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[542, 33824, 22467])).
% 4.37/4.76 tff(33826,plain,
% 4.37/4.76 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[8191, 33825, 33810, 33772])).
% 4.37/4.76 tff(33827,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[2758, 33826, 33733])).
% 4.37/4.76 tff(33828,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33827, 33732])).
% 4.37/4.76 tff(33829,plain,
% 4.37/4.76 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33810, 19617])).
% 4.37/4.76 tff(33830,plain,
% 4.37/4.76 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33829, 19616])).
% 4.37/4.76 tff(33831,plain,
% 4.37/4.76 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[19607])).
% 4.37/4.76 tff(33832,plain,
% 4.37/4.76 (~r(z, elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13826, 33797, 33715, 33734, 708])).
% 4.37/4.76 tff(33833,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.76 inference(symmetry,[status(thm)],[33811])).
% 4.37/4.76 tff(33834,plain,
% 4.37/4.76 (~(s(s(elem!1)) = elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[7595, 22465, 863])).
% 4.37/4.76 tff(33835,plain,
% 4.37/4.76 (~(elem!1 = s(s(elem!1)))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[5603, 33834])).
% 4.37/4.76 tff(33836,plain,
% 4.37/4.76 (~(s(elem!1) = elem!1)),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[5813, 33835])).
% 4.37/4.76 tff(33837,plain,
% 4.37/4.76 (~(elem!1 = s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1569, 33836])).
% 4.37/4.76 tff(33838,plain,
% 4.37/4.76 (~b(elem!1, s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1642, 26349, 451, 585])).
% 4.37/4.76 tff(33839,plain,
% 4.37/4.76 (r(elem!1, s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[560, 33838, 33837])).
% 4.37/4.76 tff(33840,plain,
% 4.37/4.76 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[13646, 26353, 123, 286, 2484, 8684, 33837, 624, 706, 1575, 708])).
% 4.37/4.76 tff(33841,plain,
% 4.37/4.76 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[472, 33840, 22466])).
% 4.37/4.76 tff(33842,plain,
% 4.37/4.76 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[12088, 33841, 2484, 33839])).
% 4.37/4.76 tff(33843,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[542, 33842, 22467])).
% 4.37/4.76 tff(33844,plain,
% 4.37/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33843, 33833])).
% 4.37/4.76 tff(33845,plain,
% 4.37/4.76 (b(z, s(s(s(s(z)))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[585, 22521])).
% 4.37/4.76 tff(33846,plain,
% 4.37/4.76 (~r(s(elem!1), s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[1911, 26349, 6065, 33836, 624, 323])).
% 4.37/4.76 tff(33847,plain,
% 4.37/4.76 (b(s(elem!1), s(z))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[486, 33846, 8684])).
% 4.37/4.76 tff(33848,plain,
% 4.37/4.76 (b(s(s(s(s(z)))), s(z))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33847, 19636])).
% 4.37/4.76 tff(33849,plain,
% 4.37/4.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.76 inference(rewrite,[status(thm)],[])).
% 4.37/4.76 tff(33850,plain,
% 4.37/4.76 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.76 inference(rewrite,[status(thm)],[])).
% 4.37/4.76 tff(33851,plain,
% 4.37/4.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.37/4.76 inference(monotonicity,[status(thm)],[33850])).
% 4.37/4.76 tff(33852,plain,
% 4.37/4.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.76 inference(transitivity,[status(thm)],[33851, 33849])).
% 4.37/4.76 tff(33853,plain,
% 4.37/4.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.37/4.76 inference(quant_inst,[status(thm)],[])).
% 4.37/4.76 tff(33854,plain,
% 4.37/4.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33853, 33852])).
% 4.37/4.76 tff(33855,plain,
% 4.37/4.76 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33854, 144, 33848, 304, 286, 33845])).
% 4.37/4.76 tff(33856,plain,
% 4.37/4.76 ($false),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33855, 33844])).
% 4.37/4.76 tff(33857,plain,(r(z, elem!1) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (s(z) = elem!1) | b(elem!1, s(z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~r(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.76 tff(33858,plain,
% 4.37/4.76 (~b(z, s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[33857, 33832, 304, 33747, 2484, 50, 3238, 33715, 708, 33788, 33762, 33781, 74])).
% 4.37/4.76 tff(33859,plain,
% 4.37/4.76 (r(z, s(elem!1))),
% 4.37/4.76 inference(unit_resolution,[status(thm)],[583, 33858])).
% 4.37/4.76 tff(33860,plain,
% 4.37/4.76 (r(z, s(s(s(s(z)))))),
% 4.37/4.76 inference(modus_ponens,[status(thm)],[33859, 33831])).
% 4.37/4.76 tff(33861,plain,
% 4.37/4.76 (((~![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(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(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(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(s(s(z))))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33862,plain,
% 4.37/4.77 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(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(s(s(z))))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33863,plain,
% 4.37/4.77 (((~![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(s(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(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(s(s(z)))))))))))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[33862])).
% 4.37/4.77 tff(33864,plain,
% 4.37/4.77 (((~![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(s(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(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(s(s(z))))))))))),
% 4.37/4.77 inference(transitivity,[status(thm)],[33863, 33861])).
% 4.37/4.77 tff(33865,plain,
% 4.37/4.77 ((~![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(s(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))))))))),
% 4.37/4.77 inference(quant_inst,[status(thm)],[])).
% 4.37/4.77 tff(33866,plain,
% 4.37/4.77 ((~![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(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(s(s(z)))))))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33865, 33864])).
% 4.37/4.77 tff(33867,plain,
% 4.37/4.77 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33866, 333, 33860, 33803])).
% 4.37/4.77 tff(33868,plain,
% 4.37/4.77 (~r(z, s(s(s(s(s(z))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33867, 33830])).
% 4.37/4.77 tff(33869,plain,
% 4.37/4.77 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[13107, 44, 33868])).
% 4.37/4.77 tff(33870,plain,
% 4.37/4.77 (b(z, s(s(s(s(s(z))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33869, 13087])).
% 4.37/4.77 tff(33871,plain,
% 4.37/4.77 (((~![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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33872,plain,
% 4.37/4.77 (((~r(s(s(s(s(z)))), s(s(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33873,plain,
% 4.37/4.77 (((~![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(s(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[33872])).
% 4.37/4.77 tff(33874,plain,
% 4.37/4.77 (((~![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(s(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.77 inference(transitivity,[status(thm)],[33873, 33871])).
% 4.37/4.77 tff(33875,plain,
% 4.37/4.77 ((~![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(s(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)))),
% 4.37/4.77 inference(quant_inst,[status(thm)],[])).
% 4.37/4.77 tff(33876,plain,
% 4.37/4.77 ((~![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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33875, 33874])).
% 4.37/4.77 tff(33877,plain,
% 4.37/4.77 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33876, 333, 33860, 33803])).
% 4.37/4.77 tff(33878,plain,
% 4.37/4.77 (~r(s(s(s(s(s(z))))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33877, 33830])).
% 4.37/4.77 tff(33879,plain,
% 4.37/4.77 (b(s(s(s(s(s(z))))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 33878])).
% 4.37/4.77 tff(33880,plain,
% 4.37/4.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33881,plain,
% 4.37/4.77 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33882,plain,
% 4.37/4.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[33881])).
% 4.37/4.77 tff(33883,plain,
% 4.37/4.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(transitivity,[status(thm)],[33882, 33880])).
% 4.37/4.77 tff(33884,plain,
% 4.37/4.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.37/4.77 inference(quant_inst,[status(thm)],[])).
% 4.37/4.77 tff(33885,plain,
% 4.37/4.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33884, 33883])).
% 4.37/4.77 tff(33886,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33885, 144, 33747, 33879, 33870, 33828])).
% 4.37/4.77 tff(33887,plain,(b(s(z), s(s(s(z)))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z)) | (z = elem!1) | (~r(s(s(s(z))), s(z))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33888,plain,
% 4.37/4.77 (b(s(z), s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33887, 3238, 304, 2484, 708, 74, 3193, 4])).
% 4.37/4.77 tff(33889,plain,
% 4.37/4.77 (b(s(z), elem!1)),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33888, 27517])).
% 4.37/4.77 tff(33890,plain,
% 4.37/4.77 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[3238])).
% 4.37/4.77 tff(33891,plain,
% 4.37/4.77 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 4.37/4.77 inference(symmetry,[status(thm)],[33890])).
% 4.37/4.77 tff(33892,plain,
% 4.37/4.77 ((~r(z, s(s(s(z))))) <=> (~r(z, elem!1))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[33891])).
% 4.37/4.77 tff(33893,plain,
% 4.37/4.77 (~r(z, s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[6555, 1699, 3193, 323])).
% 4.37/4.77 tff(33894,plain,
% 4.37/4.77 (b(z, s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[372, 33893])).
% 4.37/4.77 tff(33895,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[757, 33766, 33894, 123, 304])).
% 4.37/4.77 tff(33896,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33897,plain,
% 4.37/4.77 (~r(s(s(s(z))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33896, 323, 304, 123, 3193])).
% 4.37/4.77 tff(33898,plain,
% 4.37/4.77 (b(s(s(s(z))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[396, 33897])).
% 4.37/4.77 tff(33899,plain,
% 4.37/4.77 (b(elem!1, z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[380, 33898, 22465])).
% 4.37/4.77 tff(33900,plain,
% 4.37/4.77 (~r(z, elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[727, 354, 6065, 323])).
% 4.37/4.77 tff(33901,plain,
% 4.37/4.77 (b(z, elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[658, 33900, 74])).
% 4.37/4.77 tff(33902,plain,
% 4.37/4.77 (b(s(elem!1), elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33081, 33901, 8684, 2484, 123, 6065, 304, 33836, 323, 22466, 624])).
% 4.37/4.77 tff(33903,plain,
% 4.37/4.77 (~b(s(elem!1), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[916, 33902, 624, 33901])).
% 4.37/4.77 tff(33904,plain,
% 4.37/4.77 (r(s(elem!1), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[507, 33903])).
% 4.37/4.77 tff(33905,plain,
% 4.37/4.77 (~r(s(z), s(elem!1))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1235, 33904, 323, 354])).
% 4.37/4.77 tff(33906,plain,
% 4.37/4.77 (b(s(z), s(elem!1))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1244, 33905, 33789])).
% 4.37/4.77 tff(33907,plain,
% 4.37/4.77 (~b(elem!1, s(elem!1))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1730, 33906, 134, 33902])).
% 4.37/4.77 tff(33908,plain,
% 4.37/4.77 (r(elem!1, s(elem!1))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[560, 33907, 33837])).
% 4.37/4.77 tff(33909,plain,
% 4.37/4.77 (r(elem!1, s(s(s(s(z)))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33908, 19693])).
% 4.37/4.77 tff(33910,plain,
% 4.37/4.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33909, 31921])).
% 4.37/4.77 tff(33911,plain,
% 4.37/4.77 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[13646, 33904, 123, 286, 2484, 8684, 33837, 33900, 706, 624, 708])).
% 4.37/4.77 tff(33912,plain,
% 4.37/4.77 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[472, 33911, 22466])).
% 4.37/4.77 tff(33913,plain,
% 4.37/4.77 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[22516, 33912, 3238])).
% 4.37/4.77 tff(33914,plain,
% 4.37/4.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[9806, 333, 22490, 33805, 33913])).
% 4.37/4.77 tff(33915,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33914, 33910])).
% 4.37/4.77 tff(33916,plain,((~r(z, s(z))) | (~(elem!1 = s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33917,plain,
% 4.37/4.77 (~r(z, s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33916, 323, 134, 3238, 123, 286, 2484, 706, 33899, 708, 304, 74])).
% 4.37/4.77 tff(33918,plain,
% 4.37/4.77 (b(z, s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[372, 33917])).
% 4.37/4.77 tff(33919,plain,
% 4.37/4.77 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[757, 33918, 123, 304])).
% 4.37/4.77 tff(33920,plain,
% 4.37/4.77 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[279, 33919])).
% 4.37/4.77 tff(33921,plain,
% 4.37/4.77 (~r(z, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1480, 333, 22490, 33805, 33920])).
% 4.37/4.77 tff(33922,plain,
% 4.37/4.77 (~r(z, elem!1)),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33921, 33892])).
% 4.37/4.77 tff(33923,plain,
% 4.37/4.77 (b(z, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[619, 33921])).
% 4.37/4.77 tff(33924,plain,
% 4.37/4.77 (b(z, elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[609, 33923, 22465])).
% 4.37/4.77 tff(33925,plain,
% 4.37/4.77 (b(s(elem!1), elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33081, 33924, 8684, 2484, 123, 6065, 304, 33836, 323, 22466, 33899])).
% 4.37/4.77 tff(33926,plain,
% 4.37/4.77 (~b(s(elem!1), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[916, 33925, 33899, 33924])).
% 4.37/4.77 tff(33927,plain,
% 4.37/4.77 (r(s(elem!1), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[507, 33926])).
% 4.37/4.77 tff(33928,plain,
% 4.37/4.77 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[13493, 33927, 2484, 33920])).
% 4.37/4.77 tff(33929,plain,
% 4.37/4.77 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[472, 33928, 22466])).
% 4.37/4.77 tff(33930,plain,
% 4.37/4.77 (r(z, elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[13646, 33929, 123, 286, 2484, 8684, 33837, 33927, 706, 33899, 708])).
% 4.37/4.77 tff(33931,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33930, 33922])).
% 4.37/4.77 tff(33932,plain,((~r(s(z), z)) | (~(elem!1 = s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(z) = elem!1) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (z = elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33933,plain,
% 4.37/4.77 (~r(s(z), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33932, 3238, 50, 33747, 2484, 33715, 708, 304, 33889, 74, 3193])).
% 4.37/4.77 tff(33934,plain,
% 4.37/4.77 (b(s(z), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[348, 33933])).
% 4.37/4.77 tff(33935,plain,
% 4.37/4.77 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[7741, 33934, 50, 33747])).
% 4.37/4.77 tff(33936,plain,
% 4.37/4.77 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[279, 33935])).
% 4.37/4.77 tff(33937,plain,
% 4.37/4.77 (~r(z, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1480, 333, 22490, 33805, 33936])).
% 4.37/4.77 tff(33938,plain,
% 4.37/4.77 (b(z, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[619, 33937])).
% 4.37/4.77 tff(33939,plain,
% 4.37/4.77 (~r(s(s(s(z))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1340, 333, 22490, 33805, 33936])).
% 4.37/4.77 tff(33940,plain,
% 4.37/4.77 (b(s(s(s(z))), z)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[396, 33939])).
% 4.37/4.77 tff(33941,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[2156, 33940, 33938, 33888, 33934])).
% 4.37/4.77 tff(33942,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (z = elem!1) | (~r(s(s(s(z))), s(z))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33943,plain,
% 4.37/4.77 (~(elem!1 = s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33942, 33730, 708, 304, 74, 2484, 4])).
% 4.37/4.77 tff(33944,plain,
% 4.37/4.77 (r(elem!1, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1538, 33943, 12397])).
% 4.37/4.77 tff(33945,plain,
% 4.37/4.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33228, 33944, 2484, 33714])).
% 4.37/4.77 tff(33946,plain,
% 4.37/4.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[1137, 33945])).
% 4.37/4.77 tff(33947,plain,
% 4.37/4.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[22410, 33944, 2484, 33730])).
% 4.37/4.77 tff(33948,plain,
% 4.37/4.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[249, 33947])).
% 4.37/4.77 tff(33949,plain,
% 4.37/4.77 (~b(s(z), s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[2262, 33948, 50, 33946])).
% 4.37/4.77 tff(33950,plain,
% 4.37/4.77 (r(s(z), s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[172, 33949])).
% 4.37/4.77 tff(33951,plain,
% 4.37/4.77 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.37/4.77 inference(rewrite,[status(thm)],[])).
% 4.37/4.77 tff(33952,plain,
% 4.37/4.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 4.37/4.77 inference(monotonicity,[status(thm)],[33951])).
% 4.37/4.77 tff(33953,plain,
% 4.37/4.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, 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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.37/4.77 inference(transitivity,[status(thm)],[33952, 10893])).
% 4.37/4.77 tff(33954,plain,
% 4.37/4.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 4.37/4.77 inference(quant_inst,[status(thm)],[])).
% 4.37/4.77 tff(33955,plain,
% 4.37/4.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 4.37/4.77 inference(modus_ponens,[status(thm)],[33954, 33953])).
% 4.37/4.77 tff(33956,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33955, 333, 33944, 33717, 33730, 33950])).
% 4.37/4.77 tff(33957,plain,(b(elem!1, s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | b(elem!1, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (z = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33958,plain,
% 4.37/4.77 (b(elem!1, s(s(s(z))))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33957, 708, 32633, 33713, 33692, 26540])).
% 4.37/4.77 tff(33959,plain,
% 4.37/4.77 (~(s(s(s(z))) = elem!1)),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[27447, 33724])).
% 4.37/4.77 tff(33960,plain,
% 4.37/4.77 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[33711, 722, 2484, 123, 286, 706, 1368])).
% 4.37/4.77 tff(33961,plain,
% 4.37/4.77 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[319, 33960])).
% 4.37/4.77 tff(33962,plain,
% 4.37/4.77 ($false),
% 4.37/4.77 inference(unit_resolution,[status(thm)],[6004, 144, 56, 123, 2254, 304])).
% 4.37/4.77 tff(33963,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.77 tff(33964,plain,
% 4.37/4.78 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33963, 56, 123, 33961])).
% 4.37/4.78 tff(33965,plain,
% 4.37/4.78 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1137, 33964])).
% 4.37/4.78 tff(33966,plain,
% 4.37/4.78 (~r(s(s(s(z))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[23315, 33965, 33699, 2484])).
% 4.37/4.78 tff(33967,plain,
% 4.37/4.78 (~r(elem!1, s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33228, 33965, 2484, 33699])).
% 4.37/4.78 tff(33968,plain,
% 4.37/4.78 (~b(z, s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[757, 259, 123, 33961])).
% 4.37/4.78 tff(33969,plain,
% 4.37/4.78 (r(z, s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[372, 33968])).
% 4.37/4.78 tff(33970,plain,
% 4.37/4.78 (~b(s(z), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[7741, 259, 123, 286])).
% 4.37/4.78 tff(33971,plain,
% 4.37/4.78 (r(s(z), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[348, 33970])).
% 4.37/4.78 tff(33972,plain,
% 4.37/4.78 (~r(z, elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[727, 33971, 722, 33969])).
% 4.37/4.78 tff(33973,plain,
% 4.37/4.78 (b(z, elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[658, 33972, 25631])).
% 4.37/4.78 tff(33974,plain,
% 4.37/4.78 (~b(z, s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[21799, 33973, 33967, 698, 33966])).
% 4.37/4.78 tff(33975,plain,
% 4.37/4.78 (r(z, s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[619, 33974])).
% 4.37/4.78 tff(33976,plain,
% 4.37/4.78 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33963, 56, 123, 304])).
% 4.37/4.78 tff(33977,plain,
% 4.37/4.78 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1137, 33976])).
% 4.37/4.78 tff(33978,plain,
% 4.37/4.78 (~r(s(s(s(z))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[23315, 33977, 33699, 2484])).
% 4.37/4.78 tff(33979,plain,
% 4.37/4.78 (~b(z, s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[21533, 283, 286, 304, 56])).
% 4.37/4.78 tff(33980,plain,
% 4.37/4.78 (r(z, s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[619, 33979])).
% 4.37/4.78 tff(33981,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(33982,plain,
% 4.37/4.78 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(33983,plain,
% 4.37/4.78 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[33982])).
% 4.37/4.78 tff(33984,plain,
% 4.37/4.78 (((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, 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))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(transitivity,[status(thm)],[33983, 33981])).
% 4.37/4.78 tff(33985,plain,
% 4.37/4.78 ((~![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(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 4.37/4.78 inference(quant_inst,[status(thm)],[])).
% 4.37/4.78 tff(33986,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[33985, 33984])).
% 4.37/4.78 tff(33987,plain,
% 4.37/4.78 ($false),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33986, 333, 623, 2484, 6107, 51])).
% 4.37/4.78 tff(33988,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.78 tff(33989,plain,
% 4.37/4.78 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33988, 33980, 2484, 33977])).
% 4.37/4.78 tff(33990,plain,
% 4.37/4.78 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[279, 33989])).
% 4.37/4.78 tff(33991,plain,
% 4.37/4.78 (~b(z, s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[757, 33990, 123, 304])).
% 4.37/4.78 tff(33992,plain,
% 4.37/4.78 (r(z, s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[372, 33991])).
% 4.37/4.78 tff(33993,plain,
% 4.37/4.78 (~b(s(z), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[7741, 33990, 123, 286])).
% 4.37/4.78 tff(33994,plain,
% 4.37/4.78 (r(s(z), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[348, 33993])).
% 4.37/4.78 tff(33995,plain,
% 4.37/4.78 (~r(z, elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[727, 33994, 722, 33992])).
% 4.37/4.78 tff(33996,plain,
% 4.37/4.78 (b(z, elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[658, 33995, 25631])).
% 4.37/4.78 tff(33997,plain,
% 4.37/4.78 (~(s(s(s(z))) = elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[257, 33996, 33979])).
% 4.37/4.78 tff(33998,plain,
% 4.37/4.78 (~r(elem!1, z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[747, 33994, 722, 33992])).
% 4.37/4.78 tff(33999,plain,
% 4.37/4.78 (b(elem!1, z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1380, 33998, 1368])).
% 4.37/4.78 tff(34000,plain,
% 4.37/4.78 (~b(s(z), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[846, 283, 304, 56])).
% 4.37/4.78 tff(34001,plain,
% 4.37/4.78 (r(s(z), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[172, 34000])).
% 4.37/4.78 tff(34002,plain,
% 4.37/4.78 (~r(s(s(s(z))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[7314, 33994, 34001, 33992])).
% 4.37/4.78 tff(34003,plain,
% 4.37/4.78 (b(s(s(s(z))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[396, 34002])).
% 4.37/4.78 tff(34004,plain,
% 4.37/4.78 (~b(s(s(s(z))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[10565, 34003, 33999, 33996])).
% 4.37/4.78 tff(34005,plain,
% 4.37/4.78 ($false),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[704, 34004, 33997, 33978])).
% 4.37/4.78 tff(34006,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (elem!1 = z) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.78 tff(34007,plain,
% 4.37/4.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[34006, 56, 722, 123, 33961, 286, 2484, 1368])).
% 4.37/4.78 tff(34008,plain,
% 4.37/4.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[249, 34007])).
% 4.37/4.78 tff(34009,plain,
% 4.37/4.78 (b(s(s(s(z))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[704, 698, 33966])).
% 4.37/4.78 tff(34010,plain,
% 4.37/4.78 (~r(elem!1, z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[747, 33971, 722, 33969])).
% 4.37/4.78 tff(34011,plain,
% 4.37/4.78 (b(elem!1, z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1380, 34010, 1368])).
% 4.37/4.78 tff(34012,plain,
% 4.37/4.78 (~b(s(s(s(z))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[10565, 34011, 34009, 33973])).
% 4.37/4.78 tff(34013,plain,
% 4.37/4.78 (r(s(s(s(z))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[396, 34012])).
% 4.37/4.78 tff(34014,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(34015,plain,
% 4.37/4.78 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(34016,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![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)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34015])).
% 4.37/4.78 tff(34017,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![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)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 4.37/4.78 inference(transitivity,[status(thm)],[34016, 34014])).
% 4.37/4.78 tff(34018,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 4.37/4.78 inference(quant_inst,[status(thm)],[])).
% 4.37/4.78 tff(34019,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[34018, 34017])).
% 4.37/4.78 tff(34020,plain,
% 4.37/4.78 (~r(s(s(s(s(z)))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[34019, 333, 1699, 623, 27463])).
% 4.37/4.78 tff(34021,plain,
% 4.37/4.78 (b(s(s(s(s(z)))), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[4243, 44, 242, 34020])).
% 4.37/4.78 tff(34022,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(34023,plain,
% 4.37/4.78 (((~r(s(s(s(z))), z)) | (~r(s(s(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(s(s(z)))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(34024,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(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(s(s(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))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34023])).
% 4.37/4.78 tff(34025,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(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(s(s(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))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.78 inference(transitivity,[status(thm)],[34024, 34022])).
% 4.37/4.78 tff(34026,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(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(s(s(z))))))))))),
% 4.37/4.78 inference(quant_inst,[status(thm)],[])).
% 4.37/4.78 tff(34027,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[34026, 34025])).
% 4.37/4.78 tff(34028,plain,
% 4.37/4.78 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[34027, 333, 1699, 224, 27463])).
% 4.37/4.78 tff(34029,plain,
% 4.37/4.78 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[9761, 34028])).
% 4.37/4.78 tff(34030,plain,
% 4.37/4.78 ($false),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[24823, 144, 286, 259, 34029, 34021])).
% 4.37/4.78 tff(34031,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.78 tff(34032,plain,
% 4.37/4.78 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[34031, 259, 286, 34013, 34008, 33975])).
% 4.37/4.78 tff(34033,plain,
% 4.37/4.78 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[9821, 44, 219, 34032])).
% 4.37/4.78 tff(34034,plain,
% 4.37/4.78 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.78 inference(rewrite,[status(thm)],[])).
% 4.37/4.78 tff(34035,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34034])).
% 4.37/4.78 tff(34036,plain,
% 4.37/4.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.78 inference(transitivity,[status(thm)],[34035, 27070])).
% 4.37/4.78 tff(34037,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.37/4.78 inference(quant_inst,[status(thm)],[])).
% 4.37/4.78 tff(34038,plain,
% 4.37/4.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[34037, 34036])).
% 4.37/4.78 tff(34039,plain,
% 4.37/4.78 (~b(s(s(s(s(z)))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[34038, 144, 2082, 34009, 34033])).
% 4.37/4.78 tff(34040,plain,
% 4.37/4.78 (~r(s(z), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[7314, 34013, 33971, 33969])).
% 4.37/4.78 tff(34041,plain,
% 4.37/4.78 (b(s(z), s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[172, 34040])).
% 4.37/4.78 tff(34042,plain,
% 4.37/4.78 (~b(s(z), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[19991, 144, 2082, 34041, 34009])).
% 4.37/4.78 tff(34043,plain,
% 4.37/4.78 (r(s(z), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[406, 34042, 706])).
% 4.37/4.78 tff(34044,plain,
% 4.37/4.78 (~b(s(s(s(s(z)))), s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[18487, 144, 56, 34041, 34033])).
% 4.37/4.78 tff(34045,plain,
% 4.37/4.78 (r(s(s(s(s(z)))), s(z))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[24600, 34044, 24294])).
% 4.37/4.78 tff(34046,plain,
% 4.37/4.78 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[26847, 34045, 722, 34043])).
% 4.37/4.78 tff(34047,plain,
% 4.37/4.78 (s(s(s(s(z)))) = elem!1),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[24301, 34046, 34039])).
% 4.37/4.78 tff(34048,plain,
% 4.37/4.78 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34047])).
% 4.37/4.78 tff(34049,plain,
% 4.37/4.78 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34048])).
% 4.37/4.78 tff(34050,plain,
% 4.37/4.78 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.37/4.78 inference(symmetry,[status(thm)],[34049])).
% 4.37/4.78 tff(34051,plain,
% 4.37/4.78 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34050])).
% 4.37/4.78 tff(34052,plain,
% 4.37/4.78 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34051])).
% 4.37/4.78 tff(34053,plain,
% 4.37/4.78 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 4.37/4.78 inference(symmetry,[status(thm)],[34052])).
% 4.37/4.78 tff(34054,plain,
% 4.37/4.78 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34053])).
% 4.37/4.78 tff(34055,plain,
% 4.37/4.78 (~(s(s(s(elem!1))) = elem!1)),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[13793, 34054])).
% 4.37/4.78 tff(34056,plain,
% 4.37/4.78 (~(elem!1 = s(elem!1))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[2482, 34055])).
% 4.37/4.78 tff(34057,plain,
% 4.37/4.78 (~(s(elem!1) = elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[906, 34056])).
% 4.37/4.78 tff(34058,plain,
% 4.37/4.78 (elem!1 = s(s(s(s(z))))),
% 4.37/4.78 inference(symmetry,[status(thm)],[34047])).
% 4.37/4.78 tff(34059,plain,
% 4.37/4.78 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34058])).
% 4.37/4.78 tff(34060,plain,
% 4.37/4.78 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 4.37/4.78 inference(transitivity,[status(thm)],[34059, 24729])).
% 4.37/4.78 tff(34061,plain,
% 4.37/4.78 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 4.37/4.78 inference(symmetry,[status(thm)],[34060])).
% 4.37/4.78 tff(34062,plain,
% 4.37/4.78 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 4.37/4.78 inference(monotonicity,[status(thm)],[34061])).
% 4.37/4.78 tff(34063,plain,
% 4.37/4.78 (~(s(s(z)) = elem!1)),
% 4.37/4.78 inference(modus_ponens,[status(thm)],[24445, 34062])).
% 4.37/4.78 tff(34064,plain,
% 4.37/4.78 (~(s(elem!1) = s(s(s(z))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1508, 34063])).
% 4.37/4.78 tff(34065,plain,
% 4.37/4.78 (~r(s(elem!1), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[7383, 34064, 25636, 706, 56, 33971, 33972, 34013, 34056, 33969])).
% 4.37/4.78 tff(34066,plain,
% 4.37/4.78 (b(s(elem!1), z)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[507, 34065])).
% 4.37/4.78 tff(34067,plain,
% 4.37/4.78 (~b(s(elem!1), elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[916, 34066, 34011, 33973])).
% 4.37/4.78 tff(34068,plain,
% 4.37/4.78 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[33081, 34067, 25636, 2484, 123, 722, 33961, 33973, 33971, 34057, 34011])).
% 4.37/4.78 tff(34069,plain,
% 4.37/4.78 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[930, 34068])).
% 4.37/4.78 tff(34070,plain,
% 4.37/4.78 (~(elem!1 = s(s(elem!1)))),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[1216, 34069])).
% 4.37/4.78 tff(34071,plain,
% 4.37/4.78 ($false),
% 4.37/4.78 inference(unit_resolution,[status(thm)],[24637, 34070, 34069, 34047])).
% 4.37/4.78 tff(34072,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.78 tff(34073,plain,
% 4.37/4.79 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34072, 22678, 123, 722, 706, 2484, 2082, 286, 33959, 1368])).
% 4.37/4.79 tff(34074,plain,
% 4.37/4.79 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[279, 34073])).
% 4.37/4.79 tff(34075,plain,
% 4.37/4.79 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33963, 22678, 123, 33961])).
% 4.37/4.79 tff(34076,plain,
% 4.37/4.79 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1137, 34075])).
% 4.37/4.79 tff(34077,plain,
% 4.37/4.79 (~r(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[23315, 34076, 33699, 2484])).
% 4.37/4.79 tff(34078,plain,
% 4.37/4.79 (~r(elem!1, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33228, 34076, 2484, 33699])).
% 4.37/4.79 tff(34079,plain,
% 4.37/4.79 (~r(z, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33988, 34074, 2484, 34076])).
% 4.37/4.79 tff(34080,plain,
% 4.37/4.79 (b(z, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[619, 34079])).
% 4.37/4.79 tff(34081,plain,
% 4.37/4.79 (~b(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[21799, 34080, 34078, 33959, 34077])).
% 4.37/4.79 tff(34082,plain,
% 4.37/4.79 (r(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[658, 34081, 25631])).
% 4.37/4.79 tff(34083,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24187, 333, 34082, 2484, 33699, 34074])).
% 4.37/4.79 tff(34084,plain,(r(s(s(s(z))), s(z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34085,plain,
% 4.37/4.79 (r(s(s(s(z))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34084, 33698, 33696, 32633, 33695, 33958, 33690, 33691])).
% 4.37/4.79 tff(34086,plain,
% 4.37/4.79 (~(elem!1 = s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33942, 34085, 708, 33713, 33692, 32633, 26540])).
% 4.37/4.79 tff(34087,plain,
% 4.37/4.79 (~(s(s(s(z))) = elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27447, 34086])).
% 4.37/4.79 tff(34088,plain,
% 4.37/4.79 (~b(z, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[757, 259, 123, 304])).
% 4.37/4.79 tff(34089,plain,
% 4.37/4.79 (r(z, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[372, 34088])).
% 4.37/4.79 tff(34090,plain,
% 4.37/4.79 (~r(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[747, 33971, 722, 34089])).
% 4.37/4.79 tff(34091,plain,
% 4.37/4.79 (b(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1380, 34090, 1368])).
% 4.37/4.79 tff(34092,plain,
% 4.37/4.79 (~r(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[32918, 33971, 304, 722, 123, 33699, 2484])).
% 4.37/4.79 tff(34093,plain,
% 4.37/4.79 (b(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[704, 34092, 698])).
% 4.37/4.79 tff(34094,plain,
% 4.37/4.79 (~r(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[727, 34089, 722, 33971])).
% 4.37/4.79 tff(34095,plain,
% 4.37/4.79 (b(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[658, 34094, 25631])).
% 4.37/4.79 tff(34096,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[10565, 34095, 34093, 285, 34091])).
% 4.37/4.79 tff(34097,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34098,plain,
% 4.37/4.79 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34097, 285, 1368, 698, 722, 33961, 123, 2484, 286])).
% 4.37/4.79 tff(34099,plain,
% 4.37/4.79 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[279, 34098])).
% 4.37/4.79 tff(34100,plain,
% 4.37/4.79 (((~![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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.79 inference(rewrite,[status(thm)],[])).
% 4.37/4.79 tff(34101,plain,
% 4.37/4.79 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.79 inference(rewrite,[status(thm)],[])).
% 4.37/4.79 tff(34102,plain,
% 4.37/4.79 (((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.37/4.79 inference(monotonicity,[status(thm)],[34101])).
% 4.37/4.79 tff(34103,plain,
% 4.37/4.79 (((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, 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(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.37/4.79 inference(transitivity,[status(thm)],[34102, 34100])).
% 4.37/4.79 tff(34104,plain,
% 4.37/4.79 ((~![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(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))),
% 4.37/4.79 inference(quant_inst,[status(thm)],[])).
% 4.37/4.79 tff(34105,plain,
% 4.37/4.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.37/4.79 inference(modus_ponens,[status(thm)],[34104, 34103])).
% 4.37/4.79 tff(34106,plain,
% 4.37/4.79 (~r(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34105, 333, 2484, 33699, 34099])).
% 4.37/4.79 tff(34107,plain,
% 4.37/4.79 (b(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1380, 34106, 1368])).
% 4.37/4.79 tff(34108,plain,
% 4.37/4.79 (~r(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24187, 333, 2484, 33699, 34099])).
% 4.37/4.79 tff(34109,plain,
% 4.37/4.79 (b(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[658, 34108, 25631])).
% 4.37/4.79 tff(34110,plain,
% 4.37/4.79 (~b(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[10565, 34109, 285, 34107])).
% 4.37/4.79 tff(34111,plain,
% 4.37/4.79 (r(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[704, 34110, 698])).
% 4.37/4.79 tff(34112,plain,
% 4.37/4.79 (~r(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[12189, 34111, 123, 2484, 722])).
% 4.37/4.79 tff(34113,plain,
% 4.37/4.79 (b(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[406, 34112, 706])).
% 4.37/4.79 tff(34114,plain,
% 4.37/4.79 (~r(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[32918, 34111, 33961, 722, 123, 33699, 2484])).
% 4.37/4.79 tff(34115,plain,
% 4.37/4.79 (b(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[348, 34114])).
% 4.37/4.79 tff(34116,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1602, 34115, 34113, 34109, 34107])).
% 4.37/4.79 tff(34117,plain,((~b(s(s(s(z))), z)) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34118,plain,
% 4.37/4.79 (~b(s(s(s(z))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34117, 33695, 33698, 33696, 32633, 34087, 33691, 33690])).
% 4.37/4.79 tff(34119,plain,
% 4.37/4.79 (r(s(s(s(z))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[396, 34118])).
% 4.37/4.79 tff(34120,plain,
% 4.37/4.79 (~r(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33896, 34119, 33713, 33696, 34085])).
% 4.37/4.79 tff(34121,plain,
% 4.37/4.79 (b(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[348, 34120])).
% 4.37/4.79 tff(34122,plain,
% 4.37/4.79 (~b(z, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[7093, 34121, 33690, 33713])).
% 4.37/4.79 tff(34123,plain,
% 4.37/4.79 (r(z, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[372, 34122])).
% 4.37/4.79 tff(34124,plain,
% 4.37/4.79 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[7741, 34121, 33696, 33690])).
% 4.37/4.79 tff(34125,plain,
% 4.37/4.79 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[279, 34124])).
% 4.37/4.79 tff(34126,plain,
% 4.37/4.79 (~r(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34105, 333, 32633, 33694, 34125])).
% 4.37/4.79 tff(34127,plain,
% 4.37/4.79 (b(elem!1, z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1380, 34126, 33691])).
% 4.37/4.79 tff(34128,plain,
% 4.37/4.79 (~r(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24187, 333, 32633, 33694, 34125])).
% 4.37/4.79 tff(34129,plain,
% 4.37/4.79 (b(z, elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[658, 34128, 33692])).
% 4.37/4.79 tff(34130,plain,
% 4.37/4.79 (~b(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1602, 34129, 34121, 34127])).
% 4.37/4.79 tff(34131,plain,
% 4.37/4.79 (r(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[406, 34130, 33695])).
% 4.37/4.79 tff(34132,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[8673, 333, 34131, 34123, 34119, 34085])).
% 4.37/4.79 tff(34133,plain,(b(elem!1, s(z)) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34134,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34133, 32631])).
% 4.37/4.79 tff(34135,plain,
% 4.37/4.79 (~b(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[152, 34134, 32439, 50])).
% 4.37/4.79 tff(34136,plain,
% 4.37/4.79 (r(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[406, 34135, 706])).
% 4.37/4.79 tff(34137,plain,
% 4.37/4.79 (~r(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[12189, 34136, 32437, 50, 32632])).
% 4.37/4.79 tff(34138,plain,
% 4.37/4.79 (b(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[704, 34137, 22677])).
% 4.37/4.79 tff(34139,plain,
% 4.37/4.79 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[12172, 34136, 32437, 32632])).
% 4.37/4.79 tff(34140,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[319, 34139])).
% 4.37/4.79 tff(34141,plain,
% 4.37/4.79 (~b(z, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28115, 32631, 22670])).
% 4.37/4.79 tff(34142,plain,
% 4.37/4.79 (~b(elem!1, s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[18030, 34141, 22669])).
% 4.37/4.79 tff(34143,plain,
% 4.37/4.79 (~b(z, s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[18176, 34142, 22679])).
% 4.37/4.79 tff(34144,plain,
% 4.37/4.79 (r(z, s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[583, 34143])).
% 4.37/4.79 tff(34145,plain,
% 4.37/4.79 (r(elem!1, s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[560, 34142, 29713])).
% 4.37/4.79 tff(34146,plain,
% 4.37/4.79 (r(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33640, 34140, 50, 22669, 32632, 34136, 32437, 34145, 34144])).
% 4.37/4.79 tff(34147,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33307, 34146, 50, 32632, 34140, 32437])).
% 4.37/4.79 tff(34148,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24301, 34147, 26922])).
% 4.37/4.79 tff(34149,plain,
% 4.37/4.79 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33677, 34140, 32437, 22669, 50, 32632, 34145, 34146, 34136])).
% 4.37/4.79 tff(34150,plain,
% 4.37/4.79 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1137, 34149])).
% 4.37/4.79 tff(34151,plain,
% 4.37/4.79 (~r(elem!1, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27266, 34150, 34146, 34136])).
% 4.37/4.79 tff(34152,plain,
% 4.37/4.79 (b(elem!1, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1538, 34151, 22674])).
% 4.37/4.79 tff(34153,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27075, 144, 34152, 34148, 34138])).
% 4.37/4.79 tff(34154,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27512, 34153])).
% 4.37/4.79 tff(34155,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[26588, 34140, 32439, 50, 34134, 22669, 32632, 34136])).
% 4.37/4.79 tff(34156,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[9761, 34155])).
% 4.37/4.79 tff(34157,plain,
% 4.37/4.79 (~(s(elem!1) = elem!1)),
% 4.37/4.79 inference(modus_ponens,[status(thm)],[706, 29028])).
% 4.37/4.79 tff(34158,plain,
% 4.37/4.79 (~b(s(elem!1), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[462, 34134, 32439, 27196])).
% 4.37/4.79 tff(34159,plain,
% 4.37/4.79 (r(s(elem!1), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[448, 34158, 34157])).
% 4.37/4.79 tff(34160,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33689, 32631, 32437, 4])).
% 4.37/4.79 tff(34161,plain,
% 4.37/4.79 (~r(s(s(s(z))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[22912, 34137, 22670])).
% 4.37/4.79 tff(34162,plain,
% 4.37/4.79 (b(s(s(s(z))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[396, 34161])).
% 4.37/4.79 tff(34163,plain,
% 4.37/4.79 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[26913, 34150, 22669, 34144, 34162, 34160, 34140, 34136, 34159])).
% 4.37/4.79 tff(34164,plain,
% 4.37/4.79 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[249, 34163])).
% 4.37/4.79 tff(34165,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[21343, 333, 34164, 34150, 34156, 34154])).
% 4.37/4.79 tff(34166,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34167,plain,
% 4.37/4.79 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34166, 706, 4])).
% 4.37/4.79 tff(34168,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33689, 708, 32437, 4])).
% 4.37/4.79 tff(34169,plain,
% 4.37/4.79 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[33711, 721, 32437, 50, 34168, 706, 77])).
% 4.37/4.79 tff(34170,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.37/4.79 inference(monotonicity,[status(thm)],[78])).
% 4.37/4.79 tff(34171,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(symmetry,[status(thm)],[34170])).
% 4.37/4.79 tff(34172,plain,
% 4.37/4.79 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.37/4.79 inference(monotonicity,[status(thm)],[34171])).
% 4.37/4.79 tff(34173,plain,
% 4.37/4.79 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(modus_ponens,[status(thm)],[2545, 34172])).
% 4.37/4.79 tff(34174,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[283, 34173])).
% 4.37/4.79 tff(34175,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34176,plain,
% 4.37/4.79 (~(s(s(s(z))) = elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34175, 17795, 2545])).
% 4.37/4.79 tff(34177,plain,
% 4.37/4.79 (b(elem!1, s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34133, 2545])).
% 4.37/4.79 tff(34178,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 4.37/4.79 tff(34179,plain,
% 4.37/4.79 (s(s(s(s(z)))) = s(z)),
% 4.37/4.79 inference(symmetry,[status(thm)],[34178])).
% 4.37/4.79 tff(34180,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24294, 34179])).
% 4.37/4.79 tff(34181,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34182,plain,
% 4.37/4.79 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[14770, 32441, 2545])).
% 4.37/4.79 tff(34183,plain,
% 4.37/4.79 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[302, 34182])).
% 4.37/4.79 tff(34184,plain,
% 4.37/4.79 (~r(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[341, 28771, 322, 34183])).
% 4.37/4.79 tff(34185,plain,
% 4.37/4.79 (b(s(z), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[348, 34184])).
% 4.37/4.79 tff(34186,plain,
% 4.37/4.79 (b(s(elem!1), z)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[18064, 34185, 66])).
% 4.37/4.79 tff(34187,plain,
% 4.37/4.79 (b(s(elem!1), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[25335, 34186, 66])).
% 4.37/4.79 tff(34188,plain,
% 4.37/4.79 (b(elem!1, s(elem!1))),
% 4.37/4.79 inference(modus_ponens,[status(thm)],[34177, 32556])).
% 4.37/4.79 tff(34189,plain,
% 4.37/4.79 (~b(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[2262, 25522, 123, 25846])).
% 4.37/4.79 tff(34190,plain,
% 4.37/4.79 (r(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[172, 34189])).
% 4.37/4.79 tff(34191,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28690, 3559, 322, 353])).
% 4.37/4.79 tff(34192,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28694, 34191, 8677])).
% 4.37/4.79 tff(34193,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24448, 34192, 25190])).
% 4.37/4.79 tff(34194,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24997, 34193, 547, 451])).
% 4.37/4.79 tff(34195,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24301, 34194, 24296])).
% 4.37/4.79 tff(34196,plain,
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% 4.37/4.79 inference(unit_resolution,[status(thm)],[24816, 333, 34195, 2484, 2323, 3559])).
% 4.37/4.79 tff(34197,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34198,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34197, 34190, 2323, 24296, 547, 451, 25190, 8677, 322, 2484])).
% 4.37/4.79 tff(34199,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[9761, 34198])).
% 4.37/4.79 tff(34200,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28686, 34199, 25846, 25522])).
% 4.37/4.79 tff(34201,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27512, 34200])).
% 4.37/4.79 tff(34202,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28803, 707, 2323, 34201])).
% 4.37/4.79 tff(34203,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24301, 34202, 24296])).
% 4.37/4.79 tff(34204,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24997, 34203, 547, 451])).
% 4.37/4.79 tff(34205,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24448, 34204, 25190])).
% 4.37/4.79 tff(34206,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28694, 34205, 8677])).
% 4.37/4.79 tff(34207,plain,
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% 4.37/4.79 inference(unit_resolution,[status(thm)],[28671, 333, 707, 34206, 34190, 34201])).
% 4.37/4.79 tff(34208,plain,((~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34209,plain,
% 4.37/4.79 (~r(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34208, 34187, 32437, 2323, 18054, 32443, 34188, 322, 32450, 123])).
% 4.37/4.79 tff(34210,plain,
% 4.37/4.79 (b(s(s(s(z))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[704, 34209, 22891])).
% 4.37/4.79 tff(34211,plain,
% 4.37/4.79 (b(s(z), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[22716, 34185, 32441])).
% 4.37/4.79 tff(34212,plain,
% 4.37/4.79 (~b(s(s(s(z))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[4375, 34210, 34177, 34211])).
% 4.37/4.79 tff(34213,plain,
% 4.37/4.79 (r(s(s(s(z))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[2794, 34212])).
% 4.37/4.79 tff(34214,plain,
% 4.37/4.79 (~r(elem!1, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[22410, 224, 32437, 3193])).
% 4.37/4.79 tff(34215,plain,
% 4.37/4.79 (b(elem!1, s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1538, 34214, 1524])).
% 4.37/4.79 tff(34216,plain,
% 4.37/4.79 (~b(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[10692, 144, 134, 34215, 4367])).
% 4.37/4.79 tff(34217,plain,
% 4.37/4.79 (r(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[172, 34216])).
% 4.37/4.79 tff(34218,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27642, 333, 3193, 34217, 224, 322])).
% 4.37/4.79 tff(34219,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34220,plain,
% 4.37/4.79 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34219, 34213, 322, 34211, 34210, 25347])).
% 4.37/4.79 tff(34221,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[249, 34220])).
% 4.37/4.79 tff(34222,plain,
% 4.37/4.79 (~b(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[31303, 144, 34211, 123, 34221, 34210])).
% 4.37/4.79 tff(34223,plain,
% 4.37/4.79 (r(s(z), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[172, 34222])).
% 4.37/4.79 tff(34224,plain,
% 4.37/4.79 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[10422, 34223, 322, 34213])).
% 4.37/4.79 tff(34225,plain,
% 4.37/4.79 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[1137, 34224])).
% 4.37/4.79 tff(34226,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34197, 34223, 32437, 2323, 32450, 34188, 32443, 18054, 322, 34187])).
% 4.37/4.79 tff(34227,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[9761, 34226])).
% 4.37/4.79 tff(34228,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28686, 34227, 34221, 34225])).
% 4.37/4.79 tff(34229,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[27512, 34228])).
% 4.37/4.79 tff(34230,plain,
% 4.37/4.79 ($false),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[23683, 333, 3193, 25527, 353, 27463])).
% 4.37/4.79 tff(34231,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.79 tff(34232,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(z))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34231, 34229, 34213, 34223])).
% 4.37/4.79 tff(34233,plain,
% 4.37/4.79 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[28694, 34232, 18054])).
% 4.37/4.79 tff(34234,plain,
% 4.37/4.79 (b(s(s(s(s(z)))), s(elem!1))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24448, 34233, 32443])).
% 4.37/4.79 tff(34235,plain,
% 4.37/4.79 (~b(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24997, 34234, 34188, 34187])).
% 4.37/4.79 tff(34236,plain,
% 4.37/4.79 (r(s(s(s(s(z)))), elem!1)),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[24301, 34235, 32450])).
% 4.37/4.79 tff(34237,plain,
% 4.37/4.79 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[25222, 333, 34236, 32437, 2323])).
% 4.37/4.79 tff(34238,plain,
% 4.37/4.79 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[12733, 44, 34237])).
% 4.37/4.79 tff(34239,plain,
% 4.37/4.79 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.37/4.79 inference(unit_resolution,[status(thm)],[34238, 12723])).
% 4.37/4.79 tff(34240,plain,
% 4.37/4.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.79 inference(rewrite,[status(thm)],[])).
% 4.37/4.79 tff(34241,plain,
% 4.37/4.79 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.37/4.79 inference(rewrite,[status(thm)],[])).
% 4.37/4.79 tff(34242,plain,
% 4.37/4.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34241])).
% 4.46/4.80 tff(34243,plain,
% 4.46/4.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.80 inference(transitivity,[status(thm)],[34242, 34240])).
% 4.46/4.80 tff(34244,plain,
% 4.46/4.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(quant_inst,[status(thm)],[])).
% 4.46/4.80 tff(34245,plain,
% 4.46/4.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.46/4.80 inference(modus_ponens,[status(thm)],[34244, 34243])).
% 4.46/4.80 tff(34246,plain,
% 4.46/4.80 (~b(s(z), s(s(s(s(z)))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34245, 144, 123, 34227, 34239])).
% 4.46/4.80 tff(34247,plain,
% 4.46/4.80 (~r(s(z), s(s(s(s(z)))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[33326, 333, 34213, 34223, 34229])).
% 4.46/4.80 tff(34248,plain,
% 4.46/4.80 ($false),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[19906, 44, 34247, 34246, 34181])).
% 4.46/4.80 tff(34249,plain,((~(z = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34250,plain,
% 4.46/4.80 (~(z = elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34249, 322, 34167, 50, 2545])).
% 4.46/4.80 tff(34251,plain,
% 4.46/4.80 (~r(z, elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[25313, 33714, 321, 2484])).
% 4.46/4.80 tff(34252,plain,
% 4.46/4.80 (b(z, elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[658, 34251, 74])).
% 4.46/4.80 tff(34253,plain,
% 4.46/4.80 (b(elem!1, z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1380, 32635, 1368])).
% 4.46/4.80 tff(34254,plain,
% 4.46/4.80 (~r(s(z), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[341, 51, 322, 321])).
% 4.46/4.80 tff(34255,plain,
% 4.46/4.80 (b(s(z), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[348, 34254])).
% 4.46/4.80 tff(34256,plain,
% 4.46/4.80 (~b(s(z), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1602, 34255, 251, 34253])).
% 4.46/4.80 tff(34257,plain,
% 4.46/4.80 (r(s(z), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[406, 34256, 706])).
% 4.46/4.80 tff(34258,plain,
% 4.46/4.80 (~r(z, s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[14521, 34257, 322, 321])).
% 4.46/4.80 tff(34259,plain,
% 4.46/4.80 (~b(z, s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[31791, 34257, 322, 2323, 713, 34253, 51, 321])).
% 4.46/4.80 tff(34260,plain,
% 4.46/4.80 ($false),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[372, 34259, 34258])).
% 4.46/4.80 tff(34261,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1) | (~b(z, elem!1)) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34262,plain,
% 4.46/4.80 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34261, 33714, 322, 321, 6529, 34252, 730, 2484])).
% 4.46/4.80 tff(34263,plain,
% 4.46/4.80 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[279, 34262])).
% 4.46/4.80 tff(34264,plain,
% 4.46/4.80 (~b(z, s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[813, 34263, 123, 305, 34252])).
% 4.46/4.80 tff(34265,plain,
% 4.46/4.80 (r(z, s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[372, 34264])).
% 4.46/4.80 tff(34266,plain,
% 4.46/4.80 (~r(elem!1, z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[24027, 34265, 321, 33714])).
% 4.46/4.80 tff(34267,plain,
% 4.46/4.80 (b(elem!1, z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1380, 34266, 730])).
% 4.46/4.80 tff(34268,plain,
% 4.46/4.80 (~b(s(z), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[2219, 34267, 123, 6529, 322, 34252, 34263, 34265])).
% 4.46/4.80 tff(34269,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[348, 34268])).
% 4.46/4.80 tff(34270,plain,
% 4.46/4.80 ($false),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1497, 333, 34265, 34269, 322, 321])).
% 4.46/4.80 tff(34271,plain,((z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34272,plain,
% 4.46/4.80 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34271, 34250, 32437, 50, 322, 34177])).
% 4.46/4.80 tff(34273,plain,
% 4.46/4.80 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[302, 34272])).
% 4.46/4.80 tff(34274,plain,
% 4.46/4.80 (((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, 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(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(rewrite,[status(thm)],[])).
% 4.46/4.80 tff(34275,plain,
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% 4.46/4.80 tff(34276,plain,
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% 4.46/4.80 inference(monotonicity,[status(thm)],[34275])).
% 4.46/4.80 tff(34277,plain,
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% 4.46/4.80 inference(transitivity,[status(thm)],[34276, 34274])).
% 4.46/4.80 tff(34278,plain,
% 4.46/4.80 ((~![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(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.46/4.80 inference(quant_inst,[status(thm)],[])).
% 4.46/4.80 tff(34279,plain,
% 4.46/4.80 ((~![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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.80 inference(modus_ponens,[status(thm)],[34278, 34277])).
% 4.46/4.80 tff(34280,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[34279, 333, 409, 32437, 2323, 322])).
% 4.46/4.80 tff(34281,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34282,plain,
% 4.46/4.80 (~r(s(z), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34281, 322, 34167])).
% 4.46/4.80 tff(34283,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[406, 34282, 706])).
% 4.46/4.80 tff(34284,plain,
% 4.46/4.80 (b(s(z), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[30698, 8684, 4, 606])).
% 4.46/4.80 tff(34285,plain,
% 4.46/4.80 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[2541, 8676, 322, 34167])).
% 4.46/4.80 tff(34286,plain,
% 4.46/4.80 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[279, 34285])).
% 4.46/4.80 tff(34287,plain,
% 4.46/4.80 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34271, 74, 32437, 50, 322, 34177])).
% 4.46/4.80 tff(34288,plain,
% 4.46/4.80 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[302, 34287])).
% 4.46/4.80 tff(34289,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[7741, 34288, 50, 34286])).
% 4.46/4.80 tff(34290,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[348, 34289])).
% 4.46/4.80 tff(34291,plain,
% 4.46/4.80 (~b(z, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[16228, 2254, 259, 283])).
% 4.46/4.80 tff(34292,plain,
% 4.46/4.80 (r(z, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[619, 34291])).
% 4.46/4.80 tff(34293,plain,
% 4.46/4.80 (~b(s(z), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[2262, 2254, 123, 283])).
% 4.46/4.80 tff(34294,plain,
% 4.46/4.80 (r(s(z), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[172, 34293])).
% 4.46/4.80 tff(34295,plain,
% 4.46/4.80 (~r(s(s(s(z))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[27726, 34294, 34292, 10280])).
% 4.46/4.80 tff(34296,plain,
% 4.46/4.80 (b(s(s(s(z))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[396, 34295])).
% 4.46/4.80 tff(34297,plain,
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% 4.46/4.80 inference(unit_resolution,[status(thm)],[14036, 144, 34296, 2254, 286, 259])).
% 4.46/4.80 tff(34298,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34299,plain,
% 4.46/4.80 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34298, 283, 259, 286, 123])).
% 4.46/4.80 tff(34300,plain,
% 4.46/4.80 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1137, 34299])).
% 4.46/4.80 tff(34301,plain,
% 4.46/4.80 (~r(s(s(s(z))), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[23315, 34300, 32437, 2323])).
% 4.46/4.80 tff(34302,plain,
% 4.46/4.80 (~(s(s(s(z))) = elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34175, 283, 2545])).
% 4.46/4.80 tff(34303,plain,
% 4.46/4.80 (b(s(s(s(z))), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[704, 34302, 34301])).
% 4.46/4.80 tff(34304,plain,
% 4.46/4.80 (~b(s(s(s(z))), s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[4375, 34303, 34177, 134])).
% 4.46/4.80 tff(34305,plain,
% 4.46/4.80 (r(s(s(s(z))), s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[2794, 34304])).
% 4.46/4.80 tff(34306,plain,
% 4.46/4.80 (~r(s(z), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[10422, 34305, 322, 34300])).
% 4.46/4.80 tff(34307,plain,
% 4.46/4.80 (b(s(z), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[172, 34306])).
% 4.46/4.80 tff(34308,plain,
% 4.46/4.80 (~r(elem!1, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[33228, 34300, 32437, 2323])).
% 4.46/4.80 tff(34309,plain,
% 4.46/4.80 (~(elem!1 = s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[10997, 34302])).
% 4.46/4.80 tff(34310,plain,
% 4.46/4.80 (b(elem!1, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[1538, 34309, 34308])).
% 4.46/4.80 tff(34311,plain,
% 4.46/4.80 ($false),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[10692, 144, 134, 34310, 34307, 34303])).
% 4.46/4.80 tff(34312,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.80 tff(34313,plain,
% 4.46/4.80 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34312, 34284, 322, 2545, 34167, 34286, 34288, 50])).
% 4.46/4.80 tff(34314,plain,
% 4.46/4.80 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[249, 34313])).
% 4.46/4.80 tff(34315,plain,
% 4.46/4.80 (~r(s(s(s(z))), s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[20837, 34314, 322, 34290])).
% 4.46/4.80 tff(34316,plain,
% 4.46/4.80 (b(s(s(s(z))), s(z))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[2794, 34315])).
% 4.46/4.80 tff(34317,plain,
% 4.46/4.80 (~b(s(s(s(z))), elem!1)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[4375, 34316, 34177, 34284])).
% 4.46/4.80 tff(34318,plain,
% 4.46/4.80 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[27459])).
% 4.46/4.80 tff(34319,plain,
% 4.46/4.80 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 4.46/4.80 inference(symmetry,[status(thm)],[34318])).
% 4.46/4.80 tff(34320,plain,
% 4.46/4.80 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34319])).
% 4.46/4.80 tff(34321,plain,
% 4.46/4.80 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 4.46/4.80 inference(transitivity,[status(thm)],[34320, 13328])).
% 4.46/4.80 tff(34322,plain,
% 4.46/4.80 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(symmetry,[status(thm)],[34321])).
% 4.46/4.80 tff(34323,plain,
% 4.46/4.80 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34322])).
% 4.46/4.80 tff(34324,plain,
% 4.46/4.80 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[7608, 78, 706])).
% 4.46/4.80 tff(34325,plain,
% 4.46/4.80 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(modus_ponens,[status(thm)],[34324, 34323])).
% 4.46/4.80 tff(34326,plain,
% 4.46/4.80 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34319])).
% 4.46/4.80 tff(34327,plain,
% 4.46/4.80 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 4.46/4.80 inference(transitivity,[status(thm)],[34326, 15186])).
% 4.46/4.80 tff(34328,plain,
% 4.46/4.80 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 4.46/4.80 inference(symmetry,[status(thm)],[34327])).
% 4.46/4.80 tff(34329,plain,
% 4.46/4.80 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34328])).
% 4.46/4.80 tff(34330,plain,
% 4.46/4.80 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 4.46/4.80 inference(modus_ponens,[status(thm)],[863, 34329])).
% 4.46/4.80 tff(34331,plain,
% 4.46/4.80 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34319])).
% 4.46/4.80 tff(34332,plain,
% 4.46/4.80 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 4.46/4.80 inference(symmetry,[status(thm)],[34331])).
% 4.46/4.80 tff(34333,plain,
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% 4.46/4.80 inference(monotonicity,[status(thm)],[34318])).
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% 4.46/4.80 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 4.46/4.80 inference(symmetry,[status(thm)],[34333])).
% 4.46/4.80 tff(34335,plain,
% 4.46/4.80 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34334])).
% 4.46/4.80 tff(34336,plain,
% 4.46/4.80 (~b(z, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[609, 78, 606])).
% 4.46/4.80 tff(34337,plain,
% 4.46/4.80 (r(z, s(s(s(z))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[619, 34336])).
% 4.46/4.80 tff(34338,plain,
% 4.46/4.80 (~r(s(s(s(s(s(z))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[13217, 13209, 623, 323])).
% 4.46/4.80 tff(34339,plain,
% 4.46/4.80 (b(s(s(s(s(s(z))))), z)),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 34338])).
% 4.46/4.80 tff(34340,plain,
% 4.46/4.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(rewrite,[status(thm)],[])).
% 4.46/4.80 tff(34341,plain,
% 4.46/4.80 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(rewrite,[status(thm)],[])).
% 4.46/4.80 tff(34342,plain,
% 4.46/4.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34341])).
% 4.46/4.80 tff(34343,plain,
% 4.46/4.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(transitivity,[status(thm)],[34342, 34340])).
% 4.46/4.80 tff(34344,plain,
% 4.46/4.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 4.46/4.80 inference(quant_inst,[status(thm)],[])).
% 4.46/4.80 tff(34345,plain,
% 4.46/4.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.80 inference(modus_ponens,[status(thm)],[34344, 34343])).
% 4.46/4.80 tff(34346,plain,
% 4.46/4.80 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.80 inference(unit_resolution,[status(thm)],[34345, 144, 286, 259, 34339])).
% 4.46/4.80 tff(34347,plain,
% 4.46/4.80 (((~![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(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(rewrite,[status(thm)],[])).
% 4.46/4.80 tff(34348,plain,
% 4.46/4.80 (((~r(s(z), z)) | (~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.80 inference(rewrite,[status(thm)],[])).
% 4.46/4.80 tff(34349,plain,
% 4.46/4.80 (((~![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(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(s(s(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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.46/4.80 inference(monotonicity,[status(thm)],[34348])).
% 4.46/4.80 tff(34350,plain,
% 4.46/4.80 (((~![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(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(s(s(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(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.81 inference(transitivity,[status(thm)],[34349, 34347])).
% 4.46/4.81 tff(34351,plain,
% 4.46/4.81 ((~![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(s(s(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(s(s(s(z))))))))))),
% 4.46/4.81 inference(quant_inst,[status(thm)],[])).
% 4.46/4.81 tff(34352,plain,
% 4.46/4.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34351, 34350])).
% 4.46/4.81 tff(34353,plain,
% 4.46/4.81 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34352, 333, 323, 13209, 322])).
% 4.46/4.81 tff(34354,plain,
% 4.46/4.81 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[1159, 44, 34353])).
% 4.46/4.81 tff(34355,plain,
% 4.46/4.81 ($false),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34354, 34346, 19614])).
% 4.46/4.81 tff(34356,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.81 tff(34357,plain,
% 4.46/4.81 (~r(s(s(s(s(s(z))))), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34356, 34324, 259, 286, 27448, 10280, 322, 34337])).
% 4.46/4.81 tff(34358,plain,
% 4.46/4.81 (~r(s(s(elem!1)), s(z))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34357, 34335])).
% 4.46/4.81 tff(34359,plain,
% 4.46/4.81 (b(s(s(elem!1)), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[4983, 34358])).
% 4.46/4.81 tff(34360,plain,
% 4.46/4.81 (b(s(s(s(s(s(z))))), s(z))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34359, 34332])).
% 4.46/4.81 tff(34361,plain,
% 4.46/4.81 (b(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[32405, 27448, 134])).
% 4.46/4.81 tff(34362,plain,
% 4.46/4.81 (~r(s(s(s(z))), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[20837, 224, 322, 10280])).
% 4.46/4.81 tff(34363,plain,
% 4.46/4.81 (b(s(s(s(z))), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[2794, 34362])).
% 4.46/4.81 tff(34364,plain,
% 4.46/4.81 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[1109, 144, 34363, 34361, 34360])).
% 4.46/4.81 tff(34365,plain,
% 4.46/4.81 ((s(s(s(s(s(z))))) = s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[19732, 44, 34364])).
% 4.46/4.81 tff(34366,plain,
% 4.46/4.81 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34365, 34330])).
% 4.46/4.81 tff(34367,plain,
% 4.46/4.81 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[2323, 27449])).
% 4.46/4.81 tff(34368,plain,
% 4.46/4.81 (((~![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))))), z)) | (~r(z, 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(s(s(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(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34369,plain,
% 4.46/4.81 (((~r(s(s(s(z))), s(s(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(z, 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(s(s(z))))))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34370,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(z, 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(s(s(z)))))))))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34369])).
% 4.46/4.81 tff(34371,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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(z, 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(s(s(z))))))))))),
% 4.46/4.81 inference(transitivity,[status(thm)],[34370, 34368])).
% 4.46/4.81 tff(34372,plain,
% 4.46/4.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(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)))),
% 4.46/4.81 inference(quant_inst,[status(thm)],[])).
% 4.46/4.81 tff(34373,plain,
% 4.46/4.81 ((~![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))))), z)) | (~r(z, 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(s(s(z)))))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34372, 34371])).
% 4.46/4.81 tff(34374,plain,
% 4.46/4.81 (~r(s(s(s(s(s(z))))), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34373, 333, 34337, 34367, 34366])).
% 4.46/4.81 tff(34375,plain,
% 4.46/4.81 (b(s(s(s(s(s(z))))), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[13047, 44, 1444, 34374])).
% 4.46/4.81 tff(34376,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34377,plain,
% 4.46/4.81 (((~b(s(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(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34378,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34377])).
% 4.46/4.81 tff(34379,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.81 inference(transitivity,[status(thm)],[34378, 34376])).
% 4.46/4.81 tff(34380,plain,
% 4.46/4.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 4.46/4.81 inference(quant_inst,[status(thm)],[])).
% 4.46/4.81 tff(34381,plain,
% 4.46/4.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34380, 34379])).
% 4.46/4.81 tff(34382,plain,
% 4.46/4.81 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34381, 144, 123, 286, 34360, 34375])).
% 4.46/4.81 tff(34383,plain,
% 4.46/4.81 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[1146, 333, 224, 34367, 34366])).
% 4.46/4.81 tff(34384,plain,
% 4.46/4.81 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[1159, 44, 34383])).
% 4.46/4.81 tff(34385,plain,
% 4.46/4.81 ($false),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34384, 34382, 34325])).
% 4.46/4.81 tff(34386,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.81 tff(34387,plain,
% 4.46/4.81 (~(s(s(s(z))) = elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34386, 34288, 50, 34314, 34286, 322, 34167, 34284, 606, 706])).
% 4.46/4.81 tff(34388,plain,
% 4.46/4.81 (r(s(s(s(z))), elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[704, 34387, 34317])).
% 4.46/4.81 tff(34389,plain,
% 4.46/4.81 (~r(z, s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[30116, 34388, 8676, 34167])).
% 4.46/4.81 tff(34390,plain,
% 4.46/4.81 (b(z, s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[619, 34389])).
% 4.46/4.81 tff(34391,plain,
% 4.46/4.81 (~r(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[22780, 34388, 322, 34314])).
% 4.46/4.81 tff(34392,plain,
% 4.46/4.81 (b(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[172, 34391])).
% 4.46/4.81 tff(34393,plain,
% 4.46/4.81 (r(s(z), elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[29205, 34392, 34177, 34314, 34316, 34387, 34167])).
% 4.46/4.81 tff(34394,plain,
% 4.46/4.81 (~(elem!1 = s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[10997, 34387])).
% 4.46/4.81 tff(34395,plain,
% 4.46/4.81 (~b(elem!1, s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[22776, 34392, 34177, 34316])).
% 4.46/4.81 tff(34396,plain,
% 4.46/4.81 (r(elem!1, s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[1538, 34395, 34394])).
% 4.46/4.81 tff(34397,plain,
% 4.46/4.81 ($false),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[21939, 34396, 34393, 8676, 34388, 34390])).
% 4.46/4.81 tff(34398,plain,((z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, elem!1) | (s(z) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.81 tff(34399,plain,
% 4.46/4.81 (b(z, elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34398, 34250, 322, 706, 2545, 4])).
% 4.46/4.81 tff(34400,plain,
% 4.46/4.81 (~b(s(z), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[32015, 144, 34399, 34283, 50, 34273])).
% 4.46/4.81 tff(34401,plain,
% 4.46/4.81 (r(s(z), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[348, 34400])).
% 4.46/4.81 tff(34402,plain,
% 4.46/4.81 (~b(z, s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[7079, 34283, 34177, 34399])).
% 4.46/4.81 tff(34403,plain,
% 4.46/4.81 (r(z, s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[372, 34402])).
% 4.46/4.81 tff(34404,plain,
% 4.46/4.81 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[12139, 333, 34403, 34401, 322])).
% 4.46/4.81 tff(34405,plain,
% 4.46/4.81 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[279, 34404])).
% 4.46/4.81 tff(34406,plain,
% 4.46/4.81 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34312, 34405, 322, 2545, 34167, 34283, 34273, 50])).
% 4.46/4.81 tff(34407,plain,
% 4.46/4.81 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[249, 34406])).
% 4.46/4.81 tff(34408,plain,
% 4.46/4.81 (~r(s(s(s(z))), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[20837, 34407, 322, 34401])).
% 4.46/4.81 tff(34409,plain,
% 4.46/4.81 (b(s(s(s(z))), s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[2794, 34408])).
% 4.46/4.81 tff(34410,plain,
% 4.46/4.81 (~b(s(s(s(z))), elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[4375, 34409, 34177, 34283])).
% 4.46/4.81 tff(34411,plain,
% 4.46/4.81 (~r(s(z), elem!1)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34281, 322, 2323])).
% 4.46/4.81 tff(34412,plain,
% 4.46/4.81 (~b(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[29205, 698, 305, 34411, 224, 56, 2323])).
% 4.46/4.81 tff(34413,plain,
% 4.46/4.81 (r(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[172, 34412])).
% 4.46/4.81 tff(34414,plain,
% 4.46/4.81 ($false),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[22780, 34413, 12399, 322, 224])).
% 4.46/4.81 tff(34415,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.81 tff(34416,plain,
% 4.46/4.81 (s(s(s(z))) = elem!1),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34415, 322, 34407, 34410, 34177, 34409, 34167])).
% 4.46/4.81 tff(34417,plain,
% 4.46/4.81 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[12214, 34416])).
% 4.46/4.81 tff(34418,plain,
% 4.46/4.81 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[20734, 34417])).
% 4.46/4.81 tff(34419,plain,
% 4.46/4.81 (~(s(elem!1) = s(z))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[8683, 34250])).
% 4.46/4.81 tff(34420,plain,
% 4.46/4.81 (elem!1 = s(s(s(z)))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[27447, 34416])).
% 4.46/4.81 tff(34421,plain,
% 4.46/4.81 (s(elem!1) = s(s(s(s(z))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34420])).
% 4.46/4.81 tff(34422,plain,
% 4.46/4.81 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34421])).
% 4.46/4.81 tff(34423,plain,
% 4.46/4.81 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 4.46/4.81 inference(symmetry,[status(thm)],[34422])).
% 4.46/4.81 tff(34424,plain,
% 4.46/4.81 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34423])).
% 4.46/4.81 tff(34425,plain,
% 4.46/4.81 (b(s(z), s(s(s(z))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[32405, 34420, 34283])).
% 4.46/4.81 tff(34426,plain,
% 4.46/4.81 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34420])).
% 4.46/4.81 tff(34427,plain,
% 4.46/4.81 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34167, 34426])).
% 4.46/4.81 tff(34428,plain,
% 4.46/4.81 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34429,plain,
% 4.46/4.81 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34430,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34429])).
% 4.46/4.81 tff(34431,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.81 inference(transitivity,[status(thm)],[34430, 34428])).
% 4.46/4.81 tff(34432,plain,
% 4.46/4.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.81 inference(quant_inst,[status(thm)],[])).
% 4.46/4.81 tff(34433,plain,
% 4.46/4.81 ((~![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(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34432, 34431])).
% 4.46/4.81 tff(34434,plain,
% 4.46/4.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[34433, 333, 224, 6107, 27463])).
% 4.46/4.81 tff(34435,plain,
% 4.46/4.81 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34434, 27551])).
% 4.46/4.81 tff(34436,plain,
% 4.46/4.81 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[542, 34435, 537])).
% 4.46/4.81 tff(34437,plain,
% 4.46/4.81 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34436, 33833])).
% 4.46/4.81 tff(34438,plain,
% 4.46/4.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[21343, 333, 224, 6107, 27463])).
% 4.46/4.81 tff(34439,plain,
% 4.46/4.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[9761, 34438])).
% 4.46/4.81 tff(34440,plain,
% 4.46/4.81 (~b(s(elem!1), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[27477, 34439, 3238, 286, 259])).
% 4.46/4.81 tff(34441,plain,
% 4.46/4.81 (r(s(elem!1), z)),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[507, 34440])).
% 4.46/4.81 tff(34442,plain,
% 4.46/4.81 (r(s(s(s(s(z)))), z)),
% 4.46/4.81 inference(modus_ponens,[status(thm)],[34441, 19808])).
% 4.46/4.81 tff(34443,plain,
% 4.46/4.81 (~r(s(z), s(s(s(s(z)))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[33819, 333, 354, 323, 34442])).
% 4.46/4.81 tff(34444,plain,
% 4.46/4.81 (b(s(z), s(s(s(s(z)))))),
% 4.46/4.81 inference(unit_resolution,[status(thm)],[19906, 44, 34443, 34181])).
% 4.46/4.81 tff(34445,plain,
% 4.46/4.81 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.81 inference(rewrite,[status(thm)],[])).
% 4.46/4.81 tff(34446,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 4.46/4.81 inference(monotonicity,[status(thm)],[34445])).
% 4.46/4.81 tff(34447,plain,
% 4.46/4.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.46/4.82 inference(transitivity,[status(thm)],[34446, 34240])).
% 4.46/4.82 tff(34448,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 4.46/4.82 inference(quant_inst,[status(thm)],[])).
% 4.46/4.82 tff(34449,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[34448, 34447])).
% 4.46/4.82 tff(34450,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34449, 144, 34444, 123, 34439, 34437])).
% 4.46/4.82 tff(34451,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34452,plain,
% 4.46/4.82 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34451, 34420, 50, 34418, 34403, 34401, 34273, 34405, 34407, 34427])).
% 4.46/4.82 tff(34453,plain,
% 4.46/4.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[27512, 34452])).
% 4.46/4.82 tff(34454,plain,
% 4.46/4.82 (~b(s(s(s(s(z)))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[27536, 34453, 34409, 34425])).
% 4.46/4.82 tff(34455,plain,
% 4.46/4.82 (~b(s(elem!1), s(z))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[34454, 34424])).
% 4.46/4.82 tff(34456,plain,
% 4.46/4.82 (r(s(elem!1), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[486, 34455, 34419])).
% 4.46/4.82 tff(34457,plain,
% 4.46/4.82 (~b(s(elem!1), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1670, 34456, 322, 34401, 34403, 34418])).
% 4.46/4.82 tff(34458,plain,
% 4.46/4.82 (~r(s(elem!1), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1365, 34456, 34401, 34403])).
% 4.46/4.82 tff(34459,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[507, 34458, 34457])).
% 4.46/4.82 tff(34460,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34461,plain,
% 4.46/4.82 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34460, 2545, 706, 4])).
% 4.46/4.82 tff(34462,plain,
% 4.46/4.82 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[319, 34461])).
% 4.46/4.82 tff(34463,plain,
% 4.46/4.82 (~r(z, elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[25313, 321, 32437, 2323])).
% 4.46/4.82 tff(34464,plain,
% 4.46/4.82 (~r(elem!1, z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[12025, 51, 32437, 321])).
% 4.46/4.82 tff(34465,plain,
% 4.46/4.82 (~(elem!1 = z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[22716, 489, 350])).
% 4.46/4.82 tff(34466,plain,
% 4.46/4.82 (b(elem!1, z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[653, 34465, 1378])).
% 4.46/4.82 tff(34467,plain,
% 4.46/4.82 (~(z = elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18287, 34465])).
% 4.46/4.82 tff(34468,plain,
% 4.46/4.82 (b(z, elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[658, 34467, 34463])).
% 4.46/4.82 tff(34469,plain,
% 4.46/4.82 (b(z, s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[32808, 34468, 123, 321, 698, 350, 304, 489, 34466, 2323])).
% 4.46/4.82 tff(34470,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[387, 144, 34466, 34469, 489, 305])).
% 4.46/4.82 tff(34471,plain,((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = elem!1) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34472,plain,
% 4.46/4.82 (~b(s(z), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34471, 350, 123, 321, 698, 305, 304, 2323, 34464])).
% 4.46/4.82 tff(34473,plain,
% 4.46/4.82 (r(s(z), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[348, 34472])).
% 4.46/4.82 tff(34474,plain,
% 4.46/4.82 (~r(s(s(s(z))), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[13781, 34473, 123, 51, 304])).
% 4.46/4.82 tff(34475,plain,
% 4.46/4.82 (b(s(s(s(z))), z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[396, 34474])).
% 4.46/4.82 tff(34476,plain,
% 4.46/4.82 (b(elem!1, z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[653, 730, 1378])).
% 4.46/4.82 tff(34477,plain,
% 4.46/4.82 (~b(s(s(s(z))), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[10565, 24015, 285, 34476])).
% 4.46/4.82 tff(34478,plain,
% 4.46/4.82 (~b(z, s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[31850, 34477, 305, 285, 698, 2323, 304, 409, 34476])).
% 4.46/4.82 tff(34479,plain,
% 4.46/4.82 (r(z, s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[372, 34478])).
% 4.46/4.82 tff(34480,plain,
% 4.46/4.82 (r(s(s(s(z))), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[704, 34477, 698])).
% 4.46/4.82 tff(34481,plain,
% 4.46/4.82 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[23315, 34480, 32437, 2323])).
% 4.46/4.82 tff(34482,plain,
% 4.46/4.82 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1137, 34481])).
% 4.46/4.82 tff(34483,plain,
% 4.46/4.82 (~b(s(z), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[2262, 34482, 123, 283])).
% 4.46/4.82 tff(34484,plain,
% 4.46/4.82 (r(s(z), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[172, 34483])).
% 4.46/4.82 tff(34485,plain,
% 4.46/4.82 (~r(z, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1519, 34484, 34480, 34479])).
% 4.46/4.82 tff(34486,plain,
% 4.46/4.82 (b(z, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[619, 34485])).
% 4.46/4.82 tff(34487,plain,
% 4.46/4.82 (~b(s(s(s(z))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33963, 34482, 123, 304])).
% 4.46/4.82 tff(34488,plain,
% 4.46/4.82 (r(s(s(s(z))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[2794, 34487])).
% 4.46/4.82 tff(34489,plain,
% 4.46/4.82 (~r(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[11876, 34488, 409, 34484])).
% 4.46/4.82 tff(34490,plain,
% 4.46/4.82 (b(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1538, 34489, 12398])).
% 4.46/4.82 tff(34491,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[8728, 144, 34476, 34490, 285, 34486])).
% 4.46/4.82 tff(34492,plain,((z = elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34493,plain,
% 4.46/4.82 (z = elem!1),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34492, 34475, 2169, 123, 304, 17795, 2323, 305, 698, 34464, 34463])).
% 4.46/4.82 tff(34494,plain,
% 4.46/4.82 (s(elem!1) = s(z)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[70, 34493])).
% 4.46/4.82 tff(34495,plain,
% 4.46/4.82 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34494])).
% 4.46/4.82 tff(34496,plain,
% 4.46/4.82 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.82 inference(symmetry,[status(thm)],[34495])).
% 4.46/4.82 tff(34497,plain,
% 4.46/4.82 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34496])).
% 4.46/4.82 tff(34498,plain,
% 4.46/4.82 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[107, 34497])).
% 4.46/4.82 tff(34499,plain,
% 4.46/4.82 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34493])).
% 4.46/4.82 tff(34500,plain,
% 4.46/4.82 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.46/4.82 inference(transitivity,[status(thm)],[34499, 1218])).
% 4.46/4.82 tff(34501,plain,
% 4.46/4.82 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34500])).
% 4.46/4.82 tff(34502,plain,
% 4.46/4.82 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[1094, 34501])).
% 4.46/4.82 tff(34503,plain,
% 4.46/4.82 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34493])).
% 4.46/4.82 tff(34504,plain,
% 4.46/4.82 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34503])).
% 4.46/4.82 tff(34505,plain,
% 4.46/4.82 (~(s(s(z)) = elem!1)),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[164, 34504])).
% 4.46/4.82 tff(34506,plain,
% 4.46/4.82 (b(s(s(s(z))), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[26887, 34493, 34475])).
% 4.46/4.82 tff(34507,plain,
% 4.46/4.82 (~b(s(s(s(z))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33963, 23185, 123, 304])).
% 4.46/4.82 tff(34508,plain,
% 4.46/4.82 (r(s(s(s(z))), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[2794, 34507])).
% 4.46/4.82 tff(34509,plain,
% 4.46/4.82 (~r(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[11876, 34508, 409, 353])).
% 4.46/4.82 tff(34510,plain,
% 4.46/4.82 (b(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1538, 34509, 1524])).
% 4.46/4.82 tff(34511,plain,
% 4.46/4.82 (~r(s(z), s(s(z)))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[23647, 333, 3193, 353, 6330])).
% 4.46/4.82 tff(34512,plain,
% 4.46/4.82 (~r(s(z), s(s(elem!1)))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[22807, 34511, 8677])).
% 4.46/4.82 tff(34513,plain,
% 4.46/4.82 (b(s(z), s(s(elem!1)))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[5484, 34512])).
% 4.46/4.82 tff(34514,plain,
% 4.46/4.82 (~r(s(s(z)), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[29992, 333, 3193, 353, 6330])).
% 4.46/4.82 tff(34515,plain,
% 4.46/4.82 (~r(s(s(elem!1)), s(elem!1))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[22871, 34514, 8677])).
% 4.46/4.82 tff(34516,plain,
% 4.46/4.82 (b(s(s(elem!1)), s(elem!1))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1283, 34515, 22759])).
% 4.46/4.82 tff(34517,plain,
% 4.46/4.82 (~b(elem!1, s(s(elem!1)))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[5494, 34516, 305, 28638, 34513])).
% 4.46/4.82 tff(34518,plain,
% 4.46/4.82 (r(elem!1, s(s(elem!1)))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[2522, 34517, 1221])).
% 4.46/4.82 tff(34519,plain,
% 4.46/4.82 (r(elem!1, s(s(z)))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[34518, 28271])).
% 4.46/4.82 tff(34520,plain,
% 4.46/4.82 (b(s(s(z)), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18895, 34516, 8677])).
% 4.46/4.82 tff(34521,plain,
% 4.46/4.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1425, 34520, 123, 304])).
% 4.46/4.82 tff(34522,plain,
% 4.46/4.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1451, 34521])).
% 4.46/4.82 tff(34523,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33242, 333, 34522, 32437, 2323, 34519])).
% 4.46/4.82 tff(34524,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34525,plain,
% 4.46/4.82 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34524, 34508, 8677, 1221, 123, 304, 305, 2323, 353])).
% 4.46/4.82 tff(34526,plain,
% 4.46/4.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18132, 34525, 8677])).
% 4.46/4.82 tff(34527,plain,
% 4.46/4.82 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[4311, 34526, 22826])).
% 4.46/4.82 tff(34528,plain,
% 4.46/4.82 (b(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18122, 34527, 8677])).
% 4.46/4.82 tff(34529,plain,
% 4.46/4.82 (~b(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33620, 34528, 4367, 34510])).
% 4.46/4.82 tff(34530,plain,
% 4.46/4.82 (r(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[7970, 34529, 1506])).
% 4.46/4.82 tff(34531,plain,
% 4.46/4.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[7952, 34528, 7926, 7927])).
% 4.46/4.82 tff(34532,plain,
% 4.46/4.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1451, 34531])).
% 4.46/4.82 tff(34533,plain,
% 4.46/4.82 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.82 inference(rewrite,[status(thm)],[])).
% 4.46/4.82 tff(34534,plain,
% 4.46/4.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34533])).
% 4.46/4.82 tff(34535,plain,
% 4.46/4.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.46/4.82 inference(transitivity,[status(thm)],[34534, 25387])).
% 4.46/4.82 tff(34536,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 4.46/4.82 inference(quant_inst,[status(thm)],[])).
% 4.46/4.82 tff(34537,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[34536, 34535])).
% 4.46/4.82 tff(34538,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34537, 333, 34532, 32437, 2323, 34530])).
% 4.46/4.82 tff(34539,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~(s(elem!1) = s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34540,plain,
% 4.46/4.82 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34539, 353, 1506, 4367, 7926, 8677, 1221, 123, 304, 305, 2323, 1524, 409])).
% 4.46/4.82 tff(34541,plain,
% 4.46/4.82 (~r(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33228, 34540, 32437, 2323])).
% 4.46/4.82 tff(34542,plain,
% 4.46/4.82 (b(elem!1, s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1538, 34541, 1524])).
% 4.46/4.82 tff(34543,plain,
% 4.46/4.82 (~r(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34537, 333, 2671, 32437, 2323])).
% 4.46/4.82 tff(34544,plain,
% 4.46/4.82 (b(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[7970, 34543, 1506])).
% 4.46/4.82 tff(34545,plain,
% 4.46/4.82 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33620, 34544, 4367, 2082])).
% 4.46/4.82 tff(34546,plain,
% 4.46/4.82 (((~![X0: $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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.46/4.82 inference(rewrite,[status(thm)],[])).
% 4.46/4.82 tff(34547,plain,
% 4.46/4.82 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.46/4.82 inference(rewrite,[status(thm)],[])).
% 4.46/4.82 tff(34548,plain,
% 4.46/4.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 4.46/4.82 inference(monotonicity,[status(thm)],[34547])).
% 4.46/4.82 tff(34549,plain,
% 4.46/4.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.46/4.82 inference(transitivity,[status(thm)],[34548, 34546])).
% 4.46/4.82 tff(34550,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.46/4.82 inference(quant_inst,[status(thm)],[])).
% 4.46/4.82 tff(34551,plain,
% 4.46/4.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.46/4.82 inference(modus_ponens,[status(thm)],[34550, 34549])).
% 4.46/4.82 tff(34552,plain,
% 4.46/4.82 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34551, 333, 2671, 32437, 6107])).
% 4.46/4.82 tff(34553,plain,
% 4.46/4.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18132, 34552, 8677])).
% 4.46/4.82 tff(34554,plain,
% 4.46/4.82 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[4311, 34553, 22826])).
% 4.46/4.82 tff(34555,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18122, 34554, 34545, 8677])).
% 4.46/4.82 tff(34556,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.82 tff(34557,plain,
% 4.46/4.82 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[34556, 34542, 4367, 8677, 1506, 34540, 2323])).
% 4.46/4.82 tff(34558,plain,
% 4.46/4.82 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1451, 34557])).
% 4.46/4.82 tff(34559,plain,
% 4.46/4.82 (~r(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[31517, 34558, 123, 305, 8677, 409, 28638, 2323])).
% 4.46/4.82 tff(34560,plain,
% 4.46/4.82 (b(s(s(z)), elem!1)),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[7970, 34559, 1506])).
% 4.46/4.82 tff(34561,plain,
% 4.46/4.82 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[33620, 34560, 4367, 34542])).
% 4.46/4.82 tff(34562,plain,
% 4.46/4.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18122, 34561, 8677])).
% 4.46/4.82 tff(34563,plain,
% 4.46/4.82 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[4311, 34562, 22826])).
% 4.46/4.82 tff(34564,plain,
% 4.46/4.82 (~b(s(s(z)), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1425, 34558, 123, 304])).
% 4.46/4.82 tff(34565,plain,
% 4.46/4.82 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18895, 34564, 8677])).
% 4.46/4.82 tff(34566,plain,
% 4.46/4.82 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[1283, 34565, 22759])).
% 4.46/4.82 tff(34567,plain,
% 4.46/4.82 (r(s(s(z)), s(z))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[22871, 34566, 8677])).
% 4.46/4.82 tff(34568,plain,
% 4.46/4.82 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[29853, 34567, 353, 34540])).
% 4.46/4.82 tff(34569,plain,
% 4.46/4.82 ($false),
% 4.46/4.82 inference(unit_resolution,[status(thm)],[18132, 34568, 34563, 8677])).
% 4.46/4.82 tff(34570,plain,((~r(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.83 tff(34571,plain,
% 4.46/4.83 (~r(s(z), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34570, 34494, 34506, 34505, 123, 304, 305, 2169, 2323, 12398, 7926, 34502])).
% 4.46/4.83 tff(34572,plain,
% 4.46/4.83 (b(s(z), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[172, 34571])).
% 4.46/4.83 tff(34573,plain,
% 4.46/4.83 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[2262, 34572, 123, 17795])).
% 4.46/4.83 tff(34574,plain,
% 4.46/4.83 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1137, 34573])).
% 4.46/4.83 tff(34575,plain,
% 4.46/4.83 (~r(elem!1, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[33228, 34574, 32437, 2323])).
% 4.46/4.83 tff(34576,plain,
% 4.46/4.83 (b(elem!1, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1538, 34575, 12398])).
% 4.46/4.83 tff(34577,plain,
% 4.46/4.83 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34556, 34576, 34506, 34494, 34505, 34574, 2323])).
% 4.46/4.83 tff(34578,plain,
% 4.46/4.83 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1451, 34577])).
% 4.46/4.83 tff(34579,plain,
% 4.46/4.83 (~b(s(s(z)), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1425, 34578, 123, 304])).
% 4.46/4.83 tff(34580,plain,
% 4.46/4.83 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[18895, 34579, 34494])).
% 4.46/4.83 tff(34581,plain,
% 4.46/4.83 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1283, 34580, 34498])).
% 4.46/4.83 tff(34582,plain,
% 4.46/4.83 (r(s(s(z)), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[22871, 34581, 34494])).
% 4.46/4.83 tff(34583,plain,
% 4.46/4.83 (s(s(elem!1)) = s(s(z))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34494])).
% 4.46/4.83 tff(34584,plain,
% 4.46/4.83 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34583])).
% 4.46/4.83 tff(34585,plain,
% 4.46/4.83 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34583, 34584])).
% 4.46/4.83 tff(34586,plain,
% 4.46/4.83 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34585])).
% 4.46/4.83 tff(34587,plain,
% 4.46/4.83 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34586])).
% 4.46/4.83 tff(34588,plain,
% 4.46/4.83 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[217, 34587])).
% 4.46/4.83 tff(34589,plain,
% 4.46/4.83 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34494])).
% 4.46/4.83 tff(34590,plain,
% 4.46/4.83 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34589])).
% 4.46/4.83 tff(34591,plain,
% 4.46/4.83 (b(elem!1, s(elem!1))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[305, 34590])).
% 4.46/4.83 tff(34592,plain,
% 4.46/4.83 (~r(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[31517, 34578, 123, 305, 34494, 2169, 34591, 2323])).
% 4.46/4.83 tff(34593,plain,
% 4.46/4.83 (b(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7970, 34592, 34505])).
% 4.46/4.83 tff(34594,plain,
% 4.46/4.83 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[33620, 34593, 34506, 34576])).
% 4.46/4.83 tff(34595,plain,
% 4.46/4.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[18122, 34594, 34494])).
% 4.46/4.83 tff(34596,plain,
% 4.46/4.83 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[4311, 34595, 34588])).
% 4.46/4.83 tff(34597,plain,
% 4.46/4.83 (r(s(s(z)), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[18132, 34596, 34494])).
% 4.46/4.83 tff(34598,plain,
% 4.46/4.83 (~b(s(s(s(z))), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[846, 34572, 304, 17795])).
% 4.46/4.83 tff(34599,plain,
% 4.46/4.83 (r(s(s(s(z))), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[2794, 34598])).
% 4.46/4.83 tff(34600,plain,
% 4.46/4.83 ($false),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[33532, 333, 2169, 34599, 34597, 34582])).
% 4.46/4.83 tff(34601,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.83 tff(34602,plain,
% 4.46/4.83 (b(s(z), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34601, 51, 304, 305, 2323, 7926, 698, 123, 321, 706])).
% 4.46/4.83 tff(34603,plain,
% 4.46/4.83 (~b(z, s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7079, 24015, 305, 134])).
% 4.46/4.83 tff(34604,plain,
% 4.46/4.83 (r(z, s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[372, 34603])).
% 4.46/4.83 tff(34605,plain,
% 4.46/4.83 (~b(s(z), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[2262, 23185, 123, 17795])).
% 4.46/4.83 tff(34606,plain,
% 4.46/4.83 (r(s(z), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[172, 34605])).
% 4.46/4.83 tff(34607,plain,
% 4.46/4.83 (~b(s(z), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1602, 24015, 134, 34476])).
% 4.46/4.83 tff(34608,plain,
% 4.46/4.83 (r(s(z), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[348, 34607])).
% 4.46/4.83 tff(34609,plain,
% 4.46/4.83 (~r(s(s(s(z))), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[13781, 34608, 123, 51, 304])).
% 4.46/4.83 tff(34610,plain,
% 4.46/4.83 (b(s(s(s(z))), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[396, 34609])).
% 4.46/4.83 tff(34611,plain,
% 4.46/4.83 (~b(s(s(s(z))), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[10565, 34610, 24015, 34476])).
% 4.46/4.83 tff(34612,plain,
% 4.46/4.83 (r(s(s(s(z))), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[704, 34611, 698])).
% 4.46/4.83 tff(34613,plain,
% 4.46/4.83 (~r(z, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1519, 34612, 34606, 34604])).
% 4.46/4.83 tff(34614,plain,
% 4.46/4.83 (b(z, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[619, 34613])).
% 4.46/4.83 tff(34615,plain,
% 4.46/4.83 (~b(elem!1, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[8728, 144, 34476, 34610, 34614])).
% 4.46/4.83 tff(34616,plain,
% 4.46/4.83 (r(elem!1, s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1538, 34615, 12398])).
% 4.46/4.83 tff(34617,plain,
% 4.46/4.83 (~r(s(s(s(s(z)))), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[32601, 34616, 32437, 23185, 17795, 34508])).
% 4.46/4.83 tff(34618,plain,
% 4.46/4.83 (r(s(s(z)), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1473, 44, 23042, 217])).
% 4.46/4.83 tff(34619,plain,
% 4.46/4.83 ($false),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[9276, 333, 323, 34508, 34618, 1430])).
% 4.46/4.83 tff(34620,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.83 tff(34621,plain,
% 4.46/4.83 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34620, 34608, 7926, 7927, 123, 304])).
% 4.46/4.83 tff(34622,plain,
% 4.46/4.83 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1451, 34621])).
% 4.46/4.83 tff(34623,plain,
% 4.46/4.83 (~r(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34537, 333, 34622, 32437, 2323])).
% 4.46/4.83 tff(34624,plain,
% 4.46/4.83 (((~![X0: $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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(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)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 4.46/4.83 inference(rewrite,[status(thm)],[])).
% 4.46/4.83 tff(34625,plain,
% 4.46/4.83 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 4.46/4.83 inference(rewrite,[status(thm)],[])).
% 4.46/4.83 tff(34626,plain,
% 4.46/4.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, 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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34625])).
% 4.46/4.83 tff(34627,plain,
% 4.46/4.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, 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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34626, 34624])).
% 4.46/4.83 tff(34628,plain,
% 4.46/4.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 4.46/4.83 inference(quant_inst,[status(thm)],[])).
% 4.46/4.83 tff(34629,plain,
% 4.46/4.83 ((~![X0: $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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[34628, 34627])).
% 4.46/4.83 tff(34630,plain,
% 4.46/4.83 (~r(s(s(z)), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34629, 333, 34622, 32437, 51])).
% 4.46/4.83 tff(34631,plain,
% 4.46/4.83 (b(s(s(z)), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1462, 44, 164, 34630])).
% 4.46/4.83 tff(34632,plain,
% 4.46/4.83 (~b(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7961, 144, 24015, 34476, 34631])).
% 4.46/4.83 tff(34633,plain,
% 4.46/4.83 (s(s(z)) = elem!1),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7970, 34632, 34623])).
% 4.46/4.83 tff(34634,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34633])).
% 4.46/4.83 tff(34635,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34634, 203])).
% 4.46/4.83 tff(34636,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(transitivity,[status(thm)],[34635, 24285])).
% 4.46/4.83 tff(34637,plain,
% 4.46/4.83 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34636])).
% 4.46/4.83 tff(34638,plain,
% 4.46/4.83 (~(s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[24445, 34637])).
% 4.46/4.83 tff(34639,plain,
% 4.46/4.83 (b(s(s(s(s(z)))), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[24301, 34638, 34617])).
% 4.46/4.83 tff(34640,plain,
% 4.46/4.83 (~b(s(s(s(s(z)))), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[12662, 144, 24015, 34476, 34639])).
% 4.46/4.83 tff(34641,plain,
% 4.46/4.83 (r(s(s(s(s(z)))), z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[4243, 44, 242, 34640])).
% 4.46/4.83 tff(34642,plain,
% 4.46/4.83 (~b(s(s(s(s(z)))), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[24594, 144, 134, 305, 34639])).
% 4.46/4.83 tff(34643,plain,
% 4.46/4.83 (r(s(s(s(s(z)))), s(z))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[27538, 34642])).
% 4.46/4.83 tff(34644,plain,
% 4.46/4.83 (((~![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(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(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.46/4.83 inference(rewrite,[status(thm)],[])).
% 4.46/4.83 tff(34645,plain,
% 4.46/4.83 (((~r(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), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.46/4.83 inference(rewrite,[status(thm)],[])).
% 4.46/4.83 tff(34646,plain,
% 4.46/4.83 (((~![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(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)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34645])).
% 4.46/4.83 tff(34647,plain,
% 4.46/4.83 (((~![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(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)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34646, 34644])).
% 4.46/4.83 tff(34648,plain,
% 4.46/4.83 ((~![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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 4.46/4.83 inference(quant_inst,[status(thm)],[])).
% 4.46/4.83 tff(34649,plain,
% 4.46/4.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[34648, 34647])).
% 4.46/4.83 tff(34650,plain,
% 4.46/4.83 ($false),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34649, 333, 34604, 34608, 34643, 34641])).
% 4.46/4.83 tff(34651,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(s(s(z))) = elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.83 tff(34652,plain,
% 4.46/4.83 (z = elem!1),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34651, 7927, 305, 51, 2323, 7926, 134, 123, 304, 698, 1378, 1575])).
% 4.46/4.83 tff(34653,plain,
% 4.46/4.83 (s(elem!1) = s(z)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[70, 34652])).
% 4.46/4.83 tff(34654,plain,
% 4.46/4.83 (s(s(elem!1)) = s(s(z))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34653])).
% 4.46/4.83 tff(34655,plain,
% 4.46/4.83 (s(s(z)) = s(s(elem!1))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34654])).
% 4.46/4.83 tff(34656,plain,
% 4.46/4.83 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34655])).
% 4.46/4.83 tff(34657,plain,
% 4.46/4.83 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34656])).
% 4.46/4.83 tff(34658,plain,
% 4.46/4.83 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34657])).
% 4.46/4.83 tff(34659,plain,
% 4.46/4.83 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.83 tff(34660,plain,
% 4.46/4.83 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.46/4.83 inference(symmetry,[status(thm)],[34659])).
% 4.46/4.83 tff(34661,plain,
% 4.46/4.83 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.83 tff(34662,plain,
% 4.46/4.83 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34661])).
% 4.46/4.83 tff(34663,plain,
% 4.46/4.83 (~(s(s(z)) = elem!1)),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[164, 34662])).
% 4.46/4.83 tff(34664,plain,
% 4.46/4.83 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.83 tff(34665,plain,
% 4.46/4.83 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654, 34664])).
% 4.46/4.83 tff(34666,plain,
% 4.46/4.83 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34665])).
% 4.46/4.83 tff(34667,plain,
% 4.46/4.83 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34666])).
% 4.46/4.83 tff(34668,plain,
% 4.46/4.83 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[217, 34667])).
% 4.46/4.83 tff(34669,plain,
% 4.46/4.83 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.83 tff(34670,plain,
% 4.46/4.83 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34669, 1218])).
% 4.46/4.83 tff(34671,plain,
% 4.46/4.83 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34670])).
% 4.46/4.83 tff(34672,plain,
% 4.46/4.83 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[1094, 34671])).
% 4.46/4.83 tff(34673,plain,
% 4.46/4.83 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34524, 34672, 34606, 34653, 123, 304, 305, 2323, 34508])).
% 4.46/4.83 tff(34674,plain,
% 4.46/4.83 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[18132, 34673, 34653])).
% 4.46/4.83 tff(34675,plain,
% 4.46/4.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[4311, 34674, 34668])).
% 4.46/4.83 tff(34676,plain,
% 4.46/4.83 (b(s(s(z)), s(s(s(z))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[18122, 34675, 34653])).
% 4.46/4.83 tff(34677,plain,
% 4.46/4.83 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7952, 34676, 7926, 7927])).
% 4.46/4.83 tff(34678,plain,
% 4.46/4.83 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[1451, 34677])).
% 4.46/4.83 tff(34679,plain,
% 4.46/4.83 (~r(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[34537, 333, 34678, 32437, 2323])).
% 4.46/4.83 tff(34680,plain,
% 4.46/4.83 (b(s(s(z)), elem!1)),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[7970, 34679, 34663])).
% 4.46/4.83 tff(34681,plain,
% 4.46/4.83 (b(s(s(elem!1)), elem!1)),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[34680, 34660])).
% 4.46/4.83 tff(34682,plain,
% 4.46/4.83 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.83 tff(34683,plain,
% 4.46/4.83 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34682])).
% 4.46/4.83 tff(34684,plain,
% 4.46/4.83 ((~r(elem!1, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34683])).
% 4.46/4.83 tff(34685,plain,
% 4.46/4.83 (~r(elem!1, s(s(z)))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[33242, 333, 34678, 32437, 2323])).
% 4.46/4.83 tff(34686,plain,
% 4.46/4.83 (~r(elem!1, s(s(elem!1)))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[34685, 34684])).
% 4.46/4.83 tff(34687,plain,
% 4.46/4.83 (b(elem!1, s(s(elem!1)))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[2522, 34686, 34672])).
% 4.46/4.83 tff(34688,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.83 tff(34689,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34688, 203])).
% 4.46/4.83 tff(34690,plain,
% 4.46/4.83 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(transitivity,[status(thm)],[34689, 24285])).
% 4.46/4.83 tff(34691,plain,
% 4.46/4.83 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34690])).
% 4.46/4.83 tff(34692,plain,
% 4.46/4.83 (~(s(s(s(s(z)))) = elem!1)),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[242, 34691])).
% 4.46/4.83 tff(34693,plain,
% 4.46/4.83 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 4.46/4.83 inference(transitivity,[status(thm)],[34661, 17961])).
% 4.46/4.83 tff(34694,plain,
% 4.46/4.83 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34693])).
% 4.46/4.83 tff(34695,plain,
% 4.46/4.83 (~(elem!1 = s(s(z)))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[164, 34694])).
% 4.46/4.83 tff(34696,plain,
% 4.46/4.83 (b(elem!1, s(s(z)))),
% 4.46/4.83 inference(unit_resolution,[status(thm)],[29812, 34685, 34695])).
% 4.46/4.83 tff(34697,plain,
% 4.46/4.83 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.83 tff(34698,plain,
% 4.46/4.83 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.83 tff(34699,plain,
% 4.46/4.83 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34698])).
% 4.46/4.83 tff(34700,plain,
% 4.46/4.83 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34699])).
% 4.46/4.83 tff(34701,plain,
% 4.46/4.83 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34653])).
% 4.46/4.83 tff(34702,plain,
% 4.46/4.83 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.83 inference(symmetry,[status(thm)],[34701])).
% 4.46/4.83 tff(34703,plain,
% 4.46/4.83 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.83 inference(monotonicity,[status(thm)],[34702])).
% 4.46/4.83 tff(34704,plain,
% 4.46/4.83 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.83 inference(modus_ponens,[status(thm)],[107, 34703])).
% 4.46/4.83 tff(34705,plain,
% 4.46/4.83 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.84 tff(34706,plain,
% 4.46/4.84 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34705])).
% 4.46/4.84 tff(34707,plain,
% 4.46/4.84 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34653])).
% 4.46/4.84 tff(34708,plain,
% 4.46/4.84 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34707])).
% 4.46/4.84 tff(34709,plain,
% 4.46/4.84 (b(elem!1, s(z)) <=> b(z, s(elem!1))),
% 4.46/4.84 inference(transitivity,[status(thm)],[34708, 34706])).
% 4.46/4.84 tff(34710,plain,
% 4.46/4.84 (b(z, s(elem!1))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[305, 34709])).
% 4.46/4.84 tff(34711,plain,
% 4.46/4.84 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.84 tff(34712,plain,
% 4.46/4.84 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 4.46/4.84 inference(symmetry,[status(thm)],[34711])).
% 4.46/4.84 tff(34713,plain,
% 4.46/4.84 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34653])).
% 4.46/4.84 tff(34714,plain,
% 4.46/4.84 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 4.46/4.84 inference(symmetry,[status(thm)],[34713])).
% 4.46/4.84 tff(34715,plain,
% 4.46/4.84 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 4.46/4.84 inference(transitivity,[status(thm)],[34714, 34712])).
% 4.46/4.84 tff(34716,plain,
% 4.46/4.84 (b(s(elem!1), z)),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[134, 34715])).
% 4.46/4.84 tff(34717,plain,
% 4.46/4.84 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34652])).
% 4.46/4.84 tff(34718,plain,
% 4.46/4.84 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.46/4.84 inference(symmetry,[status(thm)],[34717])).
% 4.46/4.84 tff(34719,plain,
% 4.46/4.84 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34654])).
% 4.46/4.84 tff(34720,plain,
% 4.46/4.84 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.46/4.84 inference(symmetry,[status(thm)],[34719])).
% 4.46/4.84 tff(34721,plain,
% 4.46/4.84 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.46/4.84 inference(transitivity,[status(thm)],[34720, 34718])).
% 4.46/4.84 tff(34722,plain,
% 4.46/4.84 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34721])).
% 4.46/4.84 tff(34723,plain,
% 4.46/4.84 (~r(s(s(elem!1)), z)),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34679, 34722])).
% 4.46/4.84 tff(34724,plain,
% 4.46/4.84 (b(s(s(elem!1)), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[5509, 34723])).
% 4.46/4.84 tff(34725,plain,
% 4.46/4.84 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[5572, 34724, 34716, 34710])).
% 4.46/4.84 tff(34726,plain,
% 4.46/4.84 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1283, 34725, 34704])).
% 4.46/4.84 tff(34727,plain,
% 4.46/4.84 (r(s(s(z)), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[22871, 34726, 34653])).
% 4.46/4.84 tff(34728,plain,
% 4.46/4.84 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 4.46/4.84 inference(rewrite,[status(thm)],[])).
% 4.46/4.84 tff(34729,plain,
% 4.46/4.84 (((~r(s(z), 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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 4.46/4.84 inference(rewrite,[status(thm)],[])).
% 4.46/4.84 tff(34730,plain,
% 4.46/4.84 (((~![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(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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34729])).
% 4.46/4.84 tff(34731,plain,
% 4.46/4.84 (((~![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(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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 4.46/4.84 inference(transitivity,[status(thm)],[34730, 34728])).
% 4.46/4.84 tff(34732,plain,
% 4.46/4.84 ((~![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(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.46/4.84 inference(quant_inst,[status(thm)],[])).
% 4.46/4.84 tff(34733,plain,
% 4.46/4.84 ((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34732, 34731])).
% 4.46/4.84 tff(34734,plain,
% 4.46/4.84 (~r(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34733, 333, 34508, 34606, 34727])).
% 4.46/4.84 tff(34735,plain,
% 4.46/4.84 (~r(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34734, 34700])).
% 4.46/4.84 tff(34736,plain,
% 4.46/4.84 (b(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1301, 34735, 1184])).
% 4.46/4.84 tff(34737,plain,
% 4.46/4.84 (b(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34736, 34697])).
% 4.46/4.84 tff(34738,plain,
% 4.46/4.84 (~b(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[26836, 144, 34676, 34737, 34696])).
% 4.46/4.84 tff(34739,plain,
% 4.46/4.84 (r(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1538, 34738, 12398])).
% 4.46/4.84 tff(34740,plain,
% 4.46/4.84 (~r(s(s(s(s(z)))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[32601, 34739, 32437, 23185, 17795, 34508])).
% 4.46/4.84 tff(34741,plain,
% 4.46/4.84 (b(s(s(s(s(z)))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[24301, 34740, 34692])).
% 4.46/4.84 tff(34742,plain,
% 4.46/4.84 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[10534, 34741, 34687, 34681])).
% 4.46/4.84 tff(34743,plain,
% 4.46/4.84 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34742, 34658])).
% 4.46/4.84 tff(34744,plain,
% 4.46/4.84 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[25349, 34652])).
% 4.46/4.84 tff(34745,plain,
% 4.46/4.84 (b(s(elem!1), elem!1)),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[134, 34714])).
% 4.46/4.84 tff(34746,plain,
% 4.46/4.84 (b(elem!1, s(elem!1))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[305, 34708])).
% 4.46/4.84 tff(34747,plain,
% 4.46/4.84 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[24997, 34741, 34746, 34745])).
% 4.46/4.84 tff(34748,plain,
% 4.46/4.84 (r(s(s(s(s(z)))), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[24448, 34747, 34744])).
% 4.46/4.84 tff(34749,plain,
% 4.46/4.84 (r(s(s(s(s(z)))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[28694, 34748, 34653])).
% 4.46/4.84 tff(34750,plain,
% 4.46/4.84 (((~![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(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)))))),
% 4.46/4.84 inference(rewrite,[status(thm)],[])).
% 4.46/4.84 tff(34751,plain,
% 4.46/4.84 (((~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)))))),
% 4.46/4.84 inference(rewrite,[status(thm)],[])).
% 4.46/4.84 tff(34752,plain,
% 4.46/4.84 (((~![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(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))))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34751])).
% 4.46/4.84 tff(34753,plain,
% 4.46/4.84 (((~![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(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)))))),
% 4.46/4.84 inference(transitivity,[status(thm)],[34752, 34750])).
% 4.46/4.84 tff(34754,plain,
% 4.46/4.84 ((~![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(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.46/4.84 inference(quant_inst,[status(thm)],[])).
% 4.46/4.84 tff(34755,plain,
% 4.46/4.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34754, 34753])).
% 4.46/4.84 tff(34756,plain,
% 4.46/4.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34755, 333, 34749, 34606, 34727])).
% 4.46/4.84 tff(34757,plain,
% 4.46/4.84 (b(s(s(s(s(z)))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[21386, 44, 24445, 34756])).
% 4.46/4.84 tff(34758,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34757, 34743])).
% 4.46/4.84 tff(34759,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34760,plain,
% 4.46/4.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34759, 34602, 2323, 7926, 123, 304, 305, 863, 51, 698, 34464, 34463])).
% 4.46/4.84 tff(34761,plain,
% 4.46/4.84 (~r(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33228, 34760, 32437, 2323])).
% 4.46/4.84 tff(34762,plain,
% 4.46/4.84 (~r(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[23315, 34760, 32437, 2323])).
% 4.46/4.84 tff(34763,plain,
% 4.46/4.84 (~r(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33988, 34760, 32437, 51])).
% 4.46/4.84 tff(34764,plain,
% 4.46/4.84 (b(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[619, 34763])).
% 4.46/4.84 tff(34765,plain,
% 4.46/4.84 (~b(z, elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[21799, 34764, 698, 34762, 34761])).
% 4.46/4.84 tff(34766,plain,
% 4.46/4.84 (z = elem!1),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[658, 34765, 34463])).
% 4.46/4.84 tff(34767,plain,
% 4.46/4.84 (s(elem!1) = s(z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[70, 34766])).
% 4.46/4.84 tff(34768,plain,
% 4.46/4.84 (s(s(elem!1)) = s(s(z))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34767])).
% 4.46/4.84 tff(34769,plain,
% 4.46/4.84 (s(s(z)) = s(s(elem!1))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34768])).
% 4.46/4.84 tff(34770,plain,
% 4.46/4.84 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34769])).
% 4.46/4.84 tff(34771,plain,
% 4.46/4.84 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 4.46/4.84 inference(transitivity,[status(thm)],[34770, 13328])).
% 4.46/4.84 tff(34772,plain,
% 4.46/4.84 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34771])).
% 4.46/4.84 tff(34773,plain,
% 4.46/4.84 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[1446, 34772])).
% 4.46/4.84 tff(34774,plain,
% 4.46/4.84 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34768])).
% 4.46/4.84 tff(34775,plain,
% 4.46/4.84 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34774])).
% 4.46/4.84 tff(34776,plain,
% 4.46/4.84 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34775])).
% 4.46/4.84 tff(34777,plain,
% 4.46/4.84 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34768])).
% 4.46/4.84 tff(34778,plain,
% 4.46/4.84 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34768])).
% 4.46/4.84 tff(34779,plain,
% 4.46/4.84 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34778])).
% 4.46/4.84 tff(34780,plain,
% 4.46/4.84 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34779])).
% 4.46/4.84 tff(34781,plain,
% 4.46/4.84 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34767])).
% 4.46/4.84 tff(34782,plain,
% 4.46/4.84 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34781])).
% 4.46/4.84 tff(34783,plain,
% 4.46/4.84 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34782])).
% 4.46/4.84 tff(34784,plain,
% 4.46/4.84 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[107, 34783])).
% 4.46/4.84 tff(34785,plain,
% 4.46/4.84 (b(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1538, 34761, 12398])).
% 4.46/4.84 tff(34786,plain,
% 4.46/4.84 (b(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[704, 34762, 698])).
% 4.46/4.84 tff(34787,plain,
% 4.46/4.84 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34766])).
% 4.46/4.84 tff(34788,plain,
% 4.46/4.84 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34787])).
% 4.46/4.84 tff(34789,plain,
% 4.46/4.84 (~(s(s(z)) = elem!1)),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[164, 34788])).
% 4.46/4.84 tff(34790,plain,
% 4.46/4.84 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34556, 34789, 34786, 34785, 34767, 34760, 2323])).
% 4.46/4.84 tff(34791,plain,
% 4.46/4.84 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1451, 34790])).
% 4.46/4.84 tff(34792,plain,
% 4.46/4.84 (~b(s(s(z)), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1425, 34791, 123, 304])).
% 4.46/4.84 tff(34793,plain,
% 4.46/4.84 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[18895, 34792, 34767])).
% 4.46/4.84 tff(34794,plain,
% 4.46/4.84 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1283, 34793, 34784])).
% 4.46/4.84 tff(34795,plain,
% 4.46/4.84 (r(s(s(z)), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[22871, 34794, 34767])).
% 4.46/4.84 tff(34796,plain,
% 4.46/4.84 (~b(s(z), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[10692, 144, 34602, 34785, 34786])).
% 4.46/4.84 tff(34797,plain,
% 4.46/4.84 (r(s(z), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[172, 34796])).
% 4.46/4.84 tff(34798,plain,
% 4.46/4.84 (~b(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[4375, 34786, 305, 34602])).
% 4.46/4.84 tff(34799,plain,
% 4.46/4.84 (r(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[2794, 34798])).
% 4.46/4.84 tff(34800,plain,
% 4.46/4.84 (~r(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34733, 333, 34799, 34797, 34795])).
% 4.46/4.84 tff(34801,plain,
% 4.46/4.84 (~r(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34800, 34780])).
% 4.46/4.84 tff(34802,plain,
% 4.46/4.84 (b(s(s(s(z))), s(s(elem!1)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1301, 34801, 863])).
% 4.46/4.84 tff(34803,plain,
% 4.46/4.84 (b(s(s(s(z))), s(s(z)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34802, 34777])).
% 4.46/4.84 tff(34804,plain,
% 4.46/4.84 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34768])).
% 4.46/4.84 tff(34805,plain,
% 4.46/4.84 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34768, 34804])).
% 4.46/4.84 tff(34806,plain,
% 4.46/4.84 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.84 inference(symmetry,[status(thm)],[34805])).
% 4.46/4.84 tff(34807,plain,
% 4.46/4.84 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34806])).
% 4.46/4.84 tff(34808,plain,
% 4.46/4.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[217, 34807])).
% 4.46/4.84 tff(34809,plain,
% 4.46/4.84 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34766])).
% 4.46/4.84 tff(34810,plain,
% 4.46/4.84 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.46/4.84 inference(transitivity,[status(thm)],[34809, 1218])).
% 4.46/4.84 tff(34811,plain,
% 4.46/4.84 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34810])).
% 4.46/4.84 tff(34812,plain,
% 4.46/4.84 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[1094, 34811])).
% 4.46/4.84 tff(34813,plain,
% 4.46/4.84 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34524, 34797, 34812, 34767, 123, 304, 305, 2323, 34799])).
% 4.46/4.84 tff(34814,plain,
% 4.46/4.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[18132, 34813, 34767])).
% 4.46/4.84 tff(34815,plain,
% 4.46/4.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[4311, 34814, 34808])).
% 4.46/4.84 tff(34816,plain,
% 4.46/4.84 (b(s(s(z)), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[18122, 34815, 34767])).
% 4.46/4.84 tff(34817,plain,
% 4.46/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[9592, 144, 34816, 17795, 34803])).
% 4.46/4.84 tff(34818,plain,
% 4.46/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34817, 34776])).
% 4.46/4.84 tff(34819,plain,
% 4.46/4.84 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34769])).
% 4.46/4.84 tff(34820,plain,
% 4.46/4.84 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.46/4.84 inference(monotonicity,[status(thm)],[34819])).
% 4.46/4.84 tff(34821,plain,
% 4.46/4.84 (~b(s(s(z)), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33620, 34816, 34786, 34785])).
% 4.46/4.84 tff(34822,plain,
% 4.46/4.84 (r(s(s(z)), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[7970, 34821, 34789])).
% 4.46/4.84 tff(34823,plain,
% 4.46/4.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[25420, 333, 32437, 2323, 34822])).
% 4.46/4.84 tff(34824,plain,
% 4.46/4.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.46/4.84 inference(modus_ponens,[status(thm)],[34823, 34820])).
% 4.46/4.84 tff(34825,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[2758, 34824, 34818, 34773])).
% 4.46/4.84 tff(34826,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34827,plain,
% 4.46/4.84 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34826, 321, 123, 304, 305, 698, 7926, 2323, 706])).
% 4.46/4.84 tff(34828,plain,
% 4.46/4.84 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[279, 34827])).
% 4.46/4.84 tff(34829,plain,
% 4.46/4.84 (~b(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33963, 2254, 123, 304])).
% 4.46/4.84 tff(34830,plain,
% 4.46/4.84 (r(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[2794, 34829])).
% 4.46/4.84 tff(34831,plain,
% 4.46/4.84 (~b(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[16228, 2254, 283, 259])).
% 4.46/4.84 tff(34832,plain,
% 4.46/4.84 (r(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[619, 34831])).
% 4.46/4.84 tff(34833,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[3031, 333, 34089, 34832, 34830, 34294])).
% 4.46/4.84 tff(34834,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34835,plain,
% 4.46/4.84 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34834, 34828, 17795, 123, 304])).
% 4.46/4.84 tff(34836,plain,
% 4.46/4.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1137, 34835])).
% 4.46/4.84 tff(34837,plain,
% 4.46/4.84 (~b(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[757, 34828, 123, 304])).
% 4.46/4.84 tff(34838,plain,
% 4.46/4.84 (r(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[372, 34837])).
% 4.46/4.84 tff(34839,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[9362, 28818])).
% 4.46/4.84 tff(34840,plain,((~(z = elem!1)) | b(z, s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34841,plain,
% 4.46/4.84 (~(z = elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34840, 34837, 305])).
% 4.46/4.84 tff(34842,plain,
% 4.46/4.84 (b(z, elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[658, 34841, 34463])).
% 4.46/4.84 tff(34843,plain,
% 4.46/4.84 (~r(elem!1, z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[24027, 34838, 321, 2323])).
% 4.46/4.84 tff(34844,plain,
% 4.46/4.84 (~(elem!1 = z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[76, 34841])).
% 4.46/4.84 tff(34845,plain,
% 4.46/4.84 (b(elem!1, z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[653, 34844, 34843])).
% 4.46/4.84 tff(34846,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[31651, 34845, 34842, 321, 698, 34838, 34836, 2323])).
% 4.46/4.84 tff(34847,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34848,plain,
% 4.46/4.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34847, 34176, 34167, 34177, 50, 34462, 7926, 706])).
% 4.46/4.84 tff(34849,plain,
% 4.46/4.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[302, 34848])).
% 4.46/4.84 tff(34850,plain,
% 4.46/4.84 (~(elem!1 = z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[14770, 34849, 2545])).
% 4.46/4.84 tff(34851,plain,
% 4.46/4.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34847, 698, 2323, 305, 123, 304, 7926, 706])).
% 4.46/4.84 tff(34852,plain,
% 4.46/4.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[302, 34851])).
% 4.46/4.84 tff(34853,plain,
% 4.46/4.84 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34298, 23185, 17795, 34852, 123])).
% 4.46/4.84 tff(34854,plain,
% 4.46/4.84 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[279, 34853])).
% 4.46/4.84 tff(34855,plain,
% 4.46/4.84 (~r(elem!1, z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34105, 333, 2484, 33699, 51])).
% 4.46/4.84 tff(34856,plain,
% 4.46/4.84 (b(elem!1, z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1380, 34855, 1368])).
% 4.46/4.84 tff(34857,plain,
% 4.46/4.84 (~r(z, elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[24187, 333, 2484, 33699, 51])).
% 4.46/4.84 tff(34858,plain,
% 4.46/4.84 (b(z, elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[658, 34857, 25631])).
% 4.46/4.84 tff(34859,plain,
% 4.46/4.84 (~b(s(s(s(z))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[10565, 34858, 4367, 34856])).
% 4.46/4.84 tff(34860,plain,
% 4.46/4.84 (r(s(s(s(z))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[396, 34859])).
% 4.46/4.84 tff(34861,plain,
% 4.46/4.84 (~r(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[13781, 34860, 123, 51, 304])).
% 4.46/4.84 tff(34862,plain,
% 4.46/4.84 (b(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[348, 34861])).
% 4.46/4.84 tff(34863,plain,
% 4.46/4.84 (~r(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[26130, 34860, 3193, 353])).
% 4.46/4.84 tff(34864,plain,
% 4.46/4.84 (b(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[372, 34863])).
% 4.46/4.84 tff(34865,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[7093, 34864, 34862, 286, 304])).
% 4.46/4.84 tff(34866,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34867,plain,
% 4.46/4.84 (~b(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34866, 34508, 123, 304, 34852, 34606, 34854, 1368, 32437])).
% 4.46/4.84 tff(34868,plain,
% 4.46/4.84 (r(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[704, 34867, 698])).
% 4.46/4.84 tff(34869,plain,
% 4.46/4.84 (~r(z, elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[30434, 34868, 304, 2323, 17795, 34852, 34508])).
% 4.46/4.84 tff(34870,plain,
% 4.46/4.84 (~r(elem!1, z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34105, 333, 32437, 2323, 34854])).
% 4.46/4.84 tff(34871,plain,
% 4.46/4.84 (~b(s(z), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34651, 34870, 305, 25631, 2323, 7926, 7927, 123, 304, 698, 34854, 34869])).
% 4.46/4.84 tff(34872,plain,
% 4.46/4.84 (r(s(z), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[406, 34871, 706])).
% 4.46/4.84 tff(34873,plain,
% 4.46/4.84 (~b(s(s(s(z))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34492, 34872, 25631, 123, 304, 17795, 2323, 305, 698, 34870, 34869])).
% 4.46/4.84 tff(34874,plain,
% 4.46/4.84 (r(s(s(s(z))), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[396, 34873])).
% 4.46/4.84 tff(34875,plain,
% 4.46/4.84 (~r(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33896, 34874, 123, 304, 34508])).
% 4.46/4.84 tff(34876,plain,
% 4.46/4.84 (b(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[348, 34875])).
% 4.46/4.84 tff(34877,plain,
% 4.46/4.84 (~r(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[26130, 34874, 34508, 34606])).
% 4.46/4.84 tff(34878,plain,
% 4.46/4.84 (b(z, s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[372, 34877])).
% 4.46/4.84 tff(34879,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[7093, 34878, 34876, 304, 34852])).
% 4.46/4.84 tff(34880,plain,(r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (s(z) = elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34881,plain,
% 4.46/4.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34880, 34176, 50, 34167, 34177, 34462, 706, 7926, 34850])).
% 4.46/4.84 tff(34882,plain,
% 4.46/4.84 (~r(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[23315, 34881, 32437, 34167])).
% 4.46/4.84 tff(34883,plain,
% 4.46/4.84 (b(s(s(s(z))), elem!1)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[704, 34882, 34176])).
% 4.46/4.84 tff(34884,plain,
% 4.46/4.84 (~(elem!1 = s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[10997, 34176])).
% 4.46/4.84 tff(34885,plain,
% 4.46/4.84 (~r(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33228, 34881, 32437, 34167])).
% 4.46/4.84 tff(34886,plain,
% 4.46/4.84 (b(elem!1, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[1538, 34885, 34884])).
% 4.46/4.84 tff(34887,plain,
% 4.46/4.84 (~b(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[21533, 56, 283, 286, 304])).
% 4.46/4.84 tff(34888,plain,
% 4.46/4.84 (r(z, s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[619, 34887])).
% 4.46/4.84 tff(34889,plain,
% 4.46/4.84 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[33988, 34888, 32437, 6107])).
% 4.46/4.84 tff(34890,plain,
% 4.46/4.84 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[279, 34889])).
% 4.46/4.84 tff(34891,plain,
% 4.46/4.84 (~b(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[7741, 34890, 123, 286])).
% 4.46/4.84 tff(34892,plain,
% 4.46/4.84 (~b(s(z), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[846, 56, 304, 283])).
% 4.46/4.84 tff(34893,plain,
% 4.46/4.84 (r(s(z), s(s(s(z))))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[172, 34892])).
% 4.46/4.84 tff(34894,plain,
% 4.46/4.84 (~r(s(z), z)),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[27739, 34890, 304, 34888, 56, 34893])).
% 4.46/4.84 tff(34895,plain,
% 4.46/4.84 ($false),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[348, 34894, 34891])).
% 4.46/4.84 tff(34896,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.84 tff(34897,plain,
% 4.46/4.84 (~b(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[34896, 34849, 50, 34462, 34881, 17795])).
% 4.46/4.84 tff(34898,plain,
% 4.46/4.84 (r(s(s(s(z))), s(z))),
% 4.46/4.84 inference(unit_resolution,[status(thm)],[2794, 34897])).
% 4.46/4.85 tff(34899,plain,
% 4.46/4.85 (~r(elem!1, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[33228, 6107, 32437, 34167])).
% 4.46/4.85 tff(34900,plain,
% 4.46/4.85 (~r(s(s(s(z))), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[23315, 6107, 32437, 34167])).
% 4.46/4.85 tff(34901,plain,
% 4.46/4.85 (b(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[30698, 350, 4, 25636])).
% 4.46/4.85 tff(34902,plain,
% 4.46/4.85 (~b(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[21799, 34901, 698, 34900, 34899])).
% 4.46/4.85 tff(34903,plain,
% 4.46/4.85 (r(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[619, 34902])).
% 4.46/4.85 tff(34904,plain,
% 4.46/4.85 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[33988, 34903, 32437, 6107])).
% 4.46/4.85 tff(34905,plain,
% 4.46/4.85 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[279, 34904])).
% 4.46/4.85 tff(34906,plain,
% 4.46/4.85 (~b(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7741, 34905, 50, 286])).
% 4.46/4.85 tff(34907,plain,
% 4.46/4.85 (r(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[348, 34906])).
% 4.46/4.85 tff(34908,plain,
% 4.46/4.85 (b(s(s(s(z))), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[704, 34900, 698])).
% 4.46/4.85 tff(34909,plain,
% 4.46/4.85 (~b(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[757, 34905, 50, 304])).
% 4.46/4.85 tff(34910,plain,
% 4.46/4.85 (r(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[372, 34909])).
% 4.46/4.85 tff(34911,plain,
% 4.46/4.85 (~r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1376, 2169, 354, 323])).
% 4.46/4.85 tff(34912,plain,
% 4.46/4.85 (~b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[10565, 34901, 4367, 285])).
% 4.46/4.85 tff(34913,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[653, 34912, 34911, 1368])).
% 4.46/4.85 tff(34914,plain,(b(s(z), elem!1) | (elem!1 = z) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34915,plain,
% 4.46/4.85 (~b(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34914, 34910, 34908, 1368, 350, 34907, 4, 706])).
% 4.46/4.85 tff(34916,plain,
% 4.46/4.85 (~r(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[33896, 34907, 50, 304, 3193])).
% 4.46/4.85 tff(34917,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[396, 34916, 34915])).
% 4.46/4.85 tff(34918,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (elem!1 = z) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34919,plain,
% 4.46/4.85 (b(s(z), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34918, 34898, 34462, 34850, 4, 706, 34849, 34881, 34176])).
% 4.46/4.85 tff(34920,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[10692, 144, 134, 2082, 838, 4367])).
% 4.46/4.85 tff(34921,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34922,plain,
% 4.46/4.85 (~b(s(z), s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34921, 34919, 34886, 34883])).
% 4.46/4.85 tff(34923,plain,
% 4.46/4.85 (r(s(z), s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[172, 34922])).
% 4.46/4.85 tff(34924,plain,
% 4.46/4.85 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34866, 34923, 50, 34462, 34849, 34883, 34898, 34850, 32437])).
% 4.46/4.85 tff(34925,plain,
% 4.46/4.85 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[279, 34924])).
% 4.46/4.85 tff(34926,plain,
% 4.46/4.85 (~b(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[757, 34925, 50, 34462])).
% 4.46/4.85 tff(34927,plain,
% 4.46/4.85 (r(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[372, 34926])).
% 4.46/4.85 tff(34928,plain,
% 4.46/4.85 (~r(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[26130, 34927, 34898, 34923])).
% 4.46/4.85 tff(34929,plain,
% 4.46/4.85 (b(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[396, 34928])).
% 4.46/4.85 tff(34930,plain,
% 4.46/4.85 (~b(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[294, 34929, 17795, 34849])).
% 4.46/4.85 tff(34931,plain,
% 4.46/4.85 (r(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[619, 34930])).
% 4.46/4.85 tff(34932,plain,
% 4.46/4.85 (~b(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7741, 34925, 50, 34849])).
% 4.46/4.85 tff(34933,plain,
% 4.46/4.85 (r(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[348, 34932])).
% 4.46/4.85 tff(34934,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[11278, 333, 34933, 34931, 34898, 34923])).
% 4.46/4.85 tff(34935,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34936,plain,
% 4.46/4.85 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34935, 2545, 706, 4])).
% 4.46/4.85 tff(34937,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[18738, 333, 707, 32437, 2323, 224])).
% 4.46/4.85 tff(34938,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34939,plain,
% 4.46/4.85 (~r(s(s(s(z))), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34938, 34936, 34167])).
% 4.46/4.85 tff(34940,plain,
% 4.46/4.85 (s(s(s(z))) = elem!1),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[704, 55, 34939])).
% 4.46/4.85 tff(34941,plain,
% 4.46/4.85 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[12214, 34940])).
% 4.46/4.85 tff(34942,plain,
% 4.46/4.85 (~(s(s(elem!1)) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7595, 34940, 863])).
% 4.46/4.85 tff(34943,plain,
% 4.46/4.85 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[5603, 34942])).
% 4.46/4.85 tff(34944,plain,
% 4.46/4.85 (~(s(elem!1) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[5813, 34943])).
% 4.46/4.85 tff(34945,plain,
% 4.46/4.85 (~r(s(s(s(z))), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34938, 224, 34167])).
% 4.46/4.85 tff(34946,plain,
% 4.46/4.85 (s(s(s(z))) = elem!1),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[704, 55, 34945])).
% 4.46/4.85 tff(34947,plain,
% 4.46/4.85 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34946])).
% 4.46/4.85 tff(34948,plain,
% 4.46/4.85 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 4.46/4.85 inference(transitivity,[status(thm)],[34947, 18283])).
% 4.46/4.85 tff(34949,plain,
% 4.46/4.85 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.46/4.85 inference(transitivity,[status(thm)],[34948, 18284])).
% 4.46/4.85 tff(34950,plain,
% 4.46/4.85 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34949])).
% 4.46/4.85 tff(34951,plain,
% 4.46/4.85 (~(elem!1 = z)),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[392, 34950])).
% 4.46/4.85 tff(34952,plain,
% 4.46/4.85 (~(s(s(elem!1)) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7595, 34946, 863])).
% 4.46/4.85 tff(34953,plain,
% 4.46/4.85 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[5603, 34952])).
% 4.46/4.85 tff(34954,plain,
% 4.46/4.85 (~(s(elem!1) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[5813, 34953])).
% 4.46/4.85 tff(34955,plain,
% 4.46/4.85 (s(s(s(s(z)))) = s(elem!1)),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34946])).
% 4.46/4.85 tff(34956,plain,
% 4.46/4.85 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34955])).
% 4.46/4.85 tff(34957,plain,
% 4.46/4.85 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34956])).
% 4.46/4.85 tff(34958,plain,
% 4.46/4.85 (~(s(elem!1) = s(z))),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[24294, 34957])).
% 4.46/4.85 tff(34959,plain,
% 4.46/4.85 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[12214, 34946])).
% 4.46/4.85 tff(34960,plain,
% 4.46/4.85 (b(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[30698, 350, 4, 34958])).
% 4.46/4.85 tff(34961,plain,
% 4.46/4.85 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7741, 259, 123, 489])).
% 4.46/4.85 tff(34962,plain,
% 4.46/4.85 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[302, 34961])).
% 4.46/4.85 tff(34963,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[14366, 259, 32437, 123, 55, 1368, 350])).
% 4.46/4.85 tff(34964,plain,
% 4.46/4.85 (~r(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[31748, 34089, 123, 1722, 1, 489, 350, 2323, 706, 259, 432])).
% 4.46/4.85 tff(34965,plain,
% 4.46/4.85 (b(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[448, 34964, 433])).
% 4.46/4.85 tff(34966,plain,
% 4.46/4.85 (~b(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[916, 34965, 251, 34963])).
% 4.46/4.85 tff(34967,plain,
% 4.46/4.85 (r(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[507, 34966])).
% 4.46/4.85 tff(34968,plain,
% 4.46/4.85 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[14540, 34967, 34962, 34089])).
% 4.46/4.85 tff(34969,plain,
% 4.46/4.85 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[472, 34968, 432])).
% 4.46/4.85 tff(34970,plain,
% 4.46/4.85 (~r(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[25313, 34962, 32437, 2323])).
% 4.46/4.85 tff(34971,plain,
% 4.46/4.85 (b(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1653, 34967, 1, 1722, 34089, 706, 34970])).
% 4.46/4.85 tff(34972,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[869, 144, 34971, 123, 304, 34969])).
% 4.46/4.85 tff(34973,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34974,plain,
% 4.46/4.85 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34973, 34960, 304, 34959, 34958, 706, 50, 34954, 34167, 489, 350, 55, 34951])).
% 4.46/4.85 tff(34975,plain,
% 4.46/4.85 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[279, 34974])).
% 4.46/4.85 tff(34976,plain,
% 4.46/4.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[33963, 56, 50, 304])).
% 4.46/4.85 tff(34977,plain,
% 4.46/4.85 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1137, 34976])).
% 4.46/4.85 tff(34978,plain,
% 4.46/4.85 (~r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34105, 333, 32437, 34167, 34975])).
% 4.46/4.85 tff(34979,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[653, 34978, 34951])).
% 4.46/4.85 tff(34980,plain,
% 4.46/4.85 (b(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24196, 34979, 34946])).
% 4.46/4.85 tff(34981,plain,
% 4.46/4.85 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[11642, 34980, 224, 34977, 34975])).
% 4.46/4.85 tff(34982,plain,
% 4.46/4.85 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1451, 34981])).
% 4.46/4.85 tff(34983,plain,
% 4.46/4.85 (~b(s(s(z)), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1425, 34982, 50, 304])).
% 4.46/4.85 tff(34984,plain,
% 4.46/4.85 (r(s(s(z)), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1429, 44, 34983, 1416])).
% 4.46/4.85 tff(34985,plain,
% 4.46/4.85 (~b(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[2273, 34980, 56, 489])).
% 4.46/4.85 tff(34986,plain,
% 4.46/4.85 (r(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[372, 34985])).
% 4.46/4.85 tff(34987,plain,
% 4.46/4.85 (((~![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(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), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 4.46/4.85 inference(rewrite,[status(thm)],[])).
% 4.46/4.85 tff(34988,plain,
% 4.46/4.85 ((~![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(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 4.46/4.85 inference(quant_inst,[status(thm)],[])).
% 4.46/4.85 tff(34989,plain,
% 4.46/4.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[34988, 34987])).
% 4.46/4.85 tff(34990,plain,
% 4.46/4.85 (~r(s(s(z)), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34989, 333, 2169, 34986, 34984])).
% 4.46/4.85 tff(34991,plain,
% 4.46/4.85 (b(s(s(z)), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1462, 44, 164, 34990])).
% 4.46/4.85 tff(34992,plain,
% 4.46/4.85 (~(s(s(z)) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[14611, 34946, 706])).
% 4.46/4.85 tff(34993,plain,
% 4.46/4.85 (~r(s(s(z)), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[28548, 34984, 34167, 2169])).
% 4.46/4.85 tff(34994,plain,
% 4.46/4.85 (b(s(s(z)), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7970, 34993, 34992])).
% 4.46/4.85 tff(34995,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7961, 144, 34960, 34979, 34994, 34991])).
% 4.46/4.85 tff(34996,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (s(z) = elem!1) | b(s(s(s(z))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(34997,plain,
% 4.46/4.85 (b(s(z), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34996, 489, 224, 56, 304, 706, 55, 4])).
% 4.46/4.85 tff(34998,plain,
% 4.46/4.85 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34948])).
% 4.46/4.85 tff(34999,plain,
% 4.46/4.85 (~(z = elem!1)),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[392, 34998])).
% 4.46/4.85 tff(35000,plain,
% 4.46/4.85 (~r(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[33988, 51, 32437, 6107])).
% 4.46/4.85 tff(35001,plain,
% 4.46/4.85 (b(z, s(s(s(z))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[619, 35000])).
% 4.46/4.85 tff(35002,plain,
% 4.46/4.85 (b(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[609, 35001, 78])).
% 4.46/4.85 tff(35003,plain,
% 4.46/4.85 (~b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1602, 35002, 489, 134])).
% 4.46/4.85 tff(35004,plain,
% 4.46/4.85 (r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1380, 35003, 30262])).
% 4.46/4.85 tff(35005,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[34105, 333, 35004, 32437, 2323, 51])).
% 4.46/4.85 tff(35006,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35007,plain,
% 4.46/4.85 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35006, 489, 34167, 34997, 34946, 34977])).
% 4.46/4.85 tff(35008,plain,
% 4.46/4.85 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[279, 35007])).
% 4.46/4.85 tff(35009,plain,
% 4.46/4.85 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[7741, 35008, 50, 489])).
% 4.46/4.85 tff(35010,plain,
% 4.46/4.85 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[302, 35009])).
% 4.46/4.85 tff(35011,plain,
% 4.46/4.85 (~r(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[25313, 35010, 32437, 34167])).
% 4.46/4.85 tff(35012,plain,
% 4.46/4.85 (b(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[658, 35011, 34999])).
% 4.46/4.85 tff(35013,plain,
% 4.46/4.85 (~b(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[757, 35008, 50, 304])).
% 4.46/4.85 tff(35014,plain,
% 4.46/4.85 (r(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[372, 35013])).
% 4.46/4.85 tff(35015,plain,
% 4.46/4.85 (~r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24027, 35010, 35014, 34167])).
% 4.46/4.85 tff(35016,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[653, 35015, 34951])).
% 4.46/4.85 tff(35017,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1602, 35016, 35012, 489, 34997])).
% 4.46/4.85 tff(35018,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(z) = elem!1) | b(s(s(s(z))), elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35019,plain,
% 4.46/4.85 (~b(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35018, 55, 34936, 56, 706, 34462, 4])).
% 4.46/4.85 tff(35020,plain,
% 4.46/4.85 (r(s(z), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[348, 35019])).
% 4.46/4.85 tff(35021,plain,
% 4.46/4.85 (s(s(s(s(z)))) = s(elem!1)),
% 4.46/4.85 inference(monotonicity,[status(thm)],[34940])).
% 4.46/4.85 tff(35022,plain,
% 4.46/4.85 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[35021])).
% 4.46/4.85 tff(35023,plain,
% 4.46/4.85 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[35022])).
% 4.46/4.85 tff(35024,plain,
% 4.46/4.85 (~(s(elem!1) = s(z))),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[24294, 35023])).
% 4.46/4.85 tff(35025,plain,
% 4.46/4.85 (b(z, elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[30698, 350, 4, 30225])).
% 4.46/4.85 tff(35026,plain,
% 4.46/4.85 (~r(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1392, 34089, 1722, 323, 1368, 251, 409])).
% 4.46/4.85 tff(35027,plain,
% 4.46/4.85 (b(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[486, 35026, 1])).
% 4.46/4.85 tff(35028,plain,
% 4.46/4.85 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[869, 144, 35027, 123, 304])).
% 4.46/4.85 tff(35029,plain,
% 4.46/4.85 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[472, 35028, 432])).
% 4.46/4.85 tff(35030,plain,
% 4.46/4.85 (~r(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24672, 333, 32437, 2323, 35029])).
% 4.46/4.85 tff(35031,plain,
% 4.46/4.85 (b(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[448, 35030, 433])).
% 4.46/4.85 tff(35032,plain,
% 4.46/4.85 (~b(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[916, 35031, 251, 34963])).
% 4.46/4.85 tff(35033,plain,
% 4.46/4.85 (r(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[507, 35032])).
% 4.46/4.85 tff(35034,plain,
% 4.46/4.85 (~r(elem!1, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24371, 333, 32437, 2323, 35029])).
% 4.46/4.85 tff(35035,plain,
% 4.46/4.85 (b(elem!1, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[560, 35034, 1722])).
% 4.46/4.85 tff(35036,plain,
% 4.46/4.85 (~b(s(z), s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[4409, 35035, 305, 35027])).
% 4.46/4.85 tff(35037,plain,
% 4.46/4.85 (r(s(z), s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1244, 35036, 1237])).
% 4.46/4.85 tff(35038,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1235, 35037, 35033, 323, 34089])).
% 4.46/4.85 tff(35039,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (elem!1 = z) | (~r(s(z), elem!1)) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35040,plain,
% 4.46/4.85 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35039, 35025, 30268, 305, 323, 14076, 34167, 14872, 50, 304, 30225, 30262, 2169, 55, 350])).
% 4.46/4.85 tff(35041,plain,
% 4.46/4.85 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[279, 35040])).
% 4.46/4.85 tff(35042,plain,
% 4.46/4.85 (~r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[417, 35041, 323, 2169])).
% 4.46/4.85 tff(35043,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[653, 35042, 30262])).
% 4.46/4.85 tff(35044,plain,
% 4.46/4.85 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[13493, 509, 32437, 51])).
% 4.46/4.85 tff(35045,plain,
% 4.46/4.85 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[472, 35044, 432])).
% 4.46/4.85 tff(35046,plain,
% 4.46/4.85 (~r(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[18515, 333, 323, 509, 51])).
% 4.46/4.85 tff(35047,plain,
% 4.46/4.85 (b(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[486, 35046, 1])).
% 4.46/4.85 tff(35048,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[869, 144, 35047, 123, 304, 35045])).
% 4.46/4.85 tff(35049,plain,((~r(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35050,plain,
% 4.46/4.85 (~r(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35049, 35041, 304, 30225, 323, 50, 14872])).
% 4.46/4.85 tff(35051,plain,
% 4.46/4.85 (b(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[507, 35050])).
% 4.46/4.85 tff(35052,plain,
% 4.46/4.85 (~b(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[916, 35051, 35025, 35043])).
% 4.46/4.85 tff(35053,plain,
% 4.46/4.85 (r(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[448, 35052, 14076])).
% 4.46/4.85 tff(35054,plain,
% 4.46/4.85 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[15009, 333, 35053, 32437, 34167])).
% 4.46/4.85 tff(35055,plain,
% 4.46/4.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[31731, 35053, 305, 304, 34167, 14077, 30225, 50, 2169, 14872])).
% 4.46/4.85 tff(35056,plain,
% 4.46/4.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[302, 35055])).
% 4.46/4.85 tff(35057,plain,
% 4.46/4.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[3246, 27448, 706])).
% 4.46/4.85 tff(35058,plain,
% 4.46/4.85 (~r(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1392, 354, 13979, 323, 30262, 251, 409])).
% 4.46/4.85 tff(35059,plain,
% 4.46/4.85 (b(s(elem!1), s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[486, 35058, 30225])).
% 4.46/4.85 tff(35060,plain,
% 4.46/4.85 (~r(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[417, 51, 323, 409])).
% 4.46/4.85 tff(35061,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[653, 35060, 30262])).
% 4.46/4.85 tff(35062,plain,
% 4.46/4.85 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.46/4.85 inference(monotonicity,[status(thm)],[78])).
% 4.46/4.85 tff(35063,plain,
% 4.46/4.85 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 4.46/4.85 inference(symmetry,[status(thm)],[35062])).
% 4.46/4.85 tff(35064,plain,
% 4.46/4.85 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 4.46/4.85 inference(transitivity,[status(thm)],[35063, 12981])).
% 4.46/4.85 tff(35065,plain,
% 4.46/4.85 (s(s(s(z))) = s(s(s(elem!1)))),
% 4.46/4.85 inference(modus_ponens,[status(thm)],[1000, 35064])).
% 4.46/4.85 tff(35066,plain,
% 4.46/4.85 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[9479, 30225])).
% 4.46/4.85 tff(35067,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35066, 35065])).
% 4.46/4.85 tff(35068,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35069,plain,
% 4.46/4.85 (~(s(s(s(elem!1))) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35068, 78])).
% 4.46/4.85 tff(35070,plain,
% 4.46/4.85 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[869, 144, 35059, 123, 304])).
% 4.46/4.85 tff(35071,plain,
% 4.46/4.85 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[472, 35070, 14872])).
% 4.46/4.85 tff(35072,plain,
% 4.46/4.85 (~r(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[13493, 35071, 32437, 51])).
% 4.46/4.85 tff(35073,plain,
% 4.46/4.85 (b(s(elem!1), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[507, 35072])).
% 4.46/4.85 tff(35074,plain,
% 4.46/4.85 (~b(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[916, 35073, 251, 35061])).
% 4.46/4.85 tff(35075,plain,
% 4.46/4.85 (r(s(elem!1), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[448, 35074, 13978])).
% 4.46/4.85 tff(35076,plain,
% 4.46/4.85 (b(elem!1, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[25838, 35074, 32437, 78, 35070, 1184])).
% 4.46/4.85 tff(35077,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[18357, 35076, 35075, 35069, 251, 30268, 323, 3127, 35061, 354, 35059, 714])).
% 4.46/4.85 tff(35078,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z)) | (~(s(s(s(z))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35079,plain,
% 4.46/4.85 (~r(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35078, 35025, 323, 35057, 713, 78, 863, 35041, 50, 304, 2169])).
% 4.46/4.85 tff(35080,plain,
% 4.46/4.85 (b(z, s(z))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[372, 35079])).
% 4.46/4.85 tff(35081,plain,
% 4.46/4.85 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24106, 144, 35051, 35080, 304, 35056])).
% 4.46/4.85 tff(35082,plain,
% 4.46/4.85 ($false),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[542, 35081, 35054, 22256])).
% 4.46/4.85 tff(35083,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.85 tff(35084,plain,
% 4.46/4.85 (b(s(z), elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[35083, 35020, 34177, 34462, 34940, 55, 4, 706])).
% 4.46/4.85 tff(35085,plain,
% 4.46/4.85 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 4.46/4.85 inference(monotonicity,[status(thm)],[94])).
% 4.46/4.85 tff(35086,plain,
% 4.46/4.85 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 4.46/4.85 inference(symmetry,[status(thm)],[35085])).
% 4.46/4.85 tff(35087,plain,
% 4.46/4.85 (~(s(s(s(z))) = s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[1934, 24264])).
% 4.46/4.85 tff(35088,plain,
% 4.46/4.85 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[3398, 32438])).
% 4.46/4.85 tff(35089,plain,
% 4.46/4.85 (b(elem!1, z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[14247, 670, 2545, 123, 30225, 354, 259, 323, 34177, 35088, 134, 706, 78])).
% 4.46/4.85 tff(35090,plain,
% 4.46/4.85 (b(s(s(s(z))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[24196, 35089, 78])).
% 4.46/4.85 tff(35091,plain,
% 4.46/4.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[25313, 670, 32437, 2323])).
% 4.46/4.85 tff(35092,plain,
% 4.46/4.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[302, 35091])).
% 4.46/4.85 tff(35093,plain,
% 4.46/4.85 (~b(z, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[14148, 20701, 32437, 259, 286, 285, 1948, 491])).
% 4.46/4.85 tff(35094,plain,
% 4.46/4.85 (r(z, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[583, 35093])).
% 4.46/4.85 tff(35095,plain,
% 4.46/4.85 (~r(elem!1, s(elem!1))),
% 4.46/4.85 inference(unit_resolution,[status(thm)],[4052, 35094, 670, 20701])).
% 4.46/4.86 tff(35096,plain,
% 4.46/4.86 (b(elem!1, s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[560, 35095, 1722])).
% 4.46/4.86 tff(35097,plain,
% 4.46/4.86 (~r(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[5456, 35096, 706, 670, 1, 323, 354, 305, 624, 1722])).
% 4.46/4.86 tff(35098,plain,
% 4.46/4.86 (b(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[448, 35097, 433])).
% 4.46/4.86 tff(35099,plain,
% 4.46/4.86 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[4879, 144, 624, 491, 134])).
% 4.46/4.86 tff(35100,plain,
% 4.46/4.86 (~b(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35099, 35098])).
% 4.46/4.86 tff(35101,plain,
% 4.46/4.86 (r(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[486, 35100, 1])).
% 4.46/4.86 tff(35102,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1355, 333, 354, 323, 35101, 35094])).
% 4.46/4.86 tff(35103,plain,((~b(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (s(elem!1) = elem!1) | (s(z) = elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35104,plain,
% 4.46/4.86 (~b(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35103, 35089, 323, 30225, 354, 134, 14076, 706, 670, 34177, 259, 35092, 35090, 35087, 14872])).
% 4.46/4.86 tff(35105,plain,
% 4.46/4.86 (r(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[507, 35104])).
% 4.46/4.86 tff(35106,plain,
% 4.46/4.86 (~r(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1365, 35105, 323, 354])).
% 4.46/4.86 tff(35107,plain,
% 4.46/4.86 (b(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[486, 35106, 30225])).
% 4.46/4.86 tff(35108,plain,
% 4.46/4.86 (b(s(s(s(s(z)))), s(z))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[35107, 35086])).
% 4.46/4.86 tff(35109,plain,
% 4.46/4.86 (b(s(z), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[32405, 134, 27448])).
% 4.46/4.86 tff(35110,plain,
% 4.46/4.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[34451, 35092, 123, 22256, 27448, 323, 259, 354, 224, 6107])).
% 4.46/4.86 tff(35111,plain,
% 4.46/4.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[27512, 35110])).
% 4.46/4.86 tff(35112,plain,
% 4.46/4.86 (~b(s(s(s(s(z)))), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[27536, 35111, 56, 35109])).
% 4.46/4.86 tff(35113,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35112, 35108])).
% 4.46/4.86 tff(35114,plain,((~r(z, elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (s(z) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35115,plain,
% 4.46/4.86 (~r(z, elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35114, 34089, 323, 78, 134, 706, 259, 56, 123, 224, 33977, 2545, 2323])).
% 4.46/4.86 tff(35116,plain,
% 4.46/4.86 (r(elem!1, z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1380, 377, 30262])).
% 4.46/4.86 tff(35117,plain,
% 4.46/4.86 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[24027, 35116, 354, 2323])).
% 4.46/4.86 tff(35118,plain,
% 4.46/4.86 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[302, 35117])).
% 4.46/4.86 tff(35119,plain,
% 4.46/4.86 (~r(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[7383, 27487, 706, 56, 30225, 323, 24264, 1575, 14077, 354])).
% 4.46/4.86 tff(35120,plain,
% 4.46/4.86 (b(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[507, 35119])).
% 4.46/4.86 tff(35121,plain,
% 4.46/4.86 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[10345, 144, 35120, 35118, 259])).
% 4.46/4.86 tff(35122,plain,
% 4.46/4.86 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[472, 35121, 14872])).
% 4.46/4.86 tff(35123,plain,
% 4.46/4.86 (b(z, elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[658, 1575, 30222])).
% 4.46/4.86 tff(35124,plain,
% 4.46/4.86 (~r(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[13988, 35122, 2545, 377, 35118, 30262])).
% 4.46/4.86 tff(35125,plain,
% 4.46/4.86 (b(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[448, 35124, 14076])).
% 4.46/4.86 tff(35126,plain,
% 4.46/4.86 (~b(elem!1, s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[7524, 35125, 34177, 30225, 134, 35123, 323, 354])).
% 4.46/4.86 tff(35127,plain,
% 4.46/4.86 (r(elem!1, s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[560, 35126, 14077])).
% 4.46/4.86 tff(35128,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[24371, 333, 35127, 32437, 2323, 35122])).
% 4.46/4.86 tff(35129,plain,(b(elem!1, z) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(s(s(z))), s(z))) | r(z, elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35130,plain,
% 4.46/4.86 (b(elem!1, z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35129, 34089, 134, 323, 2323, 2545, 259, 706, 56, 35115, 78])).
% 4.46/4.86 tff(35131,plain,
% 4.46/4.86 (~b(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[26355, 35130, 34177, 134, 706, 35115, 14077, 30222])).
% 4.46/4.86 tff(35132,plain,
% 4.46/4.86 (r(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[448, 35131, 14076])).
% 4.46/4.86 tff(35133,plain,
% 4.46/4.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[14999, 333, 35132, 32437, 2323])).
% 4.46/4.86 tff(35134,plain,
% 4.46/4.86 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[15009, 333, 35132, 32437, 2323])).
% 4.46/4.86 tff(35135,plain,
% 4.46/4.86 (~b(z, s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[8386, 35134, 259, 22256, 35133])).
% 4.46/4.86 tff(35136,plain,
% 4.46/4.86 (r(z, s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[583, 35135])).
% 4.46/4.86 tff(35137,plain,
% 4.46/4.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[472, 35133, 14872])).
% 4.46/4.86 tff(35138,plain,
% 4.46/4.86 (~b(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[3040, 144, 123, 304, 35137])).
% 4.46/4.86 tff(35139,plain,
% 4.46/4.86 (r(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[486, 35138, 30225])).
% 4.46/4.86 tff(35140,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1355, 333, 34089, 323, 35139, 35136])).
% 4.46/4.86 tff(35141,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (s(z) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(z))) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35142,plain,
% 4.46/4.86 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35141, 35020, 50, 34462, 34167, 35084, 706, 2545, 56, 34940, 34936])).
% 4.46/4.86 tff(35143,plain,
% 4.46/4.86 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[279, 35142])).
% 4.46/4.86 tff(35144,plain,
% 4.46/4.86 (~r(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35049, 35143, 34462, 35024, 35020, 50, 34941])).
% 4.46/4.86 tff(35145,plain,
% 4.46/4.86 (b(s(elem!1), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[507, 35144])).
% 4.46/4.86 tff(35146,plain,
% 4.46/4.86 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33963, 56, 50, 34462])).
% 4.46/4.86 tff(35147,plain,
% 4.46/4.86 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1137, 35146])).
% 4.46/4.86 tff(35148,plain,
% 4.46/4.86 (~r(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33988, 35143, 32437, 35147])).
% 4.46/4.86 tff(35149,plain,
% 4.46/4.86 (b(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[619, 35148])).
% 4.46/4.86 tff(35150,plain,
% 4.46/4.86 (b(z, elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[609, 35149, 34940])).
% 4.46/4.86 tff(35151,plain,
% 4.46/4.86 (~r(s(s(s(z))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[13781, 35143, 50, 35020, 34462])).
% 4.46/4.86 tff(35152,plain,
% 4.46/4.86 (b(s(s(s(z))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[396, 35151])).
% 4.46/4.86 tff(35153,plain,
% 4.46/4.86 (b(elem!1, z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[380, 35152, 34940])).
% 4.46/4.86 tff(35154,plain,
% 4.46/4.86 (~b(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[916, 35153, 35150, 35145])).
% 4.46/4.86 tff(35155,plain,
% 4.46/4.86 (r(s(elem!1), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[448, 35154, 34944])).
% 4.46/4.86 tff(35156,plain,
% 4.46/4.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[14999, 333, 35155, 32437, 34167])).
% 4.46/4.86 tff(35157,plain,
% 4.46/4.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[472, 35156, 34941])).
% 4.46/4.86 tff(35158,plain,
% 4.46/4.86 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[11642, 35152, 34936, 35147, 35143])).
% 4.46/4.86 tff(35159,plain,
% 4.46/4.86 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1451, 35158])).
% 4.46/4.86 tff(35160,plain,
% 4.46/4.86 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[20734, 34941])).
% 4.46/4.86 tff(35161,plain,
% 4.46/4.86 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[15009, 333, 35155, 32437, 34167])).
% 4.46/4.86 tff(35162,plain,
% 4.46/4.86 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[542, 35161, 35160])).
% 4.46/4.86 tff(35163,plain,
% 4.46/4.86 (~r(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1435, 35162, 50, 35159, 856, 35020, 34462, 35157])).
% 4.46/4.86 tff(35164,plain,
% 4.46/4.86 (b(s(elem!1), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[486, 35163, 35024])).
% 4.46/4.86 tff(35165,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[869, 144, 35164, 50, 34462, 35157])).
% 4.46/4.86 tff(35166,plain,(b(s(s(s(z))), elem!1) | (s(z) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(z))), s(z))) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35167,plain,
% 4.46/4.86 (b(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35166, 56, 2545, 706, 4])).
% 4.46/4.86 tff(35168,plain,
% 4.46/4.86 (b(s(s(s(z))), elem!1) <=> b(elem!1, elem!1)),
% 4.46/4.86 inference(monotonicity,[status(thm)],[3239])).
% 4.46/4.86 tff(35169,plain,
% 4.46/4.86 (b(elem!1, elem!1) <=> b(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(symmetry,[status(thm)],[35168])).
% 4.46/4.86 tff(35170,plain,
% 4.46/4.86 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35169])).
% 4.46/4.86 tff(35171,plain,
% 4.46/4.86 (~b(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[5882, 35170])).
% 4.46/4.86 tff(35172,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[4367, 35171])).
% 4.46/4.86 tff(35173,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35174,plain,
% 4.46/4.86 (~(elem!1 = s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35173, 35167])).
% 4.46/4.86 tff(35175,plain,
% 4.46/4.86 (~(s(s(s(z))) = elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[27447, 35174])).
% 4.46/4.86 tff(35176,plain,
% 4.46/4.86 (~b(s(z), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[4375, 35167, 34177, 56])).
% 4.46/4.86 tff(35177,plain,
% 4.46/4.86 (r(s(z), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[406, 35176, 706])).
% 4.46/4.86 tff(35178,plain,
% 4.46/4.86 (~r(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33228, 35147, 32437, 34167])).
% 4.46/4.86 tff(35179,plain,
% 4.46/4.86 (b(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1538, 35174, 35178])).
% 4.46/4.86 tff(35180,plain,
% 4.46/4.86 (~b(s(z), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22776, 35179, 34177, 56])).
% 4.46/4.86 tff(35181,plain,
% 4.46/4.86 (r(s(z), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[172, 35180])).
% 4.46/4.86 tff(35182,plain,
% 4.46/4.86 (~r(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33228, 6107, 32437, 2323])).
% 4.46/4.86 tff(35183,plain,
% 4.46/4.86 (~(elem!1 = s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35173, 4367])).
% 4.46/4.86 tff(35184,plain,
% 4.46/4.86 (~(s(s(s(z))) = elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[27447, 35183])).
% 4.46/4.86 tff(35185,plain,
% 4.46/4.86 (~r(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[34938, 224, 2323])).
% 4.46/4.86 tff(35186,plain,
% 4.46/4.86 (~b(z, elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[21799, 35001, 35185, 35184, 35182])).
% 4.46/4.86 tff(35187,plain,
% 4.46/4.86 (s(elem!1) = s(z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[30698, 35186, 4, 350])).
% 4.46/4.86 tff(35188,plain,
% 4.46/4.86 (s(s(elem!1)) = s(s(z))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35187])).
% 4.46/4.86 tff(35189,plain,
% 4.46/4.86 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35188])).
% 4.46/4.86 tff(35190,plain,
% 4.46/4.86 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35188, 35189])).
% 4.46/4.86 tff(35191,plain,
% 4.46/4.86 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.86 inference(symmetry,[status(thm)],[35190])).
% 4.46/4.86 tff(35192,plain,
% 4.46/4.86 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35191])).
% 4.46/4.86 tff(35193,plain,
% 4.46/4.86 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[217, 35192])).
% 4.46/4.86 tff(35194,plain,
% 4.46/4.86 (b(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1538, 35183, 35182])).
% 4.46/4.86 tff(35195,plain,
% 4.46/4.86 (z = elem!1),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[8683, 35187])).
% 4.46/4.86 tff(35196,plain,
% 4.46/4.86 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35195])).
% 4.46/4.86 tff(35197,plain,
% 4.46/4.86 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35196])).
% 4.46/4.86 tff(35198,plain,
% 4.46/4.86 (~(s(s(z)) = elem!1)),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[164, 35197])).
% 4.46/4.86 tff(35199,plain,
% 4.46/4.86 (~r(s(s(s(z))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22912, 35195, 35185])).
% 4.46/4.86 tff(35200,plain,
% 4.46/4.86 (b(s(s(s(z))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[396, 35199])).
% 4.46/4.86 tff(35201,plain,
% 4.46/4.86 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[11642, 35200, 224, 6107, 51])).
% 4.46/4.86 tff(35202,plain,
% 4.46/4.86 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1451, 35201])).
% 4.46/4.86 tff(35203,plain,
% 4.46/4.86 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35187])).
% 4.46/4.86 tff(35204,plain,
% 4.46/4.86 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 4.46/4.86 inference(symmetry,[status(thm)],[35203])).
% 4.46/4.86 tff(35205,plain,
% 4.46/4.86 (b(elem!1, s(elem!1))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[305, 35204])).
% 4.46/4.86 tff(35206,plain,
% 4.46/4.86 (~r(s(s(z)), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[31517, 35205, 50, 305, 409, 35187, 35202, 2323])).
% 4.46/4.86 tff(35207,plain,
% 4.46/4.86 (b(s(s(z)), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[7970, 35206, 35198])).
% 4.46/4.86 tff(35208,plain,
% 4.46/4.86 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33620, 35207, 4367, 35194])).
% 4.46/4.86 tff(35209,plain,
% 4.46/4.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[18122, 35208, 35187])).
% 4.46/4.86 tff(35210,plain,
% 4.46/4.86 (~b(s(s(z)), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1425, 35202, 50, 304])).
% 4.46/4.86 tff(35211,plain,
% 4.46/4.86 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[18895, 35210, 35187])).
% 4.46/4.86 tff(35212,plain,
% 4.46/4.86 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35187])).
% 4.46/4.86 tff(35213,plain,
% 4.46/4.86 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.86 inference(symmetry,[status(thm)],[35212])).
% 4.46/4.86 tff(35214,plain,
% 4.46/4.86 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35213])).
% 4.46/4.86 tff(35215,plain,
% 4.46/4.86 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[107, 35214])).
% 4.46/4.86 tff(35216,plain,
% 4.46/4.86 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1283, 35215, 35211])).
% 4.46/4.86 tff(35217,plain,
% 4.46/4.86 (r(s(s(z)), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22871, 35216, 35187])).
% 4.46/4.86 tff(35218,plain,
% 4.46/4.86 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[29853, 35217, 6107, 353])).
% 4.46/4.86 tff(35219,plain,
% 4.46/4.86 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[18132, 35218, 35187])).
% 4.46/4.86 tff(35220,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[4311, 35219, 35209, 35193])).
% 4.46/4.86 tff(35221,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35222,plain,
% 4.46/4.86 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35221, 35147, 35181, 35167, 34177, 35177, 34167, 34462, 34936, 4, 35176])).
% 4.46/4.86 tff(35223,plain,
% 4.46/4.86 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[279, 35222])).
% 4.46/4.86 tff(35224,plain,
% 4.46/4.86 (~b(z, s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[757, 35223, 50, 34462])).
% 4.46/4.86 tff(35225,plain,
% 4.46/4.86 (~(z = elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[34840, 35224, 34177])).
% 4.46/4.86 tff(35226,plain,
% 4.46/4.86 (~(s(elem!1) = s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[8683, 35225])).
% 4.46/4.86 tff(35227,plain,
% 4.46/4.86 (b(z, elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[30698, 35226, 4, 35176])).
% 4.46/4.86 tff(35228,plain,
% 4.46/4.86 (~b(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[21799, 35227, 34939, 35175, 35178])).
% 4.46/4.86 tff(35229,plain,
% 4.46/4.86 (r(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[619, 35228])).
% 4.46/4.86 tff(35230,plain,
% 4.46/4.86 (~r(s(z), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[27739, 35229, 34462, 56, 35181, 35223])).
% 4.46/4.86 tff(35231,plain,
% 4.46/4.86 (b(s(z), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[348, 35230])).
% 4.46/4.86 tff(35232,plain,
% 4.46/4.86 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[7741, 35231, 50, 35223])).
% 4.46/4.86 tff(35233,plain,
% 4.46/4.86 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[302, 35232])).
% 4.46/4.86 tff(35234,plain,
% 4.46/4.86 (~r(elem!1, z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[32997, 35233, 32437, 35229])).
% 4.46/4.86 tff(35235,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[34471, 35234, 35233, 50, 35231, 35176, 34177, 34462, 34167, 35175])).
% 4.46/4.86 tff(35236,plain,((~b(s(s(s(z))), s(z))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35237,plain,
% 4.46/4.86 (~b(s(s(s(z))), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35236, 2545, 706, 4])).
% 4.46/4.86 tff(35238,plain,
% 4.46/4.86 (r(s(s(s(z))), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[2794, 35237])).
% 4.46/4.86 tff(35239,plain,
% 4.46/4.86 (~r(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22410, 35238, 32437, 34936])).
% 4.46/4.86 tff(35240,plain,
% 4.46/4.86 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 4.46/4.86 inference(symmetry,[status(thm)],[281])).
% 4.46/4.86 tff(35241,plain,
% 4.46/4.86 (b(s(s(s(z))), s(z))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[305, 35240])).
% 4.46/4.86 tff(35242,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[2789, 35241])).
% 4.46/4.86 tff(35243,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35244,plain,
% 4.46/4.86 (~(s(s(s(z))) = elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35243, 35237, 34177])).
% 4.46/4.86 tff(35245,plain,
% 4.46/4.86 (~(elem!1 = s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[10997, 35244])).
% 4.46/4.86 tff(35246,plain,
% 4.46/4.86 (b(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[1538, 35245, 35239])).
% 4.46/4.86 tff(35247,plain,
% 4.46/4.86 (b(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[704, 35244, 34939])).
% 4.46/4.86 tff(35248,plain,
% 4.46/4.86 (~r(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22410, 3193, 32437, 224])).
% 4.46/4.86 tff(35249,plain,
% 4.46/4.86 (~b(s(s(s(z))), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33963, 2254, 50, 304])).
% 4.46/4.86 tff(35250,plain,
% 4.46/4.86 (r(s(s(s(z))), s(z))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[2794, 35249])).
% 4.46/4.86 tff(35251,plain,
% 4.46/4.86 (~r(elem!1, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[22410, 35250, 32437, 224])).
% 4.46/4.86 tff(35252,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[26742, 333, 409, 3193, 707, 2323])).
% 4.46/4.86 tff(35253,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35254,plain,
% 4.46/4.86 (~r(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35253, 2169, 35250, 34167])).
% 4.46/4.86 tff(35255,plain,
% 4.46/4.86 (~(s(s(s(z))) = elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35243, 35249, 305])).
% 4.46/4.86 tff(35256,plain,
% 4.46/4.86 (~b(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33007, 489, 123, 2254, 838])).
% 4.46/4.86 tff(35257,plain,
% 4.46/4.86 (r(z, s(s(s(z))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[619, 35256])).
% 4.46/4.86 tff(35258,plain,
% 4.46/4.86 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[11040, 333, 35257, 3193, 224])).
% 4.46/4.86 tff(35259,plain,
% 4.46/4.86 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[279, 35258])).
% 4.46/4.86 tff(35260,plain,
% 4.46/4.86 (((~![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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.46/4.86 inference(rewrite,[status(thm)],[])).
% 4.46/4.86 tff(35261,plain,
% 4.46/4.86 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.46/4.86 inference(rewrite,[status(thm)],[])).
% 4.46/4.86 tff(35262,plain,
% 4.46/4.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.46/4.86 inference(monotonicity,[status(thm)],[35261])).
% 4.46/4.86 tff(35263,plain,
% 4.46/4.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, 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))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.46/4.86 inference(transitivity,[status(thm)],[35262, 35260])).
% 4.46/4.86 tff(35264,plain,
% 4.46/4.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.46/4.86 inference(quant_inst,[status(thm)],[])).
% 4.46/4.86 tff(35265,plain,
% 4.46/4.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.46/4.86 inference(modus_ponens,[status(thm)],[35264, 35263])).
% 4.46/4.86 tff(35266,plain,
% 4.46/4.86 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35265, 333, 35257, 3193, 224])).
% 4.46/4.86 tff(35267,plain,
% 4.46/4.86 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[302, 35266])).
% 4.46/4.86 tff(35268,plain,
% 4.46/4.86 ($false),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[7741, 35267, 35259, 123, 489])).
% 4.46/4.86 tff(35269,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.86 tff(35270,plain,
% 4.46/4.86 (~b(s(z), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[35269, 838, 35250, 224, 2254, 50])).
% 4.46/4.86 tff(35271,plain,
% 4.46/4.86 (r(s(z), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[348, 35270])).
% 4.46/4.86 tff(35272,plain,
% 4.46/4.86 (b(s(s(s(z))), elem!1)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[704, 35254, 35255])).
% 4.46/4.86 tff(35273,plain,
% 4.46/4.86 (~r(s(s(s(z))), z)),
% 4.46/4.86 inference(unit_resolution,[status(thm)],[33896, 35271, 50, 304, 35250])).
% 4.46/4.87 tff(35274,plain,
% 4.46/4.87 (b(s(s(s(z))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[396, 35273])).
% 4.46/4.87 tff(35275,plain,
% 4.46/4.87 (~(z = elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34840, 9362, 305])).
% 4.46/4.87 tff(35276,plain,
% 4.46/4.87 (elem!1 = z),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34914, 9363, 350, 4367, 285, 323, 4, 706])).
% 4.46/4.87 tff(35277,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[76, 35276, 35275])).
% 4.46/4.87 tff(35278,plain,(b(z, s(z)) | b(s(z), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35279,plain,
% 4.46/4.87 (b(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35278, 35274, 35272, 350, 35271, 4, 706, 305])).
% 4.46/4.87 tff(35280,plain,
% 4.46/4.87 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[757, 35279, 50, 304])).
% 4.46/4.87 tff(35281,plain,
% 4.46/4.87 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[279, 35280])).
% 4.46/4.87 tff(35282,plain,
% 4.46/4.87 (~r(elem!1, z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[417, 35281, 2169, 35271])).
% 4.46/4.87 tff(35283,plain,
% 4.46/4.87 (~(elem!1 = s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[10997, 35255])).
% 4.46/4.87 tff(35284,plain,
% 4.46/4.87 (b(elem!1, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1538, 35283, 35251])).
% 4.46/4.87 tff(35285,plain,
% 4.46/4.87 (~b(elem!1, z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[7247, 144, 35279, 35284, 305, 35274])).
% 4.46/4.87 tff(35286,plain,
% 4.46/4.87 (elem!1 = z),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1380, 35285, 35282])).
% 4.46/4.87 tff(35287,plain,
% 4.46/4.87 (z = elem!1),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[76, 35286])).
% 4.46/4.87 tff(35288,plain,
% 4.46/4.87 (s(elem!1) = s(z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[70, 35287])).
% 4.46/4.87 tff(35289,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35288])).
% 4.46/4.87 tff(35290,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(symmetry,[status(thm)],[35289])).
% 4.46/4.87 tff(35291,plain,
% 4.46/4.87 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35290])).
% 4.46/4.87 tff(35292,plain,
% 4.46/4.87 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[107, 35291])).
% 4.46/4.87 tff(35293,plain,
% 4.46/4.87 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35286])).
% 4.46/4.87 tff(35294,plain,
% 4.46/4.87 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.87 inference(symmetry,[status(thm)],[35293])).
% 4.46/4.87 tff(35295,plain,
% 4.46/4.87 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35294])).
% 4.46/4.87 tff(35296,plain,
% 4.46/4.87 (~(s(s(z)) = elem!1)),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[164, 35295])).
% 4.46/4.87 tff(35297,plain,
% 4.46/4.87 (~r(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[28548, 9770, 2323, 409])).
% 4.46/4.87 tff(35298,plain,
% 4.46/4.87 (b(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[7970, 35297, 1506])).
% 4.46/4.87 tff(35299,plain,
% 4.46/4.87 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[33620, 35298, 4367, 2082])).
% 4.46/4.87 tff(35300,plain,
% 4.46/4.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18122, 35299, 8677])).
% 4.46/4.87 tff(35301,plain,
% 4.46/4.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[4311, 35300, 22826])).
% 4.46/4.87 tff(35302,plain,
% 4.46/4.87 (r(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18132, 35301, 8677])).
% 4.46/4.87 tff(35303,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[9276, 333, 323, 3193, 35302, 9770])).
% 4.46/4.87 tff(35304,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35305,plain,
% 4.46/4.87 (~r(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35304, 35271, 35250, 35288, 35272, 35284, 35296, 34167, 2169])).
% 4.46/4.87 tff(35306,plain,
% 4.46/4.87 (~r(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22871, 35305, 35288])).
% 4.46/4.87 tff(35307,plain,
% 4.46/4.87 (b(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1283, 35306, 35292])).
% 4.46/4.87 tff(35308,plain,
% 4.46/4.87 (b(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18895, 35307, 35288])).
% 4.46/4.87 tff(35309,plain,
% 4.46/4.87 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1425, 35308, 50, 304])).
% 4.46/4.87 tff(35310,plain,
% 4.46/4.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[2262, 838, 123, 2254])).
% 4.46/4.87 tff(35311,plain,
% 4.46/4.87 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[249, 35310])).
% 4.46/4.87 tff(35312,plain,
% 4.46/4.87 (~r(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[31082, 333, 2671, 2323, 35311])).
% 4.46/4.87 tff(35313,plain,
% 4.46/4.87 (b(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[7970, 35312, 26795])).
% 4.46/4.87 tff(35314,plain,
% 4.46/4.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 4.46/4.87 inference(rewrite,[status(thm)],[])).
% 4.46/4.87 tff(35315,plain,
% 4.46/4.87 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 4.46/4.87 inference(rewrite,[status(thm)],[])).
% 4.46/4.87 tff(35316,plain,
% 4.46/4.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35315])).
% 4.46/4.87 tff(35317,plain,
% 4.46/4.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 4.46/4.87 inference(transitivity,[status(thm)],[35316, 35314])).
% 4.46/4.87 tff(35318,plain,
% 4.46/4.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 4.46/4.87 inference(quant_inst,[status(thm)],[])).
% 4.46/4.87 tff(35319,plain,
% 4.46/4.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[35318, 35317])).
% 4.46/4.87 tff(35320,plain,
% 4.46/4.87 (~b(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35319, 144, 1417, 838, 4367, 35313])).
% 4.46/4.87 tff(35321,plain,
% 4.46/4.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18122, 35320, 8677])).
% 4.46/4.87 tff(35322,plain,
% 4.46/4.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[4311, 35321, 22826])).
% 4.46/4.87 tff(35323,plain,
% 4.46/4.87 (r(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18132, 35322, 8677])).
% 4.46/4.87 tff(35324,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[31108, 333, 3193, 2671, 35311, 35323])).
% 4.46/4.87 tff(35325,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35326,plain,
% 4.46/4.87 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35325, 35308, 34167, 838, 35288, 35250, 35272, 50, 2254])).
% 4.46/4.87 tff(35327,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1451, 35326, 35309])).
% 4.46/4.87 tff(35328,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | b(s(z), elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35329,plain,
% 4.46/4.87 (~b(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35328, 350, 304, 305, 2254, 4, 706, 224])).
% 4.46/4.87 tff(35330,plain,
% 4.46/4.87 (r(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[172, 35329])).
% 4.46/4.87 tff(35331,plain,
% 4.46/4.87 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.46/4.87 inference(rewrite,[status(thm)],[])).
% 4.46/4.87 tff(35332,plain,
% 4.46/4.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35331])).
% 4.46/4.87 tff(35333,plain,
% 4.46/4.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 4.46/4.87 inference(transitivity,[status(thm)],[35332, 3026])).
% 4.46/4.87 tff(35334,plain,
% 4.46/4.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 4.46/4.87 inference(quant_inst,[status(thm)],[])).
% 4.46/4.87 tff(35335,plain,
% 4.46/4.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[35334, 35333])).
% 4.46/4.87 tff(35336,plain,
% 4.46/4.87 (~r(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35335, 333, 623, 3193, 353])).
% 4.46/4.87 tff(35337,plain,
% 4.46/4.87 (b(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[372, 35336])).
% 4.46/4.87 tff(35338,plain,
% 4.46/4.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[11040, 333, 623, 3193, 224])).
% 4.46/4.87 tff(35339,plain,
% 4.46/4.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[279, 35338])).
% 4.46/4.87 tff(35340,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[757, 35339, 35337, 123, 304])).
% 4.46/4.87 tff(35341,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35342,plain,
% 4.46/4.87 (~r(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35341, 35330, 304, 35250, 224, 50])).
% 4.46/4.87 tff(35343,plain,
% 4.46/4.87 (b(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[619, 35342])).
% 4.46/4.87 tff(35344,plain,
% 4.46/4.87 (~b(z, elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[21799, 35343, 35255, 35254, 35251])).
% 4.46/4.87 tff(35345,plain,
% 4.46/4.87 (s(elem!1) = s(z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[30698, 35344, 4, 350])).
% 4.46/4.87 tff(35346,plain,
% 4.46/4.87 (z = elem!1),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[8683, 35345])).
% 4.46/4.87 tff(35347,plain,
% 4.46/4.87 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35346])).
% 4.46/4.87 tff(35348,plain,
% 4.46/4.87 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35347])).
% 4.46/4.87 tff(35349,plain,
% 4.46/4.87 (~(s(s(z)) = elem!1)),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[164, 35348])).
% 4.46/4.87 tff(35350,plain,
% 4.46/4.87 (s(s(elem!1)) = s(s(z))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35345])).
% 4.46/4.87 tff(35351,plain,
% 4.46/4.87 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35350])).
% 4.46/4.87 tff(35352,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35350, 35351])).
% 4.46/4.87 tff(35353,plain,
% 4.46/4.87 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.87 inference(symmetry,[status(thm)],[35352])).
% 4.46/4.87 tff(35354,plain,
% 4.46/4.87 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35353])).
% 4.46/4.87 tff(35355,plain,
% 4.46/4.87 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[217, 35354])).
% 4.46/4.87 tff(35356,plain,
% 4.46/4.87 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35346])).
% 4.46/4.87 tff(35357,plain,
% 4.46/4.87 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.46/4.87 inference(transitivity,[status(thm)],[35356, 1218])).
% 4.46/4.87 tff(35358,plain,
% 4.46/4.87 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35357])).
% 4.46/4.87 tff(35359,plain,
% 4.46/4.87 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[1094, 35358])).
% 4.46/4.87 tff(35360,plain,
% 4.46/4.87 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34524, 35359, 35330, 35345, 50, 304, 305, 34167, 35250])).
% 4.46/4.87 tff(35361,plain,
% 4.46/4.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18132, 35360, 35345])).
% 4.46/4.87 tff(35362,plain,
% 4.46/4.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[4311, 35361, 35355])).
% 4.46/4.87 tff(35363,plain,
% 4.46/4.87 (b(s(s(z)), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18122, 35362, 35345])).
% 4.46/4.87 tff(35364,plain,
% 4.46/4.87 (~b(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[33620, 35363, 35272, 35284])).
% 4.46/4.87 tff(35365,plain,
% 4.46/4.87 (r(s(s(z)), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[7970, 35364, 35349])).
% 4.46/4.87 tff(35366,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35345])).
% 4.46/4.87 tff(35367,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(symmetry,[status(thm)],[35366])).
% 4.46/4.87 tff(35368,plain,
% 4.46/4.87 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35367])).
% 4.46/4.87 tff(35369,plain,
% 4.46/4.87 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[107, 35368])).
% 4.46/4.87 tff(35370,plain,
% 4.46/4.87 (elem!1 = z),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18287, 35346])).
% 4.46/4.87 tff(35371,plain,
% 4.46/4.87 (~b(s(z), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22716, 35370, 350])).
% 4.46/4.87 tff(35372,plain,
% 4.46/4.87 (r(s(z), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[348, 35371])).
% 4.46/4.87 tff(35373,plain,
% 4.46/4.87 (~r(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35304, 35349, 35250, 35345, 35272, 35284, 35372, 34167, 2169])).
% 4.46/4.87 tff(35374,plain,
% 4.46/4.87 (~r(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22871, 35373, 35345])).
% 4.46/4.87 tff(35375,plain,
% 4.46/4.87 (b(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1283, 35374, 35369])).
% 4.46/4.87 tff(35376,plain,
% 4.46/4.87 (b(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18895, 35375, 35345])).
% 4.46/4.87 tff(35377,plain,
% 4.46/4.87 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1425, 35376, 50, 304])).
% 4.46/4.87 tff(35378,plain,
% 4.46/4.87 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1451, 35377])).
% 4.46/4.87 tff(35379,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34537, 333, 35378, 32437, 34167, 35365])).
% 4.46/4.87 tff(35380,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35381,plain,
% 4.46/4.87 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35380, 350, 305, 4, 224, 304, 706])).
% 4.46/4.87 tff(35382,plain,
% 4.46/4.87 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1137, 35381])).
% 4.46/4.87 tff(35383,plain,
% 4.46/4.87 (b(z, elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[30698, 1, 4, 350])).
% 4.46/4.87 tff(35384,plain,
% 4.46/4.87 (~b(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[21799, 35383, 699, 698, 21019])).
% 4.46/4.87 tff(35385,plain,
% 4.46/4.87 (r(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[619, 35384])).
% 4.46/4.87 tff(35386,plain,
% 4.46/4.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[33988, 35385, 32437, 6107])).
% 4.46/4.87 tff(35387,plain,
% 4.46/4.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[279, 35386])).
% 4.46/4.87 tff(35388,plain,
% 4.46/4.87 (~b(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[757, 35387, 50, 304])).
% 4.46/4.87 tff(35389,plain,
% 4.46/4.87 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34918, 77, 304, 3193, 4, 706, 350, 6107, 698])).
% 4.46/4.87 tff(35390,plain,
% 4.46/4.87 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[302, 35389])).
% 4.46/4.87 tff(35391,plain,
% 4.46/4.87 (~r(elem!1, z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[32997, 35390, 32437, 35385])).
% 4.46/4.87 tff(35392,plain,
% 4.46/4.87 (b(elem!1, z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[653, 35391, 77])).
% 4.46/4.87 tff(35393,plain,
% 4.46/4.87 (~r(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[31651, 35392, 35383, 698, 35390, 6107, 34167])).
% 4.46/4.87 tff(35394,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[372, 35393, 35388])).
% 4.46/4.87 tff(35395,plain,((s(elem!1) = s(z)) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35396,plain,
% 4.46/4.87 (s(elem!1) = s(z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35395, 35382, 698, 304, 3193, 4, 706, 350, 34945, 35248])).
% 4.46/4.87 tff(35397,plain,
% 4.46/4.87 (z = elem!1),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[8683, 35396])).
% 4.46/4.87 tff(35398,plain,
% 4.46/4.87 (~r(s(s(s(z))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22912, 35397, 34945])).
% 4.46/4.87 tff(35399,plain,
% 4.46/4.87 (b(s(s(s(z))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[396, 35398])).
% 4.46/4.87 tff(35400,plain,
% 4.46/4.87 (b(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34840, 35397, 305])).
% 4.46/4.87 tff(35401,plain,
% 4.46/4.87 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[757, 35400, 50, 304])).
% 4.46/4.87 tff(35402,plain,
% 4.46/4.87 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[279, 35401])).
% 4.46/4.87 tff(35403,plain,
% 4.46/4.87 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[11642, 35402, 224, 35382, 35399])).
% 4.46/4.87 tff(35404,plain,
% 4.46/4.87 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1451, 35403])).
% 4.46/4.87 tff(35405,plain,
% 4.46/4.87 (~b(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1425, 35404, 50, 304])).
% 4.46/4.87 tff(35406,plain,
% 4.46/4.87 (~b(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18895, 35405, 35396])).
% 4.46/4.87 tff(35407,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35396])).
% 4.46/4.87 tff(35408,plain,
% 4.46/4.87 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(symmetry,[status(thm)],[35407])).
% 4.46/4.87 tff(35409,plain,
% 4.46/4.87 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35408])).
% 4.46/4.87 tff(35410,plain,
% 4.46/4.87 (~(s(s(elem!1)) = s(elem!1))),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[107, 35409])).
% 4.46/4.87 tff(35411,plain,
% 4.46/4.87 (r(s(s(elem!1)), s(elem!1))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1283, 35410, 35406])).
% 4.46/4.87 tff(35412,plain,
% 4.46/4.87 (elem!1 = z),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[18287, 35397])).
% 4.46/4.87 tff(35413,plain,
% 4.46/4.87 (~b(s(z), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22716, 35412, 350])).
% 4.46/4.87 tff(35414,plain,
% 4.46/4.87 (r(s(z), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[348, 35413])).
% 4.46/4.87 tff(35415,plain,
% 4.46/4.87 (b(elem!1, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[1538, 12398, 35248])).
% 4.46/4.87 tff(35416,plain,
% 4.46/4.87 (b(s(s(s(z))), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[704, 698, 34945])).
% 4.46/4.87 tff(35417,plain,
% 4.46/4.87 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35397])).
% 4.46/4.87 tff(35418,plain,
% 4.46/4.87 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.87 inference(monotonicity,[status(thm)],[35417])).
% 4.46/4.87 tff(35419,plain,
% 4.46/4.87 (~(s(s(z)) = elem!1)),
% 4.46/4.87 inference(modus_ponens,[status(thm)],[164, 35418])).
% 4.46/4.87 tff(35420,plain,
% 4.46/4.87 (~r(s(s(z)), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35304, 35419, 3193, 35396, 35416, 35415, 35414, 34167, 2169])).
% 4.46/4.87 tff(35421,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[22871, 35420, 35411, 35396])).
% 4.46/4.87 tff(35422,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35423,plain,
% 4.46/4.87 (b(s(z), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35422, 35238, 34462, 34936, 34177, 35244, 4, 706])).
% 4.46/4.87 tff(35424,plain,
% 4.46/4.87 (~b(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34921, 35423, 35247, 35246])).
% 4.46/4.87 tff(35425,plain,
% 4.46/4.87 (r(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[172, 35424])).
% 4.46/4.87 tff(35426,plain,
% 4.46/4.87 (~r(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35341, 35425, 34462, 35238, 34936, 50])).
% 4.46/4.87 tff(35427,plain,
% 4.46/4.87 (b(z, s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[619, 35426])).
% 4.46/4.87 tff(35428,plain,
% 4.46/4.87 (~b(z, elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[21799, 35427, 34939, 35244, 35239])).
% 4.46/4.87 tff(35429,plain,
% 4.46/4.87 (~b(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34921, 134, 4367, 2082])).
% 4.46/4.87 tff(35430,plain,
% 4.46/4.87 (r(s(z), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[172, 35429])).
% 4.46/4.87 tff(35431,plain,
% 4.46/4.87 (r(s(s(s(s(z)))), s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[27538, 24595])).
% 4.46/4.87 tff(35432,plain,
% 4.46/4.87 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[27512, 33319])).
% 4.46/4.87 tff(35433,plain,
% 4.46/4.87 ($false),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34231, 35432, 35431, 3193, 35430])).
% 4.46/4.87 tff(35434,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.87 tff(35435,plain,
% 4.46/4.87 (~b(s(s(s(s(z)))), elem!1)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[35434, 3193, 2082, 4367, 134, 34177])).
% 4.46/4.87 tff(35436,plain,
% 4.46/4.87 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[25313, 2311, 32437, 2323])).
% 4.46/4.87 tff(35437,plain,
% 4.46/4.87 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[302, 35436])).
% 4.46/4.87 tff(35438,plain,
% 4.46/4.87 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[34866, 35437, 123, 304, 3193, 4367, 35430, 77, 32437])).
% 4.46/4.87 tff(35439,plain,
% 4.46/4.87 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[279, 35438])).
% 4.46/4.87 tff(35440,plain,
% 4.46/4.87 (~b(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[757, 35439, 123, 304])).
% 4.46/4.87 tff(35441,plain,
% 4.46/4.87 (r(z, s(z))),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[372, 35440])).
% 4.46/4.87 tff(35442,plain,
% 4.46/4.87 (~r(s(s(s(z))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[26130, 35441, 3193, 35430])).
% 4.46/4.87 tff(35443,plain,
% 4.46/4.87 (b(s(s(s(z))), z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[396, 35442])).
% 4.46/4.87 tff(35444,plain,
% 4.46/4.87 (~b(elem!1, z)),
% 4.46/4.87 inference(unit_resolution,[status(thm)],[9164, 144, 2082, 35443, 284])).
% 4.46/4.88 tff(35445,plain,
% 4.46/4.88 (r(elem!1, z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[1380, 35444, 77])).
% 4.46/4.88 tff(35446,plain,
% 4.46/4.88 (~r(s(s(s(s(z)))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24987, 35445, 32437, 2311, 35437, 35439])).
% 4.46/4.88 tff(35447,plain,
% 4.46/4.88 (s(s(s(s(z)))) = elem!1),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24301, 35446, 35435])).
% 4.46/4.88 tff(35448,plain,
% 4.46/4.88 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24681, 885, 23985])).
% 4.46/4.88 tff(35449,plain,
% 4.46/4.88 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24691, 3687, 885])).
% 4.46/4.88 tff(35450,plain,
% 4.46/4.88 (b(s(s(s(s(z)))), s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24448, 35449, 35448])).
% 4.46/4.88 tff(35451,plain,
% 4.46/4.88 (b(s(z), s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[3262, 3674, 134])).
% 4.46/4.88 tff(35452,plain,
% 4.46/4.88 (b(s(elem!1), s(z))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[305, 886])).
% 4.46/4.88 tff(35453,plain,
% 4.46/4.88 (~b(s(s(s(s(z)))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[26255, 144, 35452, 35451, 35450])).
% 4.46/4.88 tff(35454,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[27538, 35453])).
% 4.46/4.88 tff(35455,plain,
% 4.46/4.88 (b(s(s(s(z))), s(elem!1))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[4367, 20852])).
% 4.46/4.88 tff(35456,plain,
% 4.46/4.88 (b(s(elem!1), s(s(s(z))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[2082, 21109])).
% 4.46/4.88 tff(35457,plain,
% 4.46/4.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[26247, 144, 35456, 35455, 35450])).
% 4.46/4.88 tff(35458,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[27512, 35457])).
% 4.46/4.88 tff(35459,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34231, 35458, 35454, 3193, 35430])).
% 4.46/4.88 tff(35460,plain,((~(elem!1 = s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35461,plain,
% 4.46/4.88 (~(elem!1 = s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35460, 35446, 4367, 34177, 2082, 3193, 134, 1])).
% 4.46/4.88 tff(35462,plain,
% 4.46/4.88 (r(s(elem!1), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[14240, 35461, 123, 2311, 35088, 35445, 35441, 706, 35439, 1, 134])).
% 4.46/4.88 tff(35463,plain,
% 4.46/4.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[13988, 435, 2545, 377, 35092, 1368])).
% 4.46/4.88 tff(35464,plain,
% 4.46/4.88 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[472, 35463, 432])).
% 4.46/4.88 tff(35465,plain,
% 4.46/4.88 (~r(s(elem!1), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24919, 435, 670, 2323])).
% 4.46/4.88 tff(35466,plain,
% 4.46/4.88 (b(s(elem!1), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[507, 35465])).
% 4.46/4.88 tff(35467,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[10345, 144, 35466, 35092, 35464, 259])).
% 4.46/4.88 tff(35468,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35469,plain,
% 4.46/4.88 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35468, 35462, 35439, 2311, 2323, 2545, 35444, 77])).
% 4.46/4.88 tff(35470,plain,
% 4.46/4.88 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[930, 35469])).
% 4.46/4.88 tff(35471,plain,
% 4.46/4.88 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[1216, 35470])).
% 4.46/4.88 tff(35472,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24637, 35471, 35470, 35447])).
% 4.46/4.88 tff(35473,plain,((s(elem!1) = s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35474,plain,
% 4.46/4.88 (s(elem!1) = s(z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35473, 2545, 34167, 50, 706, 35423, 35247, 35246, 35238, 35427, 34462, 35428])).
% 4.46/4.88 tff(35475,plain,
% 4.46/4.88 (z = elem!1),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[8683, 35474])).
% 4.46/4.88 tff(35476,plain,
% 4.46/4.88 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35475])).
% 4.46/4.88 tff(35477,plain,
% 4.46/4.88 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35476])).
% 4.46/4.88 tff(35478,plain,
% 4.46/4.88 (~(s(s(z)) = elem!1)),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[164, 35477])).
% 4.46/4.88 tff(35479,plain,
% 4.46/4.88 (s(s(elem!1)) = s(s(z))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35474])).
% 4.46/4.88 tff(35480,plain,
% 4.46/4.88 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35479])).
% 4.46/4.88 tff(35481,plain,
% 4.46/4.88 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35479, 35480])).
% 4.46/4.88 tff(35482,plain,
% 4.46/4.88 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.88 inference(symmetry,[status(thm)],[35481])).
% 4.46/4.88 tff(35483,plain,
% 4.46/4.88 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35482])).
% 4.46/4.88 tff(35484,plain,
% 4.46/4.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[217, 35483])).
% 4.46/4.88 tff(35485,plain,
% 4.46/4.88 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35475])).
% 4.46/4.88 tff(35486,plain,
% 4.46/4.88 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.46/4.88 inference(transitivity,[status(thm)],[35485, 1218])).
% 4.46/4.88 tff(35487,plain,
% 4.46/4.88 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35486])).
% 4.46/4.88 tff(35488,plain,
% 4.46/4.88 (~(elem!1 = s(s(elem!1)))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[1094, 35487])).
% 4.46/4.88 tff(35489,plain,
% 4.46/4.88 (~r(s(s(z)), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34524, 35488, 35238, 35425, 50, 34462, 34177, 34167, 35474])).
% 4.46/4.88 tff(35490,plain,
% 4.46/4.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[18132, 35489, 35474])).
% 4.46/4.88 tff(35491,plain,
% 4.46/4.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[4311, 35490, 35484])).
% 4.46/4.88 tff(35492,plain,
% 4.46/4.88 (b(s(s(z)), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[18122, 35491, 35474])).
% 4.46/4.88 tff(35493,plain,
% 4.46/4.88 (~b(s(s(z)), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[33620, 35492, 35247, 35246])).
% 4.46/4.88 tff(35494,plain,
% 4.46/4.88 (r(s(s(z)), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[7970, 35493, 35478])).
% 4.46/4.88 tff(35495,plain,
% 4.46/4.88 (~b(s(s(s(s(z)))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35434, 35238, 35246, 35247, 35423, 34177])).
% 4.46/4.88 tff(35496,plain,
% 4.46/4.88 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35475])).
% 4.46/4.88 tff(35497,plain,
% 4.46/4.88 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 4.46/4.88 inference(transitivity,[status(thm)],[35496, 203])).
% 4.46/4.88 tff(35498,plain,
% 4.46/4.88 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 4.46/4.88 inference(transitivity,[status(thm)],[35497, 24285])).
% 4.46/4.88 tff(35499,plain,
% 4.46/4.88 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35498])).
% 4.46/4.88 tff(35500,plain,
% 4.46/4.88 (~(s(s(s(s(z)))) = elem!1)),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[242, 35499])).
% 4.46/4.88 tff(35501,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[24301, 35500, 35495])).
% 4.46/4.88 tff(35502,plain,
% 4.46/4.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(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)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(rewrite,[status(thm)],[])).
% 4.46/4.88 tff(35503,plain,
% 4.46/4.88 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(rewrite,[status(thm)],[])).
% 4.46/4.88 tff(35504,plain,
% 4.46/4.88 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35503])).
% 4.46/4.88 tff(35505,plain,
% 4.46/4.88 (((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(transitivity,[status(thm)],[35504, 35502])).
% 4.46/4.88 tff(35506,plain,
% 4.46/4.88 ((~![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(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(quant_inst,[status(thm)],[])).
% 4.46/4.88 tff(35507,plain,
% 4.46/4.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[35506, 35505])).
% 4.46/4.88 tff(35508,plain,
% 4.46/4.88 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35507, 333, 35501, 34167, 35494])).
% 4.46/4.88 tff(35509,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35474])).
% 4.46/4.88 tff(35510,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.88 inference(symmetry,[status(thm)],[35509])).
% 4.46/4.88 tff(35511,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[34462, 35510])).
% 4.46/4.88 tff(35512,plain,
% 4.46/4.88 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35474])).
% 4.46/4.88 tff(35513,plain,
% 4.46/4.88 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(symmetry,[status(thm)],[35512])).
% 4.46/4.88 tff(35514,plain,
% 4.46/4.88 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[50, 35513])).
% 4.46/4.88 tff(35515,plain,
% 4.46/4.88 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[25349, 35475])).
% 4.46/4.88 tff(35516,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[25199, 35501, 32437, 34167, 35515, 35514, 35511])).
% 4.46/4.88 tff(35517,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[28694, 35516, 35474])).
% 4.46/4.88 tff(35518,plain,
% 4.46/4.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31939, 333, 35238, 35517, 35425])).
% 4.46/4.88 tff(35519,plain,
% 4.46/4.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[26947, 44, 26944, 35518])).
% 4.46/4.88 tff(35520,plain,
% 4.46/4.88 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34231, 35517, 35238, 35425])).
% 4.46/4.88 tff(35521,plain,
% 4.46/4.88 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[27512, 35520])).
% 4.46/4.88 tff(35522,plain,
% 4.46/4.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(rewrite,[status(thm)],[])).
% 4.46/4.88 tff(35523,plain,
% 4.46/4.88 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(rewrite,[status(thm)],[])).
% 4.46/4.88 tff(35524,plain,
% 4.46/4.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[35523])).
% 4.46/4.88 tff(35525,plain,
% 4.46/4.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.46/4.88 inference(transitivity,[status(thm)],[35524, 35522])).
% 4.46/4.88 tff(35526,plain,
% 4.46/4.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.46/4.88 inference(quant_inst,[status(thm)],[])).
% 4.46/4.88 tff(35527,plain,
% 4.46/4.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[35526, 35525])).
% 4.46/4.88 tff(35528,plain,
% 4.46/4.88 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35527, 144, 35492, 35521, 35519])).
% 4.46/4.88 tff(35529,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[20473, 44, 25543, 35528, 35508])).
% 4.46/4.88 tff(35530,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35531,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35530, 706, 4])).
% 4.46/4.88 tff(35532,plain,
% 4.46/4.88 (b(z, elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31004, 34168, 4, 35531, 1, 34167])).
% 4.46/4.88 tff(35533,plain,
% 4.46/4.88 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34281, 2169, 34167])).
% 4.46/4.88 tff(35534,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[319, 35533])).
% 4.46/4.88 tff(35535,plain,
% 4.46/4.88 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31769, 1, 35531, 50, 706, 350, 35383, 34167])).
% 4.46/4.88 tff(35536,plain,
% 4.46/4.88 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[279, 35535])).
% 4.46/4.88 tff(35537,plain,
% 4.46/4.88 (~b(z, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31959, 35383, 35531, 350, 50, 34167, 1, 706])).
% 4.46/4.88 tff(35538,plain,
% 4.46/4.88 (r(z, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[372, 35537])).
% 4.46/4.88 tff(35539,plain,
% 4.46/4.88 (~(s(s(s(z))) = elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31994, 35538, 35531, 50, 34167, 1, 2169, 35536, 706, 35383])).
% 4.46/4.88 tff(35540,plain,
% 4.46/4.88 (~r(elem!1, z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31969, 35538, 35531, 34167, 2169, 35383, 35536])).
% 4.46/4.88 tff(35541,plain,
% 4.46/4.88 (b(elem!1, z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[653, 35540, 77])).
% 4.46/4.88 tff(35542,plain,
% 4.46/4.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[880, 35541, 35531, 35383])).
% 4.46/4.88 tff(35543,plain,
% 4.46/4.88 (b(elem!1, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[33689, 35542, 32437, 4])).
% 4.46/4.88 tff(35544,plain,
% 4.46/4.88 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[302, 35542])).
% 4.46/4.88 tff(35545,plain,
% 4.46/4.88 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34826, 35544, 50, 35534, 35543, 35539, 35536, 34167, 706])).
% 4.46/4.88 tff(35546,plain,
% 4.46/4.88 (r(s(s(s(z))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31890, 35544, 35531, 2169, 50, 35534, 35383, 35536, 35539, 35541])).
% 4.46/4.88 tff(35547,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34938, 35546, 35545, 34167])).
% 4.46/4.88 tff(35548,plain,((s(elem!1) = s(z)) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35549,plain,
% 4.46/4.88 (s(elem!1) = s(z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35548, 350, 4, 706])).
% 4.46/4.88 tff(35550,plain,
% 4.46/4.88 (z = elem!1),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[8683, 35549])).
% 4.46/4.88 tff(35551,plain,
% 4.46/4.88 (elem!1 = z),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[18287, 35550])).
% 4.46/4.88 tff(35552,plain,
% 4.46/4.88 (~b(s(z), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[22716, 35551, 350])).
% 4.46/4.88 tff(35553,plain,
% 4.46/4.88 (r(s(z), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[348, 35552])).
% 4.46/4.88 tff(35554,plain,
% 4.46/4.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31402, 35549, 50, 34167, 35531, 35534, 706])).
% 4.46/4.88 tff(35555,plain,
% 4.46/4.88 (b(elem!1, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[33689, 35554, 32437, 4])).
% 4.46/4.88 tff(35556,plain,
% 4.46/4.88 (b(z, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34840, 35555, 35550])).
% 4.46/4.88 tff(35557,plain,
% 4.46/4.88 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[757, 35556, 50, 35534])).
% 4.46/4.88 tff(35558,plain,
% 4.46/4.88 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[279, 35557])).
% 4.46/4.88 tff(35559,plain,
% 4.46/4.88 (~r(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[13781, 35558, 50, 35553, 35534])).
% 4.46/4.88 tff(35560,plain,
% 4.46/4.88 (b(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[396, 35559])).
% 4.46/4.88 tff(35561,plain,
% 4.46/4.88 (b(s(s(s(z))), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[26887, 35560, 35550])).
% 4.46/4.88 tff(35562,plain,
% 4.46/4.88 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31399, 35561, 35531, 34167, 35534, 35555, 863, 35549])).
% 4.46/4.88 tff(35563,plain,
% 4.46/4.88 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[1451, 35562])).
% 4.46/4.88 tff(35564,plain,
% 4.46/4.88 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31124, 35563, 35531, 50, 863, 35549, 35561, 2169, 35534])).
% 4.46/4.88 tff(35565,plain,
% 4.46/4.88 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31355, 35563, 34167, 50, 35531, 863, 35534, 2169, 35549])).
% 4.46/4.88 tff(35566,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[1137, 35565, 35564])).
% 4.46/4.88 tff(35567,plain,(b(s(z), elem!1) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35568,plain,
% 4.46/4.88 (b(s(z), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35567, 706, 4])).
% 4.46/4.88 tff(35569,plain,
% 4.46/4.88 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[32291, 34168, 35531, 50, 35568, 713, 35532, 77])).
% 4.46/4.88 tff(35570,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[319, 35569, 34169])).
% 4.46/4.88 tff(35571,plain,(b(elem!1, s(z)) | r(s(z), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35572,plain,
% 4.46/4.88 (b(elem!1, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35571, 1, 4, 706])).
% 4.46/4.88 tff(35573,plain,
% 4.46/4.88 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[3955, 35572, 35531, 35568])).
% 4.46/4.88 tff(35574,plain,
% 4.46/4.88 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[319, 35573])).
% 4.46/4.88 tff(35575,plain,
% 4.46/4.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34271, 35574, 32437, 50, 71, 35572])).
% 4.46/4.88 tff(35576,plain,
% 4.46/4.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[302, 35575])).
% 4.46/4.88 tff(35577,plain,
% 4.46/4.88 (b(z, elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[31004, 35576, 4, 35531, 1, 34167])).
% 4.46/4.88 tff(35578,plain,
% 4.46/4.88 (~b(z, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[7079, 35577, 35572, 35568])).
% 4.46/4.88 tff(35579,plain,
% 4.46/4.88 (r(z, s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[372, 35578])).
% 4.46/4.88 tff(35580,plain,
% 4.46/4.88 (~b(elem!1, z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[880, 35576, 35531, 35577])).
% 4.46/4.88 tff(35581,plain,
% 4.46/4.88 (r(elem!1, z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[1380, 35580, 77])).
% 4.46/4.88 tff(35582,plain,
% 4.46/4.88 (~r(z, elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[30760, 35581, 35531, 50, 34167, 35574, 35576, 1, 706, 35568])).
% 4.46/4.88 tff(35583,plain,
% 4.46/4.88 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[2331, 35581, 35574, 34167])).
% 4.46/4.88 tff(35584,plain,
% 4.46/4.88 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[279, 35583])).
% 4.46/4.88 tff(35585,plain,
% 4.46/4.88 (~b(s(z), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[7741, 35584, 50, 35576])).
% 4.46/4.88 tff(35586,plain,
% 4.46/4.88 (r(s(z), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[348, 35585])).
% 4.46/4.88 tff(35587,plain,
% 4.46/4.88 (b(s(s(s(z))), s(z))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35243, 78, 305])).
% 4.46/4.88 tff(35588,plain,
% 4.46/4.88 (~b(s(elem!1), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[19646, 35587, 133, 354, 1, 323, 27448, 305, 134, 34361, 78])).
% 4.46/4.88 tff(35589,plain,
% 4.46/4.88 (r(s(elem!1), elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[448, 35588, 14076])).
% 4.46/4.88 tff(35590,plain,
% 4.46/4.88 (r(s(elem!1), s(s(s(z))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[35589, 27457])).
% 4.46/4.88 tff(35591,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[35590, 27460])).
% 4.46/4.88 tff(35592,plain,
% 4.46/4.88 (~(elem!1 = s(elem!1))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[2482, 35069])).
% 4.46/4.88 tff(35593,plain,
% 4.46/4.88 (~b(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[380, 78, 377])).
% 4.46/4.88 tff(35594,plain,
% 4.46/4.88 (r(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[396, 35593])).
% 4.46/4.88 tff(35595,plain,
% 4.46/4.88 (~r(s(elem!1), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[7383, 35594, 706, 323, 1, 35587, 24264, 1575, 35592, 354])).
% 4.46/4.88 tff(35596,plain,
% 4.46/4.88 (b(s(elem!1), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[507, 35595])).
% 4.46/4.88 tff(35597,plain,
% 4.46/4.88 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[27477, 35596, 286, 259, 27448])).
% 4.46/4.88 tff(35598,plain,
% 4.46/4.88 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[9761, 35597])).
% 4.46/4.88 tff(35599,plain,
% 4.46/4.88 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.88 inference(monotonicity,[status(thm)],[27448])).
% 4.46/4.88 tff(35600,plain,
% 4.46/4.88 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.88 inference(modus_ponens,[status(thm)],[32437, 35599])).
% 4.46/4.88 tff(35601,plain,
% 4.46/4.88 ($false),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[34027, 333, 35594, 35600, 35598, 35591])).
% 4.46/4.88 tff(35602,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(z) = elem!1) | (~r(s(z), z)) | (s(elem!1) = s(z)) | r(z, elem!1) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.88 tff(35603,plain,
% 4.46/4.88 (~(s(s(s(z))) = elem!1)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[35602, 35576, 35584, 706, 35586, 1, 35582, 35579, 35531, 35572, 35568, 35580])).
% 4.46/4.88 tff(35604,plain,
% 4.46/4.88 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[2331, 408, 19620, 2323])).
% 4.46/4.88 tff(35605,plain,
% 4.46/4.88 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[279, 35604])).
% 4.46/4.88 tff(35606,plain,
% 4.46/4.88 (~b(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[27648, 698, 133, 2323, 305, 35605, 286, 134])).
% 4.46/4.88 tff(35607,plain,
% 4.46/4.88 (r(s(s(s(z))), z)),
% 4.46/4.88 inference(unit_resolution,[status(thm)],[396, 35606])).
% 4.46/4.89 tff(35608,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2122, 35607, 12399, 354, 408])).
% 4.46/4.89 tff(35609,plain,((s(s(s(z))) = elem!1) | (~r(z, s(z))) | (~r(elem!1, z)) | b(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35610,plain,
% 4.46/4.89 (b(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35609, 35603, 35581, 35579, 35531, 34167, 35572, 35576, 35568])).
% 4.46/4.89 tff(35611,plain,
% 4.46/4.89 (~b(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[4375, 35610, 35568, 35572])).
% 4.46/4.89 tff(35612,plain,
% 4.46/4.89 (~b(s(s(s(z))), z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[27648, 35603, 35531, 34167, 35572, 35584, 35576, 35568])).
% 4.46/4.89 tff(35613,plain,
% 4.46/4.89 (r(s(s(s(z))), z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[396, 35612])).
% 4.46/4.89 tff(35614,plain,
% 4.46/4.89 (~r(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[6555, 35613, 35586, 35579])).
% 4.46/4.89 tff(35615,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2794, 35614, 35611])).
% 4.46/4.89 tff(35616,plain,((s(elem!1) = s(z)) | (s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35617,plain,
% 4.46/4.89 (s(elem!1) = s(z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35616, 706, 4])).
% 4.46/4.89 tff(35618,plain,
% 4.46/4.89 (z = elem!1),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[8683, 35617])).
% 4.46/4.89 tff(35619,plain,
% 4.46/4.89 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.46/4.89 inference(monotonicity,[status(thm)],[35618])).
% 4.46/4.89 tff(35620,plain,
% 4.46/4.89 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.89 inference(symmetry,[status(thm)],[35619])).
% 4.46/4.89 tff(35621,plain,
% 4.46/4.89 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.89 inference(modus_ponens,[status(thm)],[35531, 35620])).
% 4.46/4.89 tff(35622,plain,
% 4.46/4.89 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[31402, 35621, 50, 34167, 35531, 35617, 706])).
% 4.46/4.89 tff(35623,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[319, 35622])).
% 4.46/4.89 tff(35624,plain,
% 4.46/4.89 (~r(s(z), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[34281, 35623, 34167])).
% 4.46/4.89 tff(35625,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[31462, 35624, 35623, 35531, 50, 35617, 34167, 706])).
% 4.46/4.89 tff(35626,plain,((s(z) = elem!1) | r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35627,plain,
% 4.46/4.89 (s(z) = elem!1),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35626, 4])).
% 4.46/4.89 tff(35628,plain,
% 4.46/4.89 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[30660, 35627, 4])).
% 4.46/4.89 tff(35629,plain,
% 4.46/4.89 (s(elem!1) = s(z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[22668, 35628])).
% 4.46/4.89 tff(35630,plain,
% 4.46/4.89 (s(z) = s(elem!1)),
% 4.46/4.89 inference(symmetry,[status(thm)],[35629])).
% 4.46/4.89 tff(35631,plain,
% 4.46/4.89 (elem!1 = s(z)),
% 4.46/4.89 inference(symmetry,[status(thm)],[35627])).
% 4.46/4.89 tff(35632,plain,
% 4.46/4.89 (elem!1 = s(elem!1)),
% 4.46/4.89 inference(transitivity,[status(thm)],[35631, 35630])).
% 4.46/4.89 tff(35633,plain,
% 4.46/4.89 (~(s(s(s(elem!1))) = elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2468, 35627])).
% 4.46/4.89 tff(35634,plain,
% 4.46/4.89 (~(elem!1 = s(elem!1))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2482, 35633])).
% 4.46/4.89 tff(35635,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35634, 35632])).
% 4.46/4.89 tff(35636,plain,(r(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35637,plain,
% 4.46/4.89 (~(s(z) = elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[15132, 3, 35636])).
% 4.46/4.89 tff(35638,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.46/4.89 inference(monotonicity,[status(thm)],[22670])).
% 4.46/4.89 tff(35639,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.89 inference(symmetry,[status(thm)],[35638])).
% 4.46/4.89 tff(35640,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.46/4.89 inference(modus_ponens,[status(thm)],[32437, 35639])).
% 4.46/4.89 tff(35641,plain,
% 4.46/4.89 (b(s(z), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[22884, 35640, 35636, 22669, 32439, 35637])).
% 4.46/4.89 tff(35642,plain,
% 4.46/4.89 (~(elem!1 = s(elem!1))),
% 4.46/4.89 inference(modus_ponens,[status(thm)],[35637, 22693])).
% 4.46/4.89 tff(35643,plain,
% 4.46/4.89 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.89 inference(modus_ponens,[status(thm)],[35636, 22697])).
% 4.46/4.89 tff(35644,plain,
% 4.46/4.89 (~(elem!1 = s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[712, 35637])).
% 4.46/4.89 tff(35645,plain,
% 4.46/4.89 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[23162, 35641, 35636, 22669, 32439, 35640, 35642, 35644])).
% 4.46/4.89 tff(35646,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[319, 35645])).
% 4.46/4.89 tff(35647,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[23169, 35646, 22669])).
% 4.46/4.89 tff(35648,plain,
% 4.46/4.89 (~r(elem!1, s(elem!1))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[12088, 35647, 32437, 35643])).
% 4.46/4.89 tff(35649,plain,
% 4.46/4.89 (b(elem!1, s(elem!1))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[560, 35648, 35642])).
% 4.46/4.89 tff(35650,plain,
% 4.46/4.89 (b(z, s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[18030, 35649, 22669])).
% 4.46/4.89 tff(35651,plain,
% 4.46/4.89 (b(elem!1, s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[28115, 35650, 22670])).
% 4.46/4.89 tff(35652,plain,
% 4.46/4.89 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[23183, 35651, 32437, 35636, 35640, 22677, 35641, 22674])).
% 4.46/4.89 tff(35653,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[23247, 35651, 32437, 35636, 22669, 32439, 35641, 35647, 35652])).
% 4.46/4.89 tff(35654,plain,
% 4.46/4.89 (~r(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[30488, 35653, 35636, 35646])).
% 4.46/4.89 tff(35655,plain,
% 4.46/4.89 (b(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2794, 35654])).
% 4.46/4.89 tff(35656,plain,
% 4.46/4.89 (~b(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[4375, 35655, 35641, 35651])).
% 4.46/4.89 tff(35657,plain,
% 4.46/4.89 (~b(s(s(s(z))), z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[26887, 35656, 22670])).
% 4.46/4.89 tff(35658,plain,
% 4.46/4.89 (r(s(s(s(z))), z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[396, 35657])).
% 4.46/4.89 tff(35659,plain,
% 4.46/4.89 (~r(elem!1, s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[32460, 35658, 32437, 35653])).
% 4.46/4.89 tff(35660,plain,
% 4.46/4.89 (r(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[704, 35656, 22677])).
% 4.46/4.89 tff(35661,plain,
% 4.46/4.89 (~r(s(z), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[22780, 35660, 35646, 35653])).
% 4.46/4.89 tff(35662,plain,
% 4.46/4.89 (b(s(z), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[172, 35661])).
% 4.46/4.89 tff(35663,plain,
% 4.46/4.89 (~b(elem!1, s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[22776, 35662, 35651, 35655])).
% 4.46/4.89 tff(35664,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[1538, 35663, 35659, 22674])).
% 4.46/4.89 tff(35665,plain,(r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35666,plain,
% 4.46/4.89 (~r(elem!1, s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[23286, 333, 35636, 32437, 35665])).
% 4.46/4.89 tff(35667,plain,
% 4.46/4.89 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[26539, 35636])).
% 4.46/4.89 tff(35668,plain,
% 4.46/4.89 (elem!1 = s(z)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[720, 23326, 35666])).
% 4.46/4.89 tff(35669,plain,
% 4.46/4.89 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[27431, 35668, 35667])).
% 4.46/4.89 tff(35670,plain,
% 4.46/4.89 (~r(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[24063, 35669, 32437, 35636, 35665, 35666, 71])).
% 4.46/4.89 tff(35671,plain,
% 4.46/4.89 (b(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2794, 35670])).
% 4.46/4.89 tff(35672,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[28110, 35671, 35636, 1, 35667])).
% 4.46/4.89 tff(35673,plain,
% 4.46/4.89 (s(s(s(z))) = elem!1),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[29624, 35672, 35667, 35636, 71, 35670, 35665])).
% 4.46/4.89 tff(35674,plain,
% 4.46/4.89 (b(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[63, 35671, 57])).
% 4.46/4.89 tff(35675,plain,
% 4.46/4.89 (~(elem!1 = s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35173, 35674])).
% 4.46/4.89 tff(35676,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[27447, 35675, 35673])).
% 4.46/4.89 tff(35677,plain,((~(s(z) = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35678,plain,
% 4.46/4.89 (~(s(z) = elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35677, 1])).
% 4.46/4.89 tff(35679,plain,
% 4.46/4.89 (~(elem!1 = s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[712, 35678])).
% 4.46/4.89 tff(35680,plain,
% 4.46/4.89 (b(elem!1, s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[720, 35679, 35666])).
% 4.46/4.89 tff(35681,plain,
% 4.46/4.89 (~r(s(z), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[19114, 333, 35636, 32437, 35665])).
% 4.46/4.89 tff(35682,plain,
% 4.46/4.89 (b(s(z), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[406, 35678, 35681])).
% 4.46/4.89 tff(35683,plain,
% 4.46/4.89 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[3955, 35680, 35667, 35682])).
% 4.46/4.89 tff(35684,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[319, 35683])).
% 4.46/4.89 tff(35685,plain,
% 4.46/4.89 (b(s(z), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[406, 706, 35681])).
% 4.46/4.89 tff(35686,plain,
% 4.46/4.89 (b(elem!1, s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[720, 713, 35666])).
% 4.46/4.89 tff(35687,plain,
% 4.46/4.89 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[26276, 698, 32437, 35636, 35686, 35685, 35665])).
% 4.46/4.89 tff(35688,plain,
% 4.46/4.89 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[3955, 35686, 35667, 35685])).
% 4.46/4.89 tff(35689,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[319, 35688])).
% 4.46/4.89 tff(35690,plain,
% 4.46/4.89 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[30166, 707, 35636, 35665, 35686, 35689, 35687, 35667, 698, 706])).
% 4.46/4.89 tff(35691,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[34938, 35690, 707, 35665])).
% 4.46/4.89 tff(35692,plain,((~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35693,plain,
% 4.46/4.89 (~r(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35692, 698, 706])).
% 4.46/4.89 tff(35694,plain,
% 4.46/4.89 (b(s(s(s(z))), elem!1)),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[704, 35693, 698])).
% 4.46/4.89 tff(35695,plain,
% 4.46/4.89 (~b(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[4375, 35694, 35685, 35686])).
% 4.46/4.89 tff(35696,plain,
% 4.46/4.89 (r(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[2794, 35695])).
% 4.46/4.89 tff(35697,plain,
% 4.46/4.89 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[30488, 35696, 35636, 35689])).
% 4.46/4.89 tff(35698,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[30172, 35697, 35696, 35667, 698, 35687, 35636, 706, 35665])).
% 4.46/4.89 tff(35699,plain,((s(s(s(z))) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35700,plain,
% 4.46/4.89 (s(s(s(z))) = elem!1),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35699, 35678])).
% 4.46/4.89 tff(35701,plain,
% 4.46/4.89 (b(s(s(s(z))), s(z))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[35243, 35700, 35680])).
% 4.46/4.89 tff(35702,plain,
% 4.46/4.89 (elem!1 = s(s(s(z)))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[27447, 35700])).
% 4.46/4.89 tff(35703,plain,
% 4.46/4.89 (b(s(z), s(s(s(z))))),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[32405, 35702, 35682])).
% 4.46/4.89 tff(35704,plain,
% 4.46/4.89 ($false),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[27582, 35703, 35701, 35636, 35700, 35684, 35667, 35680, 1])).
% 4.46/4.89 tff(35705,plain,(s(elem!1) = s(z)), inference(lemma,lemma(discharge,[]))).
% 4.46/4.89 tff(35706,plain,
% 4.46/4.89 (z = elem!1),
% 4.46/4.89 inference(unit_resolution,[status(thm)],[8683, 35705])).
% 4.46/4.89 tff(35707,plain,
% 4.46/4.89 ((s(z) = z) <=> (s(z) = elem!1)),
% 4.46/4.89 inference(monotonicity,[status(thm)],[35706])).
% 4.46/4.89 tff(35708,plain,
% 4.46/4.89 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 4.46/4.89 inference(monotonicity,[status(thm)],[35707])).
% 4.46/4.89 tff(35709,plain,
% 4.46/4.89 (~(s(z) = elem!1)),
% 4.46/4.89 inference(modus_ponens,[status(thm)],[344, 35708])).
% 4.46/4.89 tff(35710,plain,
% 4.46/4.89 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 4.46/4.89 inference(monotonicity,[status(thm)],[35706])).
% 4.46/4.89 tff(35711,plain,
% 4.46/4.89 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 4.56/4.90 inference(transitivity,[status(thm)],[35710, 2])).
% 4.56/4.90 tff(35712,plain,
% 4.56/4.90 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 4.56/4.90 inference(transitivity,[status(thm)],[35711, 4795])).
% 4.56/4.90 tff(35713,plain,
% 4.56/4.90 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 4.56/4.90 inference(monotonicity,[status(thm)],[35712])).
% 4.56/4.90 tff(35714,plain,
% 4.56/4.90 (~(s(s(s(z))) = elem!1)),
% 4.56/4.90 inference(modus_ponens,[status(thm)],[392, 35713])).
% 4.56/4.90 tff(35715,plain,
% 4.56/4.90 ($false),
% 4.56/4.90 inference(unit_resolution,[status(thm)],[35699, 35714, 35709])).
% 4.56/4.90 % SZS output end Proof
% 4.56/4.91 % E exiting
%------------------------------------------------------------------------------